Constitutive Behavior Based on Crystal Plasticity

Constitutive equations are the vehicle by which our knowledge of material behavior enters into engineering design. At the very least, they should be sufficiently accurate. This could be—and frequently is—achieved by an empirical description based on data obtained under conditions that essentially duplicate those of the specific application. Of more general usefulness are relations that can be applied under a wide range of conditions and for many materials, containing a number of materials parameters (the fewer the better), which can be measured in simple tests. Such general relations can be expected to be found only if they fulfill two conditions: they must be phenomenologically sound; and they should be based on as much of the underlying physics as can be ascertained with some confidence. The closer the phenomenological description reflects the actual physical processes involved, the further it can be extrapolated beyond the range of variables for which it was measured.