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Numerical Implementation of Coupled Anisotropic Plasticity-Ductile Damage in Sheet Metal Forming Process

Published online by Cambridge University Press:  15 May 2017

R. Autay ,
S. Koubaa ,
M. Wali  and
F. Dammak
R. Autay
Affiliation:
Mechanical Modeling and Manufacturing LaboratoryNational Engineering School of SfaxUniversity of SfaxSfax, Tunisia
S. Koubaa
Affiliation:
Mechanical Modeling and Manufacturing LaboratoryNational Engineering School of SfaxUniversity of SfaxSfax, Tunisia
M. Wali*
Affiliation:
Mechanical Modeling and Manufacturing LaboratoryNational Engineering School of SfaxUniversity of SfaxSfax, Tunisia
F. Dammak
Affiliation:
Mechanical Modeling and Manufacturing LaboratoryNational Engineering School of SfaxUniversity of SfaxSfax, Tunisia
*
*Corresponding author (mondherwali@yahoo.fr)
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Abstract

This paper deals with the implementation of an anisotropic plasticity constitutive equations exhibiting non-linear isotropic, kinematic hardening and coupled continuum ductile damage models. A fully implicit integration of the coupling constitutive equations is adopted and leads to two non-linear local scalar equations solved using the Newton method. The consistent local tangent modulus is obtained in a closed form by exact linearization of the algorithm. The numerical treatment of the proposed algorithm is implemented on ABAQUS using user interface material subroutines (UMAT and VUMAT). The performance of the present algorithm is assessed and bared out by numerical examples.

Keywords

Ductile damageAnisotropic materialImplicit integration
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 4 , August 2018 , pp. 417 - 430
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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References

