Intrinsic and Extrinsic Size Effects in Plasticity by Dislocation Glide
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Intrinsic and Extrinsic Size Effects in Plasticity by Dislocation Glide
J. Gil Sevillano CEIT (Centro de Estudios e Investigaciones Técnicas de Guípúzcoa) and Faculty of Engineering, University of Navarra. P.O. Box 1555, 20080 San Sebastián, Spain. ABSTRACT A classification of size effects (SE) in plasticity is attempted. "Intrinsic" SE are perceived when any internal length scale directly influencing some process or property interferes with the size of the material region where the process is going on or when two internal length scales directly affecting the same process or property interfere. "Extrinsic" SE arise from the external imposition of spatial gradients in the plastic process or by the building up of internal gradients by the (externally induced) process itself. In dislocation-mediated plasticity plastic strain gradients are resolved by the storage of geometrically necessary dislocations (GND) leading to prominent size effects. Of course, mixed effects with intrinsic and extrinsic contributions can be found as well as superposed effects involving more than two characteristic lengths (i.e., size effects on size effects).The inclusion of both types of SE in continuum or crystallographic theories is commented. INTRODUCTION. The strong impetus experienced by a broad spectrum of micro-technologies has recently awakened the interest on the mechanical behaviour of small volumes. As it has occurred with other physical phenomena, small-scale plasticity has afforded many surprises. Some effects of size on the plastic behaviour, namely the indentation size effect, ISE, on the hardness value of a material, the torsional size effect of small wires or the ductile-brittle size transition observed on crystalline whiskers were known since a long time [1-3]. However, with the exception of the "normal size"/whisker transition, the question of their origin was far from settled and a quantitative explanation for them was not yet conceived. When the technological importance of size effects (SE) on plasticity was highlighted by the publication of a remarkable paper by Ashby and co-workers [4], interest in the exploration and understanding of plastic size effects boomed. That size matters was nothing new for materials scientists and engineers. Structural SE like the Hall-Petch effect on the strength of polycrystals or the strength dependence on the interparticle distance and particle size in precipitation or dispersion strengthened materials, crucial for structural materials design, are very well studied. The abundant structural size/plasticity relationship knowledge could guide the understanding of non-structural size effects of microtechnological interest. In fact, the aforementioned paper [4] already offered a successful link between many non-structural SE and the concept of "geometrically necessary dislocations" (GND) proposed by Nye [5]and applied by Ashby to the extra strengthening of nonhomogeneous materials [6,7]. Atomistic and discrete dislocation approaches to plasticity automatically incorporate internal lengths in t
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