The strain gradient effect on material behavior at the micron and submicron scales

Recent experiments have shown that materials display strong size effects at the micron scale. The classical plasticity theories fail to predict these observed phenomena because their constitutive models possess no internal material length scales. The theory of mechanism-based strain gradient (MSG) plasticity has been developed and proposed to investigate this observed phenomena. We extend the MSG plasticity theory to include elastic deformation in the constitutive model and develop finite element methods for MSG plasticity to analyze and model the strain gradient effect on material behavior at the micron and submicron scales. We set up an indentation model to study the micro-indentation hardness experiments. The numerical results show good agreement with the experimental data, thus providing an important self-consistent check of the theory. We also develop a simple, analytic model to investigate the influence of indenter tip radius on the microindentation hardness. Our model and numerical analysis both predict that the smaller the tip radius, the harder the hardness for the micro-indentation with spherical indenter. We use the MSG plasticity theory to model the thin film indentation behavior and show that it is capable of describing not only the decreasing hardness with increasing depth of indentation at shallow indentation, but also the rise in hardness that occurs when the indenter tip approaches the film/substrate interface. We also use MSG plasticity theory to study the particle size effect of particle-reinforced composite and find good agreements with the experiments as well as with prior numerical studies by other strain gradient plasticity theories. The conclusion is that smaller particles give larger plastic work hardening of the composite.; Finally, we focus our interest on a MEMS structure—digital micromirror device (DMD) and find that the strain gradient effect significantly increases the mechanical strain energy in the DMD and reduces the rotation time of the micromirror.