Numerical Simulation of Elastoplastic Behavior and Damage Evolution at Various Stress Triaxiality

Document Type : Research Article

Authors

1 MSc, Mahdi Ansari, School of mechanical engineering, University of Tehran

2 MSc, School of mechanical engineering, University of Tehran

Abstract

The theory of continuum damage mechanics with a phenomenological approach is able to simulate phenomena such as soft strain, local necking of materials, and their failure. Stress triaxiality is defined as the stress state in a material that strongly affects the ductile failure phenomena. In this study, two damage models, Ganjiani and Bonora, are chosen to simulate and compare the elastoplastic behavior as well as damage evolution of some metals. These damage models are sensitive to the stress triaxiality. In order to validate the capability of the models in structural response, the proposed model has been implemented into user-defined subroutines VUMAT in the finite element program ABAQUS/Explicit. For this purpose, the explicit stress integration algorithms of the model have been explained. The model has been validated by comparing the predicted results with experimental data. The simulations are performed for steel 1045, aluminum 2024-T351, and steel HY130. The details of the integration algorithm in the framework of the explicit scheme are presented. Also, the model is developed in the large strain deformation. For the determination of the constants in the models, the stress-strain, the damage-strain, and the fracture strain-triaxiality curves are used. The predicted curves of load-displacement from simulation have good agreement with corresponding experimental data.

