Crystal Plasticity from Dislocation Dynamics
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Crystal Plasticity
from Dislocation Dynamics Vasily V. Bulatov, Meijie Tang, and Hussein M. Zbib
Introduction The strength of a material is its ability to withstand an applied load without breaking or changing its shape. The strength of an ideal, defect-free crystal can be very high, but except for rather exotic materials such as micrometer-sized whiskers, crystals will fracture and/or deform plastically under stresses that are well below their ideal strength limits. The principal mechanisms of crystal plasticity involve various crystal defects such as vacancies, interstitials, and impurity atoms (point defects); dislocations (line defects); grain boundaries, heterogeneous interfaces, and microcracks (planar defects); and chemically heterogeneous precipitates, twins, and other strain-inducing phase transformations (volume defects). Most often, dislocations define plastic yield and flow behavior, either as the dominant plasticity carriers or through their interactions with the other strain-producing defects. First introduced as a mathematical concept in the 19th century, the idea of a dislocation as a crystal defect was hypothesized in 1934 simultaneously by Orowan,1 Polanyi,2 and Taylor3 largely to explain the less-than-ideal strength of crystalline materials. Only much later, in the late 1950s, was the existence of dislocations experimentally confirmed.4,5 Presently, these ubiquitous crystal defects are routinely observed by various means of electron microscopy. What a dislocation is can be easily understood by considering that a crystal can deform irreversibly by slip, that is, by shifting or sliding along one of its atomic planes. If the slip displacement is equal to a lattice vector, the material across the slip plane will preserve its lattice structure and the change of shape will become permanent. However, rather than simultaneous sliding of two half-crystals, slip displacement proceeds sequentially, starting
MRS BULLETIN/MARCH 2001
from one crystal surface and propagating along the slip plane until it reaches the other surface. The boundary between the slipped and still-unslipped crystal is a dislocation, and its motion is equivalent to slip propagation. Crystal plasticity by slip is a net result of the motion of a large number of dislocations in response to applied stress. Over the last six decades, experimental and theoretical developments have firmly established the principal role of dislocation mechanisms in defining material strength. It is now beyond any reasonable doubt that the macroscopic plasticity properties of crystalline materials are derivable, at least in principle, from the behavior of their constituent defects. However, this fundamental understanding has not translated into a quantitative physical theory of crystal plasticity based on dislocation mechanisms. One difficulty is the multiplicity and complexity of the mechanisms of dislocation motion and interactions, which leave little hope for a quantitative analytical approach. The situation is further exacerbated by the need to trace the
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