Finite-element calculations of the lattice rotation field of a tensile-loaded nickel-based alloy multicrystal and compar
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I. INTRODUCTION
IN the description of the mechanical behavior of polycrystalline materials, homogenization approaches are often used to predict the macroscopic properties.[1] According to the so-called self-consistent scheme, for instance, one computes the interaction between different phases in an unlimited area. However, parameters such as grain size and transgranular stress and strain heterogeneities are not taken into account. In the following article, a finite-element approach with a crystal-plasticity model at each integration point is used.[2,3] Thanks to the introduction of finite elements at the grain scale, the grain size and its morphology become an additional parameter in the description of the mechanical behavior of a polycrystal. In order to describe the entire microstructure of a sample, a multicrystalline microstructure is considered. The word multicrystal, instead of polycrystal, denotes a sample with a small number of large grains (Figure 1). The chosen material is the nickel-based INCO600,* a solid*INCO is a trademark of INCO Alloys International, Huntington, WV.
solution-strengthened alloy.[4] It has been heat-treated in order to obtain large recrystallized grains. The specimen studied in this work, represented in Figure 1, contains a small number of grains across the sample thickness, so that an entire meshing of the microstructure is possible. A flat sample with five grains in the gage area is considered, under tensile loading
F. EBERL, formerly Doctor with LM3, Ecole Nationale Supe´rieure d’Arts et Me´tiers Paris, 78013 Paris, France, is Research Engineer, Pechiney-CRV, 38340 Voreppe, France. S. FOREST, Researcher, and G. CAILLETAUD, Professor, are with the Centre des Mate´riaux, Ecole des Mines de Paris, 91003 Evry Cedex, France. Contact e-mail: [email protected] T. WROBLEWSKI, Professor, is with DESY-HASYLAB, D-22603 Hamburg, Germany. J.L. LEBRUN, formerly Doctor with LM3, Ecole Nationale Supe´rieure d’Arts et Me´tiers Paris, is Professor, LPMI, Ecole Nationale Supe´rieure d’Arts et Me´tiers Angers, 49100 Angers, France. Manuscript submitted June 12, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS A
conditions at room temperature. Under these conditions, only octahedral slip was expected and was, in fact, observed. The validation of the model has to be done on the grain scale and on the macroscopic scale of the entire sample. In Reference 5, the transgranular stress field was evaluated using an X-ray microbeam technique. The stress tensor could be determined at different locations within the grain and compared to the numerically calculated transgranular stress field. In the present study, the evolution of the crystallographic orientation within the grain is of interest. The introduction of a small-strain and small-rotation formalism is sufficient to calculate the lattice orientation at each integration point for each loading step, for the investigated range of tensile loading conditions. Generally, for the experimental analysis of stress and strain heterogeneities on the transgr
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