From Micro‐ to Macroplasticity

Abstract

Early results of experimental investigations on microplasticity have been gathered into collected works and treatises. [1][2][3] The plastic events taking place at lower strains are related to short-range dislocation motion [4] and are of different origin than the dislocation mechanism occurring in the macroplastic regime.[5] Therefore, macroplasticity theories based on a mechanism involving long-range dislocation motion cannot serve to predict micro-yielding. In terms of measured stressstrain behavior, the two regimes are poorly distinguished, especially when they are characterized by positive strain-hardening, i.e., an increase in strength when the microstructure is strained. To facilitate comparison of data, metallurgists have come up with the rather arbitrary 0.2 % definition of the macroscopic yield stress. [6,7] It is one of the most frequently used engineering materials parameters and very important for the precise design of functional components ranging from construction materials down to micrometer-sized microelectromechanical (MEMS) devices. In polycrystalline materials, it is taken for granted that the majority of grains are plastically deforming at the macroscopic yield stress. However, there is no easy and suitable method to verify this assumption, and the real amount of strain that should be assigned to microplasticity is unknown. Experimental studies on granular materials have predominantly been performed by precise mechanical testing using load-unload cycles accompanied by surface-visualization techniques. The first experimental investigations on the effect of grain size on microplasticity [8,9] ascribed strain-hardening predominantly to the ability of grain boundaries (GBs) to act as barriers to dislocation motion, where the strain for a given stress varied as the cube of the grain size: large grains showed more strain than smaller grains. However, it was soon recognized that the relationship between microplastic strain and stress was not so simple. When a polycrystal is subjected to an external force, an inhomogeneous state of internal stress is developed resulting from elastic anisotropy and plastic incompatibilities arising from different resolved shear stresses within the different grains. [10] In addition to the fact that plastic yielding does not start at the same time in all grains, it was recognized that internal stresses arising from the elastic interactions of neighboring grains provide additional stresses that activate non-favored slip systems in grain interiors [11] and/or change the maximum shear direction in the vicinity of a GB. The latter may result in GBs emitting dislocations [12,13] on slip systems in the GB region that are different from the primary slip system of the grain interior. [14,15] Several plasticity models have been developed to predict the mechanical behavior in terms of stress-strain and hardening as a function of grain size. Some theories are based on the postulate that geometrically necessary dislocations account for the inherent difference in the accumulation o...

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