Fatigue Crack Propagation of Short Cracks

Abstract

Previous studies have shown that both threshold stress intensity factors and fatigue crack growth rates are dependent on crack size. The average growth rates for very short cracks considerably exceed those given by conventional stress intensity-crack growth laws fitted to long crack data. Elastic and elastic plastic fracture mechanics solutions are modified to predict this behavior of short cracks by introducing an effective crack length l0 into the solutions for intensity factors and the J integral method of analysis. The threshold stress at a very short crack length approaches the fatigue limit of the material, and therefore the value of l0 can be obtained once the threshold stress intensity factor and the fatigue limit are known. The accuracy of the term l0 in predicting crack growth rates for short cracks is found to be independent of the applied strain level. It varies linearly with the grain size of the material and can be considered at the surface as a measure of the reduced flow resistance of surface grains due to their lack of constraint.

Mean stress sensitivity of ductile iron with respect to technological and statistical size effect considering defects

“…This size increases with larger specimens and coarser microstructure. The ElHaddad equation [7] has been used to estimate the fatigue limit based on supplementary crack growth experiments [2]. The calculated fatigue limits are in good agreement with the measured fatigue limits (cf.…”

Corrosion pitting and environmentally assisted small crack growth

“…This is not the case as there is no crack path through the material that would allow this upper bound growth rate; there will always be obstacles to crack growth in the small crack regime that will cause transient crack growth retardation. Alternative treatments to that of Newman [36] exist that introduce a short crack 'correction' factor to the expression for K in an empirical fashion, most notably by El Haddad et al [39], so that K is then a function of √ a + a 0 , where a 0 is the crack depth correction factor. This short crack correction worked particularly well in describing the dependence of the fatigue limit on pit size for the FV 566 martensitic stainless steel [40].…”

Gradient elasticity: a transformative stress analysis tool to design notched components against uniaxial/multiaxial high‐cycle fatigue

“…In both cases length scale parameter l was directly estimate from ∆σ0 and ∆Kth via Eq. (18). These four diagrams clearly show gradient elasticity's smoothing effect, this resulting in stress fields having, in the vicinity of the notch tip, magnitude lover than the corresponding ones calculated according to continuum mechanics.…”

“…(18). As shown in Figure 3a, gradient elasticity can simply be thought of as an operator transferring the PM linear elastic stress state determined at a distance from the notch tip equal to L/2 onto the surface of the notch itself (Fig.…”

“…The common feature of these different formalisations of the TCD is that the required critical distance can directly be determined from the plain fatigue limit range, ∆σ0, and the threshold value of the stress intensity factor range, ∆Kth, as follows [17][18][19]:…”