Mould filling simulations during powder injection moulding

Transcription

1 Mould filling simulations during powder injection moulding

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3 Mould filling simulations during powder injection moulding Proefschirft ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof. dr. ir. J.T.Fokkema, voorzitter van het College voor Promoties, in het openbaar te verdedigen op maandag juni 003 om 0:30 uur door Volodymyr Valeriyovych BILOVOL ingenieur in de poeder metallurgie, Kyiv Politechnic Institute, Oekraїne geboren te Poltava, Oekraїne

4 Dit proefschrift is goedgekeurd door de promotor: Prof. ir. L. Katgerman Toegevoegd promotor Dr.ir. J. Duszczyk Samenstelling promotiecommissie: Rector Magnificus, voorzitter Prof. ir. L. Katgerman Dr.ir. J. Duszczyk Prof. dr. ir. L. Froyen Prof. dr. L. Nyborg Prof. dr. S. J. Picken Prof. dr. R. Boom Prof. dr. D. J. Schipper Technische Universiteit Delft, promotor Technische Universiteit Delft, toegevoegd promotor Katholieke Universiteit Leuven Chalmers University of Technology Technische Universiteit Delft Technische Universiteit Delft Universiteit Twente This research was carried out under project number PM9706 in the framework of the Strategic Research Programme of the Netherlands Institute for Metals Research in the Netherlands ( Printed by Sieca Repro Turbineweg 0 67 BP Delft The Netherlands Telephone: Telefax: verkoop@sieca.nl ISBN Mould filling simulations during powder injection moulding by V. V. Bilovol, Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands. Key words: powder injection moulding, numerical simulation, stainless steel Copyright 003 by Volodymyr V. Bilovol All right reserved. No part of the material protected by this copyright notice may be reproduced or utilised in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without permission from the publisher. Printed in the Netherlands

5 Contents Contents Chapter Introduction. General principles of the powder injection moulding process. Advantages of the PIM process 4.3 Tools for powder injection moulding 5.4 Moulding cycle 6.5 Feedstock attributes 8.6 Major problem areas related to PIM technology 9.7 Process simulation.8 Scope of this thesis 3 Chapter Simulation principles 5. Fluid flow 6. Material models 7.3 Energy balance 9.4 Fluid flow momentum.5 Modelling of slip and powder-binder segregation of the PIM feedstock.6 Boundary conditions 4.7 Numerical solution 6.7. Discretisation 7.7. Pressure field solution Application of boundary conditions Solution of Energy equation Tracking of free surface 34.8 Summary 35 Chapter 3 Characterisation of BASF 36 L feedstock Feedstock attributes Viscosity measurements Fitting experimental data into viscosity models of 36 L feedstock Cross-WLF model Carreau model Carreau-Yasuda model Specific heat Thermal conductivity Summary 50 Chapter 4 Simulation programmes 5 4. C-Mold 53 V

6 Contents 4.. Powder injection moulding of simple shaped component with orifice Powder injection moulding of a component with complex shape Summary of C-Mold calculations Moldflow Examples of simulation with Moldflow Summary of C-Mold calculations ProCAST Examples of simulation with ProCAST Summary of ProCAST calculations Concluding remarks 86 Chapter 5 Comparison of the numerical results calculated with different analysis packages and their validation Experimental set-up Research mould Measuring system Measurements of pressure Measurements of temperature Parameters of powder injection moulding process 9 5. Simulation setup Comparison between numerical and experimental results Melt front advancement Temperature distribution Pressure results Computational aspects Summary 0 Chapter 6 Sensitivity of simulation results to input parameters 0 6. The effect of heat transfer coefficient 0 6. The effect of initial mould temperature The effect of mesh size The effect of viscosity Summary 7 Concluding remarks and future directions 8 References 0 Summary 4 Samenvatting 7 List of publications 30 List of symbols 3 Acknowledgements 35 VI

7 Chapter Introduction. General principles of the powder injection moulding process The modern industry requires production of various components in big quantities. Many of them have complicated shapes and small sizes. Selection of a proper production method for such components can be a difficult task. Traditional machining is expensive. Components produced by near net shape methods like casting often have low tolerances and insufficient quality of surface finish. Some types of the components can be efficiently produced by methods of powder metallurgy. But conventional powder metallurgy is applicable for production of relatively simple shapes. Isostatic pressing ensures very high quality products, but it is a low productive and expensive technology. The real breakthrough among the near net shape techniques became the powder injection moulding (PIM) process. It uses the shaping advantages of injection moulding of plastics but is applicable to metals and ceramics. The powder injection moulding process emerged as a separate branch of powder metallurgy. This process includes the following main stages:. Preparing of a mixture of powder and a binder. Moulding of green part by injection of the powder-binder mixture into the mould 3. Removal of binder 4. Sintering 5. Finishing operations (optional) Schematic diagram of the entire PIM process is shown in Figure. A powder is mixed with a binder until homogeneous distribution of powder particles is achieved. A binder is usually based on thermoplastics or other polymers such as wax, polyethylene, polyacetal, cellulose, silanes and others. The mixing takes place at the temperatures above the melting point of the binder. The mixture of powder and binder is called powder injection moulding feedstock. After mixing the feedstock is granulated or pelletised. In granulated form it is charged into the injection moulding machine. Due to the presence of the binder the PIM feedstock is able to flow at temperatures above the melting point of the binder. In the injection moulding machine the feedstock is heated to the processing temperature and thereafter injected into a mould. In this way a green part (body) is formed.

8 Chapter After the green part has been formed, the binder is removed from it. This process is called debinding. Different removal methods are used depending on the type of binder. The most common are methods of thermal or catalytic decomposition. The soluble binders are removed by immersing the green part into a proper solvent. The debinding operation is aimed at creation of the component with minimal possible amount of binder that still keeps the powder particles together. The strength of the component after debinding must be high enough to allow relocation of it from the debinding equipment to the sintering furnace. Sintering of the PIM components is performed in two stages. At the first stage the residual binder is removed. This stage requires a slow temperature increase to prevent destruction of the component by the gaseous products of the decomposing binder. At the second stage the temperature further increases to the level when the powder particles sinter into a dense structure. During sintering the component densifies and shrinks, but retains its shape. Because of shrinkage the dimensions of the sintered product, depending on the material, are reduced by to 8%, compared with the green part. The final component has a density usually greater than 97%, and the mechanical properties are not significantly, if at all, below those of wrought metal of the same composition. After sintering some finishing operations may be needed. The sintered product may be further densified, heat treated, coined, plated, or machined to complete the fabrication process. The tolerances of PIM components are %, which is high compared with the tolerances achieved by other near net shape technologies. A tolerance 0. % can generally be achieved on small, selected dimensions when the mould has been "fine-tuned". Powders used for PIM have a smaller particle size than for traditional powder metallurgy applications. Typical are PIM powders with maximum particle sizes below 0 µm. The average particle size is around 5 µm and surface roughness of PIM products is low because of the small powder diameters. Figure. A schematic diagram of powder injection moulding process Almost any shape that can be produced in thermo plastics by injection moulding can be produced in metal or ceramics by PIM. Examples of complex shapes obtainable by PIM components can be seen in Figure.

9 Introduction Figure. Typical PIM components (Courtesy of ITB Precisietechniek in Metaal en Kunstof) PIM technology can be used for any sinterable material available in powdered form. For example, products can be made from ceramics (alumina, aluminium nitride, silicon carbide, silicon nitride, zirconia, etc), and metals and alloys (stainless steel, copper, nickel, molybdenum, titanium, tungsten, duplex stainless steels, Fe-Ni and W-Cu compositions, titanium alloys, nickel superalloys, precious metals, etc) PIM technology was found suitable to produce components for many different applications. The main areas of applications are machine-building (pistons, turbochargers, air bag actuators, seat warm gear), radioelectronics (microchip substrates and radiators), computers (hard disk drive magnets, chip heat spreader), cutting tools, metallurgy (melting crucibles, thermocouple cases), medicine (medical forceps, orthodontic brackets, orthopaedic implants), tooling (nozzles for sandblast machines, drills), weapon (shotgun trigger guard, rocket nozzle guidance system), watch industry (cases, clasps, links for bracelets and bezels), household and personal applications (hear cutting shears, sporting shoe cleats), jewellery. Despite PIM is most efficient in producing small components, the variety of PIM products is quite large, from millimetres to decimetres. The smallest components produced by PIM have dimensions 50 by 480 µ m [-]. But the overwhelming majority of PIM components has the size of several centimetres. During the last ten years the popularity of PIM in the industrial world is steadily growing in terms of turnover [3]. The variety of products is also increasing. Because of obvious advantages many manufacturers frequently choose PIM technology to produce their new products. In the last decade of the 0th century PIM technology was chosen by a leading Swiss watch manufacturer to make watchcases from stainless steel [4]. This project was a tremendous success and already became a classic example of PIM technology. Depending on the type of the feedstock sometimes Metal Injection Moulding (MIM) and Ceramics Injection moulding (CIM) processes are distinguished. In this thesis for both processes the term powder injection moulding (PIM) is used. 3

10 Chapter. Advantages of the PIM process The main distinguishing characteristics of PIM can be summarised as follows:. Technological characteristics: - ability to produce complex shaped components - wide range of materials - low production costs - automatic production lines - no waste. Process characteristics: - minimal density gradients in the green body - fine powders - uniform and predictable shrinkage 3. End product features: - high density after sintering - high surface finish - superior mechanical properties as compared with traditional powder metallurgy products Detailed description of all aspects of the powder injection moulding technology can be found in [5]. The authors identified the main advantageous characteristics of PIM as the following: low production costs, shape complexity, tight tolerances, applicability to a wide range of materials and high final properties. These are key features that make powder injection moulding processing attractive for the industry. PIM overcomes the property limitations inherent to plastics, the shape limitations of traditional powder compaction, the costs of machining, the productivity limits of isostatic pressing and slip casting and the defect and tolerance limitations of shape casting. The shaping capabilities of PIM are very impressive. Producing both internal and external threads in the component is possible, avoiding post-sintering machining. Also waffle and insignias can be moulded directly into the component. The moulding stage of the PIM process can be easily automated. Some manual work is needed during preparing the mouldings for debinding and for sintering. But both debinding and sintering stages are performed without human participation. One more positive feature of the PIM process is elimination of waste. The feedstock from the damaged mouldings and from the delivery system of the mould (sprue and the runners) is completely recycled. This is especially important for expensive materials. The conventional die compaction method creates compacts with high density gradients. During sintering such compacts may be distorted. To avoid distortion, sintering at lower temperatures can be used. The disadvantage of low temperature sintering is higher porosity and lower mechanical properties of the product. If the product warps during sintering it requires machining, which is additional operation that increases production costs. As compared with conventional powder compaction, PIM reduces density gradients in the green body. Because of this the PIM products shrink uniformly to high densities and do not experience warpage at higher sintering temperatures. These advantages are complemented with high final properties of the PIM products that often are superior to the products produced by the other powder fabrication routes. The low porosity in PIM materials gives a high strength, toughness, ductility, conductivity, magnetic response, etc. Due to forming pressure gradients, sintering temperature differences, and differing performance levels, PIM and traditional powder compaction are usually not applied to the same structures. The PIM approach is suited for complex shapes sintered to near-full density, while die compaction is suited to simple shapes, sintered at lower temperatures to lower performance levels. As it was already mentioned PIM powders are finer than the usual powders for traditional powder metallurgy applications. Small powders ensure good surface finish. 4

11 Introduction.3 Tools for powder injection moulding A scheme of the mould for powder injection moulding is shown in Figure 3. A typical mould consists of two parts. In one part the cavity of desired shape is cut. The cavity is made oversized to account for shrinkage so that after sintering the final product meets the required dimensions. Often more than one cavity is made so that in one injection cycle several components are moulded. The second part of the mould does not contain the cavity. It is usually simpler than the first one. Both parts of the mould have cooling channels. They are needed for controlled cooling of the component. During the powder injection moulding process the cooling fluid is pumped through the channels. Its temperature determines the temperature of the mould and, consequently, the heat flux from the feedstock. Typical cooling fluids are water and oil. The mould material must have high strength and wear resistance, because feedstocks are abrasive. The usual mould material is hardened tool steel. Figure 3. Scheme of a two-cavity mould for powder injection moulding The melt delivery system of a mould consists of a sprue and runners. The sprue serves for transporting the feedstock from the nozzle of the injection moulding machine to the runners. The runner makes a path to the cavity. The runner is connected to the cavity by a gate, which has a smaller cross section than the runner. The gate is needed to make weak structural segments between the runner and the cavity so that the runner could be easily separated from the moulded component. To eject the green body from the cavity special ejection pins are used. The dimensions and layout of the runners significantly affect the moulding conditions. The longer is the runner, the higher is the required injection pressure and the heat losses in the feedstock on the way from the sprue to the cavity. Therefore sprue and runners should be kept as short as possible. The lay-out of the runner also depends on the gating position. Gating position is chosen with regards to several factors, the most important of which are the cavity filling pattern and maximum injection pressure. The roughness of the cavity surface determines the quality of the moulding and, eventually, the quality of the surface of the final PIM product. Therefore the mould should be machined to low roughness. To increase productivity the industrial moulds contain multiple cavities. Due to complex shapes the moulds for PIM are expensive. High price of the mould limits the application area of PIM to high scale production of complex-shaped components. 5

12 Chapter.4 Moulding cycle Figure 4 shows schematically the injection moulding machine and a mould. The powder injection moulding cycle is similar to the polymers injection moulding cycle. In the initial moment the mould is opened, while the screw (ram) is set to the leftmost (in the figure) position. When the feedstock is heated to the processing temperature, the mould closes and the screw pushes the feedstock out of the barrel into the mould. The feedstock fills the mould cavity and solidifies. To compensate for shrinkage during solidification, backpressure is maintained on the feedstock until the gate freezes. Until the gate is frozen additional portions of feedstock are forced into the mould during the cooling stage. After the component has completely solidified pressure is removed, the mould opens and the component is ejected. Then the cycle is repeated. The sequence of powder injection moulding stages is shown in Figure 5. Figure 4. Scheme of mould filling during injection moulding Figure 5. Powder injection moulding cycle The quality of the green part depends on the processing parameters one of which is the injection rate. Variable injection rates can be used to control velocity of the injected material inside the cavity. This method is often applied during manufacturing of large parts from polymers. When the cavity has variable cross sections, increasing or decreasing accordingly of the injection rate allows minimising velocity variations of the melt front during filling. Avoiding fast accelerations of the 6

13 Introduction melt front positively affects quality of the product, in particular, improves surface finish and diminishes chances for powder-binder segregation. Injection rate is related to the velocity of the ram. To force the injection rate varying according to the desirable law the velocity of the ram should vary, respectively. The velocity profile versus ram displacement is preset in the injection moulding machine. However, the pre-set values are true only when injecting "in air", i.e. without the cavity. The real ram velocity differs from the preset one because of resistance to the injection and the inertia of the machine. An example of the preset and experimentally measured injection rate profiles can be seen in Figure 6 [6]. The difference between the pre-set and the real velocity profiles increases with the reducing fill time. When the fill time is very short the ram velocity has to alter very fast. Due to non-zero response time of any injection moulding machine alterations of the ram velocity cannot be done faster than a certain limit. Typical response time of hydraulic injection moulding machines is about s. Response time of electric injection moulding machines is about 4 times smaller. However, the use of the electric injection moulding machines is not a universal solution because their velocity controlling capabilities are also limited. Besides that due to higher prices the electric injection moulding machines are less frequently used than the hydraulic ones. Taking into account the above powder injection moulding of small components is usually performed with hydraulic injection moulding machines at a constant ram velocity (and, consequently, constant injection rate). During filling with constant preset velocity the hydraulic pressure gradually increases. Hydraulic pressure and pressure within the cavity correlate as shown in Figure 7. To avoid pressure spikes at the end of the filling stage the process control scheme switches over to pressure control when the cavity is filled by 98-99%. At this moment the pressure reduces to about 80% of the maximum pressure achieved in the cycle. This pressure is maintained until the cavity is filled. During the post filling stage the pressure is still applied to compensate for the shrinkage of the feedstock. However, the magnitude of pressure is decreased as compared with the maximum developed pressure. In the simplest case, like the one shown in Figure 7, there is only one pressure level until pressure is completely removed. Alternatively, pressure may be pre-set to decrease in several steps. The moulded component remains in the cavity until its temperature decreases and it obtains the necessary strength for safe ejection. After ejection of the component the whole system returns into the original state and becomes ready for the next moulding cycle. Injection speed, cm3/s 0 Preset 5 Real Screw displacement, mm Figure 6. Preset and real injection speed profiles Figure 7. Typical a) hydraulic pressure; and b) cavity pressure during PIM 7

14 Chapter.5 Feedstock attributes The quality of PIM feedstock depends on the characteristics of the equipment, duration of the process and properties of the mixed materials. Properties of the feedstock are affected, in particular by the granulometric composition of the powder, shape of the particles, surface condition, type of the binder and type and amount of wetting additives, etc. In the early stages of development of PIM technology the PIM producers mainly produced feedstocks in house. This situation is partially preserved till present time. Especially it concerns feedstocks with rarely used powders and compositions. The disadvantage of in-house production was that it was difficult to obtain feedstocks with the same properties. Depending on the source of the ingredients the properties of the feedstocks varied up to 0% [5]. Feedstocks supplied by the different producers usually had different properties even if the declared composition was the same. With growing PIM market the increasing need for feedstocks with reproducible properties led to creation of a new industry dealing with manufacturing of pre-formulated feedstocks. The market overviews show steady increase of the number of feedstock producers and available types of feedstock formulations [3]. The standard pre-formulated feedstocks are characterised by reproducible properties [7] and are available in big quantities. Due to stable quality standard feedstocks became very popular among PIM manufacturers. Sometimes the demand to use pre-formulated standard feedstock is put forward by the end user of the PIM product. Standard PIM feedstocks became a subject of studies relatively recently. Until now information on properties of PIM feedstocks in the open literature is scattered and incomplete. A good feedstock has homogeneously distributed powder in a binder without agglomerates and voids. To secure homogeneity the mixing is performed in the equipment where high shear rates are developed. Usually attritors and twin-screw mixers are used. The volume fraction of powder in a PIM feedstock is called solid loading. It is an important parameter that determines porosity of the brown part. The theoretical maximum solid loading is determined by the volume of powder particles that are densely packed. Using powders with wide particles size distribution increases solid loading because small particles fit in pores between the big ones. However, preparation of high quality mixture of powder with wide particles size distribution is difficult. There is a danger that small particles agglomerate. Technologically much easier is the preparation of a feedstock from monodispersed spherical powders. Particles of such powders arrange in densely packed structures. Feedstocks with spherical metal powder have solid loading vol.% and more. Powders with non-spherical particles pack less efficient. Examples are the ceramic powders. Many feedstocks with ceramics powders have lower solid loading ranging from 50 to 55 vol.%. Solid loading in the real feedstocks is lower than the theoretical maximum, because the binder is added in the amount that slightly exceeds the total volume of pores. It is necessary for facilitating of rearrangement of powder particles in the liquid feedstock. Insufficient amount of binder leads to creation of voids between the particles and increasing of viscosity of the feedstock. Excessive binder also is not desirable. After the green body is moulded the binder becomes redundant. Keeping the amount of binder low permits reducing debinding time and keep porosity of the brown part low. Therefore the amount of binder is kept at minimal possible level. This level is determined by the ability of the feedstock to fill the cavity. When calculating the amount of binder needed to produce a feedstock thermal expansion of both the binder and the powder should be taken into account. Most polymers have high thermal expansion coefficients as compared with the powders. That means that during heating the binder expands more than the powder. With the increase of temperature the volume fraction of the binder increases, and consequently, solid loading decreases. Due to this effect the solid loading in the molten feedstock may decrease by several percent as compared to solid loading at the room temperature. For example, in the feedstock of iron powder with polymer wax solid loading decreases from 60 to 56 vol.% while heating to 00 C from the room temperature [5]. Solid loading is also affected by pressure because compressibility of polymers is higher than compressibility of powders. 8

15 Introduction One of the most important characteristics of the feedstock is its viscosity. Most of polymers in a liquid state have properties of a non-newtonian fluid and show viscoelastic effects [8]. Usually viscosity decreases with increasing shear rate. This phenomenon is known as shear thinning. PIM feedstocks in the liquid state behave in a similar way. But their viscosity is higher compared with viscosity of pure polymers. Typical viscosity plots for a PIM feedstock and a pure binder are shown in Figure 8. Figure 8. Typical viscosities of a polymer and PIM feedstock using this polymer as a binder The other properties, which are important for powder injection moulding are specific heat and thermal conductivity. The specific heat determines the amount of heat, which can be stored in the feedstock during the heating process and the internal friction in the barrel. Usually specific heat of PIM feedstocks is several times lower then specific heat of pure binder material [9]. On the contrary, thermal conductivity of powder materials usually is higher then thermal conductivity of polymers. Because of high solid loading it can be several times higher than that of pure binders [0]. Properties of PIM feedstocks are explained in detail in Chapter 3..6 Major problem areas related to PIM technology Ideally, a green part should have an uniform distribution of the powder in the binder. It should have a high quality surface and no defects. It should not warp neither after moulding nor during sintering. In the areas where two melt fronts meet together the so-called weld and meld lines are formed. These lines should be preferably avoided. In cases when there is no possibility to avoid weld lines, the filling pattern should be organised in such a way that they appear in the uncritical positions. The entire moulding process should take the shortest possible time. The actual flow of the feedstock during the filling of the cavity is determined by complex interplay of numerous parameters. As typical PIM component has complicated shape, the cross section at the melt front may significantly vary along the filling path. The velocity control by variable injection rate is usually not possible due to inertia of the injection moulding machine. Depending on the cross sections of the cavity, the velocity of the melt front increases in small cross sections and decreases in the large ones. The feedstock experiences fast accelerations and decelerations. When moulding the components with complex shape the flow direction sharply changes. The feedstock has high thermal conductivity and low specific heat. Moulds are usually made of tool steels, which have relatively high thermal conductivity. As the feedstock under pressure has good contact with the mould surface, the heat transfer coefficient on the feedstock-mould interface is high. Therefore the heat flux from the feedstock to the mould is limited mainly by the difference of 9

