EXPERIMENTAL STRESS ANALYSIS OF ALFA COMPOSITES USING MACHINE VISION SYSTEM

Transcription

1 CHAPTER 4 EXPERIMENTAL STRESS ANALYSIS OF ALFA COMPOSITES USING MACHINE VISION SYSTEM 4.1: INTRODUCTION 4.1.1: Upsetting Between Flat Platens Stresses in most of the metal forming processes, such as cold heading, riveting etc. are compressive in nature. Upset test at room temperature gives a representative behavior during metal forming. Upsetting of solid cylinders is an important metal forming process and an important stage in the forging sequence of many products. Though extensive studies have been reported by various authors on friction studies little attention has been given to the compression of taller cylinders, where the initial height/diameter (H 0 /D 0 ) ratio equals or exceeds unity. To be comprehensive and practical, a model of the forging process should permit determination of not only the platen forces and pressure distributions affecting tool life, but also the internal flow of the forging influencing die-design and forging sequence and the properties of final product dictating in-service performance. A systematic detailed study of free deformation can be used to predict how metal would flow under various working conditions and with various tool and work piece geometries. This information can then be used to design better forgings, make improved intermediated dies and to avoid the defects and failure of the materials during plastic working. Some specific examples are as follows: (a) Avoiding forging defects (b) Avoiding failure of materials (c) Design of forgings and intermediate stage dies (d) Economic advantages 4.1.2: Machine Vision System and Its Advantages Use of optical measuring technologies (Machine Vision System) in metal forming and tooling industry has increased during recent years. The main 56

2 applications include digitiing of metal parts and tools, to perform forming analysis of parts and tools and determination of material properties. Good interfaces to conventional CAD/CAM and numerical simulation systems made such optical measuring system a part of complex process chains. These process chains mainly focus on optimiing the development of products and production processes, improving the product quality using optical systems, considerably decreasing the development time for products and production while improving the quality. Conventional methods of analying the deformation behaviour during upsetting by measuring grid distortions on tool maker s microscope were available in literature. Adoption of Machine vision system to analye the flow behaviour of materials during upsetting has been proposed in the present work. The advantage of this method is that the experiment need not be intermittently stopped after certain deformation to measure the strains from grid. When the experiment is stopped intermittently, elastic deflections in specimen and tooling may be relieved causing inaccuracies in the next step of deformation. By the use of vision system, the experiment need not be stopped during deformation process. Offline analysis can be done latter. One of the most common analysis and evaluation methods used for the metal stamping process in measuring the extent of deformation is sometimes related to forming severity, where the level of deformation is categoried as safe, marginal or failure. In many press shops, strain measurement is used as a way to asses the formability of a stamping. Surface strain data can be used effectively to diagnose production problems, and identify potential failure sites. These data also are used to verify predicted results from finite element analysis programs (FEA) : Friction in Metal Forming Friction is the great importance in many metal forming operations. They affect the material flow, deformation characteristics of the work piece, wear and fatigue failure of the tool, and the mechanical properties of the formed parts. Furthermore, minimiing friction is profitable since it reduces the force and energy required for a given operation. This will lessen the stresses induced in the forming tool and prevent direct tool to work piece contact, which contribute to longer tool life and better quality control. 57

3 A number of studies have already been made in an attempt to obtain quantitative data on friction in metal processing by using the actual metal working operation or by using simulative laboratory tests. Use of the particular metal working process for these investigations has the disadvantage that it is difficult to separate the force necessary to overcome friction from the force necessary to give the required deformation, and more difficult to control the secondary process variables. Laboratory tests may furnish valuable measurements of frictional behavior under controlled conditions provided that these tests are capable of simulating process conditions such as temperature, deformation speed and deformation pressure : The Ring Compression Test The ring test technique involves a simple forging operation performed on a flat ring-shaped specimen; the change in diameter produced by a given amount of compression in the thickness direction is related to the interfacial friction condition. If friction were equal to ero, the ring would deform in the same way as a solid disk, with each element flowing radially outwards at a rate proportional to its distance from the center. With a small but finite interfacial friction force, outward flow takes place at a lower rate and for the same degree of compression; the outside diameter is smaller than with ero friction. If the frictional force exceeds a critical vale, it is energetically favorable for only part of the ring to flow outwards and for the remainder to flow inward towards the center; thus the outside diameter after compression is still further reduced. Measurement of the final internal diameter of compressed rings provides a particular sensitive means for studying interface friction since the internal diameter increases if the friction is small and decreases if the friction is large. The ring test has an advantage when applied to the study of friction at elevated temperatures and/or high speeds; no direct measurement of force is required and no yield strength values of the deforming material are needed, hence the major difficulties of evaluation of compression tests under these conditions are eliminated. Correlation of changes in internal diameter with numerical values of friction can be obtained either by independent calibration or by the application of available theoretical analysis. 58

