Size-Dependent Thermomechanical Responses of Nano-Sized Multilayers

Abstract

The mechanical behavior of materials/structures at nanoscales has been shown, either experimentally or numerically, to be size-dependent. An accurate analysis of a nano-sized multilayer film/substrate structure subject to temperature variation is developed in the present paper. The size-dependent character is captured by adopting the modified couple stress theory. In addition, the effect of bonding imperfection between any two consecutive layers in the structure is considered by using a linear slip-type weak interface model. In the analysis, each layer is modeled as a non-classical Euler-Bernoulli beam incorporating the couple stress. An efficient state-space formulation for the multilayer structure is presented. Comparisons of the axial force, deflection and interfacial shear stress predicted by the present model with those by the classical beam model are made in cases of a Ni film/Epoxy substrate bilayer and of a Ni film/Ni film/Epoxy substrate trilayer. The results show that a nano-sized structure can exhibit a significant size-dependent phenomenon, and the presence of weak interfaces may alter strikingly the response of a multilayer.