NUMERICAL SIMULATION OF PLASTIC DEFORMATION PROCESSES FROM CAST IRON PARTS

Transcription

1 NUMERICAL SIMULATION OF PLASTIC DEFORMATION PROCESSES FROM CAST IRON PARTS Tudor CHERECHES 1, Paul LIXANDRU 1, Sergiu MAZURU 2, Pavel COSOVSCHI 3 and Daniel DRAGNEA 1 ABSTRACT: One of the various roceedings for material cold-work hardening is the smooth finishing by suerficial lastic deformation with hard tools from metallic carbide or diamond. According to this rocedure, the active workiece faces are ressed with a tool, generally ball-shaed, which has a satial comound movement. The contact between tool and workiece, also in motion, is force/dislacement controlled. This aer describes a numerical simulation for study of the such-like rocedure, used for cast iron arts. An accurate hysical model for technological rocess was stated. The attention was focused on the material elastic-lastic roerties and on constitutive equations. The finite element discretization with more fine mesh in the suerficial layers of the workiece active faces was achieved. The LS-DYNA exlicit dynamic code was used for solving and analyses. The numerical simulation was alied on workieces of revolution, manufactured by contour turning. KEYWORDS: numerical simulation, LS-DYNA, hysical model, mathematical model, numerical solution. 1 INTRODUCTION In resent days numerical simulation became an imortant tool of engineering. The numerical simulations follow a similar rocedure to all the scientific aroaches, which consist in assing through several stages. Starting from henomenon or rocess, the hysical model is created. A mathematical model exresses the hysical laws under quantitative shae with the aid of the governing equations. The following stage, very imortant for the user of this numerical rocedure, is the discrete model design. In this stage, the investigator, using one of the available rerocessing codes, creates an adequate mesh or nodal grid in the roblem domain. A well-chosen mesh (grid) satisfies the two antagonistic conditions: a good accuracy and reasonable comutational effort. After meshing, all roblem conditions are inserted and the re-rocessing is finished. In the next stage, the code solver takes over whole comutational effort and gives the roblem solution under numerical form. The last stage consists in data ost-rocessing, which has as goal the solution comleting, 1 SC UPS PILOT ARM SRL, Dragomiresti, , România 2 UTM FIMCM, Str. Studentilor, 9, Blocul de Studii nr. 6, MD-2045, Chisinau, Moldova Reublic 3 FABRICA DE STICLA, Chisinau, str.transnistria nr. 20, Moldova Reublic tudor.chereches@yahoo.com; s_mazuru@mail.utm.md; c.ashag@gmail.com; danieldrg2003@yahoo.com additional comutations and result analysis. Excet the mathematical model, in this work were crossed all numerical simulation stages, with articular attention on the hysical model configuration, esecially on the material models and on the final solution analysis. 2 PHYSICAL MODEL The configuration of the smooth finishing rocess hysical model for workieces of revolution, considered in resent study, shown in Fig. 1a consists in: the mandrel with jaws, the tool with active art in ball-shae and workiece. The tool action is controlled using some fictive transducers for force measurement. The simulated working of the regime arameters are: the machine sindle seed and the longitudinal and radial advances. During off the smooth finishing rocess the sindle seed and, consequently, workiece seed remain constant. The two advancing movements are correlated in order to obtain the desired rofile. In all alications, the longitudinal (axial) advance is constantly ket, following that the radial advance to be adjusted according to the contact surface rofile. To achieve the major goals of numerical simulation of the lastic deformation technological rocess, there are conceived the model bodies with three tyes of active surfaces: cylindrical, conical and cubic sline rofiled shae, as resented in Fig. 1b. On the active surfaces, a random roughness was generated. In hysical model design, an imortant lace is reserved for material model formulation. ACADEMIC JOURNAL OF MANUFACTURING ENGINEERING, VOL. 12, ISSUE 2/

