An Investigation into the Effect of Strain Rate on Damage Evolution in Pure Copper Using a Modified Bonora Model

Document Type : Original Research Paper

Authors

Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran.

Abstract

Strain rate is an effective parameter in characterization of ductile materials. In this work, the influence of strain rate on damage evolution in copper is investigated through analytical approach, experiment, and numerical simulation. In the analytical approach, a modified damage model is proposed to take account of the effect of strain rate on damage parameter based on Continuum Damage Mechanics (CDM). A new technique is used for evaluation of damage evolution in tensile dog bone specimens using a Split Hopkinson Tensile Bar (SHTB). The results of high strain rate tests are used to validate the modified damage model. The proposed model is based on Bonora ductile damage model in which the effect of strain rate is incorporated. The numerical simulations are performed by implementing the proposed model in the finite element commercial code, ABAQUS/Explicit using VUSDFLD subroutines. A reasonable agreement was observed between the experimental data and the proposed damage model.  

Keywords


[1] L.M. Kachanov, Introduction to Continuum Damage Mechanics, Springer Science & Business Media, Dordrecht, 10 (2013).
[2] A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part I-Yield criteria and flow rules for porous ductile media, J. Eng. Mater. Technol., 99(1) (1977) 2-15.
[3] C.C. Chu, A. Needleman, Void nucleation effects in biaxially stretched sheets, J. Eng. Mater. Technol., 102(3) (1980) 249-256.
[4] G. Rousselier, Finite deformation constitutive relations including ductile fracture damage, Threedimensional Constitutive Relations and Ductile Fracture, (1981) 318-343.
[5] G. Rousselier, Ductile fracture models and their potential in local approach of fracture, Nucl. Eng. Des., 105(1) (1987) 97-111.
[6] J. Lemaitre, A continuous damage mechanics model for ductile fracture, J. Eng. Mater. Technol., 107(1) (1985) 83-89.
[7] G.Z. Voyiadjis, P.I. Kattan, A plasticity-damage theory for large deformation of solids-I, Theoretical formulation, Int. J. Eng. Sci., 30(9) (1992) 1089-1108.
[8] N. Bonora, A nonlinear CDM model for ductile failure, Eng. Fract. Mech., 58(1-2) (1997) 11-28.
[9] L.M. Kachanov, Time of the rupture process under creep conditions, Izu. Akad. Nauk SSR Otd. Tech., 8 (1958) 26-31.
[10] L. Hao, P. Ke, W. June, An anisotropic damage criterion for deformation instability and its application to forming limit analysis of metal plates, Eng. Fract. Mech., 21(5) (1985) 1031-1054.
[11] J. Lemaitre, A Course on Damage Mechanics, Springer Science
& Business Media, (2012).
[12] N. Bonora, G. Testa, A. Ruggiero, G. Iannitti, D. Gentile, Continuum damage mechanics modelling incorporating stress triaxiality effect on ductile damage initiation, Fatigue Fract. Eng. Mater. Struct., 43(8) (2020) 1755-1768.
[13] 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.
[14] C. Pei, W. Zeng, H. Yuan, A damage evolution model based on micro-structural characteristics for an additive manufactured superalloy under monotonic and cyclic loading conditions, Int. J. Fatigue, 131 (2020) 105279.
[15] Z. Guo, D. Huang, X. Yan, X. Zhang, M. Qi, J. Fan, A damage coupled elastic-plastic constitutive model and its application on low cycle fatigue life prediction of turbine blade, Int. J. Fatigue, 131 (2020) 105298.
[16] A. Yadollahi, N. Shamsaei, Y. Hammi, M.F. Horstemeyer, Quantification of tensile damage evolution in additive manufactured austenitic stainless steels, Mater. Sci. Eng. A, 657 (2016) 399-405.