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[1] A. Pirondi, N. Bonora, D. Steglich, W. Brocks, D. Hellmann, Simulation of failure under cyclic plastic loading by damage models, International Journal of Plasticity, 22(11) (2006) 2146-2170.
[2] C. Chow, X. Yang, A generalized mixed isotropic-kinematic hardening plastic model coupled with anisotropic damage for sheet metal forming, International Journal of damage mechanics, 13(1) (2004) 81-101.
[3] N. Bonora, G. Testa, A. Ruggiero, G. Iannitti, D. Gentile, Continuum damage mechanics modelling incorporating stress triaxiality effect on ductile damage initiation, Fatigue & Fracture of Engineering Materials & Structures,  (2020).
[4] S. Chandrakanth, P.C. Pandey, An isotropic damage model for ductile material, Engineering Fracture Mechanics, 50(4) (1995) 457-465.
[5] N. Bonora, A nonlinear CDM model for ductile failure, Engineering Fracture Mechanics, 58(1) (1997) 11-28.
[6] Y. Lou, H. Huh, S. Lim, K. Pack, New ductile fracture criterion for prediction of fracture forming limit diagrams of sheet metals, International Journal of Solids and Structures, 49(25) (2012) 3605-3615.
[7] Y. Lou, J.W. Yoon, H. Huh, Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality, International Journal of plasticity, 54 (2014) 56-80.
[8] Y. Lou, L. Chen, T. Clausmeyer, A.E. Tekkaya, J.W. Yoon, Modeling of ductile fracture from shear to balanced biaxial tension for sheet metals, International Journal of Solids and Structures, 112 (2017) 169-184.
[9] Y. Lou, H. Huh, Extension of a shear-controlled ductile fracture model considering the stress triaxiality and the Lode parameter, International Journal of Solids and Structures, 50(2) (2013) 447-455.
[10] Y. Lou, J.W. Yoon, A User-Friendly Anisotropic Ductile Fracture Criterion for Sheet Metal under Proportional Loading, International Journal of Solids and Structures,  (2021).
[11] X. Zhuang, Y. Meng, Z. Zhao, Evaluation of prediction error resulting from using average state variables in the calibration of ductile fracture criterion, International Journal of Damage Mechanics, 27(8) (2018) 1231-1251.
[12] Y. Bao, T. Wierzbicki, On fracture locus in the equivalent strain and stress triaxiality space, International Journal of Mechanical Sciences, 46(1) (2004) 81-98.
[13] I. Barsoum, J. Faleskog, Rupture mechanisms in combined tension and shear—Experiments, International Journal of Solids and Structures, 44(6) (2007) 1768-1786.
[14] M. Brünig, O. Chyra, D. Albrecht, L. Driemeier, M. Alves, A ductile damage criterion at various stress triaxialities, International Journal of Plasticity, 24(10) (2008) 1731-1755.
[15] Y. Zhu, M.D. Engelhardt, A nonlocal triaxiality and shear dependent continuum damage model for finite strain elastoplasticity, European Journal of Mechanics-A/Solids, 71 (2018) 16-33.
[16] J.R. Rice, D.M. Tracey, On the ductile enlargement of voids in triaxial stress fields, Journal of the Mechanics and Physics of Solids, 17(3) (1969) 201-217.
[17] F. Yu, P.-Y.B. Jar, M.T. Hendry, Constitutive analysis of pressure-insensitive metals under axisymmetric tensile loading: A stress triaxiality-dependent plasticity damage model, International Journal of Mechanical Sciences, 142 (2018) 21-32.
[18] Y. Bai, T. Wierzbicki, A new model of metal plasticity and fracture with pressure and Lode dependence, International journal of plasticity, 24(6) (2008) 1071-1096.
[19] Y. Bai, T. Wierzbicki, Application of extended Mohr–Coulomb criterion to ductile fracture, International Journal of Fracture, 161(1) (2010) 1.
[20] L. Malcher, E. Mamiya, An improved damage evolution law based on continuum damage mechanics and its dependence on both stress triaxiality and the third invariant, International Journal of Plasticity, 56 (2014) 232-261.
[21] J. Lemaitre, A continuous damage mechanics model for ductile fracture, Journal of Engineering Materials and Technology, 107 (1985) 83-89.
[22] H. Liu, M. Fu, Prediction and analysis of ductile fracture in sheet metal forming—Part I: A modified Ayada criterion, International Journal of Damage Mechanics, 23(8) (2014) 1189-1210.
[23] M. Ayada, Central bursting in extrusion of inhomogeneous materials, in:  Proceedings of 2nd International Conference on Technology for Plasticity, Stuttgart, 1987, 1987, pp. 553-558.
[24] T. Cao, J. Gachet, P. Montmitonnet, P. Bouchard, A Lode-dependent enhanced Lemaitre model for ductile fracture prediction at low stress triaxiality, Engineering Fracture Mechanics, 124 (2014) 80-96.
[25] N. Bonora, G. Testa, A. Ruggiero, G. Iannitti, G. Domenico, Modification of the Bonora damage model for shear failure, Frattura ed Integrità Strutturale, 12(44) (2018) 140-150.
[26] G. La Rosa, G. Mirone, A. Risitano, Effect of stress triaxiality corrected plastic flow on ductile damage evolution in the framework of continuum damage mechanics, Engineering Fracture Mechanics, 68(4) (2001) 417-434.
