Role of Anisotropic Strength and Stiffness in Governing the Initiation and Propagation of Yielding in Polycrystalline So
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CRYSTALS exhibit both elastic and plastic anisotropy. The elastic anisotropy is intrinsically linked to the crystal structure making it dependent on crystallographic orientation. Plastic deformation due to crystallographic slip occurs on a limited number of slip systems, a mechanism referred to as restricted slip. For a prescribed stress state, some crystallographic orientations are more favorable for slip than others. Thus, the directional strength of a crystal also exhibits orientational dependence. For uniaxial loading, the elastic response is characterized by the directional modulus (stiffness) and the orientational dependence of strength is typically characterized by either the Schmid or Taylor factor.[1] The Schmid factor is based on an isostress assumption, which satisfies equilibrium, whereas the Taylor factor is based on an isostrain assumption, which satisfies compatibility. Both factors relate the macroscopic yield stress (strength) to the critical resolved shear stress on a slip system. While these metrics are useful for describing an individual crystal’s properties, neither is effective for predicting the onset of yielding in the context of a polycrystal. In polycrystals, crystals yield when the stress reaches the critical resolved shear stress,
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: [email protected] Manuscript submitted June 9, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS A
just as with single crystals. However, neither the stresses nor the strains among the crystals are identical, owing to the anisotropy of the elastic behavior. As explained below, the onset of yielding depends on both the strength and the stiffness of the constituent crystals, and a parameter that embodies both of these is needed to contrast the relative responses of crystals to predict the onset of yielding. In Reference 2 it was demonstrated for uniaxial loading that it is the ratio of directional strength to directional stiffness, rather than the directional strength alone, which correlates with the order in which crystals yield. Stiffness is important in determining the order in which crystals yield because of the deformation compatibility constraints imposed on a grain in a polycrystalline aggregate by its neighbors. To illustrate this point, the authors presented a simple analogy of two materials, one stiff and strong and the other weak and compliant, loaded in parallel between two rigid plates. For this isostrain condition, they showed that the stiff, strong material can yield at a lower applied stress than the weak compliant material—it is the ratio of strength-to-stiffness that governs which material yields first. They developed two formulations for the strength-to-stiffness parameter. The first, which they termed the single-crystal strength-to-stiffness, was formulated for isolated single crystals. In this case, the strength-to-stiffness ratio is defined as the ratio of the reciprocal Schmid factor to the d
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