[17] M. Kumar, P.M. Dixit, A nonlinear ductile damage growth law, Int. J. Damage Mech., 24(7) (2014) 1070-1085.
[18] S. Chandrakanth, P.C. Pandey, An isotropic damage model for ductile material, Eng. Fract. Mech., 50(4) (1995) 457-465.
[19] B.K. Thakkar, P.C. Pandey, A high-order isotropic continuum damage evolution eodel, Int. J. Damage Mech., 16(4)(2007) 403-426.
[20] A.J. Gillard, S.F. Golovashchenko, A.V. Mamutov, Effect of quasi-static prestrain on the formability of dual phase steels in electrohydraulic forming, J. Manuf. Process., 15(2) (2013) 201-218.
[21] A. Hassannejadasl, D.E. Green, S.F. Golovashchenko, F. Sergey, J. Samei, C. Maris, Numerical modelling of electrohydraulic free-forming and die-forming of DP590 steel, J. Manuf. Proc., 16(3) (2014) 391-404.
[22] M. Brünig, S. Gerke, J. Tix, Micro-mechanical numerical analyses on the effect of stress state on ductile damage under dynamic loading conditions, Lat. Am. J. Solids Struct., 15(8) (2018) e85.
[23] G.H. Majzoobi, K. Rahmani, A. Atrian, An experimental investigation into wear resistance of MgSiC nanocomposite produced at high rate of compaction, J. Stress Anal., 3(1) (2018) 35-45.
[24] G.H. Majzoobi, K. Rahmani, M. Kashfi, The effect of pre-compaction on properties of Mg/SiC nanocomposites compacted at high strain rates, J. Stress Anal., 4(2) (2020) 19-28.
[25] N. Bonora, D. Gentile, P.P. Milella, G. Newaz, F. Iacoviello, Ductile damage evolution under different strain rate conditions, Proceedings of the ASME 2000 International Mechanical Engineering Congress and Exposition. Crashworthiness, Occupant Protection and Biomechanics in Transportation Systems. Orlando, Florida, USA, 246 (2000)
145-153.
[26] I. Sari Sarraf, D.E. Green, A. Jenab, Damage evolution and void coalescence in finite-element modelling of DP600 using a modified Rousselier model, Eng. Fract. Mech., 196 (2018) 168-190.
[27] G.R. Johnson, W. Cook, A constitutive model and data for materials subjected to large strains, high strain rates, and high temperatures. In Proceedings of the 7th International Symposium on Ballistics, Hague, Netherlands, (1983).
[28] E. Voce, The relationship between stress and strain for homogeneous deformation, J. Inst. Met., 74 (1948) 537-562.
[29] Y. Cao, B. Karlsson, J. Ahlström, Temperature and strain rate effects on the mechanical behavior of dual phase steel, Mater. Sci. Eng. A, 636 (2015) 124-132.
[30] A.S. Khan, R. Liang, Behaviors of three BCC metal over a wide range of strain rates and temperatures: experiments and modeling, Int. J. Plast., 15(10) (1999) 1089-1109.
[31] C. Husson, S. Ahzi, L. Daridon, T. Courtine, Continuum damage modeling for ductile metals under high strain rate deformation, J. phys. IV (Proceedings), 110 (2003) 63-68.
[32] S.S. Jafari, G.H. Majzoobi, E. Khademi, M. Kashfi, Development of a new technique for measuring damage accumulation at high strain rates, Eng. Fract. Mech., 209 (2019) 162-172.
[33] G.H. Majzoobi, A.H. Mahmoudi, S. Moradi, Ductile to brittle failure transition of HSLA-100 Steel at high strain rates and subzero temperatures, Eng. Fract. Mech., 158 (2016) 179-193.
[34] G.R. Johnson, W.H. Cook, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng. Fract. Mech., 21(1) (1985) 31-48.
[35] T. Holmquist, G. Johnson, Determination of constants and comparison of results for various constitutive models, J. phys., IV, EDP Sciences, 01 (C3) (1991) C3-853-C3-860.
[36] S. Walsh, D. Diamond, Non-linear curve fitting using microsoft excel solver, Talanta, 42(4) (1995) 561-572.
[37] N. Bonora, A. Ruggiero, D. Gentile, S. De Meo, Practical applicability and limitations of the elastic modulus degradation technique for damage measurements in ductile metals, Strain, 47(3) (2011) 241-254.