The aim of this study is to investigate the problem of pipe cracking based on T-stress analysis and the influence of other parameters, using a numerical computation performed by extended isogeometric analysis (X-IGA). This article examines the T-stress, which defines the second term of the Williams’ series expansion. T-stress provides effective elastic modeling at the crack tip. Using the extended iso-geometric analysis (X-IGA), we determined the distribution of T-stress at the crack tip in a pipe under internal pressure as a function of internal pressure, crack size, and Poisson’s ratio. To validate the promising findings, the results are expanded with a comparison to the extended finite element (X-FEM) method and existing research in this field, and we obtained an error between 0.2% and 4.6%. This work demonstrated the significance of T-stress in fracture description, the effect of Poisson’s ratio and size on T-stress, and that X-IGA provided accurate numerical results by precisely describing the geometry of the crack and enriching it.

In order to examine the significance of Stress Intensity Factor and T-stress (K-T parameters) in modeling pressure-cracked structures, we propose a novel method known as the Isogeometric Over-Deterministic Method IG-ODM. IG-ODM utilizes the computation of stress and displacement fields through Extended Isogeometric Analysis to improve the geometry and enhance the crack. Subsequently, these results are incorporated into the Williams expression, resulting in a set of deterministic equations that can be solved using a common solving method; this particular combination has never been attempted before. IG-ODM enables the computation of stress intensity factor SIF, T-stress, and higher-order parameters in the Williams expansion. To validate the effectiveness of this method, we conducted tests on a single-edge uniaxial-stress-cracked plate and a central uniaxial-stress-cracked plate. The results showed an error ranging from 0.06% to 2%. The obtained results demonstrate accuracy and satisfaction when compared to existing findings.