The influence of the bauschinger effect on the combined stress intensity factors for 3-D internal radial cracks in a fully or partially autofrettaged gun barrel

The influence of the Bauschinger Effect (BE) on K_IN- the combined, Mode I, 3-D Stress Intensity Factor (SIF) distributions for arrays of radial, internal, surface cracks emanating from the bore of a fully or partially autofrettaged gun barrel is investigated. A thorough comparison between the combined SIFs for a "realistic" - Bauschinger Effect Dependent Autofrettage (BEDA) and those for an "ideal" - Bauschinger Effect Independent Autofrettage (BEIA) is performed. The 3-D analysis is performed via the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BDIA, are simulated using an equivalent temperature field and more than 1200 different crack configurations are analyzed. SIFs for numerous crack arrays (n=1 to 64 cracks), a wide range of crack depth to wall thickness ratios (a/t=0.01 to 0.2), various ellipticities (a/c=0.5 to 1.5), several values of the yield-stress to pressure ratio (Ψ=σ_yp/p=1.93 to 3.55) and different levels of autofrettage (ε=30% to 100%) are evaluated. The level of autofrettage efficiency for all BEDA cases is determined, and is thoroughly compared with that of BEIA. The largest combined SIF K_Nmax can be found at any angular location along the crack front and can reach its largest values for arrays of any number of cracks from 1 to 16, and therefore needs to be evaluated for each particular case. The Bauschinger Effect is found to have a dramatic detrimental impact on the fatigue life of the gun barrel. Even in the case were autofrettage has its minimal beneficial effect, (Ψ=1.93), the BE can reduce the fatigue life of the barrel by a factor of 2 to 5. In other cases this factor can reach orders of magnitude, and in extreme cases, when autofrettage completely overcomes the pressure yielding a nil K_Nmax, this factor might become infinite, i.e., an infinite fatigue life for BEIA versus a finite fatigue life for BEDA. For a partially autofrettaged barrel, it is found that the lower the level of autofrettage, the smaller the Bauschinger Effect is. Increasing the level of autofrettage beyond ε=60% is found to be counterproductive, and therefore, it is not recommended.