Constraint and Failure Assessment Diagram Under Biaxial Loading on Semi-Elliptic Surface Cracks

Three-dimensional finite element analysis has been performed for several configurations of the semi-elliptic surface crack in an X100 pipeline steel plate under various biaxial loading conditions. The biaxial loading ratio (λ) is defined as the ratio of loading parallel to the crack face in the plate width direction to the loading perpendicular to the crack. The constraint level and the J-integral along the semi-elliptic crack front were calculated with J-A₂ constraint theory in fracture mechanics, in which A₂ is considered as the constraint parameter. It was found that λ influences the J values along the crack front. As λ varies from −1 to 0 then to +1, the location of the maximum J has a tendency to move from the deepest point of the crack to a location near the surface as the load increases, especially for a deeper crack. The constraint level (A₂) along the crack front behaves similarly to the J-integral. At λ = −1, the value of A₂ increases from the near surface to the deepest penetration when the load increases. In the case of uniaxial tension (λ = 0), the A₂ values do not vary significantly except near the surface. When the equibiaxial condition is reached (λ = 1), the location of the highest constraint moves to the near surface. However, in this region the higher constraint level is unable to maintain as the load increases (i.e., the peak value of A₂ decreases with increasing load). Finally, the failure assessment diagrams (FAD) at the deepest point of the semi-elliptic crack were constructed with the J-A₂ fracture theory. The crack stability regions are apparently smaller in the cases of λ = −1 and 2 than those for λ = 0 (uniaxial tension) or λ = 1 (equibiaxial tension).