Crystal plasticity: micro-shear banding in polycrystals using voronoi tessellation
Crystal plasticity: micro-shear banding in polycrystals using voronoi tessellation
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DOI：
10.1016/s0749-6419(98)00022-9
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发表时间：
1998-10
影响因子：
9.8
通讯作者：
O. Watanabe;H. Zbib;Eiji Takenouchi
中科院分区：
文献类型：
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作者：
O. Watanabe;H. Zbib;Eiji Takenouchi
泰勒型多晶模型以及新的时间积分方案已被开发并实施到有限元程序中，以模拟面心立方金属单晶和多晶中微剪切带的发展。为了利用与对称刚度矩阵相关的数值优势，由晶体塑性公式产生的刚度张量被对称化，并相应地重新排列本构方程。结果表明，这种方法可以显着减少计算时间，而不影响数值结果。使用 Voronoi 曲面细分分析多晶的介观行为，其中使用 Delaunay 网络生成微观结构的随机性，从该网络生成晶粒的随机分布。研究了使用 3 节点和 4 节点单元来分析多晶中的剪切带现象。结果表明，使用三角形单元来捕获多晶中的剪切带现象主要取决于网格设计，因为所得网格高度不均匀。然而，这个问题通过使用集成度降低的 4 节点单元得到了解决，说明了使用不均匀网格在多晶中形成微剪切带。
A Taylor-type polycrystalline model, together with a new time-integration scheme, has been developed and implemented into a finite element program to simulate the development of micro shear bands in single- and polycrystal of fcc metals. In order to take numerical advantages associated with a symmetric stiffness matrix, the stiffness tensor which arises from the crystal plasticity formulation is symmetrized and the constitutive equation is rearranged accordingly. It is shown that this approach yields significant reduction in computational time without affecting the numerical results. The mesoscopic behavior of polycrystals is analyzed using Voronoi tessellation in which the randomness of the microstructure is generated using a Delaunay network from which a random distribution of grains is generated. The use of 3-node and 4-node elements to analyze the phenomena of shear banding in polycrystals is investigated. It is shown that the use of triangular elements to capture the shear banding phenomenon in polycrystals depends critically on the mesh design, since the resulting mesh is highly nonuniform. However, this problem is resolved by using a 4-node element with reduced integration, illustrating the formation of micro shear bands in a polycrystal using a nonuniform mesh.