Modeling of polycrystals using a gradient crystal plasticity theory that includes dissipative micro-stresses |
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| Authors: | Swantje Bargmann B Daya Reddy |
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| Institution: | 1. Institute of Mechanics, University of Dortmund, Leonhard–Euler-Str. 5, 44227 Dortmund, Germany;2. Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, South Africa;3. Centre for Research in Computational and Applied Mechanics, University of Cape Town, 7701 Rondebosch, South Africa;1. Guangxi Colleges and Universities Key Laboratory of Novel Energy Materials and Related Technology, College of Physics Science and Technology, Guangxi University, Nanning 530004, China;2. Guangxi Key Laboratory for the Relativistic Astrophysics, Guangxi University, Nanning 530004, China;3. Key Lab of Engineering Disaster Prevention and Structural Safety of China Ministry of Education, Guangxi University, Nanning 530004, China;4. Institute of Physics Science and Engineering Technology, Yulin Normal University, Yulin 537000, China;1. School of Materials Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, PR China;2. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, PR China;1. Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China;2. School of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China;3. School of Materials Science and Engineering, Lanzhou University of Technology, Langongping Road 287, Lanzhou 730050, China |
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| Abstract: | This study investigates thermodynamically consistent dissipative hardening in gradient crystal plasticity in a large-deformation context. A viscoplastic model which accounts for constitutive dependence on the slip, the slip gradient as well as the slip rate gradient is presented. The model is an extension of that due to Gurtin (Gurtin, M. E., J. Mech. Phys. Solids, 52 (2004) 2545–2568 and Gurtin, M. E., J. Mech. Phys. Solids, 56 (2008) 640–662)), and is guided by the viscoplastic model and algorithm of Ekh et al. (Ekh, M., Grymer, M., Runesson, K. and Svedberg, T., Int. J. Numer. Meths Engng, 72 (2007) 197–220) whose governing equations are equivalent to those of Gurtin for the purely energetic case. In contrast to the Gurtin formulation and in line with that due to Ekh et al., viscoplasticity in the present model is accounted for through a Perzyna-type regularization. The resulting theory includes three different types of hardening: standard isotropic hardening is incorporated as well as energetic hardening driven by the slip gradient. In addition, as a third type, dissipative hardening associated with plastic strain rate gradients is included. Numerical computations are carried out and discussed for the large strain, viscoplastic model with non-zero dissipative backstress. |
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