Stress Localization Resulting from Grain Boundary Dislocation Interactions in Relaxed and Defective Grain Boundaries
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UCTION
DURING the plastic deformation of metals, stress and strain can be highly localized near grain boundaries (GBs). These localization phenomena can be due to GB plasticity mechanisms such as sliding and migration of, and the interaction of dislocations with, the grain boundary. Upon encountering a grain boundary, dislocations may be piled up against the boundary, obstructed, absorbed, reflected, or transferred to the adjacent grain. The development of stresses caused by dislocation–GB interactions depends on the extent to which each of these mechanisms is activated, which in turn is dependent on the details of the orientation and relaxation state of the grain boundary.[1–3]
BRYAN KUHR and DIANA FARKAS are with the Department of Materials Science and Engineering, Virginia Polytechnic Institute and State University, 213 Holden Hall, 445 Old Turner Street Blacksburg, VA 24061. Contact e-mail: [email protected] IAN M. ROBERTSON is with the Department of Materials Science and Engineering, University of Wisconsin, 1415 Engineering Drive, Madison, WI 53706. DREW JOHNSON and GARY WAS are with the Nuclear Engineering and Radiological Sciences Department, University of Michigan, Ann Arbor, MI 48109. Manuscript submitted June 12, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS A
A high concentration of dislocations near the GB can result in strain and stress localization. For example, stress localization caused by dislocation channeling has been identified as a contributing mechanism to the loading response of irradiated polycrystalline FCC metals.[4–7] When dislocation slip is not transferred to the adjacent grain, dislocation pile-up induces a region of highly localized stress and strain at the intersection.[8–14] These highly localized stresses could be an important contribution to irradiation assisted stress corrosion cracking, for example by the cracking of the native oxide to expose the base metal in stainless steel to the water coolant.[15] Understanding the evolution of the local stress fields as dislocations arrive and pile up at a grain boundary is therefore critical. One possible approach is to use continuum solutions. Continuum solutions by Stroh[16] and Eshelby[17] assume that n dislocations are piled up in a channel behind a single locked dislocation and that n is a large number. These dislocations are found to be in force equilibrium when their positions along the channel correspond to the zeroes of an nth order Laguerre polynomial. The spacing between dislocations scales with the distance from the pinning point. The stored dislocation concentration in a crystal can be calculated given the curvature of lattice distortions using the relations established by Nye.[18] Such distortions can
be estimated experimentally using electron backscattering diffraction (EBSD).[19,20] The continuum solutions by Stroh and Eshelby[16,17] calculate the stress along a half line originating at the GB and continuing into the opposite grain. This stress decays from its maximum amplitude at that pinned location with the inverse root of
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