An empirical correlation for stress intensity factors in thick-walled pressure vessels with semi-elliptical surface cracks using a meshfree e-RPIM approach

Accurate estimation of Mode I stress-intensity factors (SIFs) is essential for evaluating the structural integrity and fracture resistance of thick-walled pressure vessels, where longitudinal semi-elliptical surface cracks often serve as primary failure sites. In this study, the Radial Point Interpolation Method (RPIM), a meshfree numerical technique, is employed to investigate the SIF distribution along the crack front of a thick-walled cylindrical vessel subjected to internal pressure and to develop an empirical correlation for the dimensionless SIF parameter T based on geometric and angular parameters. The displacement field is constructed using multiquadric (MQ) radial basis functions combined with first-order polynomial terms, ensuring smooth and accurate stress gradients without the need for meshing. Parametric analyses were conducted for aspect ratios a / b = 0.4, 0.5, and 0.6 and several crack-depth ratios b / t , with a constant thickness-to-inner-radius ratio ( t / r i = 0.25). The MQ parameters were optimized through systematic calibration, yielding α = 3.0 and q = 1.03, which reduced the average relative error to below 4% compared with finite element (FEM) simulations and reference data. Validation of the RPIM results against Zheng’s numerical data demonstrated excellent agreement and numerical stability across all cases. Furthermore, an empirical correlation was developed to relate the dimensionless parameter T to geometric ratios ( b / a , b / t , t / r i ) and the crack-front angle (θ), achieving a determination coefficient of R 2 = 0.97, with a maximum error of 12.1% and an average error of 3.3%. These findings confirm that RPIM, enhanced through optimized MQ parameters and empirical correlation modeling, provides an accurate and computationally efficient tool for analyzing fracture behavior in thick-walled pressure vessels.