Applications And Development Of Taylor-Based Nonlocal Theory Of Plasticity

There is mounting experimental evidence that materials display strong size effects when the characteristic length scale associated with non-uniform plastic deformation is on the order of microns. The classical plasticity theories possess no internal length scale and can not explain the size dependence of plasticity, which may also be important in explaining the cleavage fracture in ductile materials. Micro-indentation experiments and cleavage fracture in ductile materials, including static crack and quasi-static steady state crack growth, are studied in this paper employing Taylor-based nonlocal theory (TNT) of plasticity, and a finite deformation version of TNT flow theory is developed. The following objectives have been achieved in this paper.1. Effective and robust finite element methods are developed for both infinitesimal TNT deformation theory and flow theory.2. Micro-indentation experiments are investigated using the finite element method. It is established that TNT plasticity agrees well with the micro-indentation hardness data measured from experiments. This demonstrates that TNT plasticity can characterize the plasticity behavior of materials rather accurately at the micron and submicron scales, and this also provides an important self-validation of TNT plasticity.3. Plane strain, mode I static crack tip field is investigated employing the finite element method. It is established that the stress level in the vicinity of crack tip in TNT plasticity is significantly larger than that in classical plasticity. The crack tip stress singularity in TNT plasticity is not only larger than that in HRR field in classical plasticity theory, but also exceeds or equals to the square-root singularity. Moreover, the stress singularity is independent of the plastic hardening exponent. In conjunction with the dislocation mechanism of plasticity deformation, a multiple scale view of fracture is proposed to give a rather good explanation of cleavage fracture in ductile materials.4. Plane strain, mode I quasi-static steady state crack growth is investigated utilizing the finite element method. It is once again established that TNT plasticity can significantly increase the stress level near the crack tip. The crack tip stress singularity is higher than or equal to the square-root singularity of elastic K field and is also independent of the plastic hardening exponent. Once more, this indicates that TNT plasticity provides an alternative mechanism for cleavage fracture in ductile materials.5. The finite deformation version of TNT flow theory is developed under the framework of Rice-Hill finite deformation elastic-plastic theory. Two schemes of finite deformation constitutive relations are given in which the yielding conditions are proposed separately in the initial configuration and the current configuration. An effective finite element method is developed for the second kind of finite deformation constitutive relation scheme and is used to study the plane strain, mode I static crack tip field. Once more, it is established that TNT plasticity can predict a significant stress increase in the vicinity of crack tip. Compared with that in infinitesimal TNT plasticity, the crack tip stress singularity in finite deformation TNT plasticity is closer to the square-root singularity of classical elastic K field.