Multi-scale stochastic study of the grain orientation and roughness effects on polycrystalline thin structures

When studying micro-electro-mechanical systems (MEMS) made of poly-crystalline materials, as the size of the device is only one or two orders of magnitude higher than the size of the the grains, the structural properties exhibit a scatter at the macro-scale due to the existing randomness in the grain size, grain orientation, surface roughness... In order to predict the probabilistic behavior at the structural scale, the authors have recently developed a stochastic 3-scale approach [1]. In this method, stochastic volume elements (SVEs) [2] are defined by considering random grain orientations in a tessellation. For each SVE realization, a meso-scopic apparent material tensor can be obtained using the computational homogenization theory. The extracted meso-scopic apparent material tensors can then be used to defined a spatially correlated meso-scale random field, which is in turn used as input for stochastic finite element simulations. In this work we intend to study the effect of different material-related uncertainty sources on the structural behavior of vibrating micro-devices manufactured using low pressure chemical vapor deposition. First, the effect of preferred grain orientation on vibrating micro-structures is assessed. To this end, SVEs are generated so that their grain orientation distributions follow XRD measurements. Second, the effect of the roughness of the vibrating micro-structures is studied. Toward this end, SVEs, whose rough surface statistical properties follow AFM measurements, are generated. A second-order computational homogenization [3] applied on the different SVE realizations allows defining a meso-scale random field of the in-plane and out-of-plane meso-scale shell properties. Stochastic shell finite elements can then be applied to predict the MEMS probabilistic behavior. [1] V. Lucas, et al., Comp. Meth. in Appl. Mech. and Eng., 294, 141-167, 2015 [2] M. Ostoja-Starzewski, X.Wang, Comp. Meth. in Appl. Mech. and Eng., 168, 35–49, 1999 [3] E.W.C. Coenen, V. Kouznetsova, M.G.D. Geers. Int. J. for Numer. Meth. in Eng., 83, 1180–1205, 2010.3SMVIB: The research has been funded by the Walloon Region under the agreement no 1117477 (CT-INT 2011-11-14) in the context of the ERA-NET MNT framework.; The authors gratefully acknowledge the financial support from F. R. S. - F. N. R. S. under the project number FRFC 2.4508.11