Modeling On The Size Dependent Mechanical Behavior Based On The Strain Gradient Crystal Theory

Recently, a large number of experiments suggest that a strong size effect of mechanical behavior exists at a length scale on the order of microns or sub-microns. Classical plasticity theories based on the continuum mechanics do not process internal material length parameters, and thus can’t explain this size-dependent phenomenon. In addition, in the field of industrial manufacturing or MEMS/NEMS, there is an urgent need to solve the problems of mechanical theory and simulations at the micron scale. Therefore, research on scale effect in recent years has been a hot topic in the field of academic.After Cosserat first proposed a couple stress theory, various strain gradient continuum theories have been proposed to include the length scale in order to model the strain-gradient or size dependent mechanical behaviors. It is well known that, the crystal materials has very obvious mechanical anisotropy, which have great influence on the macroscopic mechanical properties of metallic materials.Although traditional crystal plasticity theories can characterize the anisotropy of crystal materials, they do not include the scale parameter and cannot predict the size effect. Therefore, the introduction of strain gradient into the traditional crystal plasticity theory is particularly important.We introduce the scale parameters into the framework of traditional crystal plasticity theory by the UMAT. Then, using this UMAT, the size effects of micro torsion and bending of single crystal Cu, the Hall-Petch relation of polycrystalline materials, as well as the porous material with micron/submicron sized voids, have been investigated carefully. Obviously, the developed crystal plasticity UMAT with strain gradient also can predict the size effect of different two-phase materials effectively.