1. Lemaitre, J. and Chaboche, J. L., Mechanics of Solid Materials, University Press, Cambridge (1990).Google Scholar
2. Krajcinovic, D., Damage Mechanics, Elsevier, North-Holland, Amsterdam (1996).Google Scholar
3. Lemaitre, J., A Course on Damage Mechanics, 2nd Edition, Springer-Verlag, Berlin (1996).Google Scholar
4. Yeh, H.-Y. and Cheng, J.-H., “Forming Limits Prediction of the Sheet Metal Forming Process by the Energy-Based Damage Model,” Journal of Mechanics, 22, pp. 43–50 (2006).Google Scholar
5. Yang, X.-H., Zhang, Y., Hu, Y.-T. and Chen, C.-Y., “Continuum Damage Mechanics for Thermo-Piezoelectric Materials,” Journal of Mechanics, 22, pp. 93–98 (2006).Google Scholar
6. Benabou, L., Sun, Z., Pougnet, P. and Dahoo, P. R., “Continuum Damage Approach for Fatigue Life Prediction of Viscoplastic Solder Joints,” Journal of Mechanics, 31, pp. 525–531 (2015).Google Scholar
7. Benallal, A., Billardon, R. and Doghri, I., “An Integration Algorithm and the Corresponding Consistent Tangent Operator for Fully Coupled Elasto-Plastic and Damage Equations,” Communications in Applied Numerical Methods, 4, pp. 731–740 (1988).Google Scholar
8. De Souza Neto, E. A. and Peric, D., “A Computational Framework for a Class of Models for Fully Coupled Elastoplastic Damage at Finite Strains with Reference to the Linearization Aspects,” Computer Methods in Applied Mechanics and Engineering, 130, pp. 179–193 (1996).Google Scholar
9. De Souza Neto, E. A., Peric, D. and Owen, D. R. J., “Continuum Modelling and Numerical Simulation of Material Damage at Finite Strains,” Archive for Computer Methods in Engineering, 5, pp. 311–384 (1998).Google Scholar
10. Doghri, I., “Numerical Implementation and Analysis of a Class of Metal Plasticity Models Coupled with Ductile Damage,” International Journal for Numerical Methods in Engineering, 38, pp. 3403–3431 (1995).Google Scholar
11. Singh, A. K. and Pandey, P. C., “An Implicit Integration Algorithm for Plane Stress Damage Coupled Elastoplasticity,” Mechanics Research Communications, 26, pp. 693–700 (1999).Google Scholar
12. Vaz, M. Jr. and Owen, D. R. J., “Aspects of Ductile Fracture and Adaptive Mesh Refinement in Damaged Elastoplastic Materials,” International Journal for Numerical Methods in Engineering, 50, pp. 29–54 (2001).Google Scholar
13. De Souza Neto, E. A., “A Fast, One-Equation Integration Algorithm for the Lemaitre Ductile Damage Model,” Communications in Numerical Methods in Engineering, 18, pp. 541–554 (2002).Google Scholar
14. Andrade Pires, F. M., César de Sa, J. M. A., Costa Sousa, L. and Natal Jorge, R. M., “Numerical Modelling of Ductile Plastic Damage in Bulk Metal Forming,” International Journal of Mechanical Sciences, 45, pp. 273–294 (2003).Google Scholar
15. Andrade Pires, F. M., De Souza Neto, E. A. and Owen, D. R. J., “On the Finite Element Prediction of Damage Growth and Fracture Initiation in Finitely Deforming Ductile Materials,” Computer Methods Applied in Mechanical Engineering, 193, pp. 5223–5256 (2004).Google Scholar
16. Malcher, L. and Mamiya, E. N., “An Improved Damage Evolution Law Based on Continuum Damage Mechanics and its Dependence on Both Stress Tri-Axiality and the Third Invariant,” International Journal of Plasticity, 56, pp. 232–261 (2014).Google Scholar
17. Bonora, N., Majzoobi, G. H. and Khademi, E., “Numerical Implementation of a New Coupled Cyclic Plasticity and Continum Damage Model,” Computational Materials Science, 81, pp. 538–547 (2014).Google Scholar
18. Bonora, N., “A Nonlinear CDM Model for Ductile Failure,” Engineering Fracture Mechanics, 58, pp. 11–28 (1997).Google Scholar
19. Hill, R., “A Theory of the Yielding and Plastic Flow of Anisotropic Metals,” Proceedings of the Royal Society A, 193, pp. 281–297 (1948).Google Scholar
20. Hill, R., “Theoretical Plasticity of Textured Aggregates,” Mathematical Proceedings of the Cambridge Philosophical Society, 85, pp. 179–191 (1979).Google Scholar
21. Hill, R., “Constitutive Modelling of Orthotropic Plasticity in Sheet Metals,” Journal of the Mechanics and Physics of Solids, 38, pp. 405–417 (1990).Google Scholar
22. Hill, R., “A User-Friendly Theory of Orthotropic Plasticity in Sheet Metals,” International Journal of Mechanical Sciences, 35, pp. 19–25 (1993).Google Scholar
23. Karafillis, A. P. and Boyce, M., “A General Anisotropic Yield Criterion Using Bounds and a Transformation Weighting Tensor,” Journal of the Mechanics and Physics of Solids, 41, pp. 1859–1886 (1993).Google Scholar
24. Barlat, F. et al., “Yield Function Development for Aluminum Alloy Sheets,” Journal of the Mechanics and Physics of Solids, 45, pp. 1727–1763 (1997).Google Scholar
