Bimaterial curvature measurements for the CTE of adhesives: optimization, modeling, and stability

Abstract

Quantification of the coefficient of thermal expansion (CTE), the stress-free temperature, and the residual stress state is of critical importance for many applications involving bonded systems such as coatings, adhesives, and other laminated systems. This paper revisits Timoshenko's solution for the curvature of a bimaterial strip (plane stress) by identifying optimal configurations which improve the sensitivity and minimize the effects of time-dependent changes in moduli. We find that when the material system is optimized, the curvature calculation is virtually insensitive to the modulus change. A similar solution is developed from classical lamination theory (CLT) for plate-like geometries in the case of cylindrical bending. These two solutions—Timoshenko's beam solution and the cylindrical bending solution based on CLT—turn out to be the two asymptotes in the predicted curvatures, using the principle of energy minimization as shown in the numerical analysis. For thin layer systems, the bimaterial system is much more sensitive than the bulk material system in curvature measurements. This technique can be easily implemented in modern thermal mechanical analysis equipment, which is readily available in most polymer laboratories.