4 4.2: LITERATURE REVIEW 4.2.1: Friction and Ring Compression test Friction is the resistance to motion encountered when one body slides over another. In metal working processes it arises from sliding of the work piece against the die [1]. In the interest of clarity, friction forces are often neglected. In many real metal working processes friction is the predominant factor [2]. Shaw et al. [3] discussed the significance of axisymmetric compression, and then the mechanical/manufacturing properties of materials, to estimate forming limits up to plastic instability and fracture. Considerable attention has been devoted to the analysis of platen forces and pressure distributions in upsetting, particularly for thin discs [4-8]. Of the many laboratory tests utilied for friction studies the ring test technique originated by Kunogi [9] and further developed by Male and Cockroft [10] has the greatest capability for quantitatively measuring friction under normal processing conditions. Before a satisfactory mathematical solution for the compression of a ring was available, a pioneering independent calibration was made by experimentation [11]. Subsequent theoretical analyses [12, 13] have made possible more accurate and less laborious calibration of the ring test by mathematical computation. The first satisfactory analysis of the compression of a flat ring was made by Avitur [12] through an optimum upper bound mathematical solution and later verified by Hawkyard and Johnson [13] using a stress analysis approach. Both solutions are based on assumptions that (a) there is no non-uniform distortion of cylindrical elements due to frictional constraint, i.e., no barreling; (b) the ring material obeys Mises stress-strain rate laws, implying no strain hardening effect, no elastic deformation and no volumetric change; and (c) a constant friction factor, m, for a given die and material under constant surface and temperature conditions such that the interfacial frictional shear stress, τ i, is given by τ m σ 0 i = 3 Where σ 0 = basic yield stress of the ring material. The assumptions of constant m and constant σ 0 automatically means that τ i is constant. Certain investigations [14-16] on friction indicate that, for metal working conditions, the assumption of a constant interfacial friction stress may be reasonably justified. When 59

5 strain hardening of ring material occurs (i.e., assumption (b) is violated) it is necessary that interpretation of the ring test results with the mathematical solution should be cautious. The theoretical solutions of Avitur [12] and Hawkyard and Johnson [13] both yield the following mathematical relationships for a ring specimen under compression (Figure 4.1), where R n is the radius of the metal flow divide within the ring (sometimes referred to as the neutral or no-slip ): 1. When R n R i 4 R i X R 3 R0 n = R R i X ( X 1) 1 X 4 R0 2 1/ 2 X R R Ri m Ri T R0 0 0 exp (1) 2. When R i R n R 0 R m T 4 4 R R i R 0 R0 R n = ln R 4 2 i R n 2 1+ R i R R0 R0 Rn Eq.(1) is valid when R n lies between R i and O and (2) Eq.(2) is valid when Rn lies between mr 1 3( R / R ) T i ln 4 R i 2 1 R R0 Ri R 0 + i R and R0 and (3) 60

6 mr 1 3( R / R ) T i ln 4 R i 2 1 R R0 Ri (4) Direction of metal flow R n Upper die R i Ring specimen T R 0 Lower die Figure 4.1: Compression of flat ring-shaped specimen between flat dies. Neither the basic yield stress of the material, σ 0, nor the interfacial shear stress, τ, appear in the final equations in terms of absolute values, only as a ratio, m. The basic assumption in the analysis is that this ratio remains constant for the material and deformation conditions. If the analysis is carried out for a small increment of deformation, σ 0 and τ can be assumed to be approximately constant for this increment and the solution is valid. Thus, if the shear factor m is constant for the whole operation, it would appear justifiable to continue the mathematical analysis in a series of small deformation increments using the final ring geometry from one increment as the initial geometry for the subsequent increment and so on. As long as the ratio of the interfacial shear stress, τ, and the material flow stress, σ 0, remained constant it would not be of consequence if the ring material strain hardened during deformation provided that the increase in work hardening in any one single deformation increment could be neglected. The progressive increase in interfacial shear stress accompanying strain hardening would also be of no consequence provided that it could be assumed to be constant over the entire die/ring interface during any one deformation increment. Thus it is possible that the analysis could be justifiably applied to real materials even though it was initially assumed that the material would behave according to the 61

7 Mises stress-strain rate laws provided that the assumption of a constant interfacial shear factor, m, is correct. The ring compression test, developed by Male and Cockroft [10] is the most commonly employed method for determining friction characteristics. The test involves the compression of a hollow, thick-walled cylinder, or ring, and the determination of the variation of the internal bore diameter with the height reduction. The variation of the bore with height has been shown to depend on friction between the ring and the platens, and to provide a good method for its evaluation [17]. The test is reasonably easy to carry out at room temperature, since an interrupted compression test (with the associated loss in accuracy because of the load reversal) can be employed, with the bore diameter being measured at each interruption. Calibrating curves for the ring compression test have been obtained using a range of methods with various simplifying assumptions. Probably the most wellknown calibration curves are those determined by Hawkyard and Johnson [13]. In their analysis of the ring, it is assumed that the material behaves with rigid perfect plasticity and that no barreling occurs so that the deformation is completely homogeneous, with uniform states of stress and strain. The ring compression test is perceived by many as the standard procedure for determination of friction between the billet and die in forging operation. In addition, it is sometimes assumed that it is a test for which a universal calibration can be used. The friction arises due to the work piece coming in contact with a tool or die [18, 19]. The mechanics of friction are complex. The fundamentals of this phenomenon have been much studied [5, 14, 20-22], yet very little that is known would facilitate formulation of exact functional relationship between τ and the other variables. Friction can be described by a coefficient of friction (µ), defined as: µ= F / R=τ / p =τ / hardness i Where: F = force of friction, R = normal reaction, p = interface pressure σ 0, and τ i = interface shear stress. i 62

