applied fracture mechanics

190Applied Fracture Mechanicsincreases, that is, 150 N/mm-pressure results in the minimum fretting fatigue strength forsample A.4.4. ΔKth from small fretting pre-cracksFigure 18 shows ΔKs obtained from plain fatigue tests by using fretting pre-crackspecimens, where open marks mean non-fracture and closed marks mean fracture. In thisfigure, ΔKths for long crack are also shown. Estimated ΔKths for small cracks, as boundariesbetween open and closed marks, were confirmed to depend on the crack length as a slope of1/3 in the double logarithmic plots under various R. This slope of 1/3 agrees well withMurakami’s empirical rule (Murakami & Endo, 1986). Some data slightly deviated from theapproximate line, which was probably caused by inclined pre-crack effects and residualcompressive stress due to previous fretting tests.Threshold values for small cracks are modelled as Eq. (4) using ΔKth, 0.1, ΔKth at aeq=0.1mm onthe 1/3 slope line, and threshold for long cracks, ΔKth,l. The variation of ΔKth, 0.1 is shown inFig. 19 as a function of R for samples A and B obtained from plain fatigue tests using frettingpre-crack specimens. It was confirmed that the values of ΔKth, 0.1 for sample B (higher staticstrength) are higher than those of sample A under all R.K K ath,s th, 0.1 eq 1/3/ 0.1 ,K K , when K K,th th,s th,s th,lK K , when K K.th th,l th,s th,l(4)Figure 18. The value of ΔKth obtained by plain fatigue tests using fretting pre-crack specimens for (a)Sample A and (b) Sample B under various stress ratios