2 NOTE: Testing machine was not rogrammed to correct the comliance and therefore, deformation was calculated over the entire measurement loo. All curves are distorted near the origin. The causes of this defective: -non-arallelism of the samle s faces; -no flatness of the samle s front faces; -using an inaroriate lubricant. a Aarent Young s Modulus Sec. I II III E a [GPa] Sec. IV V VI E a [GPa] b Figure 1. The hysical model for the technological rocess of cold lastic deformation and workiece model 3 MATERIAL MODEL Sec. R02[MPa] Rm[MPa] E[GPa] I II III IV V VI Aver Err. 5% 8% - Generally, in ractice, arts made of iron cast with lamellar grahite are often used. This is the - R 02[MPa] R m[mpa] study case. The lasticity of the lamellar grahite Aver gray cast iron in stress state in which revail Err. 5% 5% tractions is very low and therefore it is necessary to avoid aarition of the tensile stress in workieces during smooth finishing rocess. In the lastic R02 Rm E Sec. [MPa] [MPa] [GPa] deformations of metals, besides the mechanical I roerties, some thermal roerties are involved. II III Basic elastic-lastic roerties of the materials used IV V in alications are distinguished through VI characteristic diagrams of cast iron in simle comression tests which were carried out at attested laboratories. Additionally, in the same laboratories Brinell and Vickers hardness tests were erformed. In the comression test, three lots of standard Figure 2. Comresion characteristics diagrams for lot secimens, taken from different casting charges no. 1 a) recorded curves in raw form; b) recorded have been tried. The conversion of the raw recorded curves reaired in origin; c) conventional characteristic diagrams; d) real characteristic curves obtained in comression tests in real (true) diagrams characteristic diagrams, shown in Fig. 2, was 30 ACADEMIC JOURNAL OF MANUFACTURING ENGINEERING, VOL. 12, ISSUE 2/2014

3 Table 1. Mechanical characteristics Secimen Yield Lot Stress [MPa] Ultimate Stress [MPa] Brinell Hardness [HB] a b Figure 3. Comliance correction and viscosity effect; a) Comliance correction, b) Viscosity effect achieved using a secial rocedure which has some stes. The raw curves conditioning are based on the assumtion of the testing machine comliance linearity and was made according to Fig. 3a. The conventional curves were transformed in real characteristic diagrams changing the engineering stress in true stress and the strain in logarithmic strain. From sace economy reasons, the exerimental comression data exhibition of the lot no. 1 was exosed, only, but the real mechanical roerties are comletely given in the Table 1. The value disersion of the exerimental data varies from lot by lot and even from one samle to another in the same lot, in wide limits, exressed in last column of Table 1. In this work are used averaged values on a lot. The numerical simulations of the smooth finishing rocesses by lastic deformation on the workieces emloy several tyical material elastovisco-lastic models, which are below formulated and exressed by their own constitutive equations. Secimen Err. 5 6 Aver. Yield Lot [%] Stress [MPa] Ultimate Stress [MPa] Brinell Hardness [HB] CONSTITUTIVE EQUATIONS In the lasticity, stated on lastic flow theory, the main constitutive equations have an incremental form (Khachanov, 1974) and exress roortionality between the increments of lastic strain, dε ij, and comonents of stress deviator, s ij, dλ being an infinitesimal factor (Eq. 1). These equations have in lasticity the same imortance as Hooke s law in elasticity. d i, j ds i, j. (1) Additionally, the lasticity constitutive equations contain a connection which exresses the deendence of the yield stress on the material state, lastic strain, lastic strain rate and temerature. The yield stress equation models the material resonse in action and is exclusively based on exerimental data, obtained from static and dynamic testes, at normal, low and high temeratures. The lastic stress-strain curves are obtained from real characteristic curves (Fig. 2d) eliminating the elastic comonent of strain. In this case, the lastic characteristic curve begins with initial yielding stress (Fig. 3b). In numerical simulations erformed in this work a most oular schematization exonentially exressed by binomial equation was used, y n A B, where y is the yielding stress, - effective lastic strain and A, B and n are material constants (2) ACADEMIC JOURNAL OF MANUFACTURING ENGINEERING, VOL. 12, ISSUE 2/

