Inverse Analysis of the Coefficient of Thermal Expansion of Dissimilar Materials Using the Virtual Fields Method

Abstract

This paper proposes a method for identifying the coefficient of thermal expansion of dissimilar materials that are simulating electronic packaging. Mismatch of the coefficient of thermal expansion in a substrate structure is simulated using dissimilar materials with silver solder composed two kinds of metals. The displacement distribution under a uniform thermal load is measured using digital image correlation and the coefficient of thermal expansion is obtained by performing inverse analysis from the measured displacement result as an input. The virtual fields method based on the principle of virtual work is employed as the method for the inverse analysis. Each coefficient of thermal expansion that is an unknown parameter is determined by preparing the virtual displacements as many as the number of materials in the structure. The effectiveness of the inverse analysis method is demonstrated by identifying the coefficients of thermal expansion of dissimilar materials. Results show that the coefficient of thermal expansion can be obtained by the proposed method.