On large-strain finite element solutions of higher-order gradient crystal plasticity
On large-strain finite element solutions of higher-order gradient crystal plasticity
复制标题
高阶梯度晶体塑性的大应变有限元解
DOI：
10.1016/j.ijsolstr.2011.08.008
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发表时间：
2011
影响因子：
3.6
通讯作者：
M. Kuroda
中科院分区：
文献类型：
--
作者：
M. Sato;Y. Matsuki;I. Hayashi;M. Kuroda;M. Kuroda
将考虑几何必要位错(GND)产生的背应力效应的有限应变高阶梯度晶体塑性模型应用于平面应变有限元分析。对不同的单元类型进行了试验，以寻找一种可靠的、对解决严重塑性变形问题有用的单元公式。在目前的有限元公式中，GND密度率被选为附加节点自由度。采用不同阶次的形函数对位移速率和GND密度速率进行内插。通过考虑三个边值问题：约束层(膜)的简单剪切、位错不能穿透加载表面的压缩问题和涉及剪切带形成的拉伸问题，详细考察了它们对解的影响。在所有情况下，对于位移速率和GND密度率，分别采用八节点减积单元和四节点全积分单元的公式给出了合理的解。除了讨论有限元的选择外，还利用得到的可靠计算结果研究了梯度相关固体中的详细行为，如GND密度的累积和每个滑移系统上的背应力分布。
A finite-strain higher-order gradient crystal plasticity model accounting for the backstress effect originating from the existence of geometrically necessary dislocations (GNDs) is applied to plane strain finite element analysis. Different element types are tested to seek out an element formulation that is reliable and useful for solving problems involving severe plastic deformation. In the present finite element formulation, the GND density rates are chosen to be additional nodal degrees of freedom. Different orders of shape functions are employed for the interpolation of displacement rates and GND density rates. Their effects on solutions are examined in detail by considering three boundary value problems: a simple shear of a constrained layer (a film), a compression problem with loading surfaces impenetrable to dislocations, and a tension problem involving shear band formation. In all the cases, the formulation in which eight-node elements with reduced integration and four-node elements with full integration are used respectively for displacement rates and the GND density rates gives reasonable solutions. In addition to the discussion on the choice of finite elements, detailed behavior in gradient-dependent solids, such as the accumulation of GND density and the distribution of backstress on each slip system, is investigated by utilizing the reliable computational results obtained.