16 Chapter temperatures between the mould and the feedstock. In such conditions temperature of the feedstock strongly depends on temperature of the mould. Injecting feedstock in the mould at room temperature is usually not possible due to premature solidification of the feedstock. To facilitate the injection process the mould temperature is controlled by the cooling liquid. Ideally the mould temperature should be uniform. In reality it is not uniform. The exact temperature distribution in the mould depends on the lay out of the cooling channels and the shape and dimensions of the mould. The feedstock thus flows though the mould with non-uniform temperature distribution and accordingly non-uniformly cools down. On the other hand, the feedstock experiences internal frictional heating. During filling there is velocity gradient in the moving feedstock across the cavity. In the thin cavity the layers of the feedstock that are adjacent to the mould surface have lower velocity as compared with the layers in the middle plane of the cavity. In principle, similar velocity gradient is present while filling the cavity of any arbitrary shape. In any case, the movement of the feedstock can be considered as movement of certain layers that have different velocity. Friction between such layers causes heating of the feedstock. As it will be shown later, the amount of generated heat due to friction is proportional to the viscosity of the feedstock and squared shear rate. Due to high injection rate and the above mentioned velocity gradient the shear rates are high. The shear rates are also non uniform across the thickness of the cavity and depend on the size of the cross section. In the narrow cross sections very high shear rates are observed. In the larger cross sections the shear rates decrease. Therefore the local viscous heating of the feedstock during filling is also non-uniform. Together with the non-uniform heat flux from the feedstock to the mould, the viscous heating contributes to the development of non-uniform temperature field in the feedstock. It can be seen that a real PIM component is formed by the feedstock that moves with high velocity and has temperature gradients. In such conditions there is a chance of development of undesirable effects. High accelerations and decelerations of the feedstock as well as abrupt changes of the flow direction may cause segregation of the powder and the binder. The consequence of such segregation is density gradient and non-uniform shrinkage during sintering. Segregation of the powder and binder can also take place in areas of high shear rates, because the polymer binder at shear rates exceeding the certain level disintegrates. The critical shear rate levels are material properties. They are known for the standard polymer materials. Disintegration of the binder may cause the destruction of the separating layers between the powder particles and creation of conglomerates, which later develop into the structural defects. Since the melt front velocity of the feedstock varies while filling different parts of the cavity, in some cases the melt front velocity may decrease to almost zero. In such cases it is called "hesitation" of the melt front. Hesitation also negatively affects the structure of the component mainly due to the danger of premature solidification and formation of strong weld lines. Non-uniform temperatures of the feedstock leads to development of internal stresses in the moulded component. These stresses may cause warpage or destruction of the component at the debinding stage when the strength of the component decreases. The problems with the filling may be diminished or completely avoided by choosing the proper powder injection moulding processing conditions and design of the mould. The weld lines can be shifted from the undesirable areas by changing the gating position. Position of the gate also affects the entire flow pattern and, in particular, melt front velocity. Changing the gating position therefore is one of the most frequently used methods for optimisation of the mould filling process. The melt front velocity can be also changed by adjusting accordingly the injection rate. However, the processing window during PIM is usually narrow because, on one side, the feedstock must be injected fast enough to fill the cavity, and, on the other side, it should be injected at the rate that prevents development of excessive shear rates and frictional heating. Most of the filling problems may be prevented if the powder injection moulding takes place with the optimal processing conditions (injection rate, feedstock temperature, mould temperature) into a properly designed mould. Important are gating position, shape and length of the runners and cooling channels. The major difficulty with optimisation of the mould design and the processing 0

17 Introduction conditions during PIM is that there are many factors that are not completely known. To get the clear picture of the moulding stage it is necessary to know pressure, temperature, shear rates and position of free surface of the feedstock during the filling of the mould. These characteristics cannot be analytically calculated for most of the complex shaped PIM components. It is also difficult, and in many cases not possible at all to measure them experimentally. Therefore optimisation of the powder injection moulding process is a difficult task. So far it is usually done by trial and error method. The success of optimisation depends very much on the experience of a design engineer and an operator of an injection moulding machine. Error and trial method has low efficiency and does not guarantee that the optimal solution will be found within reasonable time. The effect of the proposed improvements can be estimated only after the whole process is performed again from the beginning to the end with a new mould and/or moulding conditions. With such an approach a lot of efforts, expensive feedstock, labour and time are wasted. In case optimal conditions are finally found, there is little information on the insight of the process, and similar problems often cannot be prevented while starting production of another component..7 Process simulation Essential help in solving problems, which are often encountered while starting production of a new product by PIM method can be expected from numerical simulations. If the process is properly simulated then there is a possibility of simulating its parameters, including but not limited to temperatures, shear rates, pressures, and velocities of the melt front. Knowledge of such data allows prediction of the flow pattern and comparison of different options of mould design and process conditions. To simulate the powder injection moulding it is necessary to have: - mathematical model of the process - properties of the materials - initial conditions - boundary conditions. A mathematical model is a set of equations representing a physical process. The physical process during powder injection moulding is the flow of the feedstock under non-isothermal conditions. Mould filling simulations are performed using Computational Fluid Dynamics (CFD) principles based on solving equations of conservation of momentum, mass and energy (Navier-Stokes equations). These equations describe the motion of a fluid in non-isothermal conditions. For some simple geometries and boundary conditions the Navier-Stokes equations can be solved analytically. For most of real complex-shaped geometries the solution can be found only using numerical methods. Modelling of flow of a PIM feedstock should take into account its heterogeneous nature and characteristics of the flow like slip. The main problem in simulating PIM is that the flow of a mixture of powder and polymer is difficult to describe mathematically. A material model of the PIM feedstock actually does not exist yet. There are two main materials whose properties are required. These are the material of the mould and PIM feedstock. In the simulations the mould is assumed to be a non-deformable body. Therefore only thermal properties are relevant for the mould material. The feedstock is injected in the liquid state and solidifies in the mould. For simulation of these processes it is necessary to have rheological, thermal and mechanical properties of the feedstock. Initial conditions are determined from the real PIM process. Boundary conditions are extracted from the assumptions that are always made while describing the process mathematically. For example, it is assumed that the mould does not deform, that the velocity of the feedstock at the injection point is uniform and constant. At the mould surface the velocity of the feedstock usually is assumed to be zero. This

18 Chapter boundary condition is known as "no slip condition". Boundary conditions impose certain limits to the simulated process. For CFD calculations a number of special analysis packages have been developed. These packages include the programmes for defining geometry of the component, imposing the boundary and initial conditions and solving numerically the governing equations. The first analysis packages could simulate the flow only in two dimensions. They were primarily oriented for simulation of the injection moulding of polymers since most of polymer components are thin-walled and can be represented by the thin walled models. The two-dimensional analysis provided good results for the injection moulding of polymers. Later on the two-dimensional analysis packages were improved to analyse the injection moulding of three-dimensional thin walled components like a mailbox. In each wall of such an object the flow is assumed to be two-dimensional, but the walls could be arbitrary positioned in the 3-D space. Analysis of such thin walled three-dimensional models received the name of.5-d analysis. Programmes for.5-d analysis became very popular in the polymer industry. The first experimental codes were followed by a number of commercial packages for.5-d analysis. Last 0 years such packages are widely used by the producers of plastic components for optimisation of the moulds and the process parameters. The analysis packages developed for polymer industry implement non-newtonian material models because most polymers in liquid state behave as non-newtonian fluids. Within one package usually several material models that describe the material viscosity as a function of shear rates and temperature are available. The,5-D analysis packages can hardly be used for simulation of filling of a thick body, which cannot be adequately represented by a thin-walled model. The need to develop an analysis tool for simulation of metal casting process led to the development of 3-D simulation programmes, because products of metallurgy produced by casting usually are "bulky". Metals in the liquid state often behave as a Newtonian fluid. Therefore analysing packages that were primarily oriented for casting industry usually include few non-newtonian material models. For simulation of the metal flow viscosity is often assumed to be constant. Simulating the 3-D flow problem requires solving much more equations as compared with the same problem described in two-dimensional space. Therefore 3-D simulations are very time consuming. When the first programmes for analysis of fluid flow started to appear the computers were relatively slow and had limited memory. The 3-D programmes became intensively developed relatively recently, when fast computer have been developed. The continuously increasing computing power of modern computers allows including in the new versions of the analysis packages new tools that extent their application limits. For example, the analysis packages that were developed for simulation of injection moulding of polymers now are capable to perform analysis in 3-D models. On the other side, the programmes originally developed for the simulation of casting extent the number of incorporated material models to the models for non-newtonian fluids. Simulation programmes specifically for powder injection moulding process are being developed, but none of them so far was produced in a commercial version. So far the analysing packages for powder injection moulding are available only at the research centres where they were developed. The new features of the available commercial simulation packages allow using them for simulation of the powder injection moulding process. Simulation of PIM with such packages will be subjected to some limitations because PIM feedstock in this case must be assumed to be an isotropic homogeneous fluid. For example, with such an assumption it will not be possible simulating the powder-binder segregation phenomena. However, this approach is justified because it allows simulating a number of other important parameters and help optimising the entire PIM process. While using the commercially available analysis packages for simulation of PIM the feedstock needs to be defined as a new "polymer" or "metal", depending on the type of the programme used, with certain properties. For that properties of the feedstock are required. The few available in the open literature data on viscosity, thermal conductivity and specific heat of PIM feedstocks are

19 Introduction scattered and incomplete. Therefore, in most cases they must be specifically measured for the simulation..8 Scope of this thesis The quality of the final product made by PIM depends on the quality of the feedstock and the processing routes during moulding, debinding and sintering stages. Defects caused by low quality of feedstocks are not the issue any more since high quality standard feedstocks became available. The main sources of defects during PIM are the non-optimised moulding conditions and wrongly designed tools (moulds). Among all processing stages of PIM, the moulding stage is the most critical one. Debinding and sintering stages concern removal of the binder from the component and bonding the powder particles into a solid body, respectively. These stages are relatively well studied. Processing regimes for theses stages are known and can be used without changes for a variety of products with different shapes. On the contrary, the moulding stage for every new product requires adjustment of the injection parameters. Manufacturing a new type of product requires a new mould. The technological parameters and the mould design are the uncertainties that have to be clarified during the optimisation period. The main difficulty is that there are no standard methods for performing such an optimisation. The purpose of this thesis was to investigate the moulding stage of the powder injection moulding process using numerical simulation analysis and compare applicability of different commercial simulation packages for such simulation by experimental verification of the obtained numerical results. The choice of the analysis packages for the study was determined by the following criteria: - availability on the market - availability of material models for the non-newtonian fluid -,5-D and 3-D models. In this work three commercial codes: C-Mold, Moldflow and ProCAST were used. The first two of them were developed for analysis of injection moulding of polymers, which is quite similar process to PIM. C-Mold is a pure,5-d package. First versions of Moldflow also were twodimensional, but the last versions are already capable to analyse 3-D models. In this study the 3-D version of Moldflow was used. The third simulation package, ProCAST was developed for casting industry. Because of similarity of the injection moulding of polymers and PIM there were attempts to use both C-Mold and Moldflow packages for simulation of powder injection moulding. But the results of simulation with these packages need additional validation. It was also our goal to compare them with ProCAST, which has several features that make it attractive for simulation of powder injection moulding. In particular, ProCAST is fully three-dimensional package and has the possibility to include in the analysis the exact model of the mould. The last feature theoretically gives to ProCAST an additional advantage among all three considered programmes. Regarding all above the task of this study shall be formulated as follows: Implementation of 3D numerical simulation of the PIM process aimed at optimisation of the tool and technological parameters of the powder injection moulding The aim is to find answers to the following questions: Which parameters of the powder injection moulding process can be simulated with the existing commercial analysing packages? How realistic are the results of simulation and what are the main reasons for errors? What are the limitations of the simulation performed with the existing analysis packages? 3

20 Chapter How useful are the simulation results for the manufacturers? What shall be improved in the existing analysing packages from the point of view of the end users? Because of the reasons mentioned above the simulation results of the PIM process needs to be validated. The results of validation are to be used as guidelines for ) application of the existing software for optimisation of PIM process and for ) further development of the simulation software. The structure of the thesis is as follows: Chapter has introduced the powder injection moulding process and explained the subject of the study. Chapter describes the general principles of numerical simulation. It addresses modelling of flow of viscous fluid, finite elements method, meshing and boundary conditions. Brief introduction to C-Mold, Moldflow and ProCAST analysing packages is given. Chapter 3 is devoted to characterisation of the standard feedstock of stainless steel, used in this study. Results of measurements of viscosity, thermal conductivity and specific heat are presented. The importance of the measurements of those properties in the nonequilibrium conditions, close to those during the real powder injection moulding process is emphasised. The approaches, simulation set-up, initial and boundary conditions used in three analysing packages C-Mold, Moldflow and ProCAST, and examples of simulation of the powder injection moulding are presented in Chapter 4. This Chapter provides insight on the advantages and disadvantages of the C-Mold, Moldflow and ProCAST packages. It is shown that ProCAST produces more detailed output data than two other analysing packages. This feature of ProCAST combined with better viewing capabilities of ProCAST offers more opportunities for the optimisation of the PIM process. Chapter 5 presents the experimental set-up, equipment and methods of measurements of pressure and temperature during the validation experiments. The experimental results are compared with the simulated ones. From the validation experiments the quantitative data for estimation of applicability of commercial simulation packages for simulation of powder injection moulding process have been obtained. Analysis of sensitivity of simulation results of ProCAST to the input parameters is reported in Chapter 6. The obtained results permitted estimating the requirements to the accuracy of different input data. The role of mould temperature, heat transfer coefficient on the melt-mould interface, viscosity model and quality of the mesh was estimated. In particular it has been demonstrated that representation of viscosity of the feedstock by a constant provides unacceptably erroneous results. Chapter 7 includes the experimental and numerical results obtained for the powder injection moulding of the component with the variable thickness. Efficiency of the numerical simulation for the investigation of the problem of powder injection moulding is illustrated with the examples. The thesis is closed by Conclusions, where summary on the obtained results and future direction are given. This research has been carried out at the Laboratory of Materials Science at the Delft University of Technology. It was financed by the Netherlands Institute for Metal Research (NIMR) in the framework of the Strategic Research programme. 4

21 Chapter Simulation principles Numerical modelling of a physical process requires description of this process by a number of mathematical equations. These equations have to take into account the phenomena, which we consider to be important to the behaviour of the physical process. During modelling the real process is replaced by an imaginable one, which is made of certain assumptions. Assumptions help to define the model. They can simplify the process and permit an easy solution. However, incorrect assumptions may distort the results. There is no strict criterion for determining which phenomena are important, and which are not. Increasing the number of phenomena that are taken into consideration while creating the mathematical model helps to avoid misrepresentation of the process. But simultaneously the model becomes complex and the solution may be difficult. A good model shall be a compromise between complexity and accuracy of the produced results. In case of powder injection moulding process in the first approximation the feedstock can be considered as a homogeneous isotropic viscous fluid. If so, the flow of the feedstock can be described by the equations of motion of a viscous fluid and heat exchange between it and the mould. This approach is beneficial because the mathematical model can be made of the same equations, which are used for simulation of injection moulding of plastics and metal casting. The difference between these processes from the mathematical point view lies mainly in the properties of material being used. Till recent time simulation principles of injection moulding and metal casting were developed relatively independently. In a recent book on simulation of material processing [] it is demonstrated that both processes are based on the same principles and, therefore, the same solution methods are suitable for simulation of them. Differences in a particular process can be taken into account by assuming specific properties of the material and applying relevant for each case boundary conditions. This principle can also be extended for the powder injection moulding process. The disadvantage of any simplification is the reduction of accuracy of the calculated output data and inability to predict phenomena, which were not included in the model. Assumption that the PIM feedstock is an isotropic fluid does not allow for prediction of any phenomena that are related to powder binder interactions, like powder segregation. If those phenomena are the primary concern of the simulations then the model of the feedstock assuming that it is an isotropic fluid is irrelevant and more complicated model shall be used. However, at present such a model does not

22 Chapter exist yet, taking into account a wide size distribution of powder particles. On the other side, many details of the powder injection moulding process can be predicted without regards to the complex composition of the feedstock. The Computational Fluid Dynamics (CFD) principles, used for such type of simulations, are presented below.. Fluid flow Mathematical formulation for the flow of a viscous fluid in the mould comprises governing equations of conservation of mass and momentum: For a material with density ρ, specific heat at constant pressure C p in most general form these equations can be written as follows: Conservation of mass: where notation Dρ + ρ( v) = 0, () Dt D Dt = + v t (a) means material derivative, which is a particular kind of time derivative, in which the material point is held constant. Conservation of momentum: Dv ρ Dt = p + τ + ρb () In the equations ( ) v is the velocity vector, p is the pressure, τ is the stress tensor and b is the vector of the body force per unit mass acting on the fluid. Equations ( ) are sufficient to describe the fluid flow. But there is no method to solve them analytically in such general form. For practical needs these equations are simplified. Typical simplifications are based on the assumptions that allow excluding less important terms from the equations. Usually isotropic material and symmetric stress tensor are assumed. If material density is assumed to be constant, the equation of conservation of mass () reduces to v = 0 (3) One should take into account that simplified equation (3) holds only for materials, which are not only incompressible but also have low thermal heat expansion coefficient, i.e. their density does not change much with temperature. Assumption of constant material density during the PIM filling stage does not introduce big error because most of fluids are practically incompressible at the pressures encountered at the filling stage. Compressibility of polymers is usually taken into account, but comparing with the PIM feedstock they have higher volume fraction of polymer (00% against 35-40% in the feedstock). In normal processing conditions the only body force 6

23 Simulation principles acting on the injected material is gravity. Therefore proportional to shear rate (rate of deformation), i.e.: b = g. For a Newtonian fluid stress τ is τ µγ = (4) The coefficient of proportionality µ is called the shear viscosity. If two-dimensional flow is concerned, rate of deformation is equal to velocity gradient across the thickness of the plane, where the flow takes place. For example, shear rate in y -direction in the x z flow plane will be: v τ = µ x = µγ yx. (5) y The viscosity of a Newtonian fluid µ is independent on shear rate. If the viscosity is assumed constant, and the only body force that acts at the material is gravity, momentum equation () can be re-written without stress tensor notation in simpler form: Dv ρ = p + µ v + ρg. (6) Dt Equation (6) is referred to as Navier-Stocks equation for a Newtonian fluid. Most of polymers are non-newtonian fluids. One common feature of non-newtonian fluids is that equation (5) does not hold for them. Since viscosity of non-newtonian fluids depends on shear rate, the equation (5) should be modified as follows: τ = ηγ ( ) D, (7) where D is the rate of deformation tensor. For a simple shear flow equation (7) becomes τ η( ) γ γ =. (8) Fluids for which equation (7) holds are called generalised Newtonian fluids. Term "Generalised Newtonian Fluid" sometimes is confusing, because it is used for actual non-newtonian fluids. The function η(γ ) is called non-newtonian viscosity. Type of the viscosity function depends on the material properties. If the curve at the viscosity versus shear rate plot turns downward with the increase of shear rate, then the fluid is called shear thinning or pseudoplastic. Most of polymers exhibit this type of non-newtonian behaviour. PIM feedstocks, as materials based on polymer binders, have the same type of viscosity.. Material models At the plots of shear stress versus shear rate for pseudoplastic fluids three regions can be determined. The first one is the region at small shear rates, where practically Newtonian behaviour is observed. Second is the region of shear thinning, and the third is the region of second Newtonian behaviour [8]. The third region is observed only for part of the known polymers at very high shear rates. The shear-thinning regime can be described by a number of empirical, semi- 7

24 Chapter empirical or theoretical functions. The simplest is the power law function, which defines viscosity as s function of shear rate as follows: n η = mγ (9) In the formula (9) m is a material constant, n is the power coefficient, which takes the values between 0 and for shear thinning materials. It can be defined from the plot of ln η versus ln γ. To cover both Newtonian and non-newtonian regions of viscosity and to take into account the effect of pressure on the viscosity, Cross and Carreau models and their modifications are often used for representation of viscosity of PIM feedstocks [ - 5]. For any pseudoplastic polymer it is possible to determine critical shear rate corresponding to shear stress τ *, when viscosity changes from Newtonian to shear thinning one. Using parameter τ *, the two flow regimes can be described by the Cross model as follows: η0 η = η 0γ + ( ) * τ n, (0) where η 0 is the so-called zero-shear rate viscosity. It is defined by the 5-constant model: Tb η 0 = B exp( )exp( βp), () T * The model constants are τ, B, T b, n and β. The constants T b and β are the characteristics of sensitivity of zero shear rate viscosity η 0 on temperature and pressure ( p ), respectively. Factor (-n) characterises the slope of the shear-thinning curve, while B fixes the level of η0 at a certain temperature. Cross-William-Landel-Ferry (Cross-WLF) is a modified Cross model. According to this model temperature and pressure influence on the zero-shear viscosity η 0 is defined by the 7-constant model: A ( T T*) η 0 = D exp[ ~ ], () A + D3 p + ( T T*) where T* = D + D3 p (3) ~ Here D, D, D3, A and A are the additional model constants. Coefficients D and D 3 characterise the glass-transition temperature at low pressure and the linear pressure dependence of T *( p), respectively. T * represents the reference temperature usually taken as the glasstransition temperature of the polymer material. For description of viscosity in all three regions of the flow curves including the second Newtonian region, Carreau model is often used [6]: η η η η 0 = + ( n ) / [ ( λγ ) ], (4) 8

25 Simulation principles η is the viscosity at zero shear rate, n is a where η is the viscosity at infinite shear rate, 0 constant with the same interpretation as in the power law model. The zero shear rate viscosity is defined as in the Cross model (equation ). If there is no pressure dependent data, then coefficient β is assumed to be zero. The constant λ is an inverse critical shear rate λ = / γ cr, where γ cr represents shear rate when shear thinning becomes noticeable. Sometimes λ is also called phase shift coefficient or time constant. This model has been modified by Yasuda [7]. Due to additional parameter a proposed by Yasuda the modified Carreau-Yasuda model obtained additional flexibility and became applicable for describing viscosity versus shear rate curves, which have several regions of different character. Mathematically Carreau-Yasuda model can be written in the following form: n a [ ] a ( ) ( λ / η = η γ, (5) + ( η 0 η ) + ) η is the viscosity at infinite shear rate, η0 is the viscosity at zero shear rate, λ is phase where shift coefficient, γ - shear rate and a - is Yasuda parameter. The experimental data are used to define the coefficients η0, η, λ, a and n. Temperature dependence of viscosity is taken into account by different sets of the coefficients for each temperature, at which viscosity is measured. There exist other viscosity models, besides the considered ones [8]. However, the mentioned models are most frequently used in the analysis packages for numerical simulation of fluid flow. In Chapter 3 rheological properties of the feedstock used in this work will be described using Cross-WLF, Carreau and Carreau-Yasuda models. These models have been used for simulation of the PIM process with the analysis packages C-Mold, Moldflow and ProCAST, respectively, as described in Chapter 4..3 Energy balance During powder injection moulding a hot feedstock enters into relatively cold mould. After the contact between the feedstock and the mould is established the feedstock cools down because the heat from the feedstock is transferred to the mound. At the same time heat is generated inside the flowing feedstock due to internal friction. Governing equation for heat flow states that heat is conserved provided that all heat sources and heat sinks are included. It can be written in the form: Dε DV ρ = q ρp + τ : D + ρ R. (6) Dt Dt The left-hand side of this equation is the rate of change of internal energy, and the terms on the right-hand side represent heat transferred by conduction, work done by compression, work done by shape change at constant volume, and internal heat generation, respectively. In equation (6) q - is the heat flux vector, V - volume per unit mass; D is the rate of deformation tensor and R is the rate of generation of internal heat per unit mass. The heat flux is defined by the Fourier's law, which states that the heat flux is proportional to the temperature gradient: 9

