Reducing Computational Cost and Allowing Automatic Remeshing in FEM Models of Metal Forming Coupled With Polycrystal Plasticity

Reprinted with permission from AIP Conf. Proc May 17, 2007 Volume 908, pp. 387-392 MATERIALS PROCESSING AND DESIGN; Modeling, Simulation and Applications; NUMIFORM '07; Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Processes; doi:10.1063/1.2740842. Copyright 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of PhysicsInternational audienceThe paper proposes an original use of the Lagrangian particles concept for finite element computation of microstructure evolution in metal forming. The method amounts to distributing incomplete representations of the microstructure among the integration points of the mesh while a complete microstructure is associated with each Lagrangian particle. This decreases the computation time and enables the transport of microstructural variables when remeshing. While the method is presented for any kind of discretized microstructure, it is applied here to the prediction of mechanical anisotropy induced by crystallographic texture. In this specific case, the numerical predictions are validated against experiment by considering compression of a textured aluminium alloy (AA7175). The model accuracy is assessed with respect to mechanical anisotropy but texture evolution is also considered

Modeling of microscopic strain heterogeneity during wire drawing of pearlite

An original strategy is proposed in order bto perform computationally affordable, direct micro-macro simulations of metal forming operations. The model is implemented as a user-defined material law in the abaqus finite element code. This allows accounting for the evolving microstructure in both single and multiphase metallic alloys undergoing large plastic deformation. The model is used here to predict strength and texture development in pearlitic steel. At the scale of individual lamellae, stress equilibrium is enforced across cementite-ferrite interfaces and plasticity is achieved by dislocation glide. Three hypotheses are tested about the interaction of adjacent colonies, including a simplified - so called “multisite”- modeling of the stress and strain partitioning on either sides of planar grain boundary segments. The latter approach gives rise to a slower and more realistic prediction of the texture development and the progressive alignment of cementite lamellae with the loading axis

Prediction of intergranular strains in cubic metals using a multisite elastic-plastic model

A novel approach is adopted for determining the elastic and plastic strains of individual grains within a deformed polycrystalline aggregate. In this approach, termed “multisite modeling”, the deformation of a grain does not merely depend on the grain lattice orientation. It is also significantly influenced by the interaction with one or several of the surrounding grains. The elastic-plastic constitutive law is integrated by identifying iteratively which dislocation slip systems are activated within the grains, and the local stress tensor is shown to be the solution of a linear equation set. Several micro–macro averaging schemes are considered for the distribution of the macroscopic load over the polycrystalline aggregate. These averaging schemes are tested by simulating the development of intergranular strains during uniaxial tension of MONEL-400 as well as commercial purity aluminium. Neutron diffraction measurements of the elastic lattice strains are used as a reference in order to discriminate between the various predictions. The results demonstrate the relevance of “multisite” grain interactions in f.c.c. polycrystals

Finite element prediction of the swift effect based on Taylor-type polycrystal plasticity models

peer reviewedThis paper describes the main concepts of the stress-strain interpolation model that has been implemented in the non-linear finite element code Lagamine. This model consists in a local description of the yield locus based on the texture of the material through the full constraints Taylor’s model. The prediction of the Swift effect is investigated: the influence of the texture evolution is shown up. The LAMEL model is also investigated for the Swift effect prediction

Prediction of the plastic anisotropy of rolled sheets under a combined effect of texture, grain shape and grain size

The present study explores a way to improve predictions of the mechanical anisotropy of textured polycrystalline aggregates. The underlying hypothesis is that grain-shape-dependent backstresses developed during the elastic-plastic transition influence the selection of active slip systems inside individual grains. Recently, a model was developed and applied successfully to electro-deposited pure iron with a columnar grain structure \cite{Delannay2011}. In the present study, we first suggest another definition of the boundary separation distance experienced by individual slip systems. Then, the model is adapted from the case of spheroidal grains, considered initially, to the more general situation of ellipsoidal grains. A combined effect of grain size, grain shape and texture on plastic anisotropy at yielding is illustrated in case of a rolled IF steel sheet

Mean field modelling of the plastic behaviour of co-continuous dual-phase alloys with strong morphological anisotropy

This work addresses the plastic flow properties of a composite material in which the reinforcing phase is continuous and cannot be suitably represented by isolated ellipsoidal inclusions. The dual-phase metal under consideration is composed of a network of Inconel-601 fibres infiltrated by pure aluminium. Hence, both phases exhibit elastic-plastic behaviour and are continuous in the three dimensions of space. The fibre network presents a large morphological anisotropy that is reflected in the mechanical response of the composite. The modelling is based on Eshelby's equivalent inclusion theory. Strain partitioning between the phases is computed incrementally based on tangent operators derived from the isotropic response of individual phases. Assessment of the model relies on extensive experimental data. Uniaxial tensile tests, involving measurement of the Lankford coefficient, have been performed at various temperatures on samples containing different volume fractions of fibres. Measurement of the phase stresses by neutron diffraction supplements the information provided by the macroscopic stress-strain curves. It is demonstrated that predictions are valid only when the micro-macro averaging scheme accounts for the co-continuous character of the constitutive phases. (c) 2006 Elsevier Ltd. All rights reserved

Crystal plasticity prediction of Lankford coefficient using the MULTISITE model: influence of the critical resolved shear stresses

The MULTISITE model [1] is based on polycrystalline plasticity and the underlying hypotheses of the model are (i) that the deformation of each grain is significantly influenced by the interaction with a limited number of adjacent grains, and (ii) that local strains deviate from their macroscopic average according to specific “relaxation modes”. The LAMEL model [2] is reformulated into the more general elastic-viscoplastic MULTISITE model permitting various relaxation modes. This model has been validated for cubic materials but hexagonal close-packed (HCP) crystals usually demonstrate larger anisotropy than cubic crystals. The model was used to simulate uniaxial tensile tests performed on rolled sheets made of Ti-6Al-4V. The Lankford coefficients (r) calculated in various directions in the plane of the sheet were analysed. In this study, different grain interaction hypotheses were tested. Besides, it appeared that the value of the critical resolved shear stresses (CRSS) of the different slip system families of the HCP metal had significant effects on the results. Their influence as well as the influence of the strain rate sensitivity parameter was examined

A texture discretization technique adapted to polycrystalline aggregates with non-uniform grain size

This paper presents a new procedure for the sampling of crystallographic textures into discrete lattice orientations. The method is, for example, useful in order to assign initial grain orientations in crystal-plasticity-based finite element simulation of forming processes. The discretization technique ensures that the orientation sampling is statistically representative of a known orientation distribution function (ODF). Contrary to previous discretization techniques, the new method is valid also when the model microstructure consists of grains with non-uniform size. The accuracy of the texture representation is assessed in the case of cold rolled IF steel. Crystal plasticity theory coupled to finite element modeling is used to predict mechanical planar anisotropy of the sheet. Comparison is made between model predictions assuming, respectively, a uniform or a heterogeneous grain-size distribution. (c) 2005 Elsevier B.V. All rights reserved