4 which are obtained based on the minimum errors. For n=1 linear lastic with or without hardening model results. The additional constitutive equation for material of the lot no. 1 was written in both forms, linear and exonential, with the coefficients given in the Table 1. For comarison, beside arameters A, B and n, in last column, the quadratic errors in band of effective lastic strain from 0 u to 0.32 are resented. Many comlex lastic models integrate the exonential reresentation of the material behavior. One of them is the Johnson-Cook material model [2] which, additionally, takes into account, the strain rate and thermal effects and is exressed by the equation n A B x y m T T (3) r m x 1 ln 1 Tmelt Tr m, where, beside Eq. 2, new terms aear. C is a coefficient, m - thermal exonent, T local material temerature and is relative effective lastic strain rate. In this stage, in work, a simlified Johnson-Cook without thermal effect was used. As an examle, for the lot no. 1 were used the following arameters: A=210 [MPa], B=660 [MPa], n=0.58 and C= Other ossibility to take in account the viscosity effect is to use the Cower-Symond multilier. Using the Johnson-Cook date, C and n were aroximate: C=7100 s -1 =3.32. The viscouslastic model for first two material lots used in simulations, shown in Fig, 3b, is obtained by the combination of the iecewise linear lasticity with Cower-Symond multilier. The viscosity effect, taken in account with the Cower-Symond multilier is shown in Fig. 3b for different effective lastic strain rate. The selection of the best material models was made by the comarison of Brinell test simulation results with exerimental data. In Fig. 4 there are given the artial model of the simulation and effective lastic strain fields in remanent stage for both used materials. For Johnson-Cook materials model the values of Brinell simulated hardness (122 and 140) are comarable with the exerimental data values (118 and 140) averaged on each material lot (Table 2). This method for material model validation is very roer, esecially in the redominant comressive lastic deformations. The Johnson-Cook model is used in following simulations. Lot No. Figure 4. Brinell simulation test SIMULATION The finite element discretization of the hysical model (Fig. 1) was erformed with the variable density mesh by using 3D-hexaedral elements. d 1 [mm] d 2 [mm] d aver [mm] h [mm] HB ACADEMIC JOURNAL OF MANUFACTURING ENGINEERING, VOL. 12, ISSUE 2/2014

5 advance: mm/rev; the deth: mm. The random roughness was established in according with the middle turning oeration (Ra= μm). For each established regime, the inut data were introduced in the LS-DYNA command, file and then the LS-DYNA solver was started. The comlete solution is obtained. The result analysis accentuates the imortance of the numerical simulation on the smooth finishing rocess. The surface quality may be interret on the effective lastic strain field as that shown in Fig. 5 The field homogeneity and intensity indicate an imrovement of the surface quality by hardening. By an esecial rocedure, using nodal coordinate in final stage, the surface roughness is evaluate. The residual stress field, reresented in the same figure, relieves one of the disadvantages of this rocessing. The contact forces, as time functions, are shown in Fig. 6. The final lastic strain field (Fig. 5) and force variations (Fig. 6) reveals that a better control on the radial advance, for deformation uniformity, is necessary. Figure 6. Simulated contact forces Figure 5. The workiece discretization, effective lastic strain field and von Mises stress on active surface The suerficial layer of the workiece was meshed with high density (Fig. 5). The various simulation work regimes were established within of the following arameter limits: the sindle seed: rm; the longitudinal Figure 7. Workieces a) before and b) after real smooth finishing Fig. 8 enables qualitative analysis of machined surface deending on radial ressure force. It's a visible difference in quality, assessed by roughness of machined surfaces. In the simulation case of a radial force of 250 N, the tool failed to roduce ACADEMIC JOURNAL OF MANUFACTURING ENGINEERING, VOL. 12, ISSUE 2/

6 smoothing and reduce roughness to accetable values. The above interretation is suorted by the aearance of the machined surface of Fig. 9, which is the rofile of the machined surface deending on the radial force. Workiece surface rofile was reresented by one of its generators in the yoz lane. The surface of the workiece is divided into two arts. In front of attack's frontline of the sherical body of the tool, in the left side is found the initial ortion which resents roughness randomly generated with mentioned values on the figure. Behind of the attack's frontline, the machined surface, smoothed to a certain level is found. To highlight workiece surface rofile, radial dimension is multilied 10 times. Figure 9. Machined surface rofile deending on radial force Figure 8. Qualitative analysis of machined surface deending on radial ressure force Machining under radial force of 500 N gives a smooth surface with low roughness. Machining with larger force of 1000 N, greatly reduce roughness but roduces larger deviations form by corrugations. The data obtained by numerical simulation shows that the rocessing of the baseline data in the radial force of 250 N is not effective. Remaining roughness exceeds half from the initial one. A better smoothing with a ressing force on the tool of 500 N was erformed. It is found that on the machined surface, with some eriodicity, corrugations occur. These corrugations give a deviation form which, relative to the average radius is between -3.4 and +3.4 μm. Largest corrugations occur when the ush force increases. Selection of the working regime of radial force in the smoothing rocess and hardening of the arts made of cast iron with lamellar grahite is made deending on the urose and the initial state of the surfaces. For smoothing rocess of the surfaces with low roughness, on the sherical head of the tool smaller 34 ACADEMIC JOURNAL OF MANUFACTURING ENGINEERING, VOL. 12, ISSUE 2/2014

