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 Δ σ np for crack propagation. It is found that Δ σ n | ERC , 1.58 L ≅ Δ σ n | LM , 2 L holds for all the investigated notches. Here, Δ σ n | ERC , 1.58 L denotes the predicted value by the ERC with the intrinsic crack length l c = 1.58 L , and Δ σ n | LM , 2 L denotes the predicted value by the LM with the characteristic distance d LM = 2 L (L is the El Haddad’s material characteristic length). The validity of the LM in predicting the fatigue limit of Δ σ np 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 , Δ σ n | LM , 2 L 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 Δ K th ( l ) | Kitagawa here. However, to each specified notch root radius ρ , Δ σ n | LM , 2 L may be a conservative solution, and theoretically Δ σ np ⩽ Δ σ n | LM , 2 L holds. The reason is that: (1) most of the curves of crack driving force at a nominal stress of Δ σ n | LM , 2 L are above the resistance curve of Δ K th ( l ) | Kitagawa ; (2) the actual resistance curve of the material is generally below the resistance curve of Δ K th ( l ) | Kitagawa .