The Progress And Applications Of Conventional Theory Of Mechanism-based Strain Gradient Plasticity (CMSG)

Recent experiments at the micron scale have repeatedly shown that metallic materials display significant size effect. Classical plasticity theories do not possess internal material lengths and therefore cannot explain the observed size dependence of material behavior. Strain gradient theories have been established to deal with design and manufacturing issues at the level of microns and submicrons, and to explain the cleavage fracture in ductile materials. Based on the Conventional theory of Mechanism-based Strain Gradient plasticity (CMSG) developed by Huang et al. 2004, a series of problems have been investigated and some objectives have been achieved.1. The constitutive relations of CMSG theory for the case that combined isotropic and kinematic hardening rule are introduced, with consideration of the back stress. By the method of characteristics for nonlinear partial differential equations, for the problems of an infinite layer in shear and a uniaxial tension bar subject to a constant body force, we have obtained the"domain of determinacy"for CMSG theory. It is established that, as the applied stress increases, the"domain of determinacy"shrinks and eventually vanishes. Outside the"domain of determinacy", the solution may not be unique. Additional, non-classical boundary conditions are required to prescribe for the well-posedness of CMSG theory. This peoblem exists not only in CMSG theory but also all the lower-order strain gradient plasticity theories.2. Some problems in micro- and nanoindentation are studied using finite element method based on CMSG theory.First of all, the effect of indenter angles on the microindentation hardness is studied. It is shown that the Nix-Gao relation between the microindentation hardness and indentation depth holds for all the six indenter angles. The effect of friction is negligible for relatively flat indenters (e.g., Berkovich indenter), but may be significant for sharp indenters (e.g., cubic indenter). Secondly, the equivalence rules between triangular pyramid indenter and conical indenter are investigated. It is shown that the base area equivalence rule is no longer applicable in microindentation. We establish a new rule, called the angle equivalence rule, to deal with the angles between the two types of indenters. Numerical results confirmed the angle equivalence rule for indenters with six different angles.Lastly, the nanoindentation under spherical indenter is studied. We extend the finite element method for CMSG theory by taking into account the maximum allowable density of geometrically necessary dislocations (GND). The numerical results agree very well with both micron- and nanoindentation hardness data for iridium. But the maximum allowable density of GND is not a material constant. Its value depends on not only the material property but also the the indenter tip geometry.3. Mode I crack under steady-state growth and plane strain is analyzed employing CMSG theory.The results show that during growth of the crack, although lower than the static crack obtained by MSG theory, the normal separation stress will achieve considerably high value within a sensitive zone of strain gradient near the crack tip. The crack tip stress singularity within the dominance zone of CMSG theory is significantly higher, not only larger than classical plasticity (HRR field), but also equals to or exceeds the square-root singularity of elastic field. Moreover, that singularity is independent of the plastic hardening exponent. The dominance zone size of near-tip field in CMSG plasticity is smaller then that of MSG theory for static crack and insensitive to the level of the remote applied stress intensity.