Crack Degradation Model Derived From Experimental Strain-Stress Data

A new concept of lifetime prediction of solder joints is presented, based on a fatigue cycling experiment under isothermal conditions. A common approach of lifetime prediction of solder joints is based on damage model based on the Coffin-Manson equation, which uses the plastic strain range from a single hysteresis loop to calculate a number of cycles to failure. This was later modified by Engelmaier. Then Morrow developed a damage model based on strain energy density, which takes the area of a single hysteresis loop. These stress-strain hysteresis loops are calculated in FEA modelling, but with the assumption that there is no crack. Hence only engineering values of strain and stress are estimated, and the load-bearing area of a solder joint is assumed to be constant and not cracked. This is clearly an over simplification as solder will crack under fatigue conditions during thermal cycling. A further simplification is that the stress is calculated from an inverse solution of secondary creep rate equation. The correct approach should reflect the true stress and strain (measurement of force and actual load bearing area) developed inside a solder joint as a function of time. A clear correlation of solder joint area with electrical resistance can be shown to exist, hence the load bearing area can be obtained by monitoring of solder joint electrical resistance, and therefore the true stress can be calculated. Measurements following this approach show that the strain-stress hysteresis loop area does not collapse (using a constant displacement controlled profile of the solder joint), but that the hysteresis loop expands on the stress axis. Since, an expansion of a hysteresis loop on the stress axis would cause a divergence of stress energy density, the true shear strain is shown to be decreasing under the same displacement in each cycle. A crack degradation model will be presented using the measured true stress strain hysteresis loop area through out the fatigue life of a solder joint.