A mode-I SIF for a deep surface crack subjected to internal pressure varying with power of the coordinate variable

This study proposes a novel numerical method based on the body force method to calculate the mode I stress intensity factor (SIF) for a deep surface crack perpendicular to a free surface. The crack is subjected to an internal pressure that is uniform in its depth direction and varies across its width direction according to a power-law distribution of coordinate variable. A key feature of this method is the introduction of a new fundamental density function based on the corresponding COD of a two-dimensional crack under plane strain conditions and subjected to the same internal power-law pressure distribution. This approach ensures a stable and highly accurate analysis, even for high-order internal-pressure distributions, by incorporating an analytical solution into the numerical scheme. After validating the strategy, a parametric study was performed. The influences of the Poisson’s ratio and the pressure power-law exponent on the mode I SIF distribution along the crack front, including its maximum values and their depths, were systematically computed, and the results were shown graphically.