Denny Tjahjanto

A novel grain cluster-based homogenization scheme

An efficient homogenization scheme, termed the relaxed grain cluster (RGC), for elasto-plastic deformations of polycrystals is presented. The scheme is based on a generalization of the grain cluster concept. A volume element consisting of eight (= 2 × 2 × 2) hexahedral grains is considered. The kinematics of the RGC scheme is formulated within a finite deformation framework, where the relaxation of the local deformation gradient of each individual grain is connected to the overall deformation gradient by the, so-called, interface relaxation vectors. The set of relaxation vectors is determined by the minimization of the constitutive energy (or work) density of the overall cluster. An additional energy density associated with the mismatch at the grain boundaries due to relaxations is incorporated as a penalty term into the energy minimization formulation. Effectively, this penalty term represents the kinematical condition of deformation compatibility at the grain boundaries.Simulations have been performed for a dual-phase grain cluster loaded in uniaxial tension. The results of the simulations are presented and discussed in terms of the effective stress–strain response and the overall deformation anisotropy as functions of the penalty energy parameters. In addition, the prediction of the RGC scheme is compared with predictions using other averaging schemes, as well as to the result of direct finite element (FE) simulation. The comparison indicates that the present RGC scheme is able to approximate FE simulation results of relatively fine discretization at about three orders of magnitude lower computational cost.

Comparison of texture evolution in fcc metals predicted by various grain cluster homogenization schemes

Abstract We introduce a new material point homogenization scheme – the ‘Relaxed Grain Cluster’ (RGC) – based on a cluster of grains and formulated in the framework of finite deformations. Two variants of this scheme, which allow for different degrees of relaxation, are compared to two variants derived from the infinitesimal-strain grain interaction model regarding the evolution of texture predicted for plane-strain compression of a commercial aluminum alloy. The RGC schemes give the closest match to experimental reference on both the -fiber and the -skeleton line. The intensity of the brass texture component is found to be rather sensitive to the homogenization scheme. However, the observed decrease in texture intensity as a function of the homogenization scheme for the Cu and S component on the -skeleton line can be correlated to the number of degrees of freedom in the cluster which are left unconstrained by the respective scheme. This is in line with the significant dependence of the Cu and S component intensity on boundary conditions reported in earlier studies.

Multiscale deep drawing analysis of dual-phase steels using grain cluster-based RGC scheme

Multiscale modelling and simulation play an important role in sheet metal forming analysis, since the overall material responses at macroscopic engineering scales, e.g. formability and anisotropy, are strongly influenced by microstructural properties, such as grain size and crystal orientations (texture). In the present report, multiscale analysis on deep drawing of dual-phase steels is performed using an efficient grain cluster-based homogenization scheme.The homogenization scheme, called relaxed grain cluster (RGC), is based on a generalization of the grain cluster concept, where a (representative) volume element consists of p?????q?????r (hexahedral) grains. In this scheme, variation of the strain or deformation of individual grains is taken into account through the, so-called, interface relaxation, which is formulated within an energy minimization framework. An interfacial penalty term is introduced into the energy minimization framework in order to account for the effects of grain boundaries.The grain cluster-based homogenization scheme has been implemented and incorporated into the advanced material simulation platform DAMASK, which purposes to bridge the macroscale boundary value problems associated with deep drawing analysis to the micromechanical constitutive law, e.g. crystal plasticity model. Standard Lankford anisotropy tests are performed to validate the model parameters prior to the deep drawing analysis. Model predictions for the deep drawing simulations are analyzed and compared to the corresponding experimental data. The result shows that the predictions of the model are in a very good agreement with the experimental measurement.