26 Chapter 0 q T = k, (7) where k is thermal conductivity of the material. In general case k is a tensor. For the simulation purposes thermal conductivity can be assumed constant. Then for a material with specific enthalpy H the energy conservation equation may be re-written as follows: ( ) : p p DT Dp C L k T R Dt Dt ρ ρ ρ + = + + D τ (8) Where specific heat p C is defined as p p T H C =, p L is latent heat of pressure change: V p H L T p = and R is the rate of generation of internal heat per unit mass. If the material has constant density and constant isotropic thermal conductivity the energy equation (6) equation can be further simplified to : p DT C k T R Dt ρ ρ = + + D τ (9) For a Newtonian fluid heat dissipation term is given by: : µγ = D τ, (0) where scalar strain rate : γ D D. In rectangular coordinates the energy balance equation finally takes the form of: = z T v y T v x T v t T C z y x p ρ = z v y v x v z T y T x T k z y x µ R z v x v y v z v x v y v x z z y y x µ + ρ () Temperature in the mould is determined only by heat conduction, since no movement of the material and no heat generation takes place. Therefore heat conduction in the mould is described

27 Simulation principles by the heat conduction equation obtained from the equation (8) by dropping terms for heat generation and convective heat transfer: T ρ C pm = km T, () t where index m marks properties of the mould..4 Fluid flow momentum Most of the mathematical models for simulation of injection moulding of polymers are based on the generalized Hele-Shaw approximation, which is a set of assumptions used to simplify the governing equations. The Hele-Shaw approximation assumes that the flow is pressure driven and takes place between parallel plates []. If the flow takes place in x y plane, pressure variation is assumed to be negligible in the thickness direction z. The primary variable is the pressure, which can be found by solving the following equation: p p S + S = 0, (3) x x y y where S is the fluidity, or flow conductance. Fluidity is defined as follows: δ z dz S =. (4) η( x, y, z) 0 The midplane lies at z = 0 and the distance between the parallel plates is δ. Velocities (z) can be found from: v x and v (z) δ p z dz vx ( z) = x, (5) η( z ) z δ p z dz v y ( z) = y, (6) η( z ) z While average velocities are given by v x v y S p = h x (7) S p =. h y (8)

28 Chapter Hele-Shaw approximation allows further simplification of the governing equations. For the twodimensional flow in the x y plane the energy equation can be reduced to [8]: T ρc t T x T y + v + v = k + ηγ, (9) p x y z T where shear rate γ takes the following simple form: where v and x respectively. v v x y γ = +, (30) z z v y are the components of velocity vector V in the directions x and y, The Hele-Shaw approximation is a standard method used to simulate injection moulding of polymers [8-9], because it dramatically simplifies the governing equations for the flow of a viscous fluid in a narrow gap. However, the Hele-Shaw approximation cannot capture physical phenomena that rely on the terms dropped during simplifying the equations. This makes the Hele Shaw solution unrealistic at the edges of the mould and at the flow front..5 Modelling of slip and powder-binder segregation of the PIM feedstock In reality PIM feedstock consists of two phases one of which (binder) undergoes phase transformation during the moulding stage, while the other (powder) one remains solid. Besides that properties of the constituents are different, the distribution of the powder in the binder may be distorted during the moulding process. Powder injection moulding is usually accompanied by slip [0]. Therefore in ideal case the governing equations used to simulate the PIM process have to be modified to account for these phenomena. Efforts undertaken in modelling of specific PIM-related phenomena resulted in a number of works [ - 7]. Hwang and Kwon [4-6] proposed twodimensional models to account for slip: slip velocity model and slip layer model. In the slip velocity model they modified velocity equations of the Hele-Shaw approximation by introducing a term for slip layer velocity as follows: ~ S p v = + b x x v xs (3) ~ S p v = + b x y v ys while equation (3) was respectively modified as follows:, (3)

29 Simulation principles ~ S x p bv x ~ + S y p y xs bv ys = 0 (33) δ ~ z S = dz η 0, (34) where v xs and v ys are components of slip layer velocity. In the slip layer model different fluidity S for the slip layer with thickness b was introduced as follows: ψ b z z S = dz + dz. (35) η Then it was substituted in the equation (3): η 0 ψ S x p + S x y p y = 0 (36) The components of average velocities can be found, respectively, from the following equations: S p u ( x, y) = (37) b x S p v( x, y) = (38) b y To simulate segregation phenomena the following diffusion equations were proposed [7]: and ~ η D = DΦ γd p (39) η Φ Φ Φ Φ + u + v t x y Φ = D x, (40) where D ~ is diffusion constant, d p is particles size and Φ is solid loading. This model was successfully used to simulate the experimentally observed 5% difference in powder concentration in the injection moulded thin plate [7]. However, the simulation was limited to a two-dimensional flow. With the purpose to simulate segregation Gelin and others [8] introduced a new formulation to describe PIM feedstock as two-phase material. In the proposed formulation different densities ρ s and ρ f were assigned to a powder and a binder, respectively. Then two separate equations of 3

30 Chapter conservation of mass for powder (solid fraction) and binder (liquid fraction), respectively, can be written: ρ s t ρ t fs + ( ρ v ) = 0, (4) s s + ( ρ v ) = 0. (4) f f Where v s and v f are the velocities of the powder and the binder, respectively. Then separated Navier-Stokes equations for each phase are: v s ρ s = = Φ s p + σ s + ρ s g + ms t (43) v f ρ f = = Φ f p + σ f + ρ f g + m f t (44) In the equations (43-44) Φ is the solid loading, p is pressure, σ is the deviator of Cauchy stress tensor, m s and m f are the momentum exchange terms ( ms = m f ), and g is gravitational acceleration. Indices s and f indicate solid and liquid phase respectively. Velocity difference is taken into account by introduction of an interaction coefficient K : m s = K v v ) (45) ( f s This approach allows calculating separately volume fraction and velocity fields for both solid and liquid phases. Despite assuming the liquid phase to be a Newtonian fluid, good correspondence of the numerical results and experimental measurement was reported [8], though only for a twodimensional model. Last years considerable efforts were made in the field of simulation of the powder injection moulding process. But the implementation of the models suitable for simulation of slip and powder binder segregation remains at the early stage. The new methods to calculate slip were applied first to the -D geometries [4-6]. In the recent study [9] simulation of slip was included in the full 3-D analysis. However, in this study the flow of the 36 L PIM feedstock was assumed to be isothermal. The only commercialised analysing package for simulation of PIM is PIMflow [30]. However, published results of simulation with PIMflow concern -D analysis [4-6]. Some results on 3-D simulation of powder injection moulding performed with the NRC-3D analysing package were reported [3]. The results of calculation with NRC-3D include mainly the flow pattern of the feedstock during the mould filling. This analysing package is not yet commercialised..6 Boundary conditions For the problem of powder injection moulding boundary conditions relate to the solution of the pressure and thermal distributions in the cavity. Since moulds are vented to allow air ahead of the 4

31 Simulation principles melt to escape, the pressure datum may be chosen at atmospheric pressure. Then pressure boundary conditions are: - The pressure is zero at the flow front: p = 0 on flow front (46) - The pressure p (or velocity V ) is defined at the points where the melt is injected. p = p in, or Vin V = at the injection points (47) - The normal pressure gradient is zero at any boundary. p n = 0, (48) Velocity boundary condition on the melt-mould interface depends on the slip value. In case slip is neglected, velocity of the melt at the mould surface is set to zero. Temperature boundary conditions are the following: - The melt temperature at the points of injection is defined: T = T in at the injection point (49) - The temperature at the cavity wall must be defined: T = T w on Γ, (50) where Γ is some subset of the total boundary. - For the two dimensional case temperature gradient in the z - direction is zero at the cavity centre line and T = 0 at z = 0 (5) z Heat flux boundary condition: k T n = q on Γ, (5) where k - is the thermal conductivity, n is unit vector normal to the surface and Γ is some subset of the total boundary Γ. Heat flux q may be specified or calculated: where h is heat transfer coefficient. q = h( T Ta ), (53) To track a moving surface of the melt a special function F ( x, y, z, t) can be introduced. This function determines the presence of the feedstock by satisfying the following conservation equation: 5

32 Chapter F t + Fu = 0 (54) The function F takes value at the locations where melt is present and value 0 at locations without the melt. So F is a distribution, which is discontinuous and not differentiable at the surface. The location of the free surface is at the transition from = F =. F to 0.7 Numerical solution The governing equations are solved using numerical techniques. The most common are methods of finite element method (FEM) and finite difference method (FDM). Some codes employ a combination of both methods. During numerical solution the governing differential equations are replaced by a system of algebraic equations, the total number and complexity of which depends on the complexity of original differential equations and used numerical method. In this chapter numerical solution is demonstrated for the two-dimensional example based on the Hele-Shaw approximation. The same approach is used for simulation of a three-dimensional flow, though the number of equations to be solved in 3-D case is larger. It can be shown [8] that for the Hele-Shaw approximation continuity and momentum equations can be combined into one pressure equation: where fluidity S is defined as p p S + S = 0, (55) x x y y δ z = dz S (56) η 0 Here viscosity η is a function of shear rate and temperature. Energy equation for the flow of incompressible fluid has the following form: T ρc t T x T y + v + v = k + ηγ, (57) p x y z T where shear rate γ is calculated as: The solution steps are the following: v v x y γ = +, (58) z z 6

33 Simulation principles. Calculate fluidity S. At the start of an analysis a nominal value of viscosity at the melt temperature is used. At an intermediate step of an analysis S is calculated using the shear rate and temperature data from a previous step. After fluidity is known, equation (55) is solved for pressure, which in turn is used to calculate velocities. A new value of shear rate may then be calculated using equation (58). Then viscosity is updated. The new viscosity value is used to determine new fluidity S. The iteration continues in this way until, on two consecutive iterations, the change in pressure becomes less than some defined tolerance.. After the pressure calculation has converged, the current value of velocities v x and v y, the shear rate γ and the viscosity η are used in equation (57) to calculate the convective and viscous heating terms. The conduction calculations are performed with finite differences methods and give the temperature field. With known temperature an updated viscosity value is calculated. This is then used to calculate the flow into each control volume on the flow front. 3. Knowing the flow rate into each control volume it is possible to predict which of these will fill in the next time increment. The flow front is then advanced accordingly. Thereafter steps, and 3 are repeated until the mould is filled..7. Discretisation Discretisation involves representing the continuous variables with a number of descrete values associated with the cells (elements) or vertices (nodes) of a computational grid (mesh). Though this process, the differential equations are approximated by a set of algebraic equations, which afterwards are solved for the unknown discrete values. For the simulation of flow, Eulerian (non-deformable) type of mesh is used. Although it is possible to use other types of mesh elements, triangular elements are most suitable for filling the complex shapes, which are typical for PIM components. Meshing with triangular elements is usually performed automatically by the analysing packages. An example of a triangular element is shown in Figure 9. Vectors n i are the unit outward normals to the element sides and the element boundary Σ is composed of the three lines Σ,Σ and Σ 3. Figure 9. Triangular mesh element 7

34 Chapter.7. Pressure field solution Pressures are calculated at the nodes of an element. Within an element pressure is approximated with linear interpolation functions. Hence the pressure at any point ( x, y) within an element is approximately given by: where N i are the linear shape functions and function i can be re-written in the following form: 3 ~ p ( x, y) = N i p i, (59) i= pi are the values of pressure at node i. Shape N equals at node i, while at other nodes it equals zero. The pressure equation (55) p p S + S = ( S p), (60) x x y y where is taken to be the two dimensional divergence and gradient operator. Hence the pressure equation (55) may be written ( S p) = 0 (6) The residual function R ( ~ p), which is the difference between the exact solution and approximating function, is given by: R( ~ p ) = ( S ~ p ) (6) According to the Galerkin method, which requires that for a residual ~ ) and shape function (k ) N i for the domain B of an element R(u ( ~ ( k ) R u ) N i db = 0, (63) D one can write the following requirement for pressure: 0 = N ir( ~ p) da, (64) A or, taking into account equation (6): 0 = N ( S ~ p) da (65) A i It can be shown [8] that equation (65) can be modified to: S ~ p N da = N S ~ p ndσ, i =,, 3. (66) A i Σ i 8

35 Simulation principles Algebraic equations obtained from equation (65) for each i =,, 3 give the relationship between pressure and flow rate for any triangular element. They can be written in matrix notation as follows: S 4A ( y ( y ( y x y y 3 3 ) + x + x 3 3 x x 3 ) ) ( y ( y ( y y 3 + x y + x 3 ) + x 3 3 x x 3 ) ) ( y ( y ( y y y x + x + x ) x x 3 3 ) p ) p p 3 Q = Q Q 3 (67) where x x x ij = i j, ij i j y = y y, pi and Q i are, respectively, the pressure and total flow rate at node i, S is the fluidity. The three by three matrix on the left hand side is called the element stiffness matrix. For isotropic fluid it is symmetric and can be further abbreviated to k k k 3 k k k 3 k k k p p p 3 Q = Q Q 3 (68) k + S A y x k S A y y x x where = / 4 ( ), = / 4 ( ), etc. Total flow rates are given by: where Q = Σ q + Σ3 q3 (69) Q = Σ3 q3 + Σ q (70) Q3 = Σ q + Σ q, (7) q = S P / n and Σ i is the length of i -side of the triangle element. The quantities i i qi may be identified as flow rates along related sides of the element. The element equations can be abbreviated further to [ ] { p} { Q} K e = (7) Equation (7) gives the relationship between pressure and flow rate for any triangular element. Real components are modelled with many mesh elements. To model the entire cavity the element equations are assembled to extend the relationship (7) to the entire solution domain. For illustration of assembly of equations, two adjacent elements like those shown in Figure 0 are enough. Elements and are defined by nodes,, 4 and nodes, 3,4, respectively. 9

36 Chapter 30 Figure 0. Assembly of two elements The element equations for Element one and Element are, respectively: = Q Q Q p p p k k k k k k k k k (73) = Q Q Q p p p k k k k k k k k k (74) The equations (73 and 74) can be combined into one equation. First the element equations can be written using 4 by 4 matrices by adding zero columns and rows as follows: = Q Q Q p p p p k k k k k k k k k (75) = Q Q Q p p p p k k k k k k k k k (76)

37 Simulation principles Then the assembled equations are obtained by adding together equations (75) and (76): k k 0 k 3 k k k k 3 + k + k 3 0 k k k 3 k k k k k 3 p p p p 3 4 Q Q = Q Q Q + Q 4 (77) Equation (77) is the matrix form of the system of equations for the two-elements cavity. The 4 by 4 matrix on the left hand side is called the global stiffness matrix. It can be very large for the real models that consist of thousands elements. During the analysis the size of stiffness matrix changes. Initially it consists of only a few elements. As the melt fills the cavity, the filled elements are added to the matrix..7.3 Application of boundary conditions For nodes on the flow front, the boundary condition that pressure is zero is enforced by deleting the rows and columns of the stiffness matrix that correspond to the node number. For example, if nodes 3,4, and 7 are on the flow front we would delete the rows and columns numbered 3, 4 and 7 from the stiffness matrix. In this way the number of equations to be solved is reduced. This is illustrated in Figure. Figure Geometry consisting of two elements For the injection nodes the known pressures or flow rates are substituted in the system equations. With the boundary conditions set, the system equations may be solved to determine the nodal pressures. These are then substituted back in the system equations to get the corresponding nodal flow rates. In Figure the injection node. Let it be node. The flow rate at this node is Q. If nodes and 4 are filled, the melt front position is in Element. Therefore pressure p 3 = 0. This means that row 3 and column 3 are deleted from the stiffness matrix (equation 77): 3

38 Chapter k k k + k p p p k k3 Q k + k k3 + k3 3 k 3 3 k 33 4 = 0 0 (78) Solution of the system of equations (78) gives nodal pressures. With nodal pressures known, the flow rate into node 3 can be found by back substitution in equation (77). There exist different solution methods to solve systems of equations defined by the matrices. One of them is Gauss Seidel iteration method. It can be explained as follows. For a simple system with a stiffness matrix that is 3 by 3 components k k k 3 k k k 3 k k k p p p 3 Q = Q Q 3 (79) new values of pressures can be estimated as: p = Q k p k p3) / = Q k p k3 p3 ) / 3 = Q3 k3 p k3 p ) / ( k p ( k (80) p ( k where new pressure values are denoted as p. For the next iteration p is replaced by p and so on. Iterations stop when the difference between pressures calculated on two consecutive iterations is less then a specified tolerance Solution of Energy equation The boundary conditions for energy equation (57) are: The temperature at the cavity wall or at some point interior to the mould is defined. That is T = T w at z = h or z = h + δ (8) The temperature gradient in the z -direction is zero at the cavity centre line. That is, T z = 0 at z = 0 (8) The melt temperature at the point of injection is defined: T = T inj at the injection point (83) 3

39 Simulation principles 33 For numerical solution it is necessary to discretise energy equation (57) in both time t and spatial dimension z. For finite difference solution in any time step the convection and viscous dissipation terms from the previous time step are treated as source terms. Naturally, there is no contribution from convection and viscous dissipation for the nodes at which temperature is below solidus (or no-flow temperature), as well as for nodes located in the mould wall. Then energy equation can be written as follows: [ ] + = + + n i n i n i y x n i p z T k y T v x T v t T C γ η ρ (84) Solution of energy equation can be performed using an explicit or implicit finite difference methods. The choice of the method is determined by the stability criterion M, which is defined by the formula: ( z) M T = α (85) where α is thermal diffusivity of the material. In case / M an explicit finite difference method is used for solution. If 0 M, then implicit finite difference method is used. In case / < M it is possible to use a mix of explicit and implicit solution schemes. In explicit method the first order forward difference approximation for the time derivative is used, i.e.: t T T t t T T t T n i n i n n i n i n i = (86) and second order central difference is used for approximating the spatial term, i.e.: z T T T z T n i n i n i + + (87) temperature at node i at new time n+ t, n+ i T,can be directly found from the equation: [ ] n i p n i y x n i n i n i n i n i C t y T v x T v t T T T T M T ) ( ) ( γ η ρ = + + (88) An implicit method uses a two point forward difference expression for the time derivative and a three point central difference expression for the spatial derivative as follows: t T T t T n i n i + (89) z T T T z T n i n i n i (90) Substituting these expressions in equation (84) and rearranging gives:

40 Chapter MT where n n+ n+ n+ n T T t [ ] n i ( M ) Ti MTi Ti t vx v y η = + + γ i x y (9) ρc i p k t M =. (9) ρ C ( z) Equation (9) holds for a grid point i at any node. The unknown values of T at the new time, n+ t are found by writing equation (9) for every filled node in the model. These equations can then be arranged in matrix form as follows: [ M ]{ T n +} = { b} M is a square matrix, { T n+ } where [ ] is a column matrix of unknown values of temperature at the new time and { b } is a column matrix of the old values of temperature and the convective and viscous heating terms. The matrix equation is solved for { T n+ } using Gauss-Seidel iteration. p (93).7.5 Tracking of free surface The flow front is advanced using a volume of fluid (VOF) method. In this scheme each node is assigned a volume. These control volumes are defined by the polygonal region formed by linking the mid-sides of a triangular element to its centroid by a straight line segments. The control volumes associated with their nodes are shown in Figure. Figure. Control volumes After solving for pressure, the flow rates into each node on the flow front can be calculated. Since the time step is known, the node can be tested to see if it is full. Once the node is filled, the flow front is advanced by incorporating all nodes connected to the last node to fill into the flow front. 34

41 Simulation principles.8 Summary In this chapter governing equations for simulation of the filling stage of the powder injection moulding and material models for shear thinning fluids are described. The governing equations include equations of conservation of mass, momentum and energy. Several material models accounting for shear thinning effect are described. Further a set of boundary conditions is defined. The sequence of the solution process is illustrated for the simulation based on the Hele-Shaw approximation. The example is given for the two-dimensional geometry. Solution in 3-D space is similar, but involves more equations to account for three coordinates. 35

42 Chapter 3 Characterisation of BASF 36 L feedstock 3. PIM feedstock attributes PIM feedstock is a mixture of a powder and a binder. Their characteristics and amount determine properties of the feedstock. The powder is characterised by particles size distribution, shape and surface condition. The binder is usually based on an organic polymer, which can be decomposed and removed from the moulded component. The ideal feedstock should have as high as possible solid loading, uniform distribution of powder particles in the binder and low viscosity that would enable easy moulding [3]. Therefore, whenever possible, the powder is selected for a high packing density. This might require adjustments to the particle size distribution or particle shape. To increase solid loading different particle sizes can be mixed to form a bimodal size distribution. Figure 3. PIM feedstock with excessive binder content The spaces between the powder particles are filled with the binder. The amount of binder plays a crucial role in the viscosity of the feedstock. An excess of binder, like in the case shown in Figure 3, ensures low viscosity but does not provide particle-to-particle contact that is required for preservation of shape of the component after debinding. Too much binder is wasteful and increases shrinkage that may cause shape distortion of the component during sintering. Removal of large amount of binder takes longer time, increasing production costs. Therefore the amount of

43 Characterisation of PIM feedstock binder should be kept at lowest possible level. On the other hand, if there is not enough binder to fill all spaces between the particles the feedstock contains small voids in the binder. Such situation is illustrated in Figure 4. Figure 4. Voids in the feedstock with insufficient binder content Solid loading has the strongest effect on practically all properties of the feedstock, including viscosity. With increasing solid loading the layer separating particles from each other becomes thinner and looses its lubricating properties. Because of increased number of direct particle to particle contacts, viscosity of the feedstock increases with the increase of solid loading. A schematic plot of viscosity versus solid loading is shown in Figure 5. At the critical solid loading Φ cr the film of the binder between the particles is destroyed and due to friction between them viscosity of the feedstock sharply increases. The optimal value should be chosen at the point just below the critical amount Φ, where direct particle-to-particle contact does not take place yet. cr Figure 5. Viscosity trend of PIM feedstock versus solid loading Viscosity of PIM feedstocks decreases at higher temperature. There are two reasons for that. The first reason is that viscosity of pure polymers decreases at higher temperature [33]. This is the result of the increased mobility of molecular chains of the polymer. Several empirical equations are known for temperature dependent viscosity. For Newtonian fluids viscosity and temperature may be related by an Arrhenius equation in the following form: E RT µ = Ae /, (94) 37

