Stress intensity factor approximate formulae for uniform crack arrays in pressurized or autofrettaged cylinders

Abstract

The presently available large number of stress intensity factor (SIF) values for uniform arrays of radial cracks, emanating from the bore of partially or fully autofrettaged cylindrical pressure vessels, results from extensive research into the fatigue and fracture processes of these vessels. The data consist of more than 400 values for K I P , the SIF due to internal pressure, for different crack arrays and for a wide range of crack lengths, as well as more than 200 values for K I A , the negative SIF due to the compressive residual stress field induced by the autofrettage process, for different configurations of crack arrays and various levels of autofrettage. A detailed analysis of all the data herein reveals that any of the above results pertains to only one of two possible categories designated “sparse crack arrays”, or “dense crack arrays”. While for sparse arrays both K I P and K I A are directly proportional to the crack length, l, in the dense case, they depend primarily on the inter-crack spacing, d, and are practically crack length independent. Furthermore, the inter-crack aspect ratio, l d , is found to be the sole parameter determining to which of the two categories each case belongs. Based on these results, and using a least-squares approach, SIF approximate formulae for K I P and K I A for sparse and dense crack arrays are developed, yielding simple expressions of very good engineering accuracy which are applicable to the whole gamut of existing results.