Parallel Computing of Multi‐scale Finite Element Sheet Forming Analyses Based on Crystallographic Homogenization Method
Since the multi-scale finite element analysis (FEA) requires large computation time, development of the parallel computing technique for the multi-scale analysis is inevitable. A parallel elastic/crystalline viscoplastic FEA code based on a crystallographic homogenization method has been developed using PC cluster. The homogenization scheme is introduced to compute macro-continuum plastic deformations and material properties by considering a poly- crystal texture. Since the dynamic explicit method is applied to this method, the analysis using micro crystal structures computes the homogenized stresses in parallel based on domain partitioning of macro-continuum without solving simultaneous linear equations. The micro-structure is defined by the Scanning Electron Microscope (SEM) and the Electron Back Scan Diffraction (EBSD) measurement based crystal orientations. In order to improve parallel performance of elastoplasticity analysis, which dynamically and partially increases computational costs during the analysis, a dynamic workload balancing technique is introduced to the parallel analysis. The technique, which is an automatic task distribution method, is realized by adaptation of subdomain size for macro-continuum to maintain the computational load balancing among cluster nodes. The analysis code is applied to estimate the polycrystalline sheet metal formability.
Development of Dynamic Explicit Crystallographic Homogenization Finite Element Analysis Code to Assess Sheet Metal Formability
The crystallographic texture evolution induced by plastic deformation in the sheet metal forming process has a great influence on its formability. In the present study, a dynamic explicit finite element (FE) analysis code is newly developed by introducing a crystallographic homogenization method to estimate the polycrystalline sheet metal formability, such as the extreme thinning and “earing.” This code can predict the plastic deformation induced texture evolution at the micro scale and the plastic anisotropy at the macro scale, simultaneously. This multi‐scale analysis can couple the microscopic crystal plasticity inhomogeneous deformation with the macroscopic continuum deformation. In this homogenization process, the stress at the macro scale is defined by the volume average of those of the corresponding microscopic crystal aggregations in satisfying the equation of motion and compatibility condition in the micro scale “unit cell,” where the periodicity of deformation is satisfied. This homogenization a...
Drawability assessment of BCC steel sheet by using elastic/crystalline viscoplastic finite element analyses
Abstract Elastic/crystalline viscoplastic finite element (FE) analyses were carried out to asses the drawability of three kinds of BCC steel sheets, such as mild steel, dual-phase steel and high-strength steel, in the cylindrical cup deep drawing processes. In this study, the crystal orientations were obtained by X-ray diffraction and orientation distribution function (ODF) analyses. The measured ODF results have revealed clearly different textures of sheets, featured by orientation fibers, skeleton lines and selected orientations in Euler angle coordinate space, which can be related to the plastic anisotropy. An orientation probability assignment method, which can be categorized as an inhomogenized material modeling, was used in this FE modeling. The orientations were determined from the measured ODF and assigned to FE integration points one by one. Numbers of integration points, which represent crystallites and can rotate individually, are employed to represent textures of the sheet metals for taking account of the initial and evolutional plastic anisotropy without introducing Taylor or Sachs homogenization assumption. The FE analyses showed how the fiber textures affect the strain localization and earing in the deep drawing operation. It was confirmed by comparison with experimental results that this FE code could predict the extreme strain localization and earing with good accuracy and assess the sheet drawability.