A tentative explanation for two parameters, C and m, in Paris equation of fatigue crack growth

Abstract

The two parameters, C and m, which characterize the Paris equation for fatigue crack growth are explained in relation to the crack closure concept suggested by Elber. It is proposed that the range of effective incremental change in stress intensity factor (ΔK) needed for crack growth should have a second power correlation with the growth rate. The crack growth is essentially determined by cumulative damage to the material in cycled plastic zone near the crack tip, and is relatively insensitive to the applied ΔK-values and the mechanical properties of material. However, the crack closure behavior is expected to depend on both the stress range and the material properties. Thus it is concluded that the exponent parameter m reflects mainly the dependency of crack closure behavior on ΔK. For example, in the case of m=4 the crack opening level increases linearly with increase in ΔK, while in the case of m=2 it remains constant. It is suggested that the cyclic straining at the crack tip possibly varies with ΔK, thus changing primarily the crack closure behavior rather than the damage accumulation process in the plastic zone.