8 4.2.2: Compression Testing of Short Cylinders The compression of a short cylinder between anvils is a much better test for measuring the flow stress in metal working applications [23-25]. The nature of tensile instability due to necking can be avoided and the test can be carried out to strains in excess of 2.0 (for ductile material). Friction between the specimen and anvils play key role. In the homogeneous upset (ero friction) test a cylinder of diameter D 0 and initial height H 0 would be compressed in height to H and spread out in diameter to D according to the law of constancy of volume. D 0 2 H 0 = D 2 H For the selection of an upsetting process the following parameters are significant: a) Geometry of the component b) Strength of the component material c) Formability characteristics of the material d) Upset ratio e) Accuracy f) Surface quality, and g) The economic considerations. For trouble-free and economic production the work piece material must be of uniform quality (chemical composition, mechanical properties and surface finish) : Engineering Stress and Engineering Strain The engineering strain e is the ratio of the change in length to the original length [26-28]. e L L L 0 1 L = = = dl L L0 0 L0 L (1) 0 The engineering stress P S = (2) A 0 63

9 4.2.4: True Stress and True Strain The engineering stress-strain curve does not give a true indication of the deformation characteristics of a material because it is based entirely on the original dimensions of the specimen and these dimensions change continuously during the test. In metal working processes the work piece undergoes appreciable change in cross sectional area. Thus measures of stress and strain which are based on the instantaneous dimensions are needed. Ludwik [29-31] first proposed the definition of true strain or natural strain ε. In this definition of strain the change in length is referred to the instantaneous gauge length, rather than to the original gage length. L dl L ε= = ln (3) L0 L L 0 ε= ln L or ε= ln(1 + e) (4) L 0 True stress is the load at any instant divided by the cross-sectional area over which it acts. True stress will be denoted by the familiar symbolσ. σ = p A (5) σ = P (1+e) or σ = S (1+e) (6) A 0 where: S = engineering stress e = engineering strain P = applied load A = instantaneous area In compression equation (6) becomes σ = P (1-e) or σ = S (1-e) (7) A 0 64

10 4.2.5: Computation of Plastic Strain Plastic strain (ε p) = (Total strain) Stress Young's modulus From figure 4.2 C = y mx=σ Eε tot C ( σ Eεtot ) ε P = C / m= = E E σ ε = ε P =εtot (8) [27] E σ σ y y = mx + C ε p ε elastic ε C ε total Figure 4.2: Elastic and plastic components of total strain 4.2.6: Optical Measurements of Strains Knowledge of material behaviour requires the measurement of mechanical parameters. Strains are usually measured by the use of strain gauges. When the specimen is distant, difficult to reach, in a hostile environment or does not support the attachment of gauges, the use of measurement techniques without contact such as optical methods, allows to determining the desired parameters. These non-contact and non-destructive methods can represent a real advance for displacement, stress and strain measurements. There are two types of experimental methods for strain measurement, indirect and direct methods. Indirect techniques allow strains to be determined by derivation of the measured displacement field. Among indirect methods the principles of ones include digital image correlation [32], speckle interferometry [33] or Morié techniques [34]. Direct methods give strains using an extensometer, gauges, three element rosettes or grid [35-37]. All these tools can only 65

11 be used for strains less than 20% and also do not allow the measurement of larger deformation. Three optical methods can be employed for large strain measurement using a grid (lines or spots) method of mark-tracking techniques. The optical measurement of strains on a specimen surface is generally achieved with a grating of crossed lines obtained by engraving or die stamping from a holographic support containing the master grating [38,39]. The mark-tracking techniques can be implemented [40] in which four grid lines are scribed or drawn with a fine marker pen. The specimen surface can be either transparent or opaque. Ductility of a material is generally defined as the ability to deform plastically without fracture. It is usually expressed as a measure of the strain at fracture in a simple test (elongation or reduction in area being the two most commonly used). For metal forming applications, effective ductility is not a unique property of the material; it depends on localied conditions of stress, strain, strain rate and temperature in combination with material characteristics such as inclusion content and grain sie, processing parameters associated with die design, work piece geometry, and lubrication determine the local stress and strain states throughout the material. Control of these parameters may thus be exercised to produce conditions favorable for enhanced deformations to fracture. The compression test on cylindrical specimens has been used by several investigators for the study of deformation behaviour under combined stresses [41-44]. During compression of a cylinder the lateral free surface barrels and fractures form at the barrel. The barreled surface results in the development of a tensile stress in the circumferential direction and a decrease in the magnitude of the axial stress below the average compressive stress in the material. In case of severe barreling the axial stress may also become tensile. Through variations in the cylinder height to diameter ratio and contact surface friction conditions, the severity of the barrel curvature can be controlled. Thus a variety of stress and strain states can be generated in the equatorial regions of the upset cylinders, providing a convenient test for deformation and fracture studies. 66

