Sensitivity of Crystal Stress Distributions to the Definition of Virtual Two-Phase Samples
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ke many other structural alloys, are complex materials that have been developed with performance in mind. Alloying and processing have been optimized to achieve excellent mechanical properties by emphasizing favorable attributes of the microstructure. However, quantitative links between microstructural attributes and consequential mechanical properties often are difficult to establish. This is due in part to efforts to model mechanical behavior being stymied by uncertainties in specifying the microstructural state and crystal properties of virtual samples. For
ANDREW C. POSHADEL and PAUL R. DAWSON are with the Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York. Contact e-mail: [email protected] MICHAEL A. GHARGHOURI is with the Canadian Nuclear Laboratories, Chalk River, ON, Canada. Manuscript submitted June 9, 2018. Article published online January 10, 2019 METALLURGICAL AND MATERIALS TRANSACTIONS A
simulations at the crystal scale, uncertainty enters in the constitutive parameters and in the instantiation of virtual samples. In this paper, we address both of these sources of uncertainty for a duplex steel—LDX-2101. The behavior of this alloy has been examined in Reference 1 in the context of the initiation and propagation of yielding under biaxial loading conditions. The justification for the choices made for the constitutive parameters and in the definition of the virtual samples is presented here based on a thorough examination of these factors. Considerable effort has been devoted to identifying a structural metric for polycrystalline alloys that is a demonstrably predictive indicator of the likelihood that crystals of a specified orientation will yield at lower or higher nominal stress than crystals with other orientations. Polycrystals, both single and polyphase, are comprised of individual crystals with anisotropic elastic and plastic properties. The lattice orientations typically are spread over the range of admissible orientations, sometimes uniformly, but more frequently non-uniformly as a
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consequence of processing. These attributes of polycrystalline solids imply that the mechanical response of polycrystals is statically indeterminate, meaning that to determine the stress and deformation fields for an applied load, the full set of field equations (equilibrium, kinematics of deformation, and constitutive equations) must be solved simultaneously. Simplifying assumptions, such that the stresses within crystals equal the nominal (average) stress, deteriorate as the level of anisotropy increases. The consequence of this behavior is that metrics for yielding that are based on strength alone are not sufficient to capture the response within polycrystals, as the stresses can vary substantially both in their magnitudes and directions (eigenvalues and eigenvectors) among anisotropic crystals. A metric that does account for stress variations as well as the orientation dependence of the strength is the strength-to-stiffness ratio. The stiffness used i
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