[27] Y. Bai, T. Wierzbicki, A comparative study of three groups of ductile fracture loci in the 3D space, Engineering Fracture Mechanics, 135 (2015) 147-167.
[28] M. Ganjiani, A damage model for predicting ductile fracture with considering the dependency on stress triaxiality and Lode angle, European Journal of Mechanics-A/Solids,  (2020) 104048.
[29] M. Ganjiani, M. Homayounfard, Development of a ductile failure model sensitive to stress triaxiality and Lode angle, International Journal of Solids and Structures, 225 (2021) 111066.
[30] Z. Yue, K. Cao, H. Badreddine, K. Saanouni, J. Gao, Failure prediction on steel sheet under different loading paths based on fully coupled ductile damage model, International Journal of Mechanical Sciences, 153 (2019) 1-9.
[31] Y. Zhu, M.D. Engelhardt, Prediction of ductile fracture for metal alloys using a shear modified void growth model, Engineering Fracture Mechanics, 190 (2018) 491-513.
[32] F. Dunne, N. Petrinic, Introduction to computational plasticity, Oxford University Press on Demand, 2005.
[33] S. Li, I.J. Beyerlein, C.T. Necker, D.J. Alexander, M. Bourke, Heterogeneity of deformation texture in equal channel angular extrusion of copper, Acta materialia, 52(16) (2004) 4859-4875.
[34] Y. Bai, X. Teng, T. Wierzbicki, On the application of stress triaxiality formula for plane strain fracture testing, Journal of Engineering Materials and technology, 131(2) (2009).
[35] M. Ganjiani, A Nonlinear Damage Model of Hardening-Softening Materials, Journal of Engineering Materials and Technology, 140(1) (2018).
[36] Z. Li, F. Wei, P. La, H. Wang, Y. Wei, Enhancing Ductility of 1045 Nanoeutectic Steel Prepared by Aluminothermic Reaction through Annealing at 873 K, Advances in Materials Science and Engineering, 2017 (2017).
[37] A. Balankin, D. Morales, O. Susarrey, I. Campos, F. Sandoval, A. Bravo, A. García, M. Galicia, Fractal properties of fracture surfaces in steel 1045, International journal of fracture, 106(2) (2000) 21-26.
[38] E. Lach, H. Nahme, I. Rohr, Dynamic properties of nitrogen alloyed 1045 iron-carbon-steel, in:  Journal de Physique IV (Proceedings), EDP sciences, 2003, pp. 857-862.
[39] C. Hua, D. Socie, Fatigue damage in 1045 steel under constant amplitude biaxial loading, Fatigue & Fracture of Engineering Materials & Structures, 7(3) (1984) 165-179.
[40] M. Lotfi, S. Amini, Effect of longitudinally intermittent movement of cutting tool in drilling of AISI 1045 steel: A three-dimensional numerical simulation, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(12) (2019) 4081-4090.
[41] X. Nan, L. Xie, W. Zhao, On the application of 3D finite element modeling for small-diameter hole drilling of AISI 1045 steel, The International Journal of Advanced Manufacturing Technology, 84(9) (2016) 1927-1939.
[42] A.A.O. Abduluyahed, Tensile stress-strain analysis of multiphase alloys,  (1986).
[43] Y. Bai, X. Teng, T. Wierzbicki, On the application of stress triaxiality formula for plane strain fracture testing, Journal of Engineering Materials and technology, 131(2) (2009) 021002.
[44] Y. Bao, Dependence of ductile crack formation in tensile tests on stress triaxiality, stress and strain ratios, Engineering fracture mechanics, 72(4) (2005) 505-522.
[45] N. Bonora, G. Testa, A. Ruggiero, G. Iannitti, D. Gentile, Modification of the Bonora Damage Model for shear failure, Frattura ed Integrità Strutturale, 12(44) (2018) 140-150.
[46] J. Papasidero, V. Doquet, D. Mohr, Ductile fracture of aluminum 2024-تی351 under proportional and non-proportional multi-axial loading: Bao–Wierzbicki results revisited, International Journal of Solids and Structures, 69 (2015) 459-474.
[47] C.Y. Tang, J. Fan, C.P. Tsui, Prediction for forming limit of AL2024T3 sheet based on damage theory using finite element method, Acta Mechanica Solida Sinica, 19(2) (2006) 174-180.
[48] L. Xue, T. Wierzbicki, Ductile fracture characterization of aluminum alloy 2024-تی351 using damage plasticity theory, International Journal of Applied Mechanics, 1(02) (2009) 267-304.
[49] M. Mashayekhi, S. Ziaei-Rad, J. Parvizian, K. Nikbin, H. Hadavinia, Numerical analysis of damage evolution in ductile solids, Structural Durability & Health Monitoring, 1(1) (2005) 67.
[50] T. Holmquist, Strength and fracture characteristics of HY-80, HY-100, and HY-130 steels subjected to various strains, strain rates, temperatures, and pressures, HONEYWELL INC BROOKLYN PARK MN ARMAMENT SYSTEMS DIV, 1987.
[51] M. Schwartz, S. Aircraft, Welding, Brazing, and Soldering, volume 6 of ASM Metals Handbook, ASM Intl,  (1993) 126-129.
[52] J.H. Giovanola, S.W. Kirkpatrick, J.E. Crocker, Fracture of geometrically scaled, notched three-point-bend bars of high strength steel, Engineering fracture mechanics, 62(2-3) (1999) 291-310.