A Model for Fatigue Thresholds at HighRRatios

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Abstract
A limited number of values of the fatigue threshold, ∆K th, for various materials can be found in the literature for R ratios (R = K min/K max) greater than 0.7. Those that exist suggest two types of behaviour; materials where the value of ∆Rth decreases with increasing R in a continuous manner as seen for lower R ratios or materials where ∆K th becomes constant at high R ratios. The decrease of ∆K th with increasing R > 0 has been attributed to the phenomenon of crack closure. Schmidt and Paris [8] proposed a constant value of effective ∆K th (∆K eff,th) and a constant value of K op, (the opening value of K) to account for the decrease in observed ∆K th. The “levelling-off” of ∆K th at high R ratios occurred when K min K op and ∆K th = ∆K eff,th. This does not, however, account for materials where the “levelling-off” is not observed. A relationship proposed by McEvily and Groeger [7], based on a constant value of alternating crack tip opening displacement (∆δ) is shown to fit most existing ∆K th – R data better than the closure model and gives a better physical explanation of crack tip processes at ∆K th. An extension of this model is proposed based on experimental results in HY–80 and A533B steels to account for materials that show a “levelling-off” of ∆K th at high R ratios when the maximum crack tip root radius, ρ, near ∆K th exceeds a critical value above which the crack behaves, under fatigue conditions, like a blunt notch. For HY–80 and A533B this was found to be between 2 and 20μm while for mild steel, which does not show the “levelling-off” effect, results in the literature indicate the critical ρ to be 150μm.

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