Non-associated plastic flow and effects on macroscopic failure mechanisms
This dissertation focuses on the implications of non-associated flow on plastic deformation. The physical basis of conventional macroscopic plasticity theories for crystalline solids is a simple slip mechanism, one that is controlled only by the shear stress on the slip plane in the direction of slip. This is somewhat, exceptional behavior since in all but FCC lattices the core structures of screw dislocations tend to be three dimensional (non-planar) and, as a result, slip depends upon so-called non-glide stresses. The effects of non-glide stresses result in non-associative flow behavior in both single and polycrystals. Frictional materials such as rock and sand are typically modeled as non-associated flow as well. ^ In this work the effects of non-glide stresses are shown to persist at macroscopic scales and strongly affect deformation behaviors. For example, the critical pressure at which cavitational instabilities occur and critical necking strains are significantly affected by non-associated flow. The structure of constitutive models is studied in detail, and new relations are proposed. In classical, rate-independent non-associated flow models uniqueness and stability of solutions to incremental boundary value problems can be lost even at small strains. However, in a corner theory, a deformation theory, or a rate-dependent theory we demonstrate that uniqueness and stability can be guaranteed at small deformations. Non-associated flow is shown to significantly alter strain localization in thin sheets (sheet necking), and this class of problems is studied in detail. The effects are most prominent near the plane strain loading state. To investigate the full three-dimensional nature of instabilities in sheet deformation, a finite element analysis is carried out for nearly rate-insensitive response using an implicit dynamics scheme. This led to the discovery of "strain bursts" as a consequence of non-associated flow, particularly for deformations near the plane strain loading state. Finally, preliminary investigations of effects of non-associated flow on crack tip fields (for plane strain conditions and Mode I loading) reveal that the crack tip fields are of the HRR type, and their amplitudes are slightly affected by non-associated flow. ^
"Non-associated plastic flow and effects on macroscopic failure mechanisms"
(January 1, 2007).
Dissertations available from ProQuest.