44 Chapter 3 where E is activation energy, R - is universal gas constant, T is absolute temperature. A is the constant of the material. In a modified form this equation is used for viscosity of polymers as follows: E η = η 0 exp. (95) R T T0 In equation (95) η0 is the viscosity at a reference temperature T 0. However, reduction of viscosity of the feedstock with temperature is larger than anticipated from the reduction of viscosity of pure binder. Another factor that causes reduction of feedstock's viscosity is the decrease of solid loading at higher temperature. This happens due to higher thermal expansion coefficient of the binder as compared to that of powder. In feedstocks thermal expansion coefficients of binder and powder may differ several times. For example in wax-iron powder mixture the thermal expansion coefficient of wax is approximately twenty times that of iron [5]. Therefore reduction of viscosity due to this factor can be very strong. Another factor that affects the feedstock's viscosity is the pressure. Increase of viscosity with pressure is determined by two reasons. The first one is the increase of viscosity of pure binder under compression. The second reason is the increase of solid loading with the increase of pressure due to higher compressibility of the binder. The dependence of viscosity of the feedstocks on pressure is not linear and becomes important at the relatively high pressures, which are rarely developed during the PIM process within the cavity. The influence of pressure on viscosity may be needed to account for in case of long runners and/or mould has several cavities. Pressure dependence of viscosity is usually accounted for in the analysis packages for simulation of flow of polymers by using the PVT-diagram's. There is little information on viscosity of PIM feedstocks in the literature. The few available results are fragmented and usually restricted to low shear rates below s - [34-37]. Taking into account the shear rate ranges in real PIM process, it is desirable to measure viscosities within wider shear rates range at several temperatures. The volume fraction of the powder (solid loading) Φ can be calculated by the following formula: ρ pwdwbnd Φ = +, (96) ρbndw pwd where W is the weight, ρ is the theoretical density. Subscripts pwd and bnd refer to powder and binder, respectively. The theoretical density ρt of a PIM feedstock based on a particular powder can be found from formula (97): ρ = Φρ + Φ) ρ = ρ + Φ( ρ ρ ) (97) t pwd ( bnd bnd pwd bnd Formula (97) can be used to determine critical solid loading. For that a number of density versus volume concentration of powder experiments have to be performed. At the critical solid loading voids begin to appear between the particles due to lack of binder. The apparent density of the mixture with voids differs from the value calculated by formula (97). The solid loading where such deviation occurs first time is the critical solid loading Φ. cr 38

45 Characterisation of PIM feedstock Thermal conductivity and specific heat of the PIM feedstock are very important properties that also influence its flow. These properties seem to be significantly affected not only by the properties of the constituents of the feedstock, but also by the total area of the particle-binder interface and state of the particle surface. Heat transfer within a feedstock depends also on the number of contacts between the particles, which, in turn, depends on solid loading and temperature. This makes difficult the calculation of thermal properties based on the relevant properties of the powder and the binder. For example, the models based on the rules of mixtures provide wrong results on thermal conductivity of the feedstock [9]. Nowadays standard pre-formulated feedstocks are available on the market. However, properties of most of them are not yet measured. In the view of fast development and wider application of numerical simulation of powder injection moulding, creation of databases on the properties of PIM feedstocks becomes especially important. In this study the standard of 36 L stainless steel feedstock produced by BASF AG was used. This feedstock contains catalytically removable binder based on semicrystalline polyacetal polymer. Despite the fact that this feedstock is widely used in the PIM industry there is little information about its properties in the open literature. To simulate the PIM process with this feedstock it was necessary to measure at least its density, viscosity, thermal conductivity and specific heat. Density of the feedstock is easily measured and usually is provided by the feedstock producer. The 36 L feedstock had density 4.95 *0 3 kg/m 3. The other properties usually are not available from the producer and had to be measured. This work presents the results of measurements of viscosity, specific heat and thermal conductivity of this feedstock. 3. Viscosity measurements Viscosity of PIM feedstocks is usually measured by the capillary viscosimetry [38, 39]. For a Newtonian fluid the following characteristics can be determined for a die with radius r and length l : Apparent shear rate Wall shear stress: 4Q γ ap =, 3 πr (98) pr τ w =, l (99) The apparent viscosity can than be calculated with the following formula: η ap τ γ w =. (00) ap Formulas (98-00) are true for a Newtonian fluid. For a non-newtonian fluid the apparent shear rate γ should be corrected using Rabinowitsch equation [33]: ap ap γ = γ (3 + ), (0) 4 n 39

46 Chapter 3 where n is the power-law index, which can be obtained from the equation: d(logτ w ) n = (0) d(log γ ) Without the Rabinowitsch correction the viscosity of a non-newtonian fluid is overestimated. Furthermore, in order to access entrance and exit pressure drops in a die, a Bagley correction is applied [38]. For polymers, a plot of pressure versus length-to-diameter ratio (l/d) of the capillary at a fixed wall shear rate gives value of pressure losses at the zero capillary length. The pressure loss may be determined by using dies of several different lengths. At least two dies with different length to diameter ratio are needed in order to collect the required data for Bagley correction. In this study the rheological characterisation of the BASF 36 L feedstock was carried out on a Göttfert capillary rheometer (Rheograph 003) in the mode of prescribed volume flow rate. Measurements were performed at four different temperatures using dies with a diameter of 0.5 mm and a length of.5 and 0 mm. The extrusion pressure was measured using a pressure transducer with a measuring range of 0 00 MPa. To estimate the degree of thermal degradation of the feedstock at high temperature before the actual measurements the feedstock was extruded through a die under constant shear rate and temperature of 0 C for 30 minutes. ap Figure 6. Stability of the 36 L feedstock at T = 0 C. l=0 mm, d=0.5 mm; apparent wall shear rate 843 s -. In Figure 6, the extrusion pressure at a constant apparent shear rate of 843s is presented as a function of the residence time of the material in the barrel. The figure shows that during the first four minutes (melting time) the pressure applied by the piston during the compression of the pellets is relaxed by viscous flow. After the start of the experiment, the extrusion pressure reaches within about.5 minutes a steady state value. The pressure remains constant throughout the whole measuring time. The decrease in pressure around 00 s is likely to be due to entrapped air in the melt. In case of any degradation reaction in the polymeric binder, pressure would decrease continuously. Thus, the measurements results were not influenced by errors originating from any thermal degradation within the measured period. 40

47 Characterisation of PIM feedstock Pressure readings were taken in the steady state for several different shear rates. The pressure remained constant throughout the whole measuring time. The viscosity results are presented in Figure 7. In this figure, measured viscosity data points for four different temperatures are plotted (after applying Rabinowitsch correction). It is to be noticed that viscosity has small dependence on temperature. The viscosity at each temperature decreases in the whole range of shear rates up to 0 5 s -. The slope of the curves slightly increases with the increase of logarithm of the shear rate. Because of variable curvature of the plot of logarithm of viscosity versus logarithm of shear rate, Rabinowitsch correction factor n for every point of the plot will be different, as it is shown in Figure 8. However, from Figure 7 it can be seen that the viscosity plots may be considered as practically linear in the range of s -. A correction factor was determined in this range using two points 30 and 0 4 s - for each temperature. An error introduced through such simplification was estimated to be about 4%. Viscosity, Pa * s C 85 C 95 C 0 C Shear rate, /s Figure 7. Viscosity of BASF 36 L feedstock at four different temperatures; D=0.5 mm; L=.5 mm. 0.6 Flow behaviour index Shear rate, /s Figure 8. Flow behaviour index for Rabinowitsch correction for T=85 C An attempt to correct the viscosity results for entrance pressure losses was not fully successful. An example of Bagley correction plots for apparent shear rates up to 6700 s -, for temperature 70 C, is given in Figure 9. Shear rates higher than 6700 s - could not be reached with the 0 mm capillary, because the maximum pressure of the transducer was reached. Intercepts of the straight 4

48 Chapter 3 lines with the y-axis should determine values for the entrance pressure loss up to apparent shear rate of 886 s -. For two higher shear rates, the linear extrapolation to zero l/d ratio yields negative values for the entrance pressure, which is physically impossible. The reason for the negative values is believed to be caused by a pressure dependence of the viscosity or the onset of wall slip. Inconsistent results of Bagley correction are typical for PIM feedstocks [34] due to their more complex behaviour as compared to pure polymers. Figure 0 shows the entrance pressure losses plotted as a function of the true wall shear stress. It can be seen that the entrance pressure losses are scattered. Comparing with the extrusion pressures, which reached 00 MPa, they are small. At higher temperatures entrance pressure losses are estimated to be even smaller and, therefore, can be neglected. Figure 9. Bagley correction plot for 36L feedstock at T = 70 C Figure 0. Entrance pressure losses at T=70 C 3.3 Fitting experimental data into viscosity models of 36 L feedstock The measured viscosity data were used to fit into Cross-WLF, Carreau, and Carreau-Yasuda viscosity models that are employed during numerical simulation by the C-Mold, Moldflow and ProCAST analysis packages, respectively, as described in Chapter 4. The approximation functions were determined using least squares fitting. All viscosity models were built for shear rates up to 0 5 s - and the temperature range 70-0 C, which covered the working temperature range during the real injection moulding. Pressure effect was not taken into account because the effect of pressure on the viscosity of PIM feedstocks is believed to take place only at high pressures above 00 MPa Cross-WLF model Cross-WLF model is described by equations (9,,) in Chapter. The coefficients for the best fitting function are shown in Table. The measured and fitted using Cross-WLF model viscosity data are plotted in Figure. D D D 3 A ~ A * τ n Table 4

49 Characterisation of PIM feedstock Viscosity, Pa*s C 85 C Experimental 95 C points 0 C ` WLF 70 C WLF 85 C WLF 95 C WLF 0 C Shear rate /s Figure. Experimentally measured viscosity and Cross-WLF viscosity functions for 36 L feedstock 3.3. Carreau model If viscosity at infinite shear rate η is assumed to be zero, and from Chapter can be re-written as follows: * λ = η 0 /τ, then formula (3) η0 η = η 0γ + * τ n (03) Equation (03) is another from for the Carreau viscosity model. The related coefficients are given in Table. Comparison of the measured and fitted viscosity results is presented in Figure. B T β * b τ n 9.9E E E E-0 Table 43

50 Chapter Viscosity, Pa*s C 85 C Experimental 95 C points 0 C Carreau 70 C Carreau 85 C Carreau 95 C Carreau 0 C Shear rate /s Figure. Experimentally measured viscosity and Carreau viscosity functions for 36 L feedstock Carreau-Yasuda model Table 3 contains coefficients of the Carreau-Yasuda viscosity function for four different temperatures. Carreau-Yasuda model treats zero shear rate viscosity η 0 as a coefficient. Therefore four sets of coefficients for 70, 85, 95 and 0 C were identified. The fitting functions, with coefficients from Table 3 and experimental viscosity data are shown in Figure 3. Table 3 Coefficients of the Carreau-Yasuda function 70 C 85 C 95 C 0 C η η λ n a

51 Characterisation of PIM feedstock Figure 3. Experimentally measured viscosity and Carreau-Yasuda viscosity functions for 36 L feedstock Results presented in Figures -3 show that all applied viscosity functions ensure good match between measured and fitted viscosity data within the wide range of shear rates (5 0 5 s - ). 3.4 Specific heat Specific heat of 36L feedstock was measured by differential scanning calorimetry (DSC) method using calorimeter Perkin Elmer DSC 7. This apparatus is equipped with liquid nitrogen cooling capability that allows measuring specific heat at high cooling rates. Calorimeter Perkin Elmer DSC 7 uses power-compensation measurement scheme. Two identical holders are used in the experiment. One holder contains sample, while another one is used as a reference. The sample holder of a DSC calorimeter is schematically shown in Figure 4. The sample and reference holders are provided with individual heaters. They are used for controlled heating or cooling during the measurements. If a temperature difference develops between the sample and reference, the power input is adjusted to remove this difference. Thus the temperature of the sample holder is always kept the same as that of the reference holder by continuous and automatic adjustment of the heater power. Temperature difference may occur because of exothermic or endothermic reactions in the sample. The device generates a signal proportional to the difference between the heat input to the sample and that to the reference. This signal is recorded. It is proportional to derivative of enthalpy with respect to time dh / dt. The sample of the feedstock of about 5 mg was put in the pan, covered by a cap and put in the sample holder, where it was heated to the temperature above the melting point of the feedstock. To prevent decomposition of the binder temperature of the sample did not exceed to 00 C. At this 45

52 Chapter 3 temperature the feedstock is supposed to be in the liquid state because the recommended by the manufacturer processing temperature is 85 C. Figure 4. Sample holder of a DSC calorimeter The measurements were performed during the cooling scan with the prescribed cooling rate. The measured specific heat data are shown in Figure 5. It can be seen that the peak values of the specific heat decrease and the curves widen as the cooling rate rises. In addition to that a shift of the peak towards lower temperatures is observed with increasing cooling rate. These phenomena can be explained by the undercooling effect of the semi-crystalline binder. During cooling with high rates the feedstock remains for some time in the liquid state at the temperatures below the melting point as compared to measurements at the thermodynamic equilibrium. Then heat of transition from liquid to solid state is released at lower temperatures. During cooling at high cooling rate the heat release is registered within wider temperature range than during cooling at low cooling rate. Cp, (J/g* C) Cooling rates, C/min: Temperature, C Figure 5. Specific heat of the 36L feedstock at different cooling rates Extrapolation of the right (on the figure) slope of the peak to the baseline gives the temperature when the binder begins solidifying. This temperature is called transition temperature. From Figure 5 transition temperature of the 36 L feedstock is estimated to be 45 C for the cooling rate 00 C/min. It can be seen that in case specific heat is measured at low cooling rate, then transition temperature is higher. Measurements at cooling rate 0 C/min results in transition temperature, which is about 4 C higher than transition temperature measured at 00 C/min. The obtained results showed the same tendency as the measurements of specific heat of 36 L feedstock performed earlier [8]. However, the experiments [8] showed stronger influence of the cooling rate on the transition temperature shift. This apparent discrepancy could be attributed to different conditions of the experiment. The response of the system shown in Figure 4 depends, in 46

53 Characterisation of PIM feedstock particular, on thermal resistance of sample and pan R s and thermal resistance between pan and holder, R 0. At a moderate cooling rate R s is small compared with the resistance between pan and holder. It has been shown [39] that the slope of the leading edge of the experimental curve is proportional to ( / R 0 ) and scanning rate. At high cooling rates influence of resistance R s increases. Then the slope of the leading edge of the endotherm will be proportional to /( R 0 + Rs ). Therefore additional temperature lag will be observed, which may contribute to further shift of the peak along the temperature axis. Value of thermal resistance Rs also depends on the quality of contact between sample and pan. If the contact is bad, thermal resistance increases and so does the temperature lag on the scanning curve. Quality of the contact between sample of the feedstock and pan depends on the state of the sample. The best contact is achieved if sample is melted. If it remains in the solid state the contact may be worse. Sample of the feedstock may retain its shape even when heated above the melting temperature, because feedstocks often possess yield stress, which must be exceeded to initiate the flow [40]. Typical sample for DSC experiments has small mass about 5 mg. The gravity force, acting on such a small sample, is also small and may be lower than the yield stress. Should it be the case, the sample holds its original shape, and thermal resistance Rs remains high. To test the effect of quality of the contact between sample and pan on the measurements of specific heat two DSC scans were performed at the same conditions. In the first experiment the sample was put in the pan, covered with the cap and heated to 00 C. Thereafter specific heat was measured at prescribed cooling rate 00 C/min. In the second experiment small pressure was applied on the cap after the sample has been heated to the temperature of 00 C. Under the applied pressure the sample of the feedstock was deformed between the cap and the pan. In this way contact between the sample and pan was improved. Then specific heat was measured again at the same cooling rate of 00 C/min. The results of these experiments are shown in Figure 6. It can be seen that the peak for the sample, which was not pressed, is shifted to lower temperatures. Since in both experiments the same sample was used, thermal resistances, excepting R s, were the same. Thus it can be concluded that the observed shift of the peak is attributed only to the change of the thermal resistance between the sample and the pan R, and possible error of measurements. s Cp, (J/g* C) Temperature, C 00 C/min (bad contact) 00 C/min (good contact) Figure 6. Effect of contact quality on the DSC scans of 36 L feedstock. Cooling rate 00 C/min. 47

54 Chapter 3 To estimate reproducibility of the measurements experiments with the same sample were repeated. Figure 7 presents the results of two different DSC scans of the same sample taken at cooling rates 50 and 00 C/min. For all measurements a good contact of the sample with the pan was secured in similar way as described above. It can be seen that error of estimation of the transition temperature in different runs is about 0.5 C. The shift observed in Figure 6 exceeds C, which is about 4 times higher than possible error due to insufficient accuracy of measurements. Cp, (J/g* C) C/min 50 C/min (nd run) 00 C/min 00 C/min (nd run) Temperature, C Figure 7. Reproducibility of the DSC scans at high cooling rates. Table 4 Tabulated specific heat of 36 L feedstock as a function of temperature Temperature, C Specific J/g* C heat, Rough estimations that can be made from the heat transfer simulation of PIM [4, 4] indicate that the cooling rate during real powder injection moulding process can exceed 00 C/min. It was, however, not possible to measure specific heat of the feedstock at higher cooling rate due to reaching the upper limit of the DSC apparatus. To minimise errors during the simulation specific 48

55 Characterisation of PIM feedstock heat measured at the highest possible cooling rate (00 C/min) shall be used. The results of measurements at 00 C/min, which can be used as input parameters are shown in Table 4. These values were extracted from the measured data and used during the numerical simulation process. 3.5 Thermal conductivity Thermal conductivity is another important property of the feedstock that must be determined for the purpose of the numerical simulation process. It controls the heat dissipation rate and eventually the temperature of the feedstock. For the simulation of the PIM process it is desirable to have thermal conductivity data for both liquid and solid states of the feedstock, measured during cooling with high rate. Because of this requirement, it is relatively difficult to conduct measurement experiments yielding high quality thermal conductivity results. The best measurement method that satisfies this requirement was found to be the laser flash method. It is based on applying a high intensity and short duration heat pulse to one face of a parallel sided test piece and monitoring the temperature rise at the opposite face as a function of time. The thermal diffusivity α of the sample is then calculated according to the formula:.37s α = (04) π t 0.5 where: s is thickness of the specimen, t 0. 5 is the time from initiation of the pulse until the rear face of the test sample reaches half of its maximum temperature. The thermal conductivity k was thereafter calculated using the relationship: k = ρ C p α (05) where ρ and sample. C p are the experimentally determined density and specific heat of the feedstock s Application of the laser flash method enabled measurements of thermal conductivity of the 36 L feedstock continuously in a wide range of temperatures [9]. The measurements were performed in both solid and liquid states of the feedstock using LFA 47 NETZSCH apparatus. The estimated accuracy of measurements of thermal conductivity was 3-4% and 7-8% in the solid and liquid states, respectively. The results of measurements are presented in Figure 8. The experimental results are compared with those calculated using the theoretical Maxwell model [43] and the semi-theoretical Lewis & Nielsen model [44]. It can be seen that the experimental and the calculated data do not match well. Both models predicted the rapid increase of the thermal conductivity during cooling in the temperature range C. The Maxwell model underestimates the measured values. Bearing in mind that during calculation, thermal conductivity values of the massive 36L steel were used, it seems that the Maxwell model substantially misjudges the thermal conductivity of the feedstock. In contrast, the Lewis & Nielsen model overestimates the measured values. However, substantial difference still remains between the theoretically calculated and measured 49

56 Chapter 3 values, in particular, in the transition temperature range and the slope of the curve. On the other hand, the transition temperature estimated from the experimental data is in a good agreement with the results obtained during DSC experiments. The results from Figure 8 undoubtedly confirm that only experimental measurements provide reliable data, which should be used as input parameters in the simulation. The measured values of thermal conductivity of the 36L feedstock to be used in the simulation are given in Table 5. Thermal conductivity, W/m*K Maxwell model Lewis & Nielsen model 4 Measured Temperature, C Figure 8. The measured and calculated thermal conductivity values of the BASF 36L feedstock Temperature, C Table 5 Thermal conductivity, W/m*K Summary In this chapter the measured properties of the standard 36 L feedstock required for simulation of the PIM process are presented. The experimental data were used to define input parameters for the simulation. Density is assumed to be constant and equal to 4.95 *0 3 kg/m 3. The viscosity was measured at four different temperatures in the wide range of shear rates up to 0 5 s -. Coefficients 50

57 Characterisation of PIM feedstock for the Cross-WLF, Carreau and Carreau-Yasuda models for modelling shear rate dependent viscosity were identified. The experimental and fitted data matched each other very well. The Cross-WLF, Carreau and Carreau-Yasuda viscosity models have been used to simulate the powder injection moulding process with C-Mold, Moldflow and ProCAST analysis packages, respectively. Measurements of specific heat were performed at several cooling rates. It has been shown that measurements taken at low cooling rates lead to overestimation of the transition temperature of the feedstock. The fastest obtained cooling rate was 00 C/min. Transition temperature defined at this cooling rate amounted 45 C. Results obtained from the measurements with that cooling rate were used to determine the input parameters related specific heat and transition temperature. It has been also shown that calculation of thermal conductivity of a PIM feedstock with theoretical models yields erroneous data. 5

58 Chapter 4 Simulation programmes Soon after simulation principles and numerical solutions for modelling of the fluid flow were developed, the results of such studies led to creation of commercial numerical codes. The first commercial numerical codes were two-dimensional, and their main application area was polymer injection moulding. Quick transformation of the simulation software into a tool for daily use at the workshop level was facilitated by the good applicability of the two-dimensional simulation to the needs of the industry of polymers. Examples of such simulation packages are early versions of C- Mold and Moldflow. Newest versions of Moldflow are three-dimensional. Another large area of application of fluid flow simulations was metallurgy. The products made by metal casting usually have intricate shape, which often cannot be represented by thin-walled models. Because of this reason one of the primary requirements for the software for simulation of shape casting processes was its ability of simulating the fluid flow in the three-dimensional space. An example of such numerical code is ProCAST. In this study, for simulation of the powder injection moulding process, C-Mold (-D version 99.), Moldflow (3-D version MPI.) and ProCAST (3-D version 3..0) were used. All these analysis packages have some common features like a modular structure consisting of a number of modules (pre-processing tools, simulation engine and post-processing tools) and a material databases. C-Mold and Moldflow contain mainly description of polymers, while the database of ProCAST consist mostly of metals and alloys. None of the programmes include PIM feedstocks. The feedstock material can be included in the database as a new userdefined "polymer" or "metal". All analysis packages for numerical simulation are based on the same physical principles, the requirements to the input data and methods of the process set-up differ from a package to package. The results of simulation also differ as in layout as well as the level of detail. This chapter presents an overview of simulation of the PIM process with C-Mold, Modlflow and ProCAST packages. Along with the description of their most important features, examples of simulation of different attributes of the PIM process are given. It is demonstrated what kind of data can be calculated with these analysis packages. All simulations were performed with the properties of the standard PIM feedstock of 36L produced by BASF AG, as described in Chapter 3.

