Partially-constrained thermomechanical fatigue of eutectic tin-bismuth/copper solder joints

Small bimetallic load-frames with reference assembly stiffness, k′, and fully-constrained shear strain, γ_fc, were used to simulate the thermo-mechanical conditions experienced by eutectic Bi-42wt.%Sn-to-Cu solder joints. Shear stress and strain were induced in the solder joint by a 45-minute, 0 to 100°C temperature cycle and were calculated from the assembly temperature, joint configuration, and measured elastic strain in the load-frame. Early in cycling, a hysteresis loop representing the maximum stress range and minimum strain range was reached. As damage accumulated in the solder, the stress range decreased and the strain range increased. The TMF life of the joints, defined by the load range drop, Φ, as a function of k′ and γ_fc, can be determined, defining an effective plastic strain range which allows data for various stiffnesses and thermal expansion mismatches to be summarized on a single Coffin-Mansion plot. The effective plastic strain range also provides an important link to conventional low cycle fatigue (LCF) data taken from an infinitely stiff load-frame.