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##### STP942

### Correlation Between Strain Singularity at Crack Tip under Overall Plastic Deformation and the Exponent of the Coffin-Manson Law

**Abstract**

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.

**Keywords:**

low-cycle fatigue, the Coffin-Manson law, small cracks, crack propagation, crack tip, strain singularity, finite element analysis, fracture ductility

**Author Information:**

Y, Murakami

*Professor, Kyushu University, Higashi-ku, Fukuoka,*

**Committee/Subcommittee:** E08.05

**DOI:** 10.1520/STP24539S

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