A theory of fatigue: A physical approach with application to lead-rich solder

A fatigue theory with its failure criterion based on physical damage mechanisms is presented for solders. The theory applies Mura's micromechanical fatigue model to individual grains of the solder structure. By introducing grain orientation (Schmid factor m) into the fatigue formula, an m-N curve at constant loading, similar to a fatigue S-N curve, is suggested for fatigue failure of grains with different orientations. A solder structure is defined as fatigued when the ratio of its failed grains reaches a critical threshold, since at this threshold the failed grains may form a cluster, according to percolation theory. Experimental data for 96.5Pb-3.5Sn (wt. %) solder bulk specimens showed good agreement with the theory and its associated failure criterion. The theory is anisotropic, and there is no size limitation to its application, which could be suitable for anisotropic small-scale (micron scale or smaller) solder joints.