7 forces are alied. When the surface roughness increases it's necessary to increase the ressing force. In the Fig. 10, the effective remanent stress field in the machined zone after 10 s is resented. Remanent stresses intensity deends directly on the size of the radial forces alied. seen that the in homogeneity of the effective stress field deends on the force. The result of numerical simulation of the rocess of smoothing and hardening by dislacement control is shown in Fig. 11 in the form of effective lastic strain field. Analysis of the reresentations in Fig. 12 highlights the high quality of the surfaces machined by this method, comared with those obtained by the controlled force. Figure 10. Remanent effective stress in the machined area after 10 s tool, whose shae continuously changes. On the three reresentations, a certain eriodicity of field In homogeneity of the remanent stress fields is justified by material wave existence in front of the sherical head of the variation can be seen. It can be Figure 11. Effective lastic strain field at t = 20 ACADEMIC JOURNAL OF MANUFACTURING ENGINEERING, VOL. 12, ISSUE 2/

8 Figure 12. The radial force deending to the set deth Dr [mm] 6. CONCLUSIONS In the work, a numerical simulation methodology for the smooth finishing rocessing of the glass mold tools, based on the LS-DYNA finite element codes, was formulated. An esecial attention was conferred to model rearation, because if the hysical model is not correctly and comletely designed, neither finite element code thoroughness, nor comuter caabilities vouch for solutions accuracy and numerical simulation success. This is an argument of the large sace assigned in the work to material tests and constitutive equation formulation. The simulated working regimes were erformed with the increased longitudinal advance. This fact was generated some non-uniformity on the smoothed surfaces. The numerical simulation of the smooth finishing rocess was validated exerimental on the secial device. In Fig. 7 is shown the result of the exerimental smooth finishing rocess, alied on the cylindrical workieces. It is visible a new quality on the workiece after rocessing. The lamellar grahite in the material structure has a negative influence on the lastic deformation, by the quality limiting. It has been established that a better smoothing by using a ressing force on the tool of 500 N is ossible. It is found that on the machined surface, with some eriodicity, corrugations occur. These corrugations varies in tight limits when is alied the force of 500 N. Largest corrugations occur when the ush force increases. Machining with forces greater than 1000 N, greatly reduces roughness but roduces larger deviations form by corrugations. The numerical simulation offers the large ossibilities for design, analysis and otimizing of the working regimes for the smooth finishing rocessing. The result of numerical simulation of the rocess of smoothing and hardening by dislacement control is that the quality of the obtained surfaces is the best. It can be considered that the numerical simulation of the rocess of smoothing and hardening by lastic deformation contributed greatly to the understanding and justification of the secific asects of this technology. 7. ACKNOWLEDGEMENTS We thank the teams of the University Polytechnic of Bucharest, National Research and Develoment Institute for Gas Turbines - COMOTI Bucharest, Technical University "Gheorghe Asachi" of Iasi for their suort in conducting numerous tests carried out in several laboratories. 8. REFERENCES Khachanov, L.M. (1974). Fundamentals of the Theory of the Plasticity, Mir Publishers, Moscow Johnson, G.R., Cook W.H. (1983). A constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temeratures, Proceedings of Seventh International Symosium on Ballistics, Hague, Bathe, K.J. (1982). Finite Element Procedures in Engineering Analysis, Prentice-Hall. Bathe, K.J., Dvorkin, E.N. (1984). A Continuum Mechanics Based Four-Node Shell Element for General Nonlinear Analysis, Engineering comutations, Vol. 1, No. 1, Cook, R.D. (1974). Concets and Alications of Finite Element Analysis, J. Wiley and Sons. Bathe, K.J., Wilson, E.L. (1976) Numerical Methods in Finite Element Analysis, Prentice-Hall. 9. NOTATION dε ij = increments of lastic strain s ij = comonents of stress deviator dλ= infinitesimal factor σ y = yielding stress - effective lastic strain A, B and n= material constants 36 ACADEMIC JOURNAL OF MANUFACTURING ENGINEERING, VOL. 12, ISSUE 2/2014