This paper is concerned with the interpretation of the Coffin-Manson law Δεp·Nfα=C [1] from the standpoint of the behavior of small cracks and also with the explanation of the uniqueness of the exponent α from the strain singularity at crack tip under overall plastic deformation.

Firstly, the characteristic behavior of small cracks in low-cycle fatigue range is discussed; then it is demonstrated that the Coffin-Manson law is virtually identical to the growth law of a small crack. This suggests that we must pay attention to the behavior of a small crack in order to solve low-cycle fatigue problems. Secondly, the singularity of strain field at crack tip is analyzed by a finite element method. It is well known that, denoting the distance from the crack tip by r, the elastic stress strain field near crack tip has the singularity of r^−0.5 and under the elastic-plastic condition the stress and strain has HRR singularity. However, under overall plastic deformation (i.e., under low-cycle fatigue range) the singularity in strain distribution near crack tip deviates from HRR singularity to r^{−(0.5∼0.7)} with increasing plastic deformation regardless of hardening exponents of materials.

It is concluded from the viewpoint of the propagation of a small crack that this exponent (0.5 ∼ 0.7) in singular strain distribution is closely related to the fact that the exponent α in Δεp·Nfα=C ranges from 0.5 to 0.7 for various materials.