Physical theory of plasticity: a multicrystal model

Abstract

Single crystal tests [1, 2] have shown that under stress, slip occurs along certain crystal directions on certain crystal planes and slip depends on the resolved shear stress and is independent of the normal stress on the sliding plane. This resolved shear stress that initiates or causes the continuation of slip is called the critical shear stress, which varies with the amount of slip. After the relation between the resolved shear stress and slip was experimentally determined for single crystals, many early attempts were made to deduce the uniaxial stress-strain relation of a polycrystal from the stress-strain relation of single crystals. The first realistic model was proposed by Taylor [2]. He assumed all grains to have the same homogeneous strain as that imposed on the aggregate and also assumed the crystals to be rigid-plastic. The neglect to elastic strain in Taylor’s model gives significant error when the elastic strain is of a comparable magnitude to the plastic strain. Lin [3] extended Taylor’s model to include elastic strain. Recently, Tokuda, Kratochvril and Ohashi [4] also assumed uniform strain, elastic plus plastic in a simplified two-dimensional polycrystal and calculated the variation of macroscopic stress under some arbitrary strain paths. The calculated values were found to agree well with experimental results. All these theories satisfy the condition of compatibility but not the condition of equilibrium across the grain boundaries.