The plane stress problem of a semi-infinite, bimetallic thermostat subjected to uniform heating or cooling is treated with the theory of elasticity. Solutions to this problem are expressed as the sum of a basic solution for a bimetallic strip of infinite length and a series of complementary solutions. Interlayer peeling stresses at the free edge of the bimetallic thermostat are shown to be singular or nonsingular (but still higher than the nominal values) depending upon whether the combination of the two Dundurs’ bimaterial constants, α (α−2β), are greater or less than zero. In an example problem, current solutions agree well with finite element results while results predicted by a modified beam theory show a large deviation from the other two solutions near the free edge. Boundary layer effects near the free edges of a bimetallic thermostat are also discussed.

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Effects of crack surface heat conductance on stress intensity factors of modes I, II, and III are investigated. The crack problem is first solved by assuming perfect (infinite) heat conductance at crack surfaces. Finite heat conductance at crack surfaces is then accounted for by imposing a set of distributed dipoles at the crack surfaces. Distribution function of the dipoles is the solution of a Fredholm integral equation. It is shown that, for cracks in a homogeneous, isotropic, linear elastic solid, the degree of thermal conductivity at crack surfaces will affect the magnitude of mode I and mode II stress intensity factors but not mode III stress intensity factor. It is also shown that, for a geometrically symmetric cracked solid, only the mode II stress intensity factor will be influenced by different crack surface heat conductance even if the thermal loading is not symmetric. More importantly, for a given material thermal conductivity (K) and crack surface heat convection coefficient (h), effects of crack surface heat conductance on stress intensity factors is found to depend upon crack size. This “size effect” implies that, for a given set of K and h, an extremely small crack can be treated as if the crack surfaces are insulated and a very long crack can be treated as if the crack surfaces are perfectly heat conductive. As an example, the problem of a finite crack in an infinite plate subjected to a constant temperature gradient at infinity is studied.

A nonlinear and time dependent finite element analysis was performed on two surface mounted electronic devices subjected to thermal cycling. Constitutive equations accounting for both plasticity and creep for 37Pb/63Sn and 90Pb/10Sn solders were assumed and implemented in a finite element program ABAQUS with the aid of a user subroutine. The FE results of 37Pb/63Sn solder joints were in reasonably good agreement with the experimental data by Hall [19]. In the case of 9OPb/1OSn solder in a multilayered transistor stack, the FE results showed the existence of strong peel stress near the free edge of the joint, in addition to the anticipated shear stress. The effect of such peel stress on the crack initiation and growth as a result of thermal cycling was discussed, together with the singular behavior of both shear and peel stresses near the free edge.