Consideration to the mean stress based line method for estimating the notch fatigue limit

Abstract

To consider a mechanistic explanation of the mean stress based line method (called LM) for estimating the notch fatigue limit, the limit values predicted by the LM are investigated from both the energy condition required to create fractured surfaces and the crack propagation condition of the linear elastic fracture mechanism.Based on the energy condition, an energy release criterion (ERC), was introduced to estimate the notch fatigue limit of Δσnp for crack propagation. It is found that Δσn|ERC,1.58L≅Δσn|LM,2L holds for all the investigated notches. Here, Δσn|ERC,1.58L denotes the predicted value by the ERC with the intrinsic crack length lc=1.58L, and Δσn|LM,2L denotes the predicted value by the LM with the characteristic distance dLM=2L (L is the El Haddad’s material characteristic length). The validity of the LM in predicting the fatigue limit of Δσnp based on stress condition was demonstrated by the correspondence relation between the average stress and the energy release in the relevant zone.Also, the growth of small cracks near the notch root is investigated using the R-curve approach. It is found that, as a universal criterion applicable to various notch root radiuses ρ, Δσn|LM,2L gives a critical condition for crack to overcome the typical resistance force represented by the simplified Kitagawa-Takahashi diagram, the values of which is denoted by ΔKth(l)|Kitagawa here. However, to each specified notch root radius ρ,Δσn|LM,2L may be a conservative solution, and theoretically Δσnp⩽Δσn|LM,2L holds. The reason is that: (1) most of the curves of crack driving force at a nominal stress of Δσn|LM,2L are above the resistance curve of ΔKth(l)|Kitagawa; (2) the actual resistance curve of the material is generally below the resistance curve of ΔKth(l)|Kitagawa.