The Plasticity of an Isotropic Aggregate of Anisotropic Face-Centered Cubic Crystals

The plasticity of a polycrystalline aggregate is expressed in terms of the plasticity of the individual grains. It is assumed that the local deviation of stress from the average stress is proportional to the local deviation of strain from the average strain, and it is assumed that plastic flow begins when there is an average of three active slip systems per grain. The plastic states of a grain are mapped as a function of the orientation of the crystallographic axes. A coexistence of different states of strain with different rotations of the axes at the same state of stress can be correlated with the occurrence of deformation bands. A range of orientations is illustrated in which the axes tend to congregate quickly and then move more slowly toward a stable end orientation. The residual strain which would be observed by x-ray diffraction after the release of stress is calculated for three sets of diffracting planes. The applications of the theory have so far been limited to face-centered cubic polycrystals with intrinsic elastic isotropy.