Strain Gradient Plasticity Theory Based On Taylor Dislocation Model With Non-classical Vector-like Stress

Many recent experiments have shown that materials display strong size effects when the characteristic length scale is on the order of microns or submicrons: the smaller, the harder. The classical plasticity theories can not predict this size dependence of material behavior because their constitutive models possess no internal length scale. Therefore, it is necessary to establish new constitutive models—strain gradient plasticity theories which possess the intrinsic material length.This dissertation is focused on lower-order strain gradient plasticity theories and higher-order strain gradient plasticity theories whose non-classical stress is a vector. Furthermore, finite deformation versions of these higher-order theories are also established.The lower-order strain gradient plasticity theory retains the essential structure of classical plasticity theory, and does not seem to require additional, non-classical boundary conditions. The well-posedness of lower-order strain gradient plasticity theory is studied by the method of characteristics for nonlinear partial differential equations. For Niordson and Hutchinson's problem of an infinite layer in shear, the "domain of determinacy" for Bassani's lower-order strain gradient plasticity theory is obtained. It is also established that, as the applied shear stress increases, the "domain of determinacy" shrinks and eventually vanishes. The additional, non-classical boundary conditions are needed for Bassani's lower-order strain gradient plasticity in order to obtain the solution outside the "domain of determinacy". Within the "domain of determinacy", the present results agree well with Niordson and Hutchinson's finite difference solution. Outside the "domain of determinacy", the solution may not be unique.Within Fleck and Hutchinson's theoretical framework of strain gradient plasticity theory and based on the Taylor dislocation model, we develop a newstrain gradient plasticity theory. We also present a few examples that display strong size effects at the micron and submicron scales, including the shear of an infinite layer, torsion of thin wires, bending of thin beams, growth of microvoids, and film-substrate subject to biaxial loading. These examples show that this new strain gradient plasticity theory based on the Taylor dislocation model captures the strong size effects.At the micron and submicron scales, film experiments and dislocation simulations are significant for the studying of size effects. We investigate Yu and Spaepen's copper-Kapton tension experiment by using our strain gradient theory. Our results can not only predict the size effects but also agree well with the relation predicted by Venkatraman et al. and Nix between the yielding stress of a film bonded to a substrate and the thickness of the film. On the other hand, we use the same strain gradient plasticity theory to investigate Shu et al.'s dislocation simulation of an infinite layer in shear, and we find that our intrinsic material length parameter is at the micron scale.We obtain the finite deformation versions of Fleck and Hutchinson's strain gradient plasticity theory as well as ours. We study the torsion of thin wires by using the finite deformation theories. Our results show that there is difference between finite deformation theories and infinitesimal deformation theories.