The Influence of the Bauschinger Effect on 3D Stress Intensity Factors for Internal Radial Cracks in a Fully or Partially Autofrettaged Gun Barrel

The influence of the Bauschinger effect (BE) on the three-dimensional, mode I, stress intensity factor (SIF) distributions for arrays of radial, internal, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. A thorough comparison between the prevailing SIFs for a “realistic” (Bauschinger effect dependent autofrettage (BEDA)) and those for an “ideal” (Bauschinger effect independent autofrettage (BEIA)) is done. The three-dimensional (3D) analysis is performed via the finite element method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. More than 300 different crack configurations are analyzed. SIFs for numerous crack arrays (⁠$n=1-64$ cracks), a wide range of crack depth to wall thickness ratios $(a∕t=0.01-0.2)$⁠, various ellipticities $(a∕c=0.5-1.5)$⁠, and different levels of autofrettage $(ε=30-100%)$ are evaluated. The Bauschinger Effect is found to considerably lower the beneficial stress intensity factor due to autofrettage, $KIA$⁠, by up to 56%, as compared to the case of ideal autofrettage. The reduction in $KIA$ varies along the crack front with a maximum at the point of intersection between the crack plane and the inner surface of the cylinder, decreasing monotonically toward the deepest point of the crack. The detrimental influence of the BE increases as the number of cracks in the array increases and as crack depth decreases. For a partially autofrettaged cylinder, as the level of overstrain becomes smaller the influence of the BE is considerably reduced. As a result, the SIFs due to 100% BEDA differ by $<10%$ as compared to 60% BEDA, and on the average the difference is only about 2–4%.