- Volume 29 Issue 2 Serial No. 233
In decades, a substantial body of work on a unified viscoplastic model which considers the mechanism of plastic deformation and creep deformation has developed. The systematic scheme for numerical analysis of unified model is necessary because the dominant failure mechanism is the defect growth and coalescence in materials. In the present study, the unified viscoplastic model for materials with defects suggested by Suquet and Michel was employed for numerical analysis. The constitutive equations are integrated based on the generalized mid-point rule and implemented into a finite element program (ABAQUS) by means of user-defined subroutine (UMAT). To evaluate the validity of the developed UMAT code and the assessment of the adopted viscoplastic model, the results obtained from the UMAT code was compared with the numerical reference solution and experimental data. The unit cell analysis also has been investigated to study the effect of strain rate, temperature, stress triaxiality and initial defect volume fraction on the growth and coalescence of the defect.
Unified Viscoplastic Constitutive Model;FEM;Generalized Mid-Point Rule;Strain Rate-Dependent Effect;Unit Cell Model
- Hui, L., Sunil, S. and Piehler, H. R., 1995, 'A Critical Evaluation and Extension of Internal State Variables Constitutive Models,' Int. J. Plasticity, Vol. 11, pp. 331-345 https://doi.org/10.1016/S0749-6419(95)00002-X
- Cocks, A. C. F., 1989, 'Inelastic Deformation of Porous Materials,' J. Mech. Phys. Solids, Vol. 37, pp. 693-715 https://doi.org/10.1016/0022-5096(89)90014-8
- Michel, J. C. and Suquet, P., 1992, 'The Constitutive Law of Nonlinear Viscous and Porous Materials,' J. Mech. Phys. Solids, Vol. 40, pp. 783-812 https://doi.org/10.1016/0022-5096(92)90004-L
- Ortiz, M. and Simo, J. C., 1986, 'An Analysis of a New Class ofIntegration Algorithms for Elasto-Plastic Constitutive Equations,' Int. J. Num. Meth. Engng., Vol. 23, pp. 353-366 https://doi.org/10.1002/nme.1620230303
- Ortiz, M. and Popov, E. P., 1985, 'Accuracy and Stability of Integration Algorithms for Elastoplastic Constitutive Relations,' Int. J. Num. Meth. Engng., Vol. 21, pp. 1561 https://doi.org/10.1002/nme.1620210902
- Hughes, T. J. R. and Winget, J., 1980, 'Finite Rotation Effects in Numerical Integration of Rate Constitutive Equations Arising in Large-Deformation Analysis,' Int. J. Num. Meth. Engng., Vol. 15, pp. 1862 https://doi.org/10.1002/nme.1620151210
- Nagtegaal, J. C., 1982, 'On the Implementation of Inelastic Constitutive Equations with Special Reference to Large Deformation Problems,' Camp. Methods Appl. Mech. Engng., Vol. 33, pp. 469 https://doi.org/10.1016/0045-7825(82)90120-7
- Lush, A. M., Weber, G and Anand, L., 1989, 'An Implicit Time-Integration Procedure for a Set of Internal Variable Constitutive Equations for Isotropic Elasto- Viscoplasticity,' Int. J. Plasticity, Vol. 5, pp. 521-549 https://doi.org/10.1016/0749-6419(89)90012-0
- Honberger, K. and Stamm, H., 1989, 'An Implicit Integration Algorithm with a Projection Method for Viscoplastic Constitutive Equations,' Int. J. Num. Meth. Engng., Vol. 28, pp. 2397 https://doi.org/10.1002/nme.1620281013
- ABAQUS, User's manual I and II, 2003, Hibbit, Karlsson, and Sorensen, USA
- Simo, J. C. and Hughes, T. J. R., 1997, Computatioal Inelasticity, Springer
- Aravas, N., 1987, 'On the Numerical Integration of a Class of Pressure-Dependent Plasticity Models,' Int. J. Num. Meth. Engng., Vol. 24, pp. 1395-1416 https://doi.org/10.1002/nme.1620240713
- Zavaliangos, A., Anand, L. and von Turkovich, B. E, 1991, 'Towards a Capability for Predicting the Formation of Defects During Bulk Deformation Processing,' Annals ofCIRP, Vol. 40, pp. 267-271 https://doi.org/10.1016/S0007-8506(07)61984-2
- Needleman, A. and Rice, J. R., 1980, 'Void growth in an Elastic-Plastic Medium,' J. Appl. Mech., Vol. 41, pp.964-970
- Koplik, J. and Needleman, A., 1988, 'Void growth and Coalescence in Porous Plastic Solids,' Int. J. Solids Struct., Vol. 24, pp. 835-853 https://doi.org/10.1016/0020-7683(88)90051-0
- Brocks, W., Sun, D. -Z. and Honig, A., 1995, 'Verification of the Transferability of Micromechanical Parameters by Cell Model Calculations with ViscoPlastic Materials,' Int. J. Plasticity, Vol. 11, pp. 971-989 https://doi.org/10.1016/S0749-6419(95)00039-9
- S. S. Youn, S. B. Lee, J. B. Kim, H. Y. Lee and B. Yoo, 2000, 'Generalization of Integration Methods for Complex Inelastic Constitutive Equations with State Variables,' Transactions of KSME(A), Vol. 24, No.5, pp. 1075 -1082
- Zhang, Z. L., 1995, 'On the Accuracy of Numerical Integration Algorithms for Gurson-Based PressureDependent Elastoplastic models,' Comp Methods Appl. Mech. Engng., Vol. 121, pp. 15-28 https://doi.org/10.1016/0045-7825(94)00706-S
- Zhang, Z. L., 1995, 'Explicit Consistent Tangent Moduli with a Return Mapping Algorithms for Pressure-Dependent Elastoplastic Constitutive Models,' Comp Methods Appl. Mech. Engng., Vol. 121, pp. 29-44 https://doi.org/10.1016/0045-7825(94)00707-T
- Govindarajan, R. M., 1992, Deformation Processing of Porous Metals, Doctorial thesis, University of Pennsylvania, U. S. A.
- Haghi, M., 1992, Elasto-Viscoplasticity of Porous Metals at Elevated Temperatures, Doctorial thesis, M. I. T, U. S.A.
- Wilkins, M. L., 1964, 'Calculation of Elastic-Plastic Flow,' in Methods of Computational Physics, Vol. 3, (ed. Alder, B., Fembach, S. and Rotenberg, M), Academic Press, New York.