A fatigue model based on M-integral in notched elastic–plastic material.

• A new fatigue model is proposed based on the M -integral in notched elastic–plastic material, in which dA D /dN (A D : the equivalent damage area of notch, plastic zone and cracks) is defined as fatigue damage evolution rate and Δ M (the M -integral range per load cycle) is defined as fatigue driving force. • An experimental method for measuring the M -integral and the fatigue damage evolution rate of elastic–plastic material is proposed according to the relationship between the M -integral and CTPE (the change of the total potential energy). • The unified fatigue model can accurately describe the two-stage fatigue process in notched elastic–plastic body, including two stages: the formation and growth of plastic zone accompanying the initiation of microcracks (Stage I); the growth of macrocracks (Stage II). In this paper, an innovative fatigue model is investigated based on the concept of M -integral in notched elastic–plastic material. The contribution of notch and plastic zone damage to the lifetime of material are taken into account in the present fatigue model. The new form of fatigue damage evolution rate (dA D /dN) and fatigue driving force (Δ M) are introduced, where A D deontes the equivalent damage area of notch, plastic zone and cracks, N is the number of cycles, and Δ M corresponds to the M -integral range per load cycle. The fatigue experimental evaluations of a typically elastic–plastic material (e.g., No. 45 steel) with a circular notch have been carried out to validate the effectiveness of the present fatigue model. For experimental study, the change of the total potential energy (CTPE) is introduced to measure the value of M -integral. The results demonstrate that dA D /dN shows an apparent power law relation with Δ M in notched elastic–plastic material. The slope n and intercept λ of lg(dA D / dN)-lg(Δ M) curve has linear correlation with the initial notch radius R , but not with applied stress σ. Moreover, the model can clearly describe the two-stage process from the initiation of microcracks to the growth of macrocracks in notched body. It is concluded that the proposed fatigue model based on M -integral can accurately predict the fatigue lifetime of the notched elastic–plastic material. [ABSTRACT FROM AUTHOR]