Small-scale plasticity critically needs a new mechanics description

Abstract

Continuum constitutive laws describe the plastic deformation of materials as a smooth, continuously differentiable process. However, provided that the measurement is done with a fine enough resolution, the plastic deformation of real materials is often found to comprise discrete events usually nanometric in size. For bulk-sized specimens, such nanoscale events are minute compared with the specimen size, and so their associated strain changes are negligibly small, and this is why the continuum laws work well. However, when the specimen size is in the micrometer scale or smaller, the strain changes due to the discrete events could be significant, and the continuum description would be highly unsatisfactory. Yet, because of the advent of microtechnology and nanotechnolgy, small-sized materials will be increasingly used, and so there is a strong need to develop suitable replacement descriptions for plasticity of small materials. As the occurrence of the discrete plastic events is also strongly stochastic, their satisfactory description should also be one of a probabilistic, rather than deterministic, nature.

Keywords

• dislocations; nanoindentation; plastic deformation; size effects; strength