59 Simulation programmes 4. C-Mold C-Mold was developed by Advanced CAE Technology, Inc. The main assumptions of C-Mold are the following: - The material is a generalised Newtonian fluid. - The flow takes place in a thin cavity with thickness z much smaller than length x and width y. - There is no heat convection in z -direction. - There is no slip at the mould surface. C-Mold works only with the geometry models created with its internal drawing tool (graphic designer). The models made in another CAD/CAE software cannot be imported. The C-Mold graphic designer allows building a thin-walled geometry model in the three-dimensional space. As it was mentioned before, such models are called,5-d models. Thickness of the two-dimensional model is assigned in C-Mold as an attribute. Besides the component C-Mold permits modelling of cooling channels. However, the mould cannot be explicitly included into analysis. C-Mold uses triangular mesh, which is generated on the basis of the linear mesh size to be defined by the user. The meshing process is automated. The model can be split into regions, with different basis mesh size. In this way creation of variable mesh density throughout the model is possible. The mesh can be manually corrected by moving particular nodes in the desirable positions. The graphic designer of C-Mold also is used for defining such boundary conditions as inlet nodes for the injected material and inlet and outlet nodes for the cooling fluid. Other boundary conditions are defined in the simulation setup. Heat flux through the surface of the component is taken into account by introducing heat boundary conditions. The list of required by C-Mold input data includes parameters that describe the injection moulding process and properties of the injected material and the cooling fluid. The list of adjustable process parameters, in particular, includes: - Fill time - Ram speed profile - Timer for valve gate - Filling-to-Post filling switch - Timer for hold pressure - Inlet melt temperature - Coolant manifold control - Ambient temperature - Hot runner manifold control - Mold-melt heat transfer coefficient. The most important input parameters are defined as follows: - Injection rate (filling speed) is defined by setting the desirable fill time. - Viscosity of the material is described by one of eight material models. - Specific heat and thermal conductivity of the material are defined as a constants or data series for different temperatures. - Temperature of the mould and the initial temperature of the feedstock are defined as constants. C-Mold performs several different types of analysis: filling EZ analysis, filling analysis and postfilling analyses. Filling EZ analysis provides a quick simulation of flow of a Newtonian fluid under isothermal conditions. Because of these simplifications the filling EZ analysis is used to evaluate preliminary designs. It serves mostly for check of the geometry and mesh and hardly can be applied for simulation of PIM. The filling analysis simulates the dynamics of fluid flow and 53

60 Chapter 4 heat transfer of the material during the filling stage of the injection moulding process. The postfilling analysis simulates the packing and cooling stages of the injection moulding process. The list of output data of C-Mold filling and post-filling analyses is quite large. It includes: - Pressure - Temperature - Velocity - Shear rate - Melt front advancement - Weld lines - Meld lines - Wall shear stress - Representative shear rate - Frozen layer fraction - Flow rate in -D elements - Air traps - Average velocity - Clamp force - Melt front area With such a comprehensive list of the output data C-Mold is capable predicting many parameters of the filling process. For example, it is possible to judge about hesitation of the melt front, gate freeze-off time, probability of appearance of sink marks and warpage of the component due to non-uniform cooling. Application of C-Mold to simulation of powder injection moulding process with more details is illustrated further. 4.. Powder injection moulding of simple shaped component with orifice The applicability of C-Mold for the problems of powder injection moulding can be demonstrated with a simple component shown in Figure 9. The chosen simple geometry permits easy comparison of the calculated results with the intuitively expected ones. The component has the shape of a flat rectangular bar with dimensions 0 x 70 x mm and an orifice in the centre. The component can be injection moulded through three different gating positions denoted by numbers to 3. In each powder injection moulding cycle only one gate was used. For that the two other gates and the related runners were removed from the model. The model included cooling channels, which were placed parallel to the cavity plane symmetrically on both sides of the component (not shown on the picture). Viscosity of the feedstock was described using the Cross-WLF model. Process conditions were the following: initial temperature of the feedstock: 85 C; temperature of the cooling liquid: 40 C. The PIM process was simulated with variable fill time (0..5 s). 54

61 Simulation programmes Figure 9. Simple rectangular model with the runners One of the most important characteristics of the filling process is the location of weld and meld lines. These lines are formed in the areas where two melt fronts meet together and constitute weak structural places in the moulded part. It seems that in such a simple geometry location of the weld lines can be easily predicted intuitively. However, intuition does not always take into account all the factors affecting the flow of the melt, and, therefore, the intuitive predictions may be erroneous. This is demonstrated by the calculated positions of the weld lines. Figure 30 shows the calculated positions of the weld lines for three different gating positions. It can be seen that common sense and simulation do not always coincide. While injecting through gate 3, the weld lines are created in an unexpected area. Such a result may be caused by the non-uniform cooling of the feedstock during the filling. The colder feedstock becomes more viscous than the hotter one. As a result, the colder melt front has a lower velocity as compared with the hotter melt front. Without simulation it would be hardly possible to predict formation of the weld lines for the injection through gate 3 (Figure 30c). Figure 30. Effect of gating position on location of weld and meld lines; fill time 0.7 s In case of complex parts, that have different wall thicknesses and complex configuration of the flow path, it is almost not possible to rely on the common sense at all. Especially difficult is predicting of weld lines when the injected material has a high thermal conductivity, low specific heat (short freezing time) and a strong dependence of viscosity on temperature and shear rates. Such combination of properties is typical for PIM feedstock containing metal powders. Change of the gating position is the easiest way to move the weld lines out from the undesirable location. But any changes of the gating position also lead to changing of the flow path. The flow path determines the injection pressure and, respectively, clamp force. These characteristics are important for determining the requirements to the injection moulding machine. The differences in the developed pressure caused by changing of the gating position can be very significant. Figure 3 shows the calculated injection pressures, while moulding the component through gates, and 55

62 Chapter 4 3. The maximum injection pressure determines the clamp force needed to keep the mould closed during the PIM cycle. The related to the pressures from Figure 3 clamp forces are shown in Figure 3. From Figure 30 one could see that injections through gates and 3 resulted in formation of weld lines in approximately the same area. However, injection pressure during injection though gate 3 turned to be about.8 times higher then that during injection though gate. The maximum and minimum injection pressures calculated for the considered example differed about 3 times. These results clearly prove that selection of optimal moulding scheme cannot be based on one criterion only. Maximum Pressure, MPa Gate Gate Gate 3 Clamp Force, ton Gate Gate Gate 3 Figure 3. Maximum injection pressure Figure 3. Clamp force During PIM, the flow of the feedstock is characterised by a high average velocity, which is one of the requirements needed for complete filling of the cavity. But the velocity of the feedstock within the cavity is different in different layers. In the thin part there exist symmetric velocity gradients across the thickness. At the wall the velocity is the lowest, while in the midplane it is the highest. If the component has a complicated shape, the velocity gradient is more complicated. But in all cases, there is a velocity gradient in the flowing feedstock. Shear between the layers of the feedstock affects its viscosity, which in turn may affect the velocity distribution in the feedstock. Another consequence of shear is the heat generation. The heat is generated due to friction between the slow and fast moving layers of the feedstock. The generated heat during the filling contributes to the temperature distribution in the feedstock. These factors should be taken into account while determining the injection rate. From an industrial point of view reduction of the fill time increases productivity. Therefore a high injection rate is desirable. Injection at high shear rates brings additional benefit because it requires less energy due to reduction of viscosity of the feedstock. In the plastic industry this phenomenon is used for reduction of the injection pressure and keeping the injected material hot longer. On the other hand, increase of injection rates lead to higher shear rates and affects the velocity and temperature distribution in the feedstock during the filling. The polymer injected at high rate may disintegrate and lead to distortion of homogeneity of the distribution of the powder particles in the feedstock. The last process is extremely undesirable. Thus, the optimal process conditions shall take advantage of the positive side effects of the shear thinning and viscous heating and, at the same time, keep the shear rates below the critical value, when disintegration of the polymer begins. The experimental measurement of shear rates in many cases is not possible. They can only be numerically calculated. An example of calculated shear rates can be seen in Figure

63 Simulation programmes Figure 33 shows distribution of shear rates across the thickness of the part calculated for nodal points located directly behind the gates. Owing to assumptions of the Hele-Shaw formulation, the distribution of shear rates calculated with C-Mold is symmetric. Shear is zero in the middle plane, while it reaches its maximum at a normalised thickness In the thin layers at a normalised thickness the shear rate is again decreasing. The observed distribution of shear rates is related to the velocity gradient. At the surface of the component the feedstock is cold. It has a high viscosity and, respectively, a low velocity, as compared to the velocity of layers in the middle plane of the part. Therefore shear rates are low adjacent to the wall layers. The inner layers have the lowest viscosity and the highest velocity. Between the cold layers at the surface and the hot layers in the middle, the highest shear rates are developed. Distribution of shear rates across the thickness has the same character for all gating positions. But the magnitude of the injection rate changes with the change of gating position. From Figure 33 one can see injection through gate 3 leads to the development of the highest shear rates. The distribution of shear rates during the real powder injection moulding process may be different from the one shown in Figure 33 because of slip phenomenon. The shear rates in Figure 33 were calculated on the basis of no-slip condition. This assumption may lead to overestimation of the shear rates calculated with C-Mold. Shear rate, /s 8.E+04 7.E+04 6.E+04 5.E+04 4.E+04 3.E+04.E+04.E+04 0.E Normalised thickness Gate ; Fill time = Gate ; Fill time = Gate 3; Fill time = Figure 33. Shear rates in vicinity of gating position. C-Mold results. Information on the temperature of the feedstock during the PIM process can be obtained from the thermal analysis. C-Mold calculates temperatures across the thickness of the component as shown in Figure 34. It is possible to draw a correlation between the calculated temperatures and shear rates. In the layers corresponding to the highest shear rates ( of the normalised thickness) temperature peaks are observed. These peaks are clearly visible at the beginning of injection stage and become smoothed out in time. It is quite obvious that temperature peaks in the area of highest shear rates are present due to viscous heating. Temperature profile changes during the injection cycle. In the beginning, the temperature of the feedstock is close to the injection temperature and almost uniform across the thickness. After the feedstock has contacted the mould, the sub-surface layers of the feedstock are cooled down. High thermal conductivity of the mould and good contact with the feedstock cause a temperature drop at the surface by approximately 7 C at s since the beginning of the filling. In the middle layers the temperature remains high. Thus in the first moments after the feedstock has contacted the mould, high temperature gradient appears in the sub-surface layers. 57

64 Chapter 4 Temperature, degrees C Normalised thickness Gate Time = Time = Time = Time = Figure 34. Temperature across the thickness of the component at different time moments At this moment the peaks of temperature become noticeable. The combined effect of cooling at the surface and viscous heating at the inner layer leads to the temperature profile with the symmetric peaks. Viscous heating takes place only when the melt flows. After the mould is filled there is neither viscous heating nor heat supply with the fresh portions of the melt. All heat sources disappear and the feedstock cools down. By the end of the filling stage (t= 0.7 s) there are only bends on the temperature curve, but not the peaks. At the moment t=.08 s (about.4 s after the end of the filling stage) sharp temperature irregularities cannot be traced any more. Further cooling leads to a relatively slow decrease of temperature and its equalisation across the cavity thickness. By the end of the post filling stage (t~5.8 s) the temperature difference at the middle and surface layers amounts - C. In the considered example, temperature rise due to viscous heating is less then 5 C above the injection temperature. However, at very high shear rates the temperature may be much more pronounced. Therefore when choosing optimal processing conditions the heating effect due to friction should also be taken into account. This can be done only with the help of numerical simulations. Another important characteristic of the PIM process is the level of shear stresses in the feedstock. It is the common opinion that a high wall shear stress negatively affects the surface finish and decreases the stability of the flow [45]. The level of shear stresses can also be used for estimating the probability of the powder-binder segregation. In the areas of high shear stresses such a probability increases. Like temperature and shear rates, the shear stresses can be numerically calculated by C-Mold. The results of the calculation of the wall shear stresses at the nodes, which are located directly behind gates, and 3, are shown in Figures 35. It should also be noticed that the injection moment occurs at all three gates at different times because of the different lengths of runners. This factor explains the different times wherein shear stress can be calculated. The level of shear stress can be controlled by proper selection of the gating position. From Figure 35 it can be seen that the lowest wall shear stress is observed while injecting though gate. While injecting through different gates, the wall shear stress levels change at different rates. For example, during injection moulding through gate 3 the wall shear stress increases faster than during the injection through gate. Besides selection of the proper gating position, the wall shear stress can be controlled by the fill time, because the level of the wall shear stress strongly depends on the injection rate. This is demonstrated in Figure 36, which shows shear stress calculated for different fill times during injection through the same gate (gate 3). It can be also seen that the rate of change of shear stress increases with decreasing fill time. At short fill times the shear stress grows faster than at long fill times. 58

65 Simulation programmes Shear stress, MPa Time, s Gate Gate Gate 3 Figure 35. Wall shear stress versus time (fill time ~0.7 s) Shear stress, Mpa Time, s Gate Fill time: Figure 36. Effect of fill time on wall shear stress at the gate The fill time is easy to control. To use it efficiently for the optimisation of the PIM process it is necessary to know its effect on the other process parameters. As it has already been shown, the process parameters during the powder injection moulding process are closely interrelated and, therefore, are non-linear. This statement is true for the injection pressure. It has been already shown that the injection pressure strongly depends on the gating position. But varying the fill time can also control this important characteristic. The calculated injection pressures for different fill times while injecting through two different gates are shown in Figure 37. It can be seen that the minimum injection pressure is achieved at some intermediate injection rate. At both very low and very high injection rates (long and short fill times, respectively) the injection pressure increases. The increase of pressure at low injection rate is caused by the increasing viscosity of the feedstock that quickly cools down. As the injection rate increases, the viscosity of the feedstock starts to decrease because of the shear thinning effect and viscous heating. As a result, the injection pressure begins to decrease. If the injection rate further increases, the resistance to the flow increases due to the inertia forces. The pressure starts to increase. As a result the curve of pressure versus fill time has local minimum. The plot has the same trend for injection through different gates. But while injecting through different gates, the minimum pressure is achieved at different injection rates. It can be seen from the shift of the local minimum on the pressure curves. 59

66 Chapter 4 Maximum Pressure, MPa Fill Time, s Figure 37. Effect of fill time on pressure Gate Gate 3 Because of the high thermal conductivity of the feedstock the fill time must be kept short to avoid premature freezing and, as a result, short shot. This requirement contradicts, however, shear stress considerations, which demand low shear stresses and shear rates. Such contradicting requirements explain the fact that the range of fill times acceptable for PIM is quite narrow. For the current example optimal fill time lies in within the range s. One more parameter that can help optimising the mould filling process is the initial temperature of the feedstock. The range of possible injection temperatures is limited, on one side, by the point of freezing of the melt (no-flow temperature), and, on the other side, by the highest admissible temperature with regard to thermal degradation of the binder. The effect of the initial temperature of the feedstock on the maximum injection pressure is illustrated in Figure 38. The presented results have been calculated with C-Mold for two gating positions (fill time t= 0.7 s) Maximum Pressure, MPa Temperature, degrees C Fill time =0.7 s Gate Pressure Gate 3 Pressure Gate Delta T Gate 3 Delta T Temperature, C Figure 38. Effect of the feedstock temperature on the injection pressure and temperature difference between the hottest and the coldest spots on the component by the end of filling stage. The same trend is observed for both gates. Injecting of the hotter feedstock leads to reduction of the filling pressure due to less resistance to the flow, and at the same time, increases the difference 60

67 Simulation programmes between the hottest and the coldest spots on the component by the end of the filling stage. It can be seen that pressure can be lowered by around 40% by increasing the injection temperature from 75 to 05 ºC. As the clamp force strongly correlates with the injection pressure, the increase of the injection temperature reduces clamp force as well. So the increase of the initial temperature of the feedstock has positive effect on the PIM process. The negative consequence of the increased initial temperature of the feedstock is the increased non-homogeneity of temperature distribution at the end of the cooling stage. To illustrate the increase of temperature non-homogeneity, the temperature differences T between the hottest and the coldest spots of the component in the end of filling stage are also plotted in Figure 38. Parameter T itself does not determine the quality of the formed part, though it can serve as an auxiliary characteristic. High temperature nonhomogeneity at the end of the cooling stage may lead to accumulation of frozen-in thermal stresses resulting in warpage after ejection of the green part from the mould or cracking during the debinding process. 4.. Powder injection moulding of a component with complex shape The simple flat model is suitable for illustration of the main features of the analysis packages. However, it is more interesting and informative to simulate the powder injection moulding of a component with complicated shape, which is typical for the PIM products. The shape of the second model is shown in Figure 39. This component was chosen for the validation experiments. Figure 39. Complex-shaped experimental component 6

68 Chapter 4 The component had two round wholes and one elongated groove. One corner of the component had the form of a thin "tail" with the purpose to study the flow of the feedstock in conditions of abrupt change of the cross-section. Three holes in the component have been introduced with the purpose to make the flow more complicated and for studying the formation of the weld lines. Due to restrictions of C-Mold, the choice of the shape of the experimental component was limited to geometries that could be represented by a mid-plane model. For that the component was flat and had constant thickness. The area of these surfaces was large enough for mounting pressure and temperature transducers in the experimental mould. On the other hand, with the purpose to test the 3-D simulation packages its thickness of the real component was set to 6 mm. As compared with the other dimensions of the component such distance ensured a "bulky" shape of it. The flat shape of the component was also convenient for studying with C-Mold of the influence of the thickness on the simulation results, because in this analysis package thickness is described as a numerical parameter. As described further, in the preliminary simulations performed with C-Mold thickness of the experimental PIM component was set to mm like in the simple rectangular model. Similar to the simple rectangular geometry the model with the complicated shape included a plane cavity, runners and cooling channels. The cooling channels were located in planes parallel to the mid-plane of the cavity. The mould was described implicitly in terms of properties of the mould material and boundary conditions. Two different gating positions were used. To make the initial conditions comparable during injection moulding through different gates, the runners in both cases were modelled as cm long channels. Modelling of injection moulding through one gate at a time was performed. For simulation of powder injection moulding through each gate a separate finite element mesh was created. Both meshes consisted of triangular D elements. The temperature changes were tracked at five different nodal points on the geometry model. Mesh elements corresponding to these points are shown in the Figure 40, which depicts -D mesh of the experimental component. Figure 40. Variable finite element mesh. Temperature results were extracted for the shown mesh elements. Top and bottom numbers correspond to the meshes for injection through the gate and gate, respectively. Properties of the material of the mould were taken for the tool steel H-3. The process parameters, if not stated differently, were as follows: part thickness mm, equivalent gate diameter 0.99 mm, equivalent runner diameter 4.4 mm, initial temperature of the feedstock 6

69 Simulation programmes 85 C, coolant material oil, coolant temperature 40 C, coolant flow rate 0 l/min, postfill time 5 s, pressure hold time s. The fill time varied from 0.05 to 0.7 s. Both filling- and post-filling stages of the injection moulding were simulated for each set of variable parameters. One of the output data of C-Mold thermal analysis is bulk temperature. The bulk temperature is the velocity-weighted average of the melt temperature from each level across the thickness and represents the energy that is transported through a particular location. When the melt stops flowing the bulk temperature becomes the average temperature. Typical bulk temperature distributions at the end of the filling stage for different fill times, are shown in Figure 4. Since the injection time is inversely proportional to the injection rate, provided that the injection rate is constant, Figure 4 permits judging about the influence of the injection rate on the bulk temperature. The visualising capabilities of C-Mold allow plotting temperature results as contour or shaded plots. In Figure 4 contour plots are shown. It can be seen that the temperature distribution is quite nonhomogeneous and its nonhomogeneity increases as the fill time becomes shorter (as the injection rate increases). When the fill time is relatively long (~0.7 s, Figure 40d) a monotonous temperature decrease is observed along the flow path. The hottest feedstock can be seen in vicinity of the gate. Along the flow path the feedstock cools down due to heat transfer to the colder mould. When the fill time decreases bulk temperature of the feedstock by the end of filling increases. It is noticeable that for the shortest fill times 0.05 s and 0. s (Figures 4a and 4b) the bulk temperature in certain areas becomes higher than the initial temperature of the feedstock (T=85 C ). This can be attributed to the viscous heating. The maximum increase of the bulk temperature is about 5 6 C. Since bulk temperature is an average temperature, it hides extremities. Temperature profiles across the thickness show the amplitude of temperatures inside the cavity. Figure 4. Bulk temperatures at the end of the filling stage; pre-set fill time: a) 0.05 s, b) 0. s, c) 0.3 s, d) 0.7 s; injection through gate. C-Mold results. The numerical results for temperature profiles across the thickness of the complicated component calculated for four different fill times are shown in Figure 4. The simulations have been performed with for different fill times: 0.05, 0., 0.3 and 0.7 s. From Figure 4 one can see that similar to the case with simple rectangular model, the temperature profiles are symmetric with respect to the midplane. At the end of the filling stage temperature distribution across the thickness have similar bell-shaped profile for all fill times. 63

70 Chapter 4 Figure 4. Temperature distribution across the thickness of the experimental component at the end of filling stage; injection through gate At the end of the filling stage with the longest fill time (tfill=0.7 s) the expected bell-shaped temperature profile is obtained. The temperature at the midplane is the highest, while surface temperature is the lowest. The biggest difference between temperatures at points on the surface and in the midplane is observed in the element at the gate (E468), the smallest - in the elements E5 and E955, where the temperature is almost uniform across the thickness. Such temperature distribution reflects a continuous cooling history: the surface temperature in all the elements lays below the point of 55 C, which is more than 30 C lower than the initial temperature. The midplane temperature depends on the distance from the gate and the duration of the melt flow through a particular element. The element E5 is left aside of the main stream of the melt flow. After it is filled at the first moments of the filling stage, no melt flows through it and, consequently, no additional heat is delivered to it. After element E5 has been was filled, its temperature decreases and equalises across the thickness because the heat from the feedstock is transferred to the mould. By the end of the filling stage temperature of this element and related temperature gradient across the thickness become the lowest among all the considered elements. The element E955 is the last one to be filled. The melt reaches this element after flowing through the longest path. On the way, the melt cools down. This is illustrated by the reduction of the midplane temperature of the elements along the flow path from the gate to the remote end: E468, E635, E873, E955 (Figure 4d). Due to the short time between the moment, when the element E955 is filled, and the end of the filling stage, the temperature gradient in this element is observed mostly in the sub-surface layers. The temperature across the thickness in the three remaining elements (E468, E635 and E873) is less uniform then in element E955. Elements E468, E635 and E873 are characterised by the relatively cold surface and hot midplane. The surface temperature calculated in all three elements is almost the same, while the midplane 64

