Plastic flow localization analysis of heterogeneous materials using homogenization-based finite element method
Plastic flow localization analysis of heterogeneous materials using homogenization-based finite element method
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DOI：
10.1016/j.ijmecsci.2013.03.015
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发表时间：
2013-07
影响因子：
7.3
通讯作者：
Y. Tadano;Kengo Yoshida;M. Kuroda
中科院分区：
文献类型：
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作者：
Y. Tadano;Kengo Yoshida;M. Kuroda
提出了一种新的预测塑性流动局部化的框架。所提出的框架结合了经典的应变局部化分析与基于均匀化的有限元方法，并具有很高的适用性，以各种类型的材料与特征的微观结构，可能有显着的异质性，只要其代表性的体积元素可以表示的有限元离散化。根据所提出的方法，在宏观分析中，仅取一个或两个材料点就可以进行塑性流动局部化分析。这意味着，涉及非常复杂的微观结构的材料的局部化分析，这是很难令人满意地处理在一个完全的微观-宏观耦合有限元分析与均匀化方法，可以进行合理的计算成本。作为该框架的实际应用，本文考虑了平面应力形式的Marciniak-Kuczyelski型（M-K）方法，计算了FCC多晶板的成形极限应变。采用晶体塑性理论作为每个晶粒的本构模型，并使用基于均匀化的有限元方法来评估用于M-K型板颈缩分析的平均材料响应。通过数值收敛分析确定了均匀化过程中代表体元的合适尺寸，并研究了晶粒几何构型对均匀化结果的影响。在此基础上，计算了织构材料的成形极限应变。计算结果与传统的泰勒型多晶模型进行了比较。
A novel framework to predict the onset of plastic flow localization is presented. The proposed framework combines a classical strain localization analysis with a homogenization-based finite element method, and has high applicability to various types of material with a characteristic microstructure that may have significant heterogeneity as long as its representative volume element can be represented by a finite element discretization. According to the proposed method, a plastic flow localization analysis can be performed taking only one or two material points in macroscopic analysis. This means that localization analysis of materials involving very complex microstructures, which is hard to be satisfactorily treated in a fully micro-macro-coupled finite element analysis with the homogenization approach, can be carried out with a reasonable computational cost. As a practical application of the proposed general framework, a plane stress version, that is, a Marciniak–Kuczyński-type (M–K) approach, is considered, then the forming limit strains of FCC polycrystalline sheets are evaluated. Crystal plasticity theory is adopted as a constitutive model for each crystal grain, and the homogenization-based finite element method is used to evaluate the average material response to be used in M–K-type sheet necking analysis. A numerical convergence analysis is conducted to determine the appropriate size of the representative volume element in the homogenization, and the effect of the geometrical configuration of crystal grains is studied. Then, the forming limit strains of a textured material are evaluated. The computational results are compared with those obtained using the conventional Taylor-type polycrystalline model.