Steps towards a qualitative dynamics of damage evolution

Basic elements of a qualitative dynamics of systems with slowly accumulating damage are presented. The relationship of averaging to equations relating damage evolution rate with current damage state and load is discussed. The particular case of a scalar damage variable with one load parameter is examined in some detail. Well-known phenomenological features of fatigue tests are used as a guide. Using asymptotic arguments for small initial damage, conditions are obtained under which the time to failure is essentially determined by the initial damage state, and essentially independent of the failure criterion. A suitable form for damage evolution equations is deduced for a class of fatigue problems. Comparisons with published data show that this qualitative dynamics approach produces a model that fits, and predicts, the data as closely as a more physically motivated fatigue model.

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