Crystal plasticity based modeling of time and scale dependent behavior of thin films



The micro and sub-micro scale dimensions of the components of modern high-tech products pose challenging engineering problems that require advanced tools to tackle them. An example hereof is time dependent strain recovery, here referred to as anelasticity, which is observed in metallic thin film components of RF-MEMS switches. Moreover, it is now well known that the properties of a thin film material strongly depend on its geometrical dimensions through so-called size effects. A strain gradient crystal plasticity formulation (SGCP) was recently proposed [1–4], involving a back stress in terms of strain gradients capturing the lattice curvature effect. In the present work, the SGCP model is used in a realistic simulation of electrostatic bending of a free standing thin film beam made of either a pure fcc metal or a particle strengthened Al-Cu alloy. The model capabilities to describe the anelastic and plastic behavior of metallic thin films in comparison with experimentally available data are thereby assessed. Simulation results show that the SGCP model is able to predict a macroscopic strain recovery over time following the load removal. The amount of the anelastic relaxation and the accompanying relaxation times result from the rate dependent modeling approach, the basis of which is phenomenological only. The SGCP model is not fully capable of describing the permanent deformations in an alloy thin beam as observed in electrostatic experiments. Hence, to incorporate realistic time constants and the influence of the microstructure into the mechanical behavior of the thin film material, an improved constitutive law for crystallographic slip is necessary within the SGCP formulation. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)