12 4.2.7: Theoritical Background of Orthogonal Axes The orthogonal axes of reference for the component of stress and strain increment on the free surface of a compression specimen are as shown in figure 4.3. It is assumed that throughout the compression test the principal axed of stress and strain increment coincide. The reference axis, r, in a principal direction because the shear stresses on a free surface are ero, and -axis is principal direction because the flow is symmetrical about the longitudinal axis, hence the -axis is also a principal direction. Longitudinal axis Equator w 0 r 0 Figure 4.3: Showing the orthogonal axes of reference For these conditions, the Von-Mises yiels criterion can be written in terms of principal stresses as σ = 3J 2 = [ σ + σ -σ ] 2 2 σ 1/ (1) Because the transverse stress component σ r is ero on the free surface. Here J 2 is the second invariant of the stress deviator. The plastic strain increment at any instant of loading is proportional to the instantaneous stress deviator, i.e. ε = σ ' dλ (2) d ij ij 67

13 Where dλ is non negative constant which may vary throughout the loading history. For σ r = 0, equation (2) yields dε dε = 2σ σ 2σ σ or σ 1+ 2α = σ α (3) Where dε α = is a parameter which can be determined by experimental dε measurements of the ratio of the principal strain components in the and directions on the free surface of the specimen. Substituting equations (3) and (1) gives the following expression for σ and σ. 1/ α 1+ 2α σ = σ (4) 2+ α α + 2 And 1+ 2α σ = σ (5) 2+ α By convention, compressive stresses are negative, thus the lower sign in equation (4) is used in evaluatingσ. σ denotes the effective flow stress for an isotropic material for the appropriate effective strain ε at the free surface. In terms of the principal strain increments 2 2 ( dε ) 1/ 2 + dε + dε dε 2 dε = (6) 3 where, the incompressibility condition dε dε + dε = 0 has been used. r + The effective strain at the free surface from equation (6) is given by ε ε = dε = 0 2 ε 1/ 2 ( 1 α α ) 2 dε (7) 0 68

14 Where the integration can be performed along the strain path provided the principal axes of the strain increment do not rotate relative to element. The equations (4),(5) and (7), will enable us to calculate the stresses and effective strains on the geometric centre of the bulge surface and are identical to the equations derived by Kudo and Aoi and David et al [41,45]. Theoretically, α may take any value between - and + but there is no real value of α for whichσ or σ would increase with out bounds. In the present experimental situation the range ofα is limited to -2 to -1/2. As α increases, the tensile stressσ increases but the hydrostatic stress and tensile which leads to a higher probability of fracture. σ = ( ) H σ + /3, becomes more σ 69

15 4.3: EXPERIMENTAL DETAILS 4.3.1: Ring Compression Test Ring compression tests were carryout to determine the friction factor m for a given set of flat platens and work piece while upsetting. These tests were performed on alloy and composites in dry condition. Standard ring shaped samples were prepared by conventional machining, turning and boring operations on a lathe machine with the ratio of Outside Diameter (OD): Inside Diameter (ID): Height (H) = 6: 3: 2. Figure 4.4 shows the ring compression sample with OD: ID: H = 15:7.5:5 mm (6: 3: 2). These ring samples were allowed to deform slowly up to 50% at the rate of 0.25 mm/sec by using computer controlled electrical screw driven 100 kn universal testing machine (Model: UT 9102; Dak System Inc). The internal diameter of the ring was measured intermittently by stopping the test up to a maximum deformation of 50% or up to fracture whichever is earlier. Figure 2.13 shows the closer view of the ring compression experimental setup. Figure 4.4: Ring compression specimen (OD: ID: H = 6:3:2) 70

16 4.3.2: EXPERIMENTAL STRAIN MEASUREMENTS : Experimental Set Up A PC based system consisting of a video camera (Logitech charge coupled device) with an integrated digitiing capacity with resolution of 640x480 pixels and 256 colour full depths attached with a magnifying glass was used. The shutter speed used was 20 pictures (full frame) per second and was sufficient enough to record the images as the run speed of the upsetting process was a slow test performed on computer controlled bench mark machine of 100 kn capacity. Figure 4.5 demonstrates the experimental setup : Materials The upsetting tests were performed on four different materials vi., AA2024 alloy, and AA2024-2% fly ash, AA2024-6% fly ash and AA % fly ash composites in the following conditions. (i) Aspect ratio (H 0 /D 0 ) of 1.0, and (ii) Aspect ratio (H 0 /D 0 ) of : Compression Testing The upset tests were performed at room temperature between two flat platens on a computer controlled UTM of 100 kn capacity universal testing machine (Model: UT 9102; Dak System inc). The compression dies of H11 grade are used for compression and the sample is placed axi-symmetrically in between the dies. The tests were conducted at a constant cross head speed for both the alloy and composites for all the specimens. Details of the process control parameters and necessary precautions were discussed in chapter 2. The compression tests were carried out until either 50% reduction in height or initiation of the fracture on the specimen surface whichever is earlier. A PC based data logging system was used to record and store the loads and displacements continuously. 71

17 Figure 4.5: Experimental set up of computer controlled 100 kn compression testing machine with on line video recording system (Model: UT 9102; Dak System inc). 72

18 CCD Camera Top Platen Upsetting Specimen Bottom Platen (a) Top Platen Upsetting Specimen Bottom Platen (b) Figure 4.6: (a) Closer view of the experimental set up of computer controlled 100 KN compression testing machine with on line video recording system (b) Closer view of the Upset sample. 73

