Ghorbani Moghaddam Masoud, Achuthan Ajit, Bednarcyk Brett A, Arnold Steven M, Pineda Evan J
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699, USA.
NASA Glenn Research Center, Cleveland, OH 44135, USA.
Materials (Basel). 2016 May 4;9(5):335. doi: 10.3390/ma9050335.
A multiscale computational model is developed for determining the elasto-plastic behavior of polycrystal metals by employing a single crystal plasticity constitutive model that can capture the microstructural scale stress field on a finite element analysis (FEA) framework. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, the stand-alone GMC is applied for studying simple material microstructures such as a repeating unit cell (RUC) containing single grain or two grains under uniaxial loading conditions. For verification, the results obtained by the stand-alone GMC are compared to those from an analogous FEA model incorporating the same single crystal plasticity constitutive model. This verification is then extended to samples containing tens to hundreds of grains. The results demonstrate that the GMC homogenization combined with the crystal plasticity constitutive framework is a promising approach for failure analysis of structures as it allows for properly predicting the von Mises stress in the entire RUC, in an average sense, as well as in the local microstructural level, , each individual grain. Two-three orders of saving in computational cost, at the expense of some accuracy in prediction, especially in the prediction of the components of local tensor field quantities and the quantities near the grain boundaries, was obtained with GMC. Finally, the capability of the developed multiscale model linking FEA and GMC to solve real-life-sized structures is demonstrated by successfully analyzing an engine disc component and determining the microstructural scale details of the field quantities.
通过采用能够在有限元分析（FEA）框架下捕捉微观结构尺度应力场的单晶塑性本构模型，开发了一种多尺度计算模型，用于确定多晶金属的弹塑性行为。采用广义单元法（GMC）细观力学模型对局部场量进行均匀化处理。首先，独立的GMC用于研究简单的材料微观结构，如在单轴加载条件下包含单晶粒或双晶粒的重复单元胞（RUC）。为了进行验证，将独立GMC得到的结果与包含相同单晶塑性本构模型的类似FEA模型的结果进行比较。然后将这种验证扩展到包含数十到数百个晶粒的样品。结果表明，GMC均匀化与晶体塑性本构框架相结合是一种很有前途的结构失效分析方法，因为它能够在平均意义上以及在局部微观结构水平（即每个单独的晶粒）上正确预测整个RUC中的von Mises应力。使用GMC在计算成本上节省了两到三个数量级，但以预测的一些精度为代价，特别是在局部张量场量的分量和晶界附近的量的预测方面。最后，通过成功分析发动机盘组件并确定场量的微观结构尺度细节，证明了所开发的将FEA和GMC联系起来的多尺度模型求解实际尺寸结构的能力。
