A Methodology to Evaluate Continuum-Scale Yield Surfaces Based on the Spatial Distributions of Yielding at the Crystal S
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A physically based methodology that explicitly incorporates a polycrystalline solid’s microstructure is presented for calculating its macroscopic yield surface. The methodology analyzes the spatial distribution of the onset of yielding at the crystal (micro) scale. This distribution is predicted using a correlation between the multiaxial strength-to-stiffness ratio and the likelihood of a crystal yielding locally that has been reported previously in References 1 and 2. The multiaxial strength-to-stiffness ratio is determined from the elastic response of a virtual sample of the solid and the single crystal yield surface for the constituent crystals. A macroscopic yield detection algorithm is employed to decide if the spatial distribution of yielding at the crystal scale is sufficient to render yielding of the full sample macroscopically. To demonstrate the new methodology, the yield surface is evaluated for the dual-phase, stainless steel, LDX-2101. This alloy has nearly equal volume fractions of austenite [face-centered cubic (FCC)] and ferrite [body-centered cubic (BCC)]. For a number of biaxial stress conditions, points on the yield surface are evaluated and then used to construct a complete plane-stress yield surface. To assess the yield surface’s
ANDREW C. POSHADEL and PAUL R. DAWSON are with the Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853. Contact e-mail: paul.dawson@ cornell.edu Manuscript submitted June 9, 2018. Article published online March 27, 2019 2640—VOLUME 50A, JUNE 2019
predictive capabilities, the stress defined by the yield surface is compared to the stress computed using an elastic-plastic finite element simulation for several different biaxial stress conditions. The latter simulations were carried out to a load sufficient to induce plastic flow throughout the sample using a formulation that had been thoroughly validated against experiments, as reported in Reference 2. A second macroscopic yield surface is constructed for the same material using different relative values of the austenite and ferrite slip system strengths. In particular, phase strengths differing by a factor of two, instead of being equal, were assumed (in both cases, the alloys have the same volume-averaged strength). The two examples effectively illustrate that the new methodology provides an efficient approach for building a continuum-scale yield surface that explicitly accounts for microstructural structural features like phase properties, phase topology, grain morphology, and crystallographic texture. The paper starts with a brief summary of yield surfaces at the single crystal and the continuum scales. Next, an overview of the complete process of evaluating the macroscopic yield surface is presented, along with summaries of the main components of the method. This includes the multiaxial strength-to-stiffness parameter, the local yield predictor, and the algorithm for detecting macroscopic yield in a sample with a distribution of local yielding. Following these summaries, the finite element
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