19 4.3.3: PREPARATION OF SAMPLES, GRID MARKING AND MEASUREMENTS Several workability tests are available to study the deformation behaviour under the combined stress and strain conditions usually found in bulk deformation process. The deformation behaviour obtained from upsetting test to a deformation 50% is worth studying to determine the flow pattern. In most of the upset forging processes such as in cold heading, riveting, plate bending, stud welding, the deformations are limited to 50% in a single stroke in order to check the die filling. The parameters that affect the die filling are friction conditions, material ductility, and aspect ratio and strain rate. In case of cold and warm forging processes the effect of strain rate can be discarded, within the reasonable limits of strain rate variation that is caused in press forging operation. Deformation behaviour for two limiting values of aspect ratio 1.5 (to avoid buckling) and 1.0 (which is used in most of the forging applications) are chosen to conduct the tests. The specimens were machined from 18 mm diameter gravity die cast and homogenied fingers to a diameter of 12 mm and to lengths 12 mm and 18 mm. Grid lines were marked at the mid height of the surfaces (4 mm x 90 0 ). The measurement and strain calculations scheme was shown in figure 4.7. Online video images of grid were recorded during the deformation process. The tests were continued till 50% deformation or till the appearance of an appreciable crack which ever is earlier. The images of grids before and after deformation for Ho/Do = 1.0 were shown in figure 4.8 (a) and (b) respectively. The distortions of grid from recorded images were analyed offline after the experiments at desired reductions. The camera was calibrated for the corresponding distances of grid to yield a fixed magnification and to take care of distortions in the images. The images were selected at deformation steps of 5% using the software animation shop 3.0 and are transported to paint shop pro 7.0 for further processing to get the enhanced noiseless images of high clarity grid. Axial ( ε ) and circumferential strain ( ε ) values were calculated from these measurements according to: ε = ln h w, and ε = ln w 0 h 0 74

20 Where: h 0 and w 0 are the initial height and width of an element (Figure 4.7a), respectively, and h i and w i are the current height and width of the element respectively (Figure 4.7b). H 0 w h 0 w h D 0 D Figure 4.7: (a) Schematic diagram of upset tests showing grids for strain measurements (a) (b) Figure 4.8: Images of grids drawn at equatorial plane for Ho/Do = 1.0 (a) before deformation (b) after deformation 75

21 4.4: RESULTS AND DISCUSSION 4.4.1: RING COMPRESSION TEST The decrease in internal diameter of the ring compression test was plotted against % of deformation on Male and Cockcroft calibration curves in increments of 10% deformation. The experimental values obtained for AA2024 alloy and fly ash composites was fitted into the Male and Cockcroft calibration curves, as shown in Figure 4.9 (a-d). These experimentally obtained curves were coinciding with the calibration curve at the friction factor m value of Hence the friction factor m for this AA 2024 alloy and the composites in dry condition was equal to The same set of flat platens was used for upsetting alloy and the composites under investigation. The same surface roughness for alloy and composites samples was maintained. Hence, the friction factor m for alloy and the composites under investigation was found to be Figure 4.10 shows the photographs of ring specimen before and after 50% deformation. The end face of a ring specimen after deformation has a polished finish; this phenomenon evident the existence of friction between the ring specimen and die during deformation under dry condition. 76

22 100 % Decrease in Internal Diameter AA 2024 alloy m=1 m=0.8 m=0.6 m=0.4 m=0.08 m=0.2 m=0.12 m= m=0 % Deformation m=0.02 (a) AA2024-2% Fly Ash Composite m=0.8 m=0.6 % Decrease in Internal Diameter m=1 60 m=0.4 m= m= m= m= % Deformation (b) m=0 m=

23 100 % Decrease in Internal Diameter AA2024-6% Fly Ash Composite m=1 m=0.04 m=0.8 m=0.6 m=0.4 m=0.08 m=0.2 m= % Deformation (c) m=0 m= % Decrease in Internal Diameter AA % Fly Ash Composite m=0.8 m=0.4 m=0.6 m=1 m=0.2 m= m=0.08 m= % Deformation m=0 m=0.02 (d) Figure 4.9: Ring test calibration curves for AA 2024 alloy and composites showing the changes of the minimum internal diameter as a function of the reduction in height for dry (Unlubricated) condition. (a) AA 2024 alloy (b) AA 2024 alloy- 2% Fly ash Composite (c) AA 2024 alloy- 6% Fly ash Composite, and (d) AA 2024 alloy- 10% Fly ash Composite. 78

24 (a) (b) Figure 4.10: Ring compression test specimen (OD: ID: H = 6:3:2) (a) Before deformation (b) after 50% deformation in dry condition 79

