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Temporal scaling in mechanical strength of materials is vital for long-term effects such as fatigue. The fatigue crack length  α  is related to the change in the stress intensity factor Δ K  by the omnipresent Paris’s law, which works well for cyclic fatigue of specific frequency and amplitude. The paper considers time scaling in fatigue and through it incorporates the effects of temporal events such as unexpected or accidental loads, impact loads, and rare events such as earthquake loads. This is achieved by theoretically incorporating the effects of delta-function type loads into fatigue. Since the time-scale decomposition of such a load contains information at all scales, the theoretical framework is easily extended to include general types of loads.

Temporal scaling in fatigue life of materials and incorporation of temporal events in Paris’s law