Modeling the size and interface effects in thin metal film-substrate systems using the strain gradient plasticity

It is well-known by now through intensive experimental studies that have been performed at the micron and nano length scales that the material mechanical properties strongly depend on the size of specimen and the microstructural features. The classical continuum mechanics fails to address this problem since no material length scale exists in its constitutive description. On the other hand, nonlocal continuum theories of integral-type or gradient-type have been to a good extent successful in predicting this type of size effect. However, they fail to predict size effects when strain gradients are minimal such as the Hall-Petch effect. This problem is the main focus of this work. The effect of the material microstructural interfaces increase as the surface-to-volume ratio increases. It is shown in this work that interfacial effects have a profound impact on the scale-dependent plasticity encountered in micro/nano-systems. This is achieved by developing a higher-order gradient-dependent plasticity theory that enforces microscopic boundary conditions at interfaces and free surfaces. These nonstandard boundary conditions relate the microtraction stress at the interface to the interfacial energy. Application of the proposed framework to size effects in shear loading of a thin-film on an elastic substrate is presented. Three film-interface conditions are modeled: soft, intermediate, and hard interfaces.