Constitutive relations for stress-reduction in solder joints of surface-mounted chip carriers.

When a surface-mounted ceramic chip carrier is subjected to thermal cycling, complex stresses and strains are generated in the solder joints. Using strain gages along with some simple assumptions we can indirectly measure the shear strain and shear force during these cycles. The force, the strain, and the temperatures are related by a simple linear equation with calculable coefficients. At any temperature, the solder simultaneously undergoes creep and stress relaxation in a process we call "stress-reduction". The rate of stress-reduction is controlled by the conventional constitutive relation in which the rate of change of shear strain at a given temperature is proportional to the shear stress raised to a constant power. The constitutive relation is used to develop an equation for stress as a function of time during isothermal stress-reduction. Experiments confirm this equation over the range of -28C to 97C. The measured time to half-stress depends on the initial stress. For typical values it was measured as one-half at 97C, one month at 33C, and (by extrapolation) 30 years at -28C.