The present study scrutinizes the manner of a 3D semi-elliptical arbitrary crack in a particular drilling pipe through adopting a comprehensive numerical simulation based on the finite element method (FEM) using ANSYS Mechanical APDL. In the current investigation, the effects of crack geometry, material properties, and loading conditions on stress intensity factors (SIFs) were explored under combined rotational, pressure, and bending stresses. A 3D finite element model of the drilling pipe was developed, incorporating a semi-elliptical surface crack positioned at critical stress concentration zones identified from preliminary stress contour analyses. SOLID186 higher-order elements and quarter-point singular elements were employed to ensure convergence and accurate representation of the crack-tip stress field. The Model simulation validation demonstrated excellent agreement, with deviations below 5%, confirming the robustness of the simulation effectiveness. The acquired results revealed that the KI fracture mode is the dominant failure mode in the cracked drilling pipe, which the maximum SIF was occurred at mid-thickness regions with the highest tensile bending stress. Increasing crack depth (ac) and aspect ratio (at) significantly elevate KI values, indicating greater crack-driving forces and higher failure risks. Conversely, Mode II (sliding) and Mode III (tearing) components diminished with increasing crack depth, elucidating that shallow surface cracks can lead to shear-driven propagation, while deeper cracks can result in opening-mode failures. Internal pressure was found to directly amplify KI almost linearly, establishing it as the primary factor influencing crack growth in pressurized conditions. In contrast, variations in Young’s modulus (70–270 GPa) and Poisson’s ratio (0.25–0.30) exhibited negligible effects on the stress intensity distribution, confirming that geometric and loading parameters dominate fracture behavior. Ultimately, the machine-learning–based surrogate modeling revealed that crack depth and internal pressure are the most influential parameters for SIFs, enabling accurate prediction of fracture behavior and reliable probabilistic failure assessment with minimal computational cost.