Fracture And Finte Deformation Of Strain Gradient Plasticity Theory

Many experiments have shown that materials display strong size effects when the characteristic length scale is on the order of microns: the smaller, the stronger. The classical plasticity theories can not predict this size dependence of material behavior at the micron scale because their constitutive models possess no internal length scale. Therefore, it is necessary to establish a micron level continuum theory (strain gradient plasticity theory) considering the intrinsic material length.This paper is focussed on the mechanism-based strain gradient (MSG) deformation plasticity theory. Furthermore, the stretch and rotation gradient (SG) theory is mentioned incidentally in some part of the research.Micro-indentation and fracture are studied using MSG theory. The results of micro-indentation show that MSG theory agree very well with experimental data, with indent depth from one tenth of a micron to several microns, indicating that MSG theory are capable of characterizing the plastic behavior rather accurately at the micron and submicron scales. The purpose of the fracture studies is focussed on the increase of stress level around the crack tip in order to explain the observed cleavage fracture in ductile materials. The results show that the stress level in MSG plasticity is significantly higher than the HRR field. MSG plasticity also predicts that the crack tip stress singularity is not only larger than that in the HRR filed, but also exceeds or equals to the square-root singularity. Moreover, the crack tip stress singularity is independent of the plastic work hardening exponent. In conjunction with other model, the results provide a multiscale view of cleavage fracture in ductile materials.MSG and SG theory are generalized to compressible material based on a new decomposition of strain gradient tensor, because the original MSG and SG theories are only suitable for incompressible materials. The results of micro-indentation and fracture show that the influence of compressibility can not be ignored. The main influence in fracture of MSG plasticity is that the crack tip stress singularity does not exceed the square-root singularity.Finite deformation theories of strain gradient are developed in this paper, for both MSG and SG theory. The constitutive relations are established in the initial configuration by two different methods. The kinematics and tensors transfer relations are provided between the initial and current configurations. The equilibrium equation and boundary conditions are developed in both configurations. The micro-indentation and fracture are studied by finite element method. The micro-indentation results show that both theories for finite and infinitesimal deformation agree well with experimental data by suitably chosen material lengths. The results for fracture show that the difference between finite and infinitesimal deformation only exists in the vicinity very close to crack tip.