The in‐plane and out‐of‐plane stress constraint factors and K‐T‐Tz description of stress fields near the border of a quarter‐elliptical corner crack

Abstract

ABSTRACTThe elastic T‐stress and stress intensity factor K for quarter‐elliptical corner cracks have been investigated in elastic plates by detailed three‐dimensional finite‐element calculations. The distributions of normalized K and T‐stress have been obtained along the crack front with aspect ratios (a/c) of 0.2, 0.3, 0.4, 0.5, 0.6, 0.8 and 1.0, and far‐field tension and the effect of Poisson's ratio have also been considered. The normalized K increases and the normalized T‐stress decreases with the increase of Poisson's ratio v. For v= 0.3, the normalized K gradually increases in the range of crack‐face angle φ≥ 22.5° and decreases in the range of φ≤ 22.5° with the increase of a/c. The normalized T‐stress increases in the beginning and then decreases with increasing φ except for a/c= 0.2 and a/c= 0.3. By fitting the numerical results with the least squares method, empirical formulae have been given for the convenience of engineering applications. Combining with the corresponding out‐of‐plane constraint factor Tz, the three‐parameter K‐T‐Tz approach has been provided, which can accurately describe the stress field around the crack front.