ABSTRACT
The reliability evaluation of components commonly includes a comparison of stresses acting in the component with stresses tolerably well by the material. Since both sides are randomly influenced in many cases also probability methods have to be applied. They lead to probability terms or safety margins, respectively. It is not trivial to extend this probability concept to complicated problems of fracture mechanics. In the paper, a method to take into account random input parameters in Finite Element analyses is described and illustrated. This so-called Stochastic FEM is based on perturbation theory and especially applicable to problems with multiple random parameters showing small scattering. The randomly influenced results like displacement or stress fields can be derived from a series expansion in the small deviations. This enables to compute mean and variance of stresses and derived terms of fracture mechanics as well as -under certain assumptions - non-exceeding probabilities.
The method is applied to the reliability evaluation of thermo-mechanically stressed micromechanical components, e.g. chip-on-board and glob top/packaging. Parameters with uncertain scattering are the geometry of the joints or packages as well as material parameters like heat transfer coefficients and Young’s moduli. The Stochastic FEM is used first of all for sensitivity analyses with respect to the level of influence of the different uncertain parameters.
