9700358 Parks A program of constitutive and computational research in crystal plasticity is proposed which is based on the concept of geometrically necessary dislocation density, proportional to certain spatial gradients of crystal shear strain, as providing a physical means to introduce size- dependent plastic response in crystals. The proposed formulation fits nicely with the underlying physical concepts, most clearly described by Ashby over 20 years ago. Among the host of applications where scale-dependent plasticity driven by this mechanism is encountered are the grain-size dependence of flow strength and work-hardening in polycrystals (Hall-Petch effect), size dependence of indentation microhardness, particle-size effects in the dispersion strengthening crystals. and others. In each case, the attainment of locally inhomogeneous shear strain,,over a characteristic geometric length scale,,results approximately in the storage of a geometrically necessary dislocations, where b is the crystal lattice constant. These "geometric" dislocations, which relieve the lattice incompatibility which would otherwise be introduced by conservative dislocation movement in producing the strain gradient, act as obstacles to other (glissile) dislocations, producing very enhanced local hardening. A review of the field shows that the computational methods proposed for dealing with this class of problems are both feasible to implement and are methodologically in good agreement with the materials science understanding. Preliminary computational results on a multi-crystalline aggregate have shown a clear Hall-Petch effect, based on "first principles." The effects of the extra dislocation density, which is concentrated near grain boundaries struggling to deform compatibly, also give rise to distinct patterning of strain within the grain. The proposed extensions of the work will address less idealized versions of the Hall-Petch phenomenon, the deformation of thin metallic layers constrained between ceramics, including thermally-induced misfit strain, and particle size effects in the dispersion strengthening of crystals. The results will be of fundamental scientific value, being a first computational thrust into quantifying scale effects in crystal plasticity and the interactions of statistically stored and geometrically necessary dislocations. Among the industrial applications which could benefit from a robust computational capability to account for scale-dependent plasticity are the mechanical behavior of multi-layer electronic devices and thin films.