71 Simulation programmes temperature substantially differs depending on the distance of the element from the gate. The element E468 has the highest midplane temperature due to the continuous flow of fresh hot melt during the whole filling stage. As the distance from the gate increases, the melt cools down and the midplane temperature decreases (elements E635 and E873). Temperature in a particular element by the end of filling depends on: the inlet feedstock temperature, the amount of the heat brought with the new portions of the melt during filling, and the time between the moment when melt front reaches the element and the moment when the melt stops to flow through this element. In case an element is located in the main stream of the melt, the last time moment coincides with the end of the filling stage. At high injection rate (short fill time) the influence of viscous heating on the temperature distribution increases. This influence becomes noticeable when heat generation rate exceeds heat dissipation rate. For the fill time of 0.3 s (Figure 4c) the temperature profiles preserve the same character as in the Figure 4d but are shifted up to higher temperature range. The midplane temperatures in all elements become closer to the initial temperature of the feedstock. It the element E468 small temperature rise is already noticeable. The temperature profile in this element has two local maximums at the layers between the midplane and the surface. This phenomenon becomes more noticeable when the fill times further decreases (Figure 4a and 4b). At the fill times 0. s and 0.05 s the temperature peaks become more pronounced and are registered in all the elements, excepting element E5. The highest increase of temperature is observed at the shortest fill time (Figure 4a). The maximum temperature rise in this case reaches 5-30 C above the initial temperature of the feedstock (85 C). It can be seen that the duration of the fill time affects position of the temperature peaks with respect to the midplane. As the fill time decreases, the peaks shift from the midplane to the surface. At the same time temperatures in the midplane of all the elements remain almost equal to the initial temperature of the feedstock (85 C). It can be now seen that increase of bulk temperature by 5 C corresponds to large temperature gradients. These gradients are maximal during the filling stage. After the cavity has been filled, temperature differences (non-homogeneity) quickly decrease. This can be seen from Figure 43, which shows temperature versus time plots for five elements. Figure 43 shows temperature data calculated for the layer where maximum temperature rise was observed. (normalised thickness 0.88). It can be seen that during the filling stage differences of temperature at the different elements are reaching C. These differences reduce to less then -3 C within s after the cavity is filled. Pre-set fill time = 0.05 s Normalised thickness = Temperature, C E468 E5 E635 E873 E Time, s Figure 43. Time-dependent temperature development in the layer at 0.88 of the normalised thickness; injection through gate 65

72 Chapter 4 A similar temperature equalisation is observed across the thickness of the part. Figure 44 illustrates the temperature distribution in different elements approximately 0.4 s after the end of the filling stage. It can be seen that within such short time, the temperature peaks completely disappeared (compare with Figure 4a). From Figures 43 and 44 it can be also seen that time period during which the overheating takes place is very short. Because of this, as well as, of the fact that the temperature rises mainly in the sub-surface layers, the experimental validation of these numerical results is practically impossible. Pre-set fill time =0.05 s time moment =0.46 s Temperature, degrees C Normalised thickness E468 E5 E635 E873 E955 Figure 44. Temperature distribution as a function of the normalised thickness at t=0.46 s; injection through gate Distribution of the melt velocity across the thickness is shown in Figure 45. The velocity profile is not parabolic. This is typical velocity distribution observed in the shear-thinning fluid. The no-slip boundary condition determines the zero velocity at the surface. The middle layers between 0.4 to 0.4 normalised thicknesses have the highest and almost uniform velocity. The highest velocity gradient is observed in the layers at the normalised thickness In this range the highest shear rate and, respectively, viscous heating effect should be expected. This observation is in good correlation with the temperature distributions, which show the hottest layers at the normalised thickness Element E468 Pre-set fill time = 0.05 s Time moment = s Velocity, m/s Normalised thickness Figure 45. Cross-sectional melt velocity distribution in the element E468 at time moment t= s; injection through gate At constant injection rate, velocity of the feedstock depends on the effective cross section of the cavity. Effective cross section is determined by the actual cross section and the thickness of the 66

73 Simulation programmes frozen layer. Figure 46 shows that midplane velocities calculated for elements E468, E635 and E873 substantially differ. The highest velocity is observed in the element E468, the lowest in the element E873. Taking into account that results shown in Figure 46 were obtained with no-slip condition, the highest midplane velocity should correspond to the highest shear rate, and consequently the highest viscous heating effect. However, the highest temperature is observed in the element E635. The seeming non-conformity of the velocities and temperatures may be attributed to the fast convective heat transfer from the element E468 to the element E635. At the filling rate corresponding to the shortest fill time the feedstock is transported with velocities about m/s. Such a high melt velocity may be a reason that heat released in one element reveals itself in the next sequential on the flow path element. Pre-set fill time =0.05 s Pre-set fill time =0.7 s 00 Velocity, m/s 0 0. E468 E635 E873 E468 E635 E Time, s Figure 46. Melt velocity in the midplane; injection through gate Therefore the temperature in the downstream element (E635) is higher, then in the upstream one (E468). When the velocity is low, the heat from the sub-surface layers reaches the surface close to the position, where it was generated. In the elements E635 and E873 velocities are much lower than in the element E468 at the gate (Figure 46). Besides that, due to the decrease of the feedstock velocity in the element E635, viscous heating becomes here negligibly low, while the rate of heat transfer from the melt to the mould remains unchanged. The process of heat transfer (cooling) starts prevailing over the heat generation. Therefore, in the couple element E635 element E873, the latter has lower temperature. Through the element E955 the melt flows during a very short time, because this is the last element to be filled. Viscous heating in this element is minimised. Besides that, the element E995 is located in the corner and therefore is in direct contact with four mould walls that ensure more extensive heat transfer to the mould as compared with the other elements. Because of these reasons only a weak temperature rise is observed in the element E995. Comparison of midplane velocities in the same element during injection with different injection times shows that midplane velocity is approximately inversely proportional to the injection time. From Figure 46 one can see that for the fill time 0.7 s, the melt velocity rates fit between 0.- m/s, while at the fill time 0.05 s they are the rage 30 m/s. At low injection rates the midplane velocities at different elements relate to each other in the same proportion as during the injection with high injection rates. That means that the effective cross sections remain practically unchanged when injection rate changes. This is indirect evidence that for the considered injection rates, thickness of the frozen layers is minimal. Despite the fact that viscous heating takes place during very short time and is localised in the thin layer of the melt, it is recommended to avoid it. Extension of the fill time seems to be the easiest 67

74 Chapter 4 way to reduce the viscous heating. Since extension of the fill time is not always acceptable because of the problems with the premature solidification, the solution may be in changing of the gating position. Figure 47 shows the calculated cross-sectional temperature distribution at the same points as shown in Figure 4a, but obtained during simulation of the filling through an alternative gating position denoted in Figure 40 as gate. All the process parameters used during this simulation were the same as in the previous case. It can be seen that change of the gate from the position to the position, may be used to decrease temperature peaks by approximately 5 C, what constitutes about 50% of the total temperature rise observed during the injection through gate. Time 0.05 s 0 0 Temperature, C Normalised thickness E55 E0 E698 E936 E006 Figure 47. Temperature distribution across the thickness of the part at the end of filling stage; injection though gate (compare with Figure 4a) 4..3 Summary of C-Mold calculations It has been demonstrated that C-Mold analysing package provides a lot of information on the PIM filling process that can be used for its optimisation. However, the absolute values of the calculated data may differ from the real ones because of the simplifying assumptions used in this package. It is especially true when the component has relatively thick walls. When a component has the shape that cannot be represented by a thin walled model, a fully 3-D simulation is required. 4. Moldflow Moldflow is an analysing package developed by Moldflow Corporation. It simulates injection moulding by using combined FEM/FDM method. First versions of Moldflow were twodimensional. The last versions of Moldflow are capable to work with 3-D models. The last versions of Moldflow include the special product suite, which got the name of Moldflow Plastic Insight (MPI). It has improved graphical interface (MPI/STUDIO), which provides tools for preparing, running and post processing an analysis of a model. A geometry model can be generated within MPI/STUDIO, or it can be imported into MPI/STUDIO from a CAD model. The last feature is a serious advantage of Moldflow as compared with C-Mold. The CAD files that can be translated into internal Moldflow format include Patran, Nastran, ANSYS, I-DEAS, STL, IGES and C-Mold formats. Based on the internally created or imported models, -D midplane mesh can be generated in Moldflow. From this point of view Moldflow is similar to C-Mold. The size of - D mesh elements is defined by setting their total number. The more elements are chosen, the finer 68

75 Simulation programmes is the resulting mesh. Moldflow is lacking 3-D meshing capability. Three-dimensional mesh cannot be created in Moldflow. If a 3-D model and mesh are needed, it has to be created outside and subsequently imported into Moldflow. Since the process of model translation and mesh generation is done automatically, the user loses control over the local mesh size. The obtained in Moldflow mesh often has to be repaired before running an analysis. The repairs can be performed with the editing tools of Moldflow. The assumptions of Moldflow analysis are similar to those of C-Mold. In particular, the injected material is assumed to be a generalised Newtonian fluid with pseudoplastic properties. Similar to C-Mold, the list of input parameters of Moldflow includes characteristics of the injection moulding process and material properties. In addition to the properties of the feedstock and the mould, Moldflow requires also recommended, maximum and minimum temperatures of the mould and the injected material. Moldflow uses also an additional parameter, which is no-flow temperature of the feedstock. It is a temperature at which the material stops to flow. It is analogous to some extent to the solidification temperature. Although the no-flow temperature is not a fundamental physical property of a material, it is commonly used in the polymer flow analysis software because of its convenience [46, 47]. The material database of Moldflow includes descriptions of standard polymer materials. Similar to C-Mold, new materials may be added. The minimum requirement for a new material is that it must have thermal and rheological properties. One of very useful features of Moldflow is the capability to generate automatically the coefficients for the material models from the tabulated viscosity values. Moldflow includes the following material models: st order model, nd order model, Cross model, Cross-WLF model, Carreau model and Matrix model. Melt density, thermal conductivity and specific heat can be defined only as constants. Boundary conditions are similar to those of C-Mold and, in particular, include injection nodes, temperature of the mould, initial temperature of the feedstock, runner dimension constraints, valve gate groups, pressure control points. Runner dimension constraints allow automatic balancing of the flow. Valve gates groups are used to modify flow pattern by injecting through more then one gate. Switching from velocity phase control to pressure phase control is possible either by the filled volume fraction (usually 98-99%) or by maximum pressure specified in the pressure control point. The output data of Moldflow, in particular, include: - Melt flow front - Temperature - Pressure - Air traps - Weld lines - Shear rate - Shear stress - Cooling time - Clamp force In Moldflow version MPI.0 there is no possibility to view temperature, pressure and shear rate data for a particular node versus time. MPI.0 is capable to perform 3-D flow analysis. The results of 3-D analysis are available only in the form of shaded contours. Shaded contours can be animated. The X-Y plots, that would depict a parameter versus time, are not available. 4.. Examples of simulation with Moldflow The capabilities of Moldflow for simulating of the PIM process are demonstrated here with the component shown in Figure 39. A 3-D model to be used for the simulation with Moldflow was made in ProEngineer and meshed in the meshing module of ProCAST. Thereafter the mesh was 69

76 Chapter 4 translated into internal Moldflow file format. The 3-D mesh obtained after translation to Moldflow is shown in Figure 48. Injection points were defined at the end of the sprue. Figure D mesh after translation in Moldflow Similarly to simulation with C-Mold, the mould material was chosen top be H3 tool steel. The temperature of the mould was set to 35 C, the injection temperature of the feedstock was 85 C. Viscosity of the feedstock was described using Carreau model. Processing parameters, initial and boundary conditions were the following: - Ejection temperature 35 C - No flow temperature 50 C - Minimum melt temperature 60 C - Maximum melt temperature 90 C - Absolute maximum of melt temperature 0 C - Minimum mold temperature 0 C - Maximum mold temperature 40 C - Recommended mould temperature 30 C (differed from the value T= 35 C defined in the boundary conditions menu). It can be seen that the boundary conditions of Moldflow include additional technological parameters, whish facilitate better formal control of the PIM process. This approach allows automatic assessment of the moulding conditions and work out a report with suggestions on the necessary improvements of the process. Some of the results calculated with Moldflow are presented below. Figure 49 shows shaded contours of the output data "fill time". In this figure positions of the melt front at different time moments are marked with different colours. There is a possibility to show for each time moment only the filled part of the cavity. A serial of pictures with the melt front positions at several sequential time moments are shown in Figure 50. Unlike in C-Mold, the progress of the melt front can be animated. 70

77 Simulation programmes Figure 49. "Fill time" results of Moldflow Figure 50. Melt front advancement calculated with Moldflow (Parameter "fill time" for different time moments) As compared with C-Mold, positions of the melt front are better visible. From the sequential pictures corresponding to different time moments, the relative melt front velocity can be estimated. Other parameters can be viewed in similar way in the form of three-dimensional shaded plots. The advantage of the 3-D plots is that they show the spacious position of the melt. The inconvenience of 3-D plots is that a large number of images similar to those shown in Figure 50 are required for studying the change of a parameter versus time. The shaded 3-D plots depict the distribution of a particular parameter over the component area, but do not allow monitoring the development of this particular parameter at a chosen node with time. Inability to depict the output data in the form of X-Y plots should be treated as a disadvantage of Moldflow. Because of this Moldflow seems to be less suitable than C-Mold for studying the evolution of a desirable parameter in time. Another peculiarity of Moldflow is that the melt front position and other output data are depicted completely independently. For example, when the pressure distribution is visualised, it is not possible to see the exact position of the melt front. It is known that pressure is zero at the melt front. However, in the 3-D plots any data are depicted by a 7

78 Chapter 4 number of shades, which correspond to the intervals rather to the exact values of the visualised data. In case of pressure plot, the melt front position will be somewhere within the pressure interval from zero to the first step of gradation. An example of it can be seen in Figure 5, which shows the calculated pressure data for two different time moments. The shaded plots depict pressure distribution in the feedstock over the cavity, but not the melt front. Figure 5. Moldflow pressure results at different time moments. The cut-off results allow viewing the isobar surfaces. An example of cut-offs for pressure results is shown in Figure 5. In Figures 5 and 5 the domains, which are not filled yet, are included in the lowest pressure gradation step. Pressure can only be monitored by comparing pictures similar to those shown in Figure 5, but made for a number of different time moments. Figure 5. Moldflow pressure results with cut-offs Unlike C-Mold, Moldflow calculates temperatures for each node and is capable to present the results without averaging over the thickness of the component. They can be presented in the form of 3-D or -D shaded plots. An example of temperature results in the form of shaded 3-D plot can be seen in Figure 53. The cut-offs permit viewing domains of the feedstock with the limited range 7

79 Simulation programmes of temperatures. An example of temperature cut-offs can be seen in Figure 54, which shows only those inner layers of the feedstock that have temperature above 65 C. Figure 53. Temperature in the end of filling. Scale is limited to C range. No temperature changes are visible on the surface Figure 54. Moldflow numerical temperature results with the "cut offs". Only domains of the feedstock, where temperature is higher then 65 C, are shown. 73

80 Chapter 4 The cut-off data like those shown in Figure 54 allow viewing "hot" feedstock inside the domain, at the melt front position. The volume of the feedstock at the temperature higher than 65 C can be seen. But temperature distribution inside and outside of that volume is unknown. Another way to see the inner layers is offered by using section planes. The model can be cut by an arbitrary plane and in the obtained cross section the studied parameter can be shown. In Moldflow the cutting plane can be dynamically moved through the model, showing how the parameter changes through the component. An example of -D cross section with temperature results can be seen in Figure 55. It provides more information on the temperature distribution than the 3-D plots (Figures 53 and 54). The cross section reveals the internal temperature non-homogeneity. In particular, in Figure 55 areas with the temperatures in the range C can be seen. The related 3-D plot (Figure 53) hardly shows any temperature gradient, because in it only surface temperature is visible. Temperature on the surface of the component is almost uniform and close to the temperature of the mould (35 C). Figure 55. Temperature in the cross section calculated with Moldflow. Comparison of data from the cutting planes needs special caution because results in the cutting plane strongly depend on its position within the model. Small difference in the positions of the cutting planes may cause great differences, for example, in the cutting plane temperature distributions. This happens because of strong temperature gradient across the component. An example of the possible temperature differences in the cutting planes of the same model is presented in Figure 56, which shows results for the same time moment of the same simulation, but from three parallel to each other the cross sections. For comparison Figure 57 shows temperature results in the cross sections for three different simulations performed with identical conditions, excepting the fill time parameter. Different temperature scale is to be noted. The differences in the temperature distributions that can be seen in both Figure 56 and Figure 57 are comparable. Therefore while comparing the cutting plane results, one should be aware that different 74

81 Simulation programmes temperatures might be attributed not only to the different moulding conditions, but also to the not identical positions of the cutting planes. Figure 56. Temperature in three parallel cross sections from one simulation. Cutting planes are parallel to each other and to the plane of the computer monitor. Figure 57. Temperature in the cross sections of three different simulations with fill times.5;.5 and.50 s. Position of the cutting planes in all cases might not be identical because of slightly different orientation of models. The advantage of 3-D plots over -D cross sections is also doubtful when studying the shear rates and velocities of the feedstock, because 3-D plots always show distribution of specific parameter only on the surface. This can be seen from comparison of Figures 58 and 59 containing 3-D plots and the cross sections with shear rates, respectively. Both figures show that the shear rates are the highest in the middle of the runner. But because the highest values of shear rates are developed in the sub-surface layers, the 3-D plots cannot reveal them. 75

82 Chapter 4 Figure 58. Shear rate. 3-D simulation of Moldflow. Figure 59. Shear rates in a cross section An example of velocity data calculated with Moldflow is shown in figure 60. This is a typical cross sectional plot similar to those described above for the temperature and shear rates distributions. Figure 60. Calculated with Moldflow velocity in the cutting plane. End of filling, t=.5 s. It is possible to locate the areas with the highest velocities. To judge about the probability of segregation it is desirable to know not only the velocity magnitude, but also velocity vectors. Unfortunately Moldflow output results do not include velocity vectors that make Moldflow less suitable for estimation of the probability of segregation. 4.. Summary of Moldflow calculations It has been demonstrated that types of results available in Moldflow make it very suitable for estimation of the melt front advancement. The scaling capabilities of Moldflow allow viewing all 76

83 Simulation programmes the peculiarities of the filling of a three-dimensional cavity. Moldflow also can be used to determine the overall effect of initial parameters on the distribution of temperatures, pressures, velocities and shear rates in the feedstock. On the other hand, absence of possibility to view the output parameters versus time in the form of X-Y plots reduces the efficiency of Moldflow for quantitative comparison of results from different simulations. 4.3 ProCAST Pro-CAST simulation code by the UES Software, Inc. has been developed for simulation of casting process. This code uses the finite element method to solve full 3-D Navier-Stokes equations without cuts along with the coupled energy equation. This makes ProCAST suitable for simulation of the PIM process of three-dimensional products, which cannot be modelled by thinwalled models. ProCAST comprises several modules that together represent a set of tools for creating a model preparing it for analysis, running the analysis and viewing the results. MeshCAST provides the capability to import geometries from commercially available CAD/CAE packages. With MeshCAST it is possible to repair models and generate both -D and 3-D meshes. PreCAST is used for defining the problem, setting up the parameters of the technological process, initial and boundary conditions and parameters of the simulation. DataCAST on the basis of information from PreCAST prepares the binary files to be used in the simulation module ProCAST. ProCAST simulates the process and generates output data. PostCAST provides the post-simulation capability to calculate derivative results, extract data from the simulation results files and format this data for further processing, analysis or viewing. ViewCAST provides the capability to view the results of the simulation. The module structure of ProCAST ensures high flexibility of this package. ProCAST allows to read 3-D meshes which have been created in commercial packages as PATRAN, IDEAS, ANVIL, ANSYS, ProEngineer, IFEM, and GFEM. It is also possible to read IGES description of geometry's surface in MeshCAST and generate 3-D mesh. Due to a large number of existing interfaces, the preparation of the analysis is short. Meshing process is completely automatic. The -D mesh is controlled by the size of linear elements. It can be made variable for every edge of the geometry. In this way variable -D mesh is created. 3-D tetrahedral mesh is generated on the basis of the surface mesh. The surface mesh has to be created for each surface of a 3-D model. The structure of set-up parameters in ProCAST is determined by the requirements of simulation of metal casting. The initial parameters describe the technological process in terms of metal casting rather then powder injection moulding. Preparation of set-up parameters for simulation in ProCAST needs relatively more work as compared to C-Mold and Moldflow. The list of adjustable process parameters, which are relevant for powder injection moulding includes: - Injection rate - Pressure - Inlet melt temperature - Temperature of the mould (surface) - Volumetric heat source or sink ProCAST allows defining of most of the input parameters as constants, or time-dependent values. In this way high flexibility of ProCAST is achieved. Typical PIM process parameters like ram speed profile, ejection temperature, minimum, maximum and suggested temperatures of the feedstock and the mould, no-flow temperature, timer for valve gate, fill to pack switch-over, timer 77

84 Chapter 4 for hold pressure, hot runner manifold control, are not present in ProCAST. Therefore the filling and cooling stages of PIM need two sequential simulations. The temperature output parameters from the simulation of the filling stage should be used as the input parameters for the simulation of the post filling stage. The major advantage of ProCAST over the two other selected analysis packages is that the PIM tooling (mould) can explicitly be included in the simulation process. The mould is modelled in the same way as the component. Such approach requires extra preliminary work but allows accounting for non-homogeneity of the mould temperature. The availability of the surface temperature of the mould permits studying the effect of the mould design on the temperature of the cavity surface and, consequently, the cooling process. When the model includes geometry the mould, the temperature distribution in the mould obtained from the thermal analysis, is used as a starting condition for the simulation of the PIM process. This simulation scheme requires more time and computer memory but makes the simulation more realistic. If the simulation is performed without the mould, then thermal boundary conditions include surface temperatures and heat transfer coefficients, which are applied to the surfaces of the model. This approach simplifies preparatory work and reduces calculation time due to less number of elements of the model, which, in such case, comprises only the component. Boundary conditions also can be defined as constants or variables. It is also possible, for example, to assign different heat transfer coefficients on different surfaces of the mould. Such approach allows precise modelling of thermal effects between parts of the mould and the mould and the component. The structure of the input database and type of input parameters in ProCAST are quite different from those of C-Mold and Moldflow. In ProCAST thermal properties of the injected material and the mould can be defined as variables, which depend on time and/or temperature. Viscosity of user-defined material may be specified as Newtonian or non-newtonian. The non- Newtonian viscosity is described by the Carreau-Yasuda [7] model (equation 5). ProCAST offers an extensive list of output parameters, which, in particular, includes: - Melt front position and velocity - Temperature - Velocity - Pressure - Shear rate - Shear stress - Frozen layer fraction - Flow rate - Heat flux - Cooling rate - Fluid velocity magnitude - Components of fluid velocity along X, Y and Z coordinates - Turbulent dissipation - Turbulent viscosity - non-newtonian Shear rate - non-newtonian viscosity. Some of the results generated by ProCAST, for example, turbulent dissipation and turbulent viscosity, are more relevant for simulation of fluid flow of metals and less important for simulation of flow of the viscous fluids like PIM feedstocks. The viewing capability of the output data of ViewCAST are superior to the viewing capabilities of C-Mold and Modlflow. Most of the output data can be presented in the forms of 3-D or -D (parameter versus time) plots. Cross sections are also available. The 3-D plots and cross sections can be animated. The only disadvantage of the viewing capability of ProCAST is that the weld lines are not explicitly indicated in the results. 78

