Inverse Hyperbolic Tangent Model of Fatigue-Crack Growth

Abstract

A fatigue-crack- propagation model was specifically developed to account for the effects of stress ratio and closely represent the sigmoidal shape of the crack-growth-rate curve. This derived functional relation was fitted to large sets of fatigue-crack -propagation data for 2024-T3, 7075-T6, and 7075-T7351 aluminum alloys, and for TJ-6A1-4V alloy taken from the literature. A statistical comparison was made between the functional relation and some commonly used fatigue-crack-propagation models as applied to these data sets. Improved representation was obtained in all cases by using the inverse hyperbolic-tangent-function model. Nomenclature a = crack length, in. da/dN = crack-growth rate, in./cycle C, n' = Paris regression coefficients C7, C2 = regression coefficients g — specimen geometric scaling function Kc = terminal stress-intensity factor, ksi-(in.)'/2 Agff = effective stress-intensity factor, ksi-(in.)1/2 ^max = maximum stress-intensity factor, ksi-(in.)1/2 K0 —threshold stress-intensity factor, ksi-(in.)1/2 M' = slope of scaling function m — Walker coefficient TV = number of loading cycles n = number of data points R = stress ratio r2 = proportion of variation explained by regression S = nominal stress, ksi SSD = standard error of estimate U = function relation accounting for effect of R W = specimen width, in. Y — dependent variable $ = scaling function $/ = intercept of scaling function