On the Causes of Deviation from the Palmgren-Miner Rule

Abstract

Based upon considerations of fatigue crack growth, explanations for the observation that the Palmgren-Miner damage summation often deviates from unity can be established. It is assumed that the fatigue lifetime is taken up entirely in fatigue crack propagation, that is the number of cycles spent in crack initiation is a negligibly small fraction of the total lifetime. This assumption permits the fatigue lifetime to be analyzed in terms of a basic constitutive relation for the rate of fatigue crack growth that is given by: dadN=A(ΔKeff−ΔKeffth)2 where a is the crack length, N is the number of cycles, A is a material-environmental constant, ΔKeff is the effective range of the stress intensity factor, i. e., Kmax - Kop, where Kmax is the maximum value of the stress intensity factor in a loading cycle, Kop is the stress intensity factor at the crack opening level, and ΔKeffth is the effective value of the stress intensity factor at the threshold level. Three variable amplitude loading conditions are considered: two-step loading, multiple two-step loading, and overload and underload loading. In each case, the cause for deviation from a Palmgren-Miner damage summation of unity is clarified.