25 4.4.2: Compressive Properties of the AA2024 alloy and Al-Fly Ash Composites Figure 4.11 shows the hardness of the AA 2024 alloy and AA 2024 alloy fly ash (ALFA) composites before and after 50% deformation. As the amount of fly ash is increasing the hardness of the composite is increasing. This increase was observed from 73 VHN for AA 2024 alloy to 130 VHN for AA % fly ash composite. This could be due to the presence of fly ash particulates which consists of majority of the alumina and silica which are hard in nature. Further, figure 4.11 also illustrates the hardness values for 50% deformed of AA 2024 alloy and AA 2024 alloy fly ash composites (2, 6 & 10 wt. % fly ash) under compression loading. The increased hardness values were observed for all the tested samples under deformed condition. This increase in hardens was higher for higher the amount of fly ash presence in the matrix. This increase was attributing from the presence of high hardness fly ash powder, which act as reinforcing phase, are dispersed in AA 2024 alloy matrix and become the obstacles to the movement of dislocation when plastic deformation occurs. From the present investigation the increase in hardness value at before and after 50% deformation for alloy and composites was observed as: for AA2024 alloy: 73 to 89 VHN, whereas for AA2024-2% fly ash composite was 85 to 115 VHN, for AA2024-6% fly ash composite was118 to 132 VHN, and for AA % fly ash composite 130 to 143 VHN respectively. Compressive properties of the synthesied Al-Fly ash (ALFA) composites (2, 6 and 10 wt. % fly ash) can be understood by studying the load displacement curves. Figure 4.12 and 4.13 shows the load displacements curves for AA2024 alloy and fly ash composites during compression testing with aspect ratios of 1.0 and 1.5 respectively; and figures 4.14 and 4.15 shows the true stress true strain curves of AA 2024 alloy and ALFA composites with aspect ratios of 1.0 and 1.5 respectively. The load requirement increased with increase in displacement for both the alloy and composites. The composites show higher loads than the unreinforced alloy; and this increase in load is more for higher the amount of fly ash, as shown in figures 4.12 and The same is confirmed from the true stress and true strain results, as shown in figures 4.14 and

26 This indicates that the fly ash addition leads to improvement in the strength of the composites. The strength of the metal matrix composites (MMC) is expected to increase by addition of solid ceramic particles due to the strengthening effects occurred in particulate reinforced composites. These effects include the transfer of stress from the matrix to the particulate, the interaction between individual dislocations and particulates, grain sie strengthening mechanism due to a reduction in composite matrix grain sie, and generation of a high dislocation density in the matrix of the composite as a result of the difference in thermal expansion between the metal matrix and particulates [46-48]. Further the experimental results shows that increased in aspect ratio decreases the load required for the same amount of deformation. For a fixed diameter, a shorter specimen will require a greater axial force to produce the same percentage of reduction in height, because of the relatively larger undoformed region [49]. Before Deformation 50% Deformation Hardness (VHN) Wt. % of fly ash Figure 4.11: Comparative hardness bar chart for AA 2024 alloy and AA % fly ash composites before and after 50% deformation 81

27 Figure 4.12: Load displacement curves for AA 2024alloy and Al-Fly ash composites at the aspect ratio (Ho/Do) =1.0 Figure 4.13: Load displacement curves for AA 2024 alloy and Al-Fly ash composites at the aspect ratio (Ho/Do) =1.5 82

28 Figure 4.14: True stress ss vs true plastic strain curves for AA 2024alloy and Al-Fly ash composites at the aspect ratio (Ho/Do) =1.0 Figure 4.15: True stress vs true plastic strain for AA 2024alloy and Al-Fly ash composites at the aspect ratio (Ho/Do) =1.5 83

29 4.4.3: HOLLOMON POWER LAW PARAMETERS True stress vs true strains were calculated from equation (7) and (8) of section with the help of the Load displacement data; which was generated during the cold upsetting of alloy and composites. The calculated true stress vs true strains were fit into well established Hollomon power law [50-56] given by: σ = K ε n Where: σ = true stress ε = true plastic strain K= strength coefficient, and n = strain hardening exponent Figures 4.14 and 4.15 shows the representative plots of σ vs ε generated from the upsetting test data carried out at slow speed with aspect ratios (H 0 /D 0 ) = 1.0 & 1.5 of the AA2024 alloy and composites respectively. This data was treated to be material property [57] and used as input for finite element analysis discussed in chapter 5. Hollomon parameters K and n are used widely to assess behaviour in both uniaxial tension and compression at room temperature [58-60]. These constants have also been used to relate properties in metal forming [61-67]. The strength coefficient (K) gives the flow stress at unit strain and it is the measure of elastic spring-back. The strain hardening exponent n is an important in metal forming. It signifies the strain hardening or work hardening characteristic of a material, that is, the higher the value of n, higher is the rate at which the material work hardens. A material with high value of n is preferred for process, which involves plastic deformation. The larger the n value, the more the material can deform before instability [68]. The strength coefficient, K found to be increasing with increasing fly ash content, figure 4.16 (a). A rise in K value was observed from 402 MPa for AA2024 alloy to 890 MPa for AA % fly ash composite. The obtained values were at 50% deformation by cold upsetting process. 84

30 Figure 4.16(b) shows the effect of fly ash particle on strain hardening exponent n. The value of n found to be increasing with fly ash addition. The strength of the metal matrix composites (MMC) is expected to increase by addition of solid ceramic particles due to the strengthening effects occurred in particulate reinforced composites. The presence of second phase particles in the continuous metal matrix phase resulted in localied internal stresses which modify the plastic properties to a great extent [69, 70]. Hence, the presence of hard fly ash particles made the composites high strength subsequently increase in strain hardening exponent n values for larger fly ash content. During metal forming the dislocation density increased by several orders of magnitude. By this, ones of higher dislocation density emerge, which represent a hindrance for moving dislocations. Therefore the dislocations can only pass by or cut across one another at an increases stress. The inner stress also cause the dislocation sources to be activated again only at higher stresses. The stress fields of the dislocations, which act against the emergence and movement of further dislocations, must be considered as the main cause of strain hardening. In polycrystalline metals, gain boundaries and the difference in orientation of the slip planes between grains act as additional obstacles for the dislocation movement. If there has no thermally activated action, such as recrystalliation or recovery, during the deformation process, the exponent n was a measure of the work hardening observed in all metallic materials. This represents the increase of flow stress σ with increase in natural strainε. Based on this phenomenon, the work hardening coefficient n was a measure of achievable maximum formability for different materials during forming with the same external restraints. A higher work hardening coefficient means a higher uniform elongation value, there by reducing the tendency for local straining in the material. Although slip planes occasionally cross grain boundaries, especially if the crystals have twin orientation or close to it as a rule deformation stops whenever a change of orientation is present not only grain boundaries but also sub boundaries acts as barriers for movement, and a pile-up of dislocations with distortion of the crystal results [71-73]. 85

