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

Strain gradient theories have been established to explain the size dependent effect and to solve the industrial problems at the micron and submicron scales. Huang et al. developed a conventional theory of mechanism-based strain gradient plasticity (CMSG), which is a low-order theory version of MSG. The major work of this dissertation is to investigate a series of problems with CMSG.At First, we improve the original CMSG and extend it to a hypoelastic-plastic constitutive model for finite deformation. And then, four problems are investigated, respectively, as follows.1. In particle-reinforced metal-matrix composite materials, particle size effect is studied with CMSG theory. Prior studies used axisymmetric models with vanishing lateral stress tractions in order to represent the uniaxial tension condition and their results fell short to agree with the experimental data. A three-dimensional (3D) unit-cell model is adopted in the present study. The periodic boundary conditions are imposed to ensure the consistency of the unit cell with its neighboring cells before and after the deformation. It is shown that the unit-cell model with the periodic boundary conditions gives much better agreements with the experimental data than the one with the traction-free boundary conditions on the lateral surfaces.2. The effect of strain gradient in surface texturing is studied by a simple indentation model, which describes the indenting of a cylinder indenter into an aluminum film on rigid substrate. We investigate the dependence of indenter force on film thickness, cylinder radius and indentation depth. With the increase of indentation depth, indenter force approaches a constant. An analytic formula is established to obtain the constants with different film thicknesses and indenter radii.3. The indentation of a hard tungsten film on soft aluminum substrate is studied with CMSG theory. We extend CxMSG to account for the effect offriction stress (intrinsic lattice resistance), which is important in body-center-cubic tungsten. The results agree well with experiments. It is also shown that the strain gradient effect is insignificant in the soft aluminum substrate, but is important in the hard tungsten thin film in shallow indentation. The strain gradient effect in tungsten, however, disappears rapidly as the indentation depth increases because the intrinsic material length in tungsten is rather small.4. At last, problems in nanoindentation are studied. The indentationhardness-depth relation established by Nix and Gao in 1998 agrees well withthe microindentation but not nanoidentation hardness data. We establish ananalytic model for nanoindentatin hardness based on the maximum allowabledensity of geometrically necessary dislocations (GND). The model gives asimple relation between indentation hardness and depth, which degenerates toNix-Gao model for microindentation. The model agrees well with bothmicron- and nanoindentation hardness data for MgO and iridium. We alsoextend CMSG to consider the maximum allowable GND density and find goodagreement with experiments. The indenter tip radius effect is also studied andthe results show that it cannot fully explain the nanoindentation size effectwithout accounting for the maximum allowable GND density.