The Interaction of a Circular Dislocation Pile-up with a Short Rigid Fiber: a 3-D Dislocation Dynamics Simulation
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The Interaction of a Circular Dislocation Pile-up with a Short Rigid Fiber: a 3-D Dislocation Dynamics Simulation Tariq A. Khraishi1 and Hussein M. Zbib2 1 Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, U.S.A. 2 School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164, U.S.A. ABSTRACT This paper presents a dislocation dynamics simulation of the interaction of a circular dislocation pile-up with a short rigid fiber, say as in metal-matrix composites. The pile-up is composed of glide dislocation loops surrounding the fiber. This problem is treated here as a boundary value problem within the context of dislocation dynamics. The proper boundary condition to be enforced is that of no or zero elastic displacements at the fiber’s surface. Such a condition is satisfied by a distribution of rectangular dislocation loops, acting as sources of elastic displacements, meshing the fiber’s surface. Such treatment is similar to crack modeling using distributed dislocations and falls under the category of “generalized image stress analysis.” The unknown in this problem is the Burgers vectors of the surface loops. Once those are found, the Peach-Koehler force acting on the circular dislocation loops, and emulating the fiber’s presence, can be determined and the dynamical arrangement of the circular pile-up evolves naturally from traditional dislocation dynamics analysis.
INTRODUCTION With regard to the interaction of particles and dislocations, most available treatments are rather simplified and consider particles of relatively small size only. This involves the interaction of a moving dislocation line, under resolved shear stress, with obstacles representing solute atoms or larger precipitates [1,2]. For overcoming small pinning points (say brought about by solute atoms), the dislocation must posses a strong enough line tension locally. Also, a gliding dislocation must either cut through precipitates or penetrate an array of them by a bowing action between the obstacles. In the latter case, the particles are relatively large in size. Here the dislocation line tension is not strong enough to shear its way through the particle. Instead, the sweeping dislocation leaves, in its wake, loops (or a pile-up of glide loops) around the obstacles in what is known as the Orowan mechanism. This is the case in metal-matrix composites which are formed by embedding hard particles in a relatively soft matrix. Metal matrix composites (MMCs) contain fibers of diameter 0.3-6.6 µm and of length 3-110 µm [3]. The formation of loops around these fibers represent a dynamic pile-up of dislocations exerting back stress on actively emitting Frank-Read sources. This causes hardening in terms of increased flow stress values [4]. Therefore this interaction problem is important in the context of investigating hardening in MMCs using the fundamental approach of dislocation dynamics. Other work on dislocation-particle interaction include calculating the interaction between an infinite sc
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