A physically based cumulative damage formalism

A general cumulative damage methodology is derived from the basic relation specifying crack growth rate (increment) as a power law function of the stress intensity factor. The crack is allowed to grow up to the point at which it becomes unstable, thereby determining the lifetime of the material under the prescribed stress program. The formalism applies for the case of creep to failure under variable stress history as well as for cyclic fatigue to failure under variable stress amplitude history. The formulation is calibrated by the creep rupture lifetimes at constant stress or the fatigue cycle lifetimes at constant stress amplitude. No empirical (non-physical) parameters are involved in the basic formulation; everything is specified in terms of experimentally determined quantities. Several examples are given showing the inadequacy of linear cumulative damage while the present nonlinear damage accumulation method overcomes these deficiencies. The present method is extended to admit probabilistic conditions.