31 (a) (b) Figure 4.16: (a) Variation of strength coefficient (K) with addition of fly ash to AA2024 alloy; (b) Variation of strain hardening exponent (n) with addition of fly ash to AA2024 alloy 86

32 4.4.4: MEASUREMENT OF EXPERIMENTAL STRAIN PATH EQUATIONS Surface strains, ε and ε were evaluated for the geometric mid-sectional grid of the specimens (figure 4.8) and the results were plotted in figures 4.17 to 4.20, for AA2024 alloy and AA to 10 wt. % fly ash composites respectively. Homogeneous deformation corresponds to ideal condition, that is, deformation without friction or barreling with a constant slope of ε 1 =. 2 ε Z Homogeneous compression resulted in straight strain paths of slope nearly equal to -1/2. From the figures 4.17 to 4.20, it was evident that upset tests with friction produced curved strain paths. The tendency of this curved strain paths was increasing with increasing frictional constraint and decreasing aspect ratio. The slope of the experimentally determined relationship between axial strain ε and circumferential strainε deviated from that corresponding to homogeneous deformation as barreling develops. The strain paths for H 0 /D 0 = 1.0 in dry conditions were much steeper than H 0 /D 0 = 1.5 of same frictional condition. This was true for the alloy and all the composites under investigation. Also it was observed that the strain path deviations from homogeneous line was less for H 0 /D 0 = 1.5 compared to H 0 /D 0 = 1.0. The line with a slope ε 1 = on ε vs ε 2 plot and which intersects the ε Z ordinates at ε 0.3 is an estimate of a fracture line for upsetting test performed on circular cylinders [74]. Though the intercept 0.3 on the ordinate may be approximately correct for steels, but may differ for material to material. Brownrigg et al [75] and H. A. Kuhn et al [76] reported these values of intercepts as 0.29, 0.32, and 0.18 for the 1045 steel, 1020 steel and 303 stainless steel respectively. In the present work these intercept values were observed to be 0.30 for AA2024 alloy and all the Al- fly ash composites. Upset tests with friction produce curved strain paths. The deviation of slope from that of homogeneous deformation to ratio between axial strain ( ε ) and 87

33 circumferential strain ( ε ) represents barreling. This deviation was less when the specimen die interface friction was low. From the experimental results, it was evident that the strain paths obtained from cylindrical specimens with aspect ratios 1.0 and 1.5 deviated from the slope 0.5 (which represents the homogeneous deformation). It was also observed that all strain paths obtained from different specimens exhibited nonlinearity from the beginning to the end of the strain path. And also it was shows that the slope at a point on the strain path increases as that point moves toward the end of the strain path or the fracture point. This means that at the fracture point, the incremental axial strain component was almost ero, while the incremental circumferential strain component was very high. This change in the slope of the strain path has a great effect on the stress state at the surface of the specimen. The curve fitting technique was used (because of the scatter in the experimental data for axial and circumferential strains) to obtain a smooth relationship between the axial strain and circumferential strain. This relationship represents the equations of the strain paths. Some of these equations of strain paths obtained from different specimens were given in table 4.1. The ends of the strain paths represent the fracture points. Joining all the fracture points on all strain paths gives the workability limit for the materials under considered. Table 4.1: Experimental strain path equations obtained by the best curve fit technique. The compression tests were carried at the friction factor m = 0.36 (Dry condition). S. No Material Aspect ratio Strain path equations 1. H 0 /D 0 =1.0 ε =0.218ε ε AA2024 alloy 2. H 0 /D 0 =1.5 ε =0.0938ε ε 3. AA2024 alloy- 2% H 0 /D 0 =1.0 ε =0.2135ε ε 4. fly ash composite H 0 /D 0 =1.5 ε =0.1579ε ε 5. AA2024 alloy- 6% H 0 /D 0 =1.0 ε =0.0929ε ε 6. fly ash composite H 0 /D 0 =1.5 ε =0.6439ε ε 7. AA2024 alloy- 10% H 0 /D 0 =1.0 ε =0.2958ε ε 8. fly ash composite H 0 /D 0 =1.5 ε =0.4193ε ε 88

34 Circumferential Strain H/D = 1.0 H/D = 1.5 Fracture Line Homogeneous Deformation Axial Strain Figure 4.17: Circumferential strain ε as a function of axial strainε at the equatorial free surface for AA2024 alloy Circumferential Strain H/D = 1.0 H/D = 1.5 Fracture Line Homogeneous Deformation Axial Strain 0 Figure 4.18: Circumferential strain ε as a function of axial strainε at the equatorial free surface for AA2024 2% fly ash composite. 89

