Constitutive Description of Isotropic and Anisotropic Plasticity for Metals
Modeling of the plastic behavior for isotropic and anisotropic metals is the topic of this article. The motivation for such work is briefly introduced. Then, a description of the main features of plastic deformation in metals at different scales is summar
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*†
and Myoung-Gyu Lee
*
* Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, Republic of Korea † Currently at Institute for Virtual Manufacturing (IVP), ETH Z¨ urich, Switzerland
Abstract Modeling of the plastic behavior for isotropic and anisotropic metals is the topic of this article. The motivation for such work is briefly introduced. Then, a description of the main features of plastic deformation in metals at different scales is summarized to prepare the subsequent choices and assumptions made in the next sections. The main properties of the Cauchy stress tensor are reviewed because it is the main variable for plastic yielding. The description of plasticity for isotropic metals is discussed, which includes the yield condition, the flow rule and strain hardening. Then, the generalization of the concepts to plastic anisotropy, which is particularly important to the case of metal sheets and plates, is outlined. Finally, the influence of the constitutive description for plasticity on failure is briefly discussed using two examples.
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Motivation
Numerical simulations based on the finite element (FE) approach are very useful to optimize manufacturing processes and predict product performances. Accurate results are achievable if sufficient consideration is given to the choice of key features, including type of mesh, boundary conditions and material constitutive behavior. The latter, in particular the plastic behavior of metals, is the topic of this paper. In plasticity, multi-scale modeling has been instrumental for understanding the relationship between macroscopic properties and microstructural features at different scales and has been successfully applied for material design (McDowell, 2010). Philosophically, multi-scale is a very comprehensive and interpretive approach to constitutive modeling. However, in many instances, it does not address very well practical needs when simple, yet accurate, material models with timeefficient implementations in commercial finite element codes are required. This is a domain where continuum descriptions are still very powerful. H. Altenbach, T. Sadowski (Eds.), Failure and Damage Analysis of Advanced Materials, CISM International Centre for Mechanical Sciences DOI 10.1007/978-3-7091-1835-1_2 © CISM Udine 2015
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F. Barlat and M. G. Lee
The goal of this article is to describe how to model plasticity for metallic materials at the continuum scale while keeping, in an approximate way, some aspects of the microstructure in the formulation. In order to develop macroscopic constitutive models that are relevant to metals and capture in a simplified way their structure, it is important to understand the relationship between macroscopic plastic properties and microscopic deformation mechanisms. These two aspects will be briefly discussed in Sect. 2. Section 3 will review the main properties of the stress tensor. The constitutive modeling of plasticity for isotropic and anisotropic metals will be introduced in Sects 4 and 5, respectively. Finally, applications
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