85 4.3. Examples of simulation with ProCAST Simulation programmes The 3-D model of the experimental component shown in Figure 39 was created with the help of ProEnginner. The model in IGES format was imported into MeshCAST module, which is part of the ProCAST package. MeshCAST checks its integrity and meshes the model. If necessary, it is possible to repair the geometry model with the editing tools of MeshCAST. Meshing was performed in two stages. During the first stage a two-dimensional surface mesh was generated. ProCAST allows creating mesh elements with variable size. The main parameter of mesh generation is basic length of mesh elements. It can be defined by the user for each edge separately, or for a set of edges. By applying different basic length, surface mesh size can be controlled. Second stage of meshing included generation of 3-D mesh. This process is fully automatic. The size and aspect ratio of 3-D elements is not controlled, because it is based on the D mesh. Quality of the 3-D mesh can be improved by smoothing operation, which is intended for equalisation of the mesh elements and reducing their aspect ratio. Surface mesh for the model of the experimental component is shown in Figure 6. On its basis, a 3-D tetrahedral mesh was created. The 3-D mesh is not shown because of too many elements, which make the mesh not legible. Figure 6. 3-D mesh of the part made with MeshCAST A 3-D geometry model including the mould is shown in Figure 6. The relevant surface mesh can be seen in Figure 63. Mesh of the component is not visible because the component is inside of the mesh of the mould. The models of the component shown in Figures 6 and 63 are equivalent. The only difference is the availability of the model of the mould around the cavity in the last case. If the model without the mould was used in the simulation, the surface temperature was defined as one of the boundary conditions. If the model with the mould was used, first step of simulation was performing of the thermal analysis. The heating-up of the mould from room temperature was simulated with the following boundary conditions: - Temperature at the internal surface of the cooling channels was 40 C - Heat transfer coefficients on the mould surface were 00 and 0 W/m /K. The higher coefficient was set up for the surfaces that were clamped by the injection moulding machine, while the lower coefficient was set up for the remaining mould surfaces. The thermal analysis was stopped when the temperature distribution became stable. In order to show the internal temperature distribution a cross section of the mould is presented in Figure 64. From this figure one can see that temperature at the surface of the cavity at different points differs by 5-7 C. While using the model without the mould, the non-uniform temperature distribution is not accounted for. 79

86 Chapter 4 Figure 6. 3-D geometry model of the experimental mould. Cavity for moulding of the component from Figure 39 and cooling channels are visible. Figure 63. Surface mesh of the mould 80

87 Simulation programmes During cavity filling simulation the following initial and boundary conditions were used: - Injection rate was m/s - Feedstock temperature was 85 C Viscosity of the feedstock was described using Carreau-Yasuda model. Figure 64. Cross section of the mould after thermal analysis. Temperature non-homogeneity in the cavity can be seen. Temperature of the cooling liquid 40 C, time 35 s. Figure 65 presents typical temperature distribution results obtained from the simulation without the mould. From the Figure 65a, which shows temperature on the surface of the injected component, position of the free surface (melt front) can be seen. Figure 65b presents the cross section plot. Example of temperature development versus time is given in Figure 66, where temperatures of the feedstock at three points, and 3 indicated in Figure 65 are shown. Temperature plots shown in Figure 66 permit monitoring of the cooling rate at different points on the surface of the component. After the feedstock has reached the point, its temperature almost instantly falls down to C. Thereafter the cooling rate sharply decreases. At all three points the cooling rates are comparable, though the cooling rate at point 3 is somewhat higher then at first two points. This can be explained by the position of point 3, which is located in the thin end of the component. From Figure 66 one can also see that the temperature data are available after melt front has reached the point. This makes possible precise timing of the melt front advancement. Temperature plots shown in Figure 66 are similar to those obtained with C-Mold (Figure 43). Examples of calculated shear rates are shown in Figure 67. Like the other parameters, the shear rates can be visualised in the forms of 3-D shaded plots or cross sections. Figure 67 shows that 8

88 Chapter 4 areas of high shear rates are located at the gate. This result is quite similar to the one calculated with Moldflow (Figure 57), though some differences in the distribution of shear rates are noticeable. These differences are most likely attributed to different material models used in the Moldflow and ProCAST. The postprocessing capabilities of ProCAST allow defining the cross section by a plane whose position is defined by coordinates. Due to this feature it is possible cutting different models with exactly the same planes, avoiding errors due to not identical positioning of the cross sections. Figure 65. Feedstock temperature during powder injection moulding. ProCAST results. Temperature, C Point 64 Point 6 Point Time, s Figure 66. Feedstock temperature as a function of time during powder injection moulding. ProCAST results. 8

89 Simulation programmes Figure 67. Shear rates during the mould filling. ProCAST results. ProCAST pressure results also can be visualised in the forms of X-Y (pressure versus time) plots or 3-d plots. An example of pressure results for two different injection rates are given in Figure 68. Figure 68. Pressure versus time at three different points for different injection rates; mould temperature 35 o C; heat transfer coefficient 8000 W/m K ; a) m/s; b) 0 m/s. ProCAST results. In this figure typical pressure versus time plots for three points located, respectively, at the nozzle, at the gate and behind the gate (inside the cavity), are shown. This type of pressure results was available in C-Mold and not available in Moldflow. The difference of the results calculated with ProCAST and C-Mold is that the ProCAST pressure results are available only for the filling stage. When the cavity is completely filled the pressure drops to zero. To simulate pressure during the filling stage another simulation has to be defined. Results presented in Figure 68 show the how pressure at a particular point changes. It can be seen that by the end of the filling stage pressure sharply increases. The observed pressure peak in the end of the filling stage is much more pronounced at the injection rate 0 m/s than at m/s. From the distances between the curves it is also possible to estimate the spacious pressure gradient within the cavity. The more information on the spacious pressure distribution during the cavity filling can be obtained form the 3-D plots. 83

90 Chapter 4 Examples of the 3-D pressure plots can be seen in Figure 69. Pressure distribution is shown at two close time moments just before and after appearance of the pressure peak on the pressure versus time plots form Figure 68. From the distances between the isobars it can be seen that low pressure gradient before the peak (Figure 69a) sharply increases by the moment when the peak has developed (Figure 69b). Figure 69. Spatial pressure distribution in the final moment of the filling stage, MPa; injection rate 0 m/s. ProCAST results. Just before the peak (Figure 69a) the pressure gradually decreases from the gate to the melt front. It can be seen that during the last moments of filling, the melt front moves in the two ends of the component. After the wider end is filled, the actual cross section of the cavity abruptly decreases and resistance to the flow suddenly increases. At this moment, the overall pressure in the cavity is increased, though non-proportionally. Figure 69b shows that near the melt front high pressure gradient is observed, while in the rest of the component it remains almost unchanged. In order to minimise residual stresses it is necessary to minimise the overall pressure magnitude and peak severity. Slow advancement of the ram in the final moments of filling can reduce peak pressure. This is illustrated in Figure 70 that shows pressure distribution by the end of the filling stage at the injection rate of m/s. Figure 70. Spatial pressure distribution in the final moment of the filling stage, MPa; injection rate m/s. ProCAST results. This result can be compared with the one presented in Figure 69b. It can be seen that during the filling with the injection rate of m/s the feedstock fills the wide and narrow ends more 84

91 Simulation programmes uniformly, than during the filling with the 0 m/s injection rate. The filling becomes more balanced at slower injection rate. The longer distances between the isobars in Figure 70 indicate that the cavity is filled till the very end with lower pressure gradient as compared to the filling with 0 m/s injection rate Summary of ProCAST calculations The main advantages of ProCAST are attributed to the combination of its ability to work with three-dimensional geometries and large number of output data, which can be presented in a form of 3-D, -D (cross sections) and "parameter versus time" plots. High flexibility of defining the initial and boundary conditions (as a constant or as a variable dependent on time and/or temperature) makes ProCAST very suitable for performing numerical simulation using "what if" principle. Like the injection rate in the considered example, any processing parameter can be modified and the simulation re-performed with the new conditions. It is easy to compare the results from different simulations including the -D shaded plots from cross sections, because in ProCAST there is a possibility to determine positions of the cross sections numerically. Among the disadvantages of ProCAST its relatively less convenient user's interface, and necessity to perform several simulations for modelling of both filling and post filling stages of PIM should be mentioned. 4.4 Concluding remarks In this chapter capabilities of C-Mold, Moldflow and ProCAST analysis packages for simulation of powder injection moulding process were demonstrated. All analysing packages calculate and visualise melt front advancement, temperature, pressure and shear rates of the feedstock. The output data of C-Mold provide overall information about the powder injection moulding process, including the melt flow front, air traps, weld lines, shear rates, pressures and temperatures of the feedstock. Because of the simplified mathematical model used in C-Mold, the results calculated with this analysing package are limited to the average data or to the data calculated with the assumption that the flow takes place between the parallel surfaces. Moldflow is goal-oriented analysing package. It is designed with the purpose to work out recommendations on the improvements of the injection moulding process. The 3-D version of Moldflow can be successfully used for monitoring of the movement of the free surface of the feedstock during filling of a three-dimensional cavity. Parameters, other then melt front position, are better viewed in the form of cross sections. Comparing with C-Mold results, results of Moldflow are less informative. Simulation of powder injection moulding with ProCAST needs relatively more preparatory work because this analysing package was not specifically designed for the injection moulding process. The main advantages of ProCAST are its capabilities to include explicitly the mould in the analysis and to define input parameters and boundary conditions as variables, which depend on time and/or temperature. ProCAST output data can be viewed in different forms, including two- and three-dimensional plots, as well as "parameter versus time" plots of X-Y type. The disadvantages of ProCAST are that it has relatively less user friendly interface than the other two analysis packages, requires manual setting up of large number of input parameters and it is not capable of simulating the filling and post-filling stages in one simulation run. 85

92 Chapter 5 Comparison of the numerical results calculated with different analysis packages and their validation In Chapter 4 the commercial analysis packages C-Mold, Moldflow and ProCAST were described. Besides the description of general capabilities of these analysis packages examples of simulation of the PIM process were given. In this Chapter the results of simulation of the PIM process calculated with all three codes are compared with the experimentally observed melt front advancement during the PIM process and measured temperatures and pressures. The validation is aimed at the estimation of the applicability of the commercially available analysis packages for simulation of the PIM process. 5. Experimental setup 5.. Research Mould The experimental measurements were made with a special research mould. The mould was made of H3 tool steel. The mould contained two identical cavities for moulding of the experimental component shown in Figure 39. Each cavity had three different gating positions, which could be opened or blocked. The gating positions on the first and the second cavity were different. Due to such design, the component could be formed by powder injection moulding through six different gating positions. The system of blocks (with and without gates) allowed injection through one or more gates simultaneously. With the purpose to modify the cavity shape, a number of inserts with different surface profiles were made. Each insert could be placed in the cavity. In this way components with variable thickness along their length could be produced. The photographs of the mould are shown in Figures General view of the mould is presented in Figure 7. Figure 7 shows in detail the design of the cavities. In this figure the lower cavity contains an insert. The mould was equipped with four Chromel-Alumel thermocouples and three Kistler piezoelectric pressure transducers for each cavity. The pressure transducers and the thermocouples were

93 Validation mounted in the plate that did not contain the cavities. The pressure transducers were mounted flush with the surface of the mould. The arrangement of the sensors was identical in each cavity and permitted registering pressure and temperature on the surface of the moulded component at different points. Positions of the sensors on the plate of the mould are shown in Figure 73. Figure 7. Experimental mould. General view of the "cavity" side. Figure 7. Cavities and lay-out of the runners Figure 73. The opposite plate of the mould with pressure transducers and thermocouples 87

94 Chapter 5 Figure 74 shows positions of the pressure transducers and thermocouples with respect to the surface of the component. Pressure transducers in the first cavity were noted as Pr, Pr and Pr 3. Pressure transducers in similar positions in the second cavity were noted as Pr 4, Pr 5 and Pr 6, respectively. Similarly positions of the thermocouples were noted as T T4 in the first cavity and T5 T8 in the second one. Figure 74. Positions of the pressure transducers and thermocouples with respect to the component. P, P and P positions of pressure transducers; T, T, T3 and T4 positions of thermocouples. Powder injection moulding is usually performed with injection moulding machines of the same types, which are used for injection moulding of polymers. In this study a standard injection moulding machine of Battenfeld, type BA50/50, Austria, was used (Figure 75). The experimental installation included the injection moulding machine, the research mould and a digital data acquisition (measuring) system. Figure 75. Battenfeld BA 50/50 injection moulding machine and digital data acquisition system 88

95 Validation 5.. Measuring system Signals from the thermocouples and pressure transducers were received by the digital amplifier DMC 90, where they were digitised and further sent to the computer via RS 3 interface wherein processed by the data measurement programme BEAM. This system possessed six channels for acquisition of the incoming signals. In the experiments three channels were used to register signals from the pressure transducers while the other three registered signals from the thermocouples. The schematic diagram of the data acquisition system is shown in Figure 76. Figure 76. Schematic diagram of the data acquisition system Because of the limited number of the temperature measuring channels (three), temperatures at any three points could be measured simultaneously during one powder injection moulding cycle. The measurements were taken with the following settings: sampling rate was 0 s -, total measurement time was 0 s. With the chosen sampling rate, the incoming signals were measured every 0.05 s. The measured data were recorded in the form ready for subsequent post processing. The tables of data were thereafter exported to a PC Microsoft EXCEL programme for further processing, where pressure versus time and temperature versus time graphs were made Measurements of pressure Typical measured pressure graphs are shown in Figure 77. The measuring system was activated manually after the beginning of the injection cycle. The period of time from the start of the injection process to the instant of the start of the measurements was not fixed. Therefore the time from the origin to the instant of the pressure rise is arbitrary in all the graphs. Because of such measuring scheme it was possible to compare only the maximum pressures achieved in different experiments and the pressure increase rate. If rates of pressure increase have to be compared, then the graphs obtained from different experiments should be shifted along the x-axis to the fixed time moment. This moment can be chosen arbitrary. For example, it can be the moment when the first transducer registers pressure rise. Before the beginning of the validation experiments the pressure transducers have been calibrated. During calibration process a prescribed pressure was applied to each transducer and compared 89

96 Chapter 5 with the response of the transducer. Each pressure transducer was tested twice. Pressure calibration graphs are shown in Figure 78. Pressure, MPa Pr0.ch) 50 Pr0.ch) 40 Pr03.ch3) Time, s Figure 77. Typical pressure graphs during the powder injection moulding cycle Calibration experiments showed high accuracy of the signals from the pressure transducers and good reproducibility of the measurements. Error attributed to the quality of the signal was found to be less then %. Another source of errors could be the fluctuations of the processing parameters of the injection process. In each shot the injection rate, temperatures of the feedstock and the mould, viscosity of the feedstock, etc., may slightly differ from each other. This may lead to different pressure distribution with the cavity. For estimation of the scattering of the measured pressure data that may occur due to fluctuations in the process parameters, ten measurements of pressure were performed in the same conditions. The results are shown in Figure 79. This figure shows the local maximums of the pressure curves. It can be seen that the maximum absolute difference between the highest and the lowest peak pressures in 0 experiments was about 3.6 Mpa, which is about 8.7 % of the maximum registered pressure. 90

97 Validation Figure 78. Pressure calibration graphs 9

98 Chapter 5 Pressure in point ; half round gate, d=4mm Pressure, MPa Time, s Exp Exp Exp 3 Exp 4 Exp 5 Exp 6 Exp 7 Exp 8 Exp 9 Exp 0 Figure 79. Scatter of maximum measured pressure. Results of ten experiments Measurements of temperature The temperature was measured by using Chromel-Alumel thermocouples. The intention was to ensure measurements of the surface temperature of the feedstock. The thermocouples were mounted in such a way, that their tips were protruding over the surface of the mould by mm as shown in Figure 80. Figure 80. Placement of a thermocouple Such placement of the thermocouples was chosen with the purpose to minimise the disturbance to the melt flow and the effect of the thermocouple casing on the measurements of temperature of the feedstock Parameters of the powder injection moulding process The validation experiments were performed with the standard feedstock of 36 L stainless steel, produced by BASF. The feedstock from the same batch was used for determination of its 9

99 Validation rheological and thermal properties and for the validation experiments. The powder injection moulding process was performed with constant preset ram speed, (constant injection rate). The injection rate was set up in the injection moulding machine in per cent to the maximum achievable injection rate. The programmes for numerical simulation often require the injection rate to be determined in the other units. For constant diameters of the barrel and the nozzle a firm relation between the injection rates expressed in per cent, in cm 3 /s and in m/s can be established. Injection rates expressed in different units for the barrel diameter 8 mm and the actual nozzle diameter 4 mm are given in Table 6. The experiments were performed with the injection rate 5%, which was equivalent to the volumetric injection rate of.78 cm 3 /s and linear injection rate 0.93 m/s. For the experimental component shown in Figure 39 the corresponding fill time was about 0.6 s. The initial temperature of the feedstock was 85 C. Table 6 Injection rates for 8 mm diameter the barrel and the 4 mm diameter nozzle, expressed in %, cm 3 /s and m/s Injection rate, Injection rate, Injection rate for % cm 3 /s nozzle opening diameter 4.0 mm; m/s The research mould was heated by oil, which was pumped through the cooling channels. Figure 8 shows temperature results measured by the thermocouple at the position T according to Figure 74 during the heating-up period. It can be seen that thermal equilibrium was reached after approximately 80 minutes of the heating. Temperature distribution in the heated mould was not uniform. The initial distributions of temperature on the surface inside the cavity could be estimated from the readings from the thermocouples at the positions T-T4. Temperatures measured in the heated mould fit in the range 7-0 C. 93

100 Chapter 5 Temperature, C Time, min Figure 8. Temperature during the heating of the experimental mould measured by the thermocouple in the position T All validation experiments were performed while injecting through gate. This gate can be seen at the leftmost side of the upper cavity shown in Figure 7. As only three temperatures at once could be recorded in one cycle, it was decided to record signals from the thermocouples T, T and T3 according to the notations in Figure 74. During the preliminary tests it was found that the signals from the pressure transducers at the points Pr and Pr3 were almost identical. Therefore in the validation experiments only transducers Pr and Pr3 were used. To study the movement of the melt front and formation of the weld lines and airtraps, the tests with deliberate short shots were performed. Positions of the weld lines were estimated by the visual check. 5. Simulation setup The initial and boundary conditions in all the simulations were kept as close as possible to the conditions during the real powder injection moulding process. Some differences, however, could not be avoided due to the different requirements regarding the set up and the input data in different analysis packages. The details are given below. The model of the experimental component used in C-Mold is shown in Figure 8. It includes the cooling channels and the runners as in the real mould. The cavity of the component itself is exactly the same as it was in Figure 40. Thickness of the model was set to 6 mm. Simulations with Moldflow and ProCAST were performed with the same models as shown in Figures 48 and 6, respectively. Figure 8. Two-dimensional model used in C-Mold. Mesh is not shown. 94

101 Validation In ProCAST and Moldflow temperature of the mould was set to 7 C. In C-Mold temperature of the mould wall in the cavity was calculated. The calculated temperature distribution at the cavity surface is shown in Figure 83. It was achieved when the temperature of the cooling fluid has been set to 5 C. The injection rate during simulation was set to the values corresponding to the 5% injection rate as defined in the injection moulding machine. In C-Mold and Moldflow the inlet boundary condition was defined through defining the fill time of 0.64 s. In ProCAST the linear inflow rate of 0.93 m/s was set. Properties of the feedstock were the same as determined in Chapter 3. Simulation with C-Mold and Moldflow were performed with PC with Athlon processor, 900 Mhz, and 56 Mb RAM. Simulation with ProCAST was performed with Hewlett Packard HP9000 J40 UNIX workstation, with dual PA-800 processor, 36MHz, 04 Mb. Figure 83. Initial mould wall temperature used in C-Mold 5.3 Comparison between numerical and experimental results 5.3. Melt front advancement The calculated positions of the melt front during cavity filling at approximately the same volumes filled are shown in Figures 84a 84c. The results of simulation can be compared with the experimental component, which was obtained by the use of deliberate short shot (Figure 84d). It can be seen that in the process of mould filling, the feedstock is split in two streams by the row of the hole-forming juts. The experimental observation (Figure 84d) shows that the feedstock fills the wider part of the cavity (the right one in Figures 84a - 84d) faster than the narrower part. In the narrower part the hesitation of the melt is observed. This effect was not predicted by C-Mold (Figure 84a). Predictions of Moldflow and ProCAST (Figures 84b and 84c) are in better agreement with the experimental observations, though the experimentally observed distance between the positions of the melt fronts in the left and the right streams is larger, than in the patterns calculated by Moldflow and ProCAST. The difference between the experimental observations and the numerical results can be explained by the lower injection rate during the short shot than during the simulations. The numerical results shown in Figure 84 are related to the time instants, when the cavity is being filled with the pre-defined injection rate of.78 cm3/s. Under such conditions the average velocities of the streams of the melt are high. In the real short-shot experiment, due to inertia of the injection moulding machine, the melt stops moving not immediately, but within a certain time period. During this period the melt velocity decreases and becomes lower than the calculated value. While moving at lower velocity, the feedstock cools to 95

102 Chapter 5 lower temperatures. At such conditions the frozen layer becomes thicker. The effective cross section of the flow path reduces, and consequently, the resistance to flow increases. The relative increase in resistance to flow is greatest in the "narrow" part of the cavity, where the relative thickness of the frozen layer is the largest. As a result, the melt experiences larger hesitation in the narrower part of the cavity. The filling pattern determines locations of the weld lines. Figure 85 shows the positions of the weld lines predicted numerically and the experimentally observed one. C-Mold explicitly marks positions of the weld lines on the model (Figure 85a). In Figures 85b and 85c positions of the weld lines can be estimated by the location of the meeting melt fronts, calculated by Moldflow and ProCAST, respectively. The experimentally observed weld line can be seen in Figure 85d. The positions of the numerically calculated weld lines and the experimentally observed ones match each other very well. All the predicted weld lines are located close to the observed weld line, though it is possible to see that the best prediction is made by ProCAST (Figure 85c). Figure 84. Melt front advancement during cavity filling; a) C-Mold; b) Moldflow; c) ProCAST; d) experimental sample Figure 85. Positions of weld lines; predicted by a) C-Mold; b) Moldflow; c) ProCAST and d) experimentally observed weld line (emphasised on the picture). C-Mold marks position of the weld line explicitly. Moldflow and ProCAST show meeting melt fronts, which form the weld line. 96

