Fatigue crack growth threshold conditions at notches. Part I: theory

Abstract

A micromechanical description of the fatigue crack growth process at notches is presented. Crack interaction with the plastic slip barriers of the material (e.g. grain boundaries) and the influence of the notch stress gradient are intrinsically taken into account in the model. Both the notch fatigue crack initiation limit and the limit for propagation up to failure (i.e. the conventional notch fatigue limit) are clearly identified and calculated. The formation of non‐propagating cracks is also explained.

Calculating fatigue limits of notched components of arbitrary size and shape with cracks growing in mode I

“…(11) in the present context is that by comparing it with the Kitagawa-Takahashi diagram of the material obtained experimentally, the sequence ðm à i =m à 1 Þ for increasing i can be obtained, as proposed by de los Rios and Navarro [10].…”

“…Thus, the limit of applied stress r Li required to propagate a crack that spans i half-grains, is given as (see [9,11,20,21]…”

“…In a first attempt to extend the treatment to mode I loading and to notches with different shapes, Vallellano et al [11,12] simply rewrote the formula for the fatigue limit in terms of the three parameters thought most relevant for the stress distribution around the notch [13], namely, the stress concentration factor (k t ), the notch root radius (r) and the notch depth (a) and substituted normal stresses for the (antiplane) shear stresses in the resulting expression. This approximate formula was compared with experimental results from the literature for different type of notches and materials (El Haddad et al [14], Frost [15], Tanaka and Akinawa [16], Lukás et al [17,18], DuQuesnay et al [19], etc.)…”

Application of the Microstructural Finite Element Alternating Method to assess the impact of specimen size and distributions of contact/residual stress fields on fatigue strength

“…(22), proposed by Vallellano [15,16], was used with an exponent . The classical equation by Peterson [48], based on critical distance methodologies, requires use of the net stress concentration factor, which is calculated as follows: Table 6 shows results for the net stress concentration factor obtained from FEA and Fig.…”

“…Several models, based on microstructural fracture mechanics, have been proposed for the analysis of notch components, as proposed by Tanaka and Mura [13], Chapetti [14], Vallellano et al [15,16] and Chaves and Navarro [17,18].…”