This work proposes a novel strategy for a two-dimensional problem that includes the approach of extended isogeometric analysis (X-IGA) in order to detect the behavior of a crack in pipeline structures. The nonrational B-Spline uniform function (NURBS) was used for the approximation of the solution fields (displacements) taking into account its geometry constrains. The modeling of the X-IGA was implemented under Abaqus/Standard software via subroutine (UEL) where the Stress Intensity Factor (KI) was extracted. The results permit detecting with accuracy the fracture toughness of a pipeline structure containing an external crack that can be submitted to critical pressures. To validate the performances of the novel strategy a careful comparison with existing literature and analytical and numerical computation methods was performed.