Interfacial Effects on Size-Dependent Strength of Nanostructured Materials and Systems

Abstract

The emerging areas of microand nano-technologies exhibit important strength differences that result from continuous modification of the material microstructural characteristics with changing size, with smaller being stronger. There are many experimental observations which indicate that, under certain specific conditions, the size of micro/nano-systems significantly affect their strength such that a length scale is required for predicting such size effects when using the classical theories of continuum mechanics. For example, experimental works have shown increase in strength by decreasing: (a) the particle size in nano-composites; (b) the diameter of nano-wires in torsion and uniaxial compression; (c) the thickness of thin films in micro-bending and uniaxial tension; (d) the grain size of nano-crystalline materials; (e) void size in nano-porous media; (f) the indentation depth in micro/nano indentation tests, etc (see Abu Al-Rub and Voyiadjis [1, 2] for a complete list of references). Therefore, 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 in 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.