35 Circumferential Strain H/D = H/D = 1.5 Fracture Line Homogeneous Deformation Axial Strain Figure 4.19: Circumferential strain ε as a function of axial strainε at the equatorial free surface for AA2024 6% fly ash composite Circumferential Strain H/D = H/D = 1.5 Fracture Line Homogeneous Deformation Axial Strain Figure 4.20: Circumferential strain ε as a function of axial strainε at the equatorial free surface for AA % fly ash composite. 90

36 4.4.5: DETERMINATION OF STRESS COMPONENTS Estimation of the effective strain,ε, on the geometrical mid section of the free surface were made from equation (7) of section The effective strain obtained by this method allowed estimates of the effective stress from the stress - strain power law relationship discussed in section The appropriate value of effective stress was then used in equation (4) and (5) of section to calculate the stresses σ and σ. The hydrostatic component of the stress, σ H = ( σ ) + σ + σ r was then 3 computed. The magnitude of the free surface stress components σ, σ andσ for H various test conditions like deformation in dry condition with aspect ratio (H o /D o ) of 1.0 and 1.5 were plotted against effective strains which were shown given in figure 4.21 to The drawn figures represent the AA2024 alloy and Al-2-10% fly ash composites respectively. As the value of σ becomes ( σ + σ )/3. H σ r on free surface was assumed to be ero, In an idealied situation of uniaxial compression, the circumferential stressσ, was ero and the axial stress σ was equal to the yield stress, σ 0. Under this condition the hydrostatic component of the stress, σ H would be equal to σ Z /3 and would always be compressive; a state of instability will never occur in homogeneous deformation. Hence according to an instability theory of fracture ductile fracture will never occur in homogenous deformation. On the other hand if the friction between the specimen and platens is such that the deformation departed from the homogeneous case and barrel was developed. The tensile circumferential surface stress component σ was non ero and the hydrostatic component of stressσ become less compressive and in some cases tensile. H The present results referring to figures 4.21 to 4.24 of AA2024 alloy and AA2024alloy fly ash composites show that with the increasing effective strain the circumferential stress component σ increasingly becomes tensile with continued deformation. The increase in its value was found to be more in case of specimens deformed for lower aspect ratio compared to the higher aspect ratio conditions. On 91

37 the other hand the axial stressesσ, for AA 2024 alloy as well as all the fly ash composites increased in the very initial stages of deformation but started becoming less compressive immediately as barreling developed. For unfractured specimens the axial stressσ, was always be compressive. surface fracture occurred both However for the specimens where σ andσ stress components became less and less H compressive as deformation progressed and became tensile. This gave rise to the so called normal fracture. Kudo and Aoi [41] and Kobayashi [43] observed both the normal and shear type of fractures in their ductile failure studies; the shear type of fracture was observed when the axial stress, σ on the surface is compressive. It is possible to speculate that when friction at the interface is so negligible that the axial stress σ is always compressive and the circumferential stress σ never reaches the critical value, shear type of fracture should occur. To verify this hypothesis Samantha [74] made his study on an Al specimen of H 0 /D 0 = 1.5 which was incrementally deformed without any strain measurements. New Teflon film was used at each incremental deformation, and the deformation was continued until shear crack appeared, after 93% reduction in height. This result gives an indication that, if the cold heading wire does not contain longitudinal surface defects such as seams and laps, and is well lubricated, ductile fracture should not be a problem in a similar process such as bolt heading, plate bending and other cold forming operations. The hydrostatic stress involves only pure tension or compression and yield stress is independent of it. But fracture strain is strongly influenced by hydrostatic stress [77, 78]. Increase in friction constraint and decrease in aspect ratio caused hydrostatic stress to be tensile and instability starts. As the hydrostatic stress becomes more and more tensile, a state of tensile instability will occur. The transformation in nature of the hydrostatic stress from compressive to tensile depends on the shape and sie of the specimen and the frictional constraint at the contact surface of the specimen with the die block. In the present work, the upsetting tests were performed in dry condition for predicting the deformation to fracture. Due to practical difficulties in observing the 92

38 crack initiation the maximum deformation is limited to 50%. For AA2024 alloy and AA2024 alloy -2% fly ash composites, no crack was observed. In case of AA2024 6% fly ash composite, the crack was observed at 48% deformation for aspect ratio of 1.0 and no crack was observed for aspect ratio of 1.5. Referring to the result obtained for AA % fly ash composite, the crack appearance was observed at 46% and 48% deformation for the aspect ratios of 1.0 and 1.5 respectively From the observation of figures 4.21 to 4.24, showing hydrostatic stress as a function of effective strain, it was concluded that for the same amount of strain the tendency of hydrostatic stress changes from compressive to tensile under for small aspect ratios. For AA2024 alloy, the extent of deformation from instability to fracture was large. But in case of all the fly ash composites (AA2024 alloy - 2 to 10 wt. %), due to presence of large portion of second phase particles, the post instability strain to fracture was small. Similar results were found with the experimental works of Edelson and Baldwin [79]. However this post instability strain to fracture can be increased by changing the microstructure via proper heat treatment as it is influenced by the grain sie and inter particle distance. Such study is beyond the scope of present work. 93