25. Barlat, F. et al., “Plane Stress Yield Function for Aluminum Alloy Sheets – Part 1: Theory,” International Journal of Plasticity, 19, pp. 1297–1319 (2003).Google Scholar
26. Barlat, F., Gracio, J. J., Lee, M. G., Rauch, E F. and Vincze, G., “An Alternative to Kinematic Hardening in Classical Plasticity,” International Journal of Plasticity, 27, pp. 1309–1327 (2011).Google Scholar
27. Banabic, D., Kuwabara, T., Balan, T., Comsa, D. S. and Julean, D., “Non-Quadratic Yield Criterion for Orthotropic Sheet Metals under Plane-Stress Conditions,” International Journal of Mechanical Sciences, 45, pp. 797–811 (2003).Google Scholar
28. Cazacu, O. and Barlat, F., “Application of the Theory of Representation to Describe Yielding of Anisotropic Aluminum Alloys,” International Journal of Mechanical Sciences, 41, pp. 1367–1385 (2003).Google Scholar
29. Khelifa, M., Oudjene, M. and Khennane, A., “Fracture in Sheet Metal Forming: Effect of Ductile Damage Evolution,” Computers and Structures, 85, pp. 205–212 (2007)Google Scholar
30. Saanouni, K., “On the Numerical Prediction of the Ductile Fracture in Metal Forming,” Engineering Fracture Mechanics, 75, pp. 3545–3559 (2008).Google Scholar
31. Khennane, A., Khelifa, M., Bleron, L. and Viguier, J., “Numerical Modelling of Ductile Damage Evolution in Tensile and Bending Tests of Timber Structures,” Mechanics of Materials, 68, pp. 228–236 (2014).Google Scholar
32. Badreddine, H., Saanouni, K. and Dogui, A., “On Non-Associative Anisotropic Finite Plasticity Fully Coupled with Isotropic Ductile Damage for Metal Forming,” International Journal of Plasticity, 26, pp. 1541–1575 (2010).Google Scholar
33. Teixeira, P., Santos, A. D., Andrade Pires, F. M. and César de Sa, J. M. A., “Finite Element Prediction of Ductile Fracture in Sheet Metal Forming Processes,” Journal of Materials Processing Technology, 177, pp. 278–281 (2006).Google Scholar
34. Wali, M., Chouchene, H., Ben Said, L. and Dammak, F., “One-Equation Integration Algorithm of a Generalized Quadratic Yield Function with Chaboche Non-Linear Isotropic/Kinematic Hardening,” International Journal of Mechanical Sciences, 92, pp. 223–232 (2015).Google Scholar
35. Mars, J., Wali, M., Jarraya, A., Dammak, F. and Dhiab, A., “Finite Element Implementation of an Orthotropic Plasticity Model for Sheet Metal in Low Velocity Impact Simulations,” Thin-Walled Structures, 89, pp. 93–100 (2015).Google Scholar
36. Ben Said, L., Wali, M. and Dammak, F., “Effects of the Tool Path Strategies on Incremental Sheet Metal Forming Process,” Mechanics & Industry, 17, 411 (2016).Google Scholar
37. Wali, M., Autay, R., Mars, J. and Dammak, F., “A Simple Integration Algorithm for a Non-Associated Anisotropic Plasticity Model for Sheet Metal Forming,” International Journal for Numerical Methods in Engineering, 107, pp. 183–204 (2016).Google Scholar
38. Chaboche, J. L., “Time-Independent Constitutive Theories for Cyclic Plasticity,” International Journal of Plasticity, 2, pp. 149–188 (1986).Google Scholar
39. Armstrong, P. J. and Frederick, C. O., A Mathematical Representation of the Multi-Axial Bauschinger Effect, Central Electricity Generating Board Report, Berkeley Nuclear Laboratories, Great Britain, RD/B/N731 (1966).Google Scholar
40. Prager, W., “A New Method of Analyzing Stresses and Strains in Work-Hardening Plastic Solids,” Journal of Applied Mechanics, 23, pp. 493–496 (1956).Google Scholar
41. Famiyesin, O. O. R., “Energy Adaptation of Non-Associeted Plasticity Tangent Matrices for Symmetric Solvers,” Computers and Structures, 79, pp. 1233–1250 (2001).Google Scholar
42. Chen, X. and Cheng, Y. G., “On Accelerated Symmetric Stiffness Techniques for Nnon-Associated Plasticity with Application to Soil Problems,” Engineering Computations, 28, pp. 1044–1063 (2011).Google Scholar
43. Lemaitre, J., “A Continuous Damage Mechanics Model for Ductile Fracture,” Journal of Engineering Materials and Technology, 107, pp. 83–89 (1985).Google Scholar
44. Krairi, K. and Doghri, I., “A Thermodynamically-Based Constitutive Model for Thermoplastic Polymers Coupling Viscoelasticity, Viscoplasticity and Ductile Damage,” International Journal of Plasticity, 60, pp. 163–181 (2014).Google Scholar
45. Simo, J. C. and Hughes, T. J. R., Computational Inelasticity, Springer, New York (1998).Google Scholar
46. Hughes, T. J. R and Winget, J., “Finite Rotation Effects in Numerical Integration of Rate Constitutive Equations Arising in Large-Deformation Analysis,” International Journal for Numerical Methods in Engineering, 15, pp. 1862–1867 (1980).Google Scholar
47. Hancock, J. W. and Mackenzie, A. C., “On the Mechanism of Ductile Fracture in High-Strength Steels Subjected to Multiaxial Stress-States,” Journal of the Mechanics and Physics of Solids, 24, pp. 147–169 (1976).Google Scholar