103 Validation 5.3. Temperature distribution The temperatures results calculated with C-Mold, Moldflow and ProCAST are shown in Figures 86a-86c, respectively. The calculated temperature results were extracted for the respective mesh nodes, which were close to the points of measurements. The experimentally measured temperatures by the thermocouples T, T and T3 are shown in Figure 86d. The measured temperature curve can be divided into three sections. The first section corresponds to the temperature of the mould with the empty cavity before the injection cycle starts. The second section depicts the temperature rise due to contact with the hot feedstock, which takes place during the filling stage, and the third section shows temperature decline after the peak was passed. The numerical results include only the temperatures for the time moments after the feedstock has reached the related point. Figure 86. Temperature results; calculated by: a) C-Mold; b) Moldflow; c) ProCAST; d) measured The temperatures measured by the thermocouples T and T rise initially to C. Despite the difference between the peak values, the cooling curves for these two thermocouples practically coincide during later stage of the cooling process. It shall be noted that the maximum temperature measured by the thermocouple T is higher than that measured by the thermocouple T, although the flow path from the gate to the position of the thermocouple T is longer. The increase of the temperature of the feedstock at the surface along the flow path may be attributed to viscous heating generated as a result of friction between the layers of the feedstock that move at different velocities. The heat released in the moving feedstock reaches the surface of the sample at the point, which is more distant from the gate than the point where it was generated. Therefore, the 97

104 Chapter 5 peak temperature measured by the thermocouple T may be higher than the peak temperature measured by the thermocouple T. This phenomena is reflected in the results obtained with C- Mold (Figure 86a), which show the peak temperatures 5 C and 6 C at the points corresponding to the thermocouples T and T, respectively. The peak temperatures calculated by ProCAST at all three nodes are very close to each other. Comparison of the numerical data of ProCAST also confirms that the peak temperature at the point corresponding to the thermocouple T is higher than that at the point corresponding to the thermocouple T. The effect of viscous heating is thus also qualitatively confirmed by ProCAST numerical results. The temperature acquired from the thermocouple T3 has a maximum value of 30 C, and then gradually decreases to 5 C at the end of the measurements period. This thermocouple is located in the thin end of the sample, which is the last part to be filled. A reduced temperature of the feedstock at the thin end of the sample can be explained by the cooling of the feedstock while flowing from the gate. It can be shown that the viscous heating term σ :{ v } from Equation (3) in the case of a generalised non-newtonian fluid can be re-written [8] as η γ, which means that viscous heating is proportional to square of the shear rate. Higher shear rates are observed in the narrow cross sections, in particular in the runners and gate. The Moldflow results show that the maximum shear rates in the gate are about s -, while in the cavity they decrease to s -. As the feedstock leaves the gate and enters the cavity the amount of heat generated due to viscous heating decreases. Between the thermocouples T and T3 the effect of viscous heating on the temperature of the feedstock becomes small. Another factor that contributes to reduction of temperature of the feedstock is the increased contact area between the feedstock and the mould due to the hole forming juts. As a result, the feedstock between the thermocouples T and T3 cools down due to the high rate of heat transfer to the mould and low heat generation rate. The decrease of the temperature of the feedstock that reaches the thermocouple T3 is correctly predicted, (qualitatively) by C-Mold. However ProCAST prediction does not show consistent evidence of temperature decrease at the point T3, which may be due to overestimation of the viscous heating effect or to the difficulties in handling non-newtonian, highly viscous fluids as those encountered in PIM. Temperature versus time plots shown in Figure 86 indicate that due to high rate of heat dissipation caused by the high thermal conductivity of the feedstock and low value of specific heat, the temperature of the material drops very quickly during the filling stage. However, the measured temperatures decrease at a lower rate than the simulated one. The observed difference in cooling rate can be explained by the relatively long response time of the thermocouples, typically about s. Due to the inertia of the measuring system, the changes of the temperature recorded over a very small period are smoothed out. If the temperature peak is very narrow it may not be visible on the measured curve. The highest cooling rate at the first instants can be expected at the thin end of the sample, because the cooling surface is relatively large there. Taking into account the assumption that the peak temperature at position T3 drops faster than it can be measured, the predictions of temperature made by both C-Mold and ProCAST match the experimental measurements. Unfortunately, the 3-D version of Moldflow MPI. does not allow to present temperature versus time results. To monitor the temperature development versus time, the shaded plots corresponding to different time instants shall be compared. An example of a shaded plot with the results of temperature calculated by Moldflow is presented in Figure 86b. This plot represents the surface temperature distribution at the end of the filling stage (the time instant 0.64 s). It can be seen that most of the surface has a temperature within the range from 0 to 30 C. Assuming that the temperature peaks by this time instant have already passed, the agreement with the experiment is 98

105 Validation good. It is however difficult to judge about the character of temperature development in the absence of the temperature versus time plot Pressure results Another numerical parameter that was experimentally verified, is in-cavity pressure. The pressure data are shown in Figure 87. C-Mold and Moldflow calculate the pressures during both filling and post-filling stages of the PIM process. The results obtained with ProCAST (Figure 87c) are available for the filling stage only. Since the pressure during the post-filling stage is a pre-set parameter (defined in the settings of the injection moulding machine), it is worth to compare the data for the filling stage only. The pressures related to the filling stage correspond to the parts of the pressure plots from zero to the maximum value. During the filling stage, the pressure increases until the cavity is filled by 98-99% at the constant velocity. The rest of the cavity is filled under constant pressure conditions. The maximum pressure measured by the transducers Pr is approximately - % higher than that measured by the transducer Pr. It means that the pressure loss within the cavity is very small. The numerical data for the in-cavity pressure calculated by C- Mold (Figure 87a) are in close agreement with the measured ones. Figure 87. Pressure results; a) C-Mold; b) Moldflow; c) ProCAST; d) measured. ProCAST underestimates the in-cavity pressure by 30-40%. The reason for that may be the high rate of pressure change at the end of the filling stage, when the pressure sharply increases to the maximum value. After the cavity has been filled, ProCAST sets the pressure value to zero. Because of this, the ProCAST pressure plot has a very narrow peak. In order to record correctly 99

106 Chapter 5 the rapid increase of the pressure at the end of filling, the time step during the calculation should be kept smaller than the width of the pressure peak. Otherwise, there is a probability that the calculated maximum pressure would be reached between the two stored steps. From Figure 87c it can be seen that the time step is of the same order of magnitude as the width of the peak. This explains not only some underestimation of the maximum pressure, but also the phenomenon that the pressure calculated at the point corresponding to the location of the transducer Pr is higher than that at the point corresponding to the transducer Pr. The time step in ProCAST is automatically controlled. The maximum time step value can however be limited by the user. It must be emphasised that, that setting the maximum time step at a very low level causes a large increase of necessary computing time and data storage capacity. Similarly to temperature results, the pressure data of Moldflow MPI.can only be viewed as contours or shades. The pressure contours at the end of the filling stage, calculated by Moldflow, are shown in Figure 87b. At this time instant, the pressure remains between the maximum and the pre-defined hold pressure, which is normally 80% of the maximum. The results from Figure 87b can be compared with the peak values from the plots in Figures 87a, 87c and 87d. It can be seen that Moldflow underestimates the pressure by a factor of 3 4. Such a large difference cannot be explained by the decrease of the pressure at the end of the filling stage from the maximum pressure. Contrary to the experimental observations, Moldflow also predicts a large pressure loss along the flow path within the cavity. Compared with the results of ProCAST and C-Mold, the Moldflow results appear to be less accurate Computational aspects From the practical point of view, the important characteristic of a particular package for numerical simulation is the time needed to perform the analysis. Some characteristics of C-Mold, Moldflow and ProCAST, including the calculation time for the analysis of the moulding of the same component are given in Table 7. In both ProCAST and Moldflow, 3-D mesh was used. This mesh was created in ProCAST and thereafter imported to Moldflow. While translating into Moldflow, the number of elements of the mesh increased from to 858. In C-Mold a -D mesh was used, which comprised 86 elements. Some characteristics of C-Mold, Moldflow and ProCAST Table 7 Dimension -D meshing 3-D meshing Automatic simulation of packing Mould description X-Y plots Cutting plane view Calculation time* C-Mold -D Yes - Yes Simplified yes - 5 min Moldflow 3-D Yes No Yes Simplified no Yes hours ProCAST 3-D Yes Yes No Full yes Yes 3 hours * Filling analysis for the component under consideration in this study It can be seen that C-Mold performs two-dimensional analysis of the filling very rapidly. The smaller number of equations to be solved and the smaller number of mesh elements explain the significantly shorter time needed for -D analysis as compared to fully 3-D analysis. The longest calculation time is required for the simulation with Moldflow. It should be noted that the calculation time depends on many other factors and can vary significantly. In general, ProCAST possesses the best combination of features needed for the simulation and analysis of fluid flow in the three-dimensional space. The only disadvantage of ProCAST is that it cannot simulate the post filling stage of the PIM process in one simulation run. However, this shortcoming is not critical as 00

107 Validation the post-filling stage can be simulated separately, using the data calculated during the filling analysis as the input parameters. 5.4 Summary Three best known commercial packages were used to simulate the powder injection moulding process. The obtained simulation results have been compared with each other and with experimentally determined ones (melt front advancement, weldline locations, in-cavity temperatures and pressures). It has been proven that the PIM process can be successfully simulated with C-Mold, Moldflow and ProCAST analysis packages. The flow pattern predicted by C-Mold appeared to be less accurate than that by ProCAST and Moldflow. The predictions of the locations of weldlines made by all three analysis packages were in good agreement with the experimental observations, and ProCAST yielded the best results. The temperatures of the feedstock predicted in the simulations were in good agreement with the experimentally measured ones. The best predictions of pressure were made by C-Mold. The in-cavity pressure values predicted by C-Mold matched well the experimentally observed ones. However, ProCAST underestimated the in-cavity pressure by 0-30 %. The Moldflow pressure results were found to be 3-4 times lower than the experimentally observed ones. Both C-Mold and Moldflow can be used for the simulation of both the filling and the post-filling stages of the PIM process. C-Mold provides temperature and pressure data that are in agreement with the experimental results. The main disadvantage of C-Mold is its limitation to -D simulation. C-Mold is therefore recommended for express analysis of PIM components, which can be represented by thin-walled models. The disadvantage of Moldflow is a lower accuracy of the predicted pressure. Another drawback of Moldflow is that the output data cannot be viewed in the form of X-Y plots. Therefore, Moldflow is recommended especially for the estimation of the melt front advancement and temperature development. ProCAST fully satisfies the requirements of an analysis package for the study on the filling stage of the powder injection moulding of bulky components. Temperatures and pressures calculated by ProCAST can be visualised in the forms of three-dimensional plots and X-Y plots. The disadvantage of ProCAST is more complicated setting up procedure for simulation and inability to simulate the filling and post-filling stages in one simulation run. Despite these drawbacks, ProCAST is capable of yielding the most reliable output results and should therefore be recommended as a preferred FEM code for the numerical simulation of the PIM process. 0

108 Chapter 6 Sensitivity of simulation results to input parameters While defining the input parameters for the simulation there is a question which accuracy level is acceptable. The simulation packages often allow defining the input data as constants of functions of time and temperature. Viscosity can be also represented by different functions of shear rates. For example, as it was already mentioned in Chapter 4, C-Mold and Moldflow include several different viscosity functions, while ProCAST uses only Carreau-Yasuda function. The temperature boundary conditions and the heat transfer coefficient also can be defined in different ways. Temperature on the surface of the formed component can be assumed uniform and constant, or it can be recalculated during the process of filling. When setting up a simulation, it is desirable to know how strongly the variations in the input parameters affect the results of the simulation. Strong interrelation between an input parameter and output data requires determination of such parameter with high accuracy. On the contrary, in case the influence of the input parameter on the results of the simulation is weak, than such a parameter can be determined approximately without large influence on accuracy of the simulation results. The use of constant parameters simplifies preparation of the simulation set-up and accelerates the analysis. Therefore constant input parameters should be preferred, when applicable. In the other cases the input parameters have to be described with high precision. The course, duration and the results of the numerical analysis also depend on the mesh of the component. Therefore the question which criteria shall be used to determine low- and high quality mesh, is also important. In this Chapter an attempt has been made to establish a correlation between some of the input parameters and the results of the numerical simulation of the PIM process. The influence of the heat transfer coefficient, the viscosity of the feedstock and mesh size have been studied. 6. The effect of heat transfer coefficient To estimate the influence of the heat transfer coefficient on the calculation of temperature on the surface of the experimental component, several simulations have been performed with the identical initial and boundary conditions, with different values of heat transfer coefficient. The PIM process

109 Sensitivity of simulation results was simulated with ProCAST. This code was chosen because it permits defining the heat transfer boundary condition as a constant, a time-depended variable, a temperature depended variable, or as a combination of all of them. Figure 88 shows the calculated temperatures at the position T according to the notations in Figure 74. The results shown in Figure 88 have been calculated with the constant initial mould temperature amounting 35 C and a number of different constant heat transfer coefficients. Temperature, C Heat transfer coefficient, 0000 W/m*K Measured temperature Time, s Figure 88. Calculated for different heat transfer coefficients and measured temperatures at the position T as a function of time. The heat transfer coefficient affects the heat flux through the feedstock-mould interface (Equation 53 from Chapter ). The high values of the coefficients correspond to the low resistance to the heat transfer from the feedstock to the mould. The heat is exchanged at high rate when the heat transfer coefficient is large. As the heat transfer coefficient increases the initial temperature of the feedstock decreases. This trend can be seen in Figure 88. For example, when the heat transfer coefficient was set to 500 and 000 W/m*K, the initial temperature of the feedstock at the time instant when it has reached the node at the position T was about 00 C. For the coefficients 0000, 5000 and 5000 W/m*K the initial temperature at the same position was, respectively, 85, 75 and 68 C. It is to be noted that the heat transfer coefficient affects the shape of the cooling curve. The cooling curve obtained from the simulations with the values of the heat transfer coefficient of 0000 W/m*K and higher have two segments corresponding to two considerably different cooling rates. The initial cooling rate is very high. The relevant segment of the cooling curve is almost parallel to the vertical axis. The initial temperature decreases at the initial cooling rate until it reaches approximately 60 C. Thereafter the cooling rate sharply decreases and the temperature change with time becomes much smaller. Further cooling takes place at the low cooling rate, which is represented by the segment of the cooling curve almost parallel to the horizontal axis. Such shape of the cooling curve indicates that the heat flux from the feedstock to the mould is controlled mainly by the thermal conductivities of the feedstock and the mould. The heat losses at the feedstock-mould interface are small and have minor influence on the temperature development. If the heat transfer coefficient value is set to 000 W/m*K (or lower), the character 03

110 Chapter 6 of the cooling curve changes. The initial cooling rate decreases. The period of time, when the cooling rate is high, is longer then in the first case and constitutes 5 and 0 seconds for the heat transfer coefficients 000 and 500 W/m*K, respectively. Such cooling mode is determined by the low heat transfer coefficient, which becomes the limiting link in the heat transfer. Data shown in Figure 88 prove that setting the heat transfer coefficient to a wrong value may completely change the prediction of the temperature development in the feedstock. One of the main difficulties in the simulation is that the heat transfer coefficient is difficult to measure. So far its value could be determined only approximately. Comparison of the measured and calculated cooling temperatures permits to conclude that the best agreement between the experimentally observed and simulated temperatures takes place at the heat transfer coefficients of 5000 W/m*K and higher. The temperature field in the feedstock affects to a certain extent its viscosity. In this way the heat transfer coefficient affects the viscosity and, eventually, the resistance of the feedstock to the injection forces, and pressure losses during the powder injection moulding process. Therefore the result of calculation of the pressure must depend on the heat transfer coefficient. The extent of this dependence can be seen in Figure 89. It shows the calculated pressures at position Pr for different heat transfer coefficients. One can see that the pressure curves practically coincide for the values of the heat transfer coefficients below 5000 W/m*K. The related peak pressures are about 6 MPa. For the value of the heat transfer coefficient 5000 W/m*K the pressure increases, reaching in the peak 7 MPa Pressure, MPa Time, s 5000 W/(m* K) 5000 W/(m* K) 000 W/(m* K) 500 W/(m* K) Figure 89. Pressure curves calculated at the position Pr for different heat transfer coefficients. The observed trend can be explained by the low dependence of the viscosity of the feedstock on temperatures above 70 C. For the heat transfer coefficient amounting to 5000 W/m*K the heat losses are so high that the temperature of the feedstock at the surface falls below 70 C during the filling stage (Figure 88). The frozen layer thickness increases. As a result, the increased pressure is required for injecting the feedstock into the mould. Figure 89 indicates that the heat transfer coefficient and the pressure within the feedstock have non-linear interrelation, i.e. gradual increase of heat transfer coefficient at certain value causes drastic increase of pressure. 04

111 6. The effect of initial mould temperature Sensitivity of simulation results The mould temperature is another principal parameter that influences the cooling rate of the feedstock and determines the thickness of the frozen layer during the filling stage of PIM, which in turn affects the filling pattern. The minimum and maximum limits of the mould temperature are determined on one side by the ability of the feedstock to fill the cavity and, on the other side, by the time needed to cool the component to the ejection temperature. Due to high thermal conductivity of the feedstock, the acceptable range of mould temperatures is narrow. Therefore the small changes of the mould temperature should have strong influence on the PIM process and, in particular, on the injection pressure. Figure 90 shows the maximum pressure developed at the nozzle calculated with different initial mould temperatures. Calculated maximum pressure at the nozzle, Mpa, at different mould temperatures Pressure, MPa T=5 C T=0 C T=5 C T=35 C T=40 C Mould temperature Figure 90. The effect of the initial mould temperature on calculated maximum pressures at the nozzle From Figure 90 it is to be noticed that five degrees difference in the mould temperature may cause the difference in the injection pressure of up to 0 30 MPa. Such difference is essential while selecting the proper injection moulding machine. The results from Figure 90 also prove that manufacturing of the same component can be done with relatively low powerful injection moulding machine if the temperature of the mould is properly chosen, and, on the contrary, the more powerful injection moulding machine does not guarantee forming of the high -quality component if the mould is too cold. Figure 9 shows the in-cavity pressure at the position Pr. The in-cavity pressure also decreases with the increase of the mould temperature. However, comparison of Figures 90 and 9 reveals that the in-cavity pressure decreases faster then the pressure at the nozzle when the mould temperature increases. Results from Figure 9 correlate with the results from Figure 89. Both figures illustrate the non-linear increase of pressure as the temperature of the feedstock decreases. The change of the temperature of the feedstock in the first instance is determined by the temperature of the mould, while in the second case it is determined by the value of the heat transfer coefficient. 05

112 Chapter 6 The results shown in Figures 90 and 9 have been obtained with the assumption of the uniform constant temperatures that changed with the 5 K step. In the real mould the temperature nonhomogeneity on the cavity surface is comparable to this difference. An example of temperature distribution on the cavity surface, calculated for the model of the experimental mould from Figure 6, is shown in Figure 9. It can be seen that the initial mould temperature non-homogeneity within the cavity surface reaches 3-4 C. As it has been demonstrated with the Figures 90 and 9 neglecting of such temperature difference may lead to large errors in calculation of pressure Pressure, MPa Mould temperature C Figure 9. Calculated maximum pressures at the position Pr for different mould temperatures. Figure 9. Calculated temperature distribution on the cavity surface after the heating-up the mould during 30 min. Nevertheless, the considered mould design shall be recognized as acceptable because the coldest and the hottest points are located at the corners of the cavity while the major part of the cavity surface has the same temperature with the accuracy ±0.5K. The non-homogeneity of the temperature distribution at the cavity surface can be significantly larger in case the lay-out of the 06

113 Sensitivity of simulation results cooling channels is not optimised. It is one of the critical issues for the optimisation of the PIM process and is a subject of improvement with the help of the numerical simulation. The temperatures of the mould and the feedstock dynamically change during the filling stage. These changes of the temperature affect the consequent process of cooling. Due to high thermal conductivities of both the feedstock and the mould, the temperature at the cavity surface changes at high rate. By the end of the filling stage the temperature distribution on the cavity surface has little in common with the initial distribution despite the filling time is usually short. To illustrate this, Figure 93 shows the temperature pattern at the cavity surface calculated at the end of the filling stage after powder injection moulding into the mould with the initial temperature distribution shown in Figure 9. It can be seen that at the end of the filling stage the temperature non-homogeneity increases. The difference between the coldest and the hottest points at the cavity surface increases to about 5 K. The change of the temperature of the mould surface affects the temperature of the formed component. Figure 94 shows the calculated temperature of the component's surface, which contacts the mould wall shown in Figure 93. As it can be seen, the temperature of the feedstock correlates with the temperature of the mould (compare temperature distributions shown in Figures 93 and 94). Figure 93. Calculated temperature distribution on the cavity surface at the end of the filling stage. The initial temperature distribution of the mould was like the one shown in Figure 9. If the constant and uniform temperature boundary condition is assumed, the calculated temperature of the feedstock differs from the one shown in Figure 94. This difference increases with time as shown in Figure 95, which depicts the calculated temperatures for approximately the same point near the position T in the models with (node 6497) and without (node 543) the mould. It can be seen that the difference between the temperatures calculated with and without the mould is minimal during the filling stage (time less than s). This difference increases during the cooling stage because the mould warms up by the heat that is transferred from the feedstock. Negligible during the first moments the temperature difference increases to about 0 K by the time =0 s. This example clearly demonstrates that constant temperature boundary condition is acceptable 07

114 Chapter 6 only during the filling stage. In case the cooling stage is to be studied, the temperature distribution in the mould must be taken into account for obtaining the meaningful results. Prediction of the cooling time with a constant temperature boundary condition will always give the underestimated values. Figure 94. Temperature distribution ( C) at the surface of the component at the end of the filling stage. Compare with Figure 93. Temperature, C Temperature at position T Time, s Figure 95. Temperature at the position T calculated with (node 6497) and without (node 543) the mould. 6.3 The effect of mesh size Calculated results should be independent of mesh size. However in practice this is not always possible. To create high quality mesh the general rules are the following:. Flow analysis requires at least two nodes across the thickness of the domain.. With smaller mesh elements the higher accuracy of simulation results is expected. 3. The finer mesh requires the longer calculation time. 4. Large aspect ratio should be avoided. Besides the size of mesh elements (density of the mesh) there are other parameters that can be used for estimation of mesh quality. These parameters are the aspect ratio of elements and dihedral 08