The flow stress in polycrystalline films: Dimensional constraints and strengthening effects

An analytical model is presented in order to derive a general expression for the flow stress in polycrystalline films which encompasses and correlates dimensional constraints and strengthening effects. The model is based on the Thompson approach, which is extended to take into account both different grain aspect ratios and distinct strengthening contributions. It allows an accurate prediction of the growth textures in polycrystalline CdTe thick films when grain growth is driven by strain energy minimization. The model also matches the experimental data concerning the grain size and film thickness dependences of the yield stress in polycrystalline Cu thin films either deposited on a substrate or freestanding. Interestingly, the yield stress is found to be fitted by a modified Hall–Petch relation resulting in a d−n dependence in which the exponent n varies between ½ and 1 as a function of the grain size for a given thickness.