Cyclic Plasticity of Engineering Materials by Guozheng Kang & Qianhua Kan

Author:Guozheng Kang & Qianhua Kan
Language: eng
Format: epub
Published: 2017-04-24T00:00:00+00:00

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Thermomechanically Coupled Cyclic Plasticity of Metallic Materials at Finite Strain

In Chapter 3, some cyclic plasticity and viscoplasticity models were established to describe the cyclic deformation (including ratchetting) of metallic materials within the framework of infinitesimal strain. However, in some cases, finite plasticity will occur during the ratchetting of metallic materials. For example, Khan et al. (2007) performed some biaxial cyclic tension–torsion tests of OFHC copper with relatively large shear strain to investigate its cyclic deformation including ratchetting. Kang et al. (2006, 2009) investigated the whole‐life ratchetting and ratchetting–fatigue interaction of SS304 stainless steel and annealed 42CrMo steel, respectively, and discussed the ratchetting of the materials within the range of finite strain, that is, the final ratchetting strain was up to 40%. It implies that a constitutive model constructed in the framework of finite plasticity is necessary to describe the cyclic plasticity of the materials presented within the range of finite strain. Recently, much effort was done to extend the nonlinear Armstrong–Frederick kinematic hardening model to describe the strain hardening of materials in the range of finite deformation, such as done by Lion (2000), Shen (2006), Shutov and Kreiig (2008), Vladimirov et al. (2008), Henann and Anand (2009), Anand (2011), Anand et al. (2012), and so on. Two kinds of procedures were used to construct the kinematic hardening rules for finite plasticity: One used the hyperelasticity theory proposed by Lion (2000), in which the inelastic part obtained in the standard Kröner multiplicative decomposition (Kröner, 1959) of finite deformation was further multiplicatively decomposed into two parts, that is, energetic and dissipative ones. The other employed the rate‐type hypoelasticity theory, in which a stress‐like internal variable was introduced to construct the kinematic hardening rule and an appropriate objective stress rate was required to establish the evolution equations agreed with the frame‐indifference. For the first procedure, additional strain‐like variables made constitutive equations very complicated and inconvenient for numerical implementation, while for the second one, no such problem occurred. In the rate‐type finite plasticity approaches, the key issue is the choice of an adequate objective stress rate. Several objective stress rates were introduced into the finite plasticity approaches, such as the Zaremba–Jaumann–Noll rate (Zaremba, 1903; Jaumann, 1911), Oldroyd rate (Oldroyd, 1950), Cotter–Rivlin rate (Cotter and Rivlin, 1955), Truesdell rate (Truesdell, 1955a, b), Green–Naghdi–Dienes rate (Green and Naghdi, 1965), Durban–Baruch rate (Durban and Baruch, 1977), Sowerby–Chu rate (Sowerby and Chu, 1984), Xia–Ellyin rate (Xia and Ellyin, 1993), and logarithmic rate (Xiao et al, 1997a, b; Bruhns et al, 1999). Xiao et al. (1997a, 1998), Bruhns et al. (1999, 2001a, b, 2005), and Meyers et al. (2003, 2006) proved that the rate‐type models were self‐consistent with the notion of elasticity and were furnished by simple, natural conditions with integrability if and only if the logarithmic rate was adopted. Based on the logarithmic stress rate, an elastoplastic cyclic constitutive model was developed by Zhu et al. (2014) in the framework of rate‐type finite plasticity. In the proposed model, the nonlinear kinematic hardening rule was constructed from extending the

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