Stress Intensity Factors for a Curved-Front Internal Crack in an Autofrettaged Tube With Bauschinger Effect

Pressure vessel steels exhibit the Bauschinger effect that significantly reduces post-autofrettage residual compressive hoop stresses in the near-bore region in comparison with ‘ideal’ (elastic-perfectly plastic) behavior. These reduced hoop stress profiles were calculated using Von Mises’ criterion via a nonlinear analysis for the case of open-end (engineering plane strain) autofrettage. These profiles were then used to obtain stress intensity factor solutions via the Boundary Integral Equation (BIE) method, commonly known as the Boundary Element Method (BEM). Results are presented for tubes of diameter ratio 2 and 2.5 with an internal semi-elliptical surface crack having a maximum depth/surface length ratio of 0.4 (i.e., an eccentricity of 0.8). Crack depths range from 20% to 80% of wall thickness and results are presented for seven locations on the crack front from maximum depth to free surface. For crack depths up to 20% of wall thickness there is a significant reduction in magnitude of autofrettage stress intensity factor due to Bauschinger effect. For typical overstrain levels this reduction is approximately 30% of “ideal” values. Such a reduction may, in turn, cause an order of magnitude reduction in the fatigue lifetime of the vessel.