Issue 35

Chahardehi et al, Frattura ed Integrità Strutturale, 35 (2016) 41-49; DOI: 10.3221/IGF-ESIS.35.05 45 dependence. As an example, Frost et al [47] found no R-ratio dependence in pure aluminium, copper, or titanium. In these materials, therefore, there is a mechanistic difference between higher R-ratios and cycles including negative stress, compared to materials where R-ratio dependence is observed. It may be concluded that where empirical formulae are derived base on positive R-ratio data, extension of these formulae to negative R-ratios is not justified . Figure 1 : Crack growth at different R-ratios following single tensile overload in 2024-T3 aluminium alloy, overload ratio =2.0 [42]. Reprinted, with permission, from ASTM STP 595 Fatigue Crack Growth Under Spectrum Loads, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428. A note on residual stresses When a component contains tensile residual stresses, such as is common in weldments, the R-ratio is always assumed to be greater than 0.5. The rationale for this is that since welds can contain residual stresses of the order of the yield strength of the material, most general engineering cyclic loading cases, when superimposed on the residual stress, would result in a fully tensile cycle with high mean stresses. However, as Allen et al [48] point out, the potential for conservative prediction should be noted. Presence of tensile residual stresses implies the presence of balancing compressive stresses, which is usually not assessed in fatigue in the conservative assumption, whereas in reality in a stress-relieved weld, the crack may close during the compression cycle, therefore removing the stress concentration at the crack tip. On the other hand, where a non-redundant structural component is welded, far-reaching residual stresses due to the misfits (or geometrical incompatibility) of the set up may be generated which have not been calculated in the modelling phase, say by using finite element method. Presence of this type of stress would increase the mean stress, and therefore should not be overlooked in assessment. Effect of thickness Some authors have correlated certain experimental observations to thickness effect - see for example [49]. However these explanations do not sufficiently deal with acceleration under plane strain conditions [41], and the question is still partly unanswered. Effect of stress range Crooker [50] showed that compressive part of the loading is more influential for low-cycle fatigue. Jones et al [23] have examined the effect of high stress ranges in fatigue crack growth, for R=-1.0. The results suggest that there is a significant difference between fatigue crack growth rate curves for small and large stress ranges, and whether the initial stress cycle closes or opens the crack: less benefit is seen when the first cycle closes the crack. Jones’s suggestion is in keeping with Crooker’s observation [50]. Effect of crack length Kurihara et al [32] performed experiments where they could show that the U parameter (ratio of effective stress intensity factor range and mathematical stress intensity factor range) is dependent on crack length (for smaller cracks), and this dependence is stronger for smaller (more negative) R-ratios. Fig. 2 shows this behaviour.