The Combined Effect of Pressure and Autofrettage on Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in Gun Barrels

Due to the repeated firing of the gun, large uniform arrays of unequal-depth fatigue cracks develop from the inner surface of the barrel. The combined effect of pressure and autofrettage on the mode I stress intensity factor (SIF) distribution along the fronts of these three-dimensional, semi-elliptical, surface cracks is herein studied. Crack depth inequality is modeled using the “two-crack depth level model” previously proposed. The analysis is performed via the finite element (FE) method employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent thermal load. The distribution of the combined stress intensity factor due to pressurization and full autofrettage $KIN=KIP+KIA,$ for numerous array configurations is evaluated for a barrel of outer to inner radii ratio of $Ro/Ri=2.$ These configurations bear $n=n1+n2=8$ to 128 cracks, a wide range of crack depth to wall thickness ratios, $a1/t=0.01$ to 0.40, and various crack depth to half-length ratios (ellipticities) $a1/c1=0.30$ to 1.50. The results for $KIN$ distributions clearly indicate that the level of effect of crack depth inequality depends on all three parameters: crack number in the array, crack depth and crack ellipticity. Furthermore, the results indicate that adjacent unequal-depth cracks influence each other only within a limited range of their depths, i.e., the “interaction range”. The range of influence between adjacent cracks on the maximal SIF $KNmax$ depends on crack ellipticity and is found to be inversely proportional to the crack density of the array. The results re-emphasize the favorable effect the residual stress field has on the fracture endurance and the fatigue life of gun barrels bearing uniform arrays of three-dimensional unequal-depth cracks at their inner surface. This favorable effect is governed by the ratio of the gun’s material yield stress to its internal pressure—$ψ=σ0/p.$ The higher ψ is, the more effective autofrettage becomes.