Solutions of T-stresses for quarter-elliptical corner cracks in finite thickness plates subject to tension and bending

The non-singular terms in the series expansion of the elastic crack-tip stress fields, commonly referred to as the T-stresses, play an important role in fracture and fatigue problems where a single fracture mechanics parameter such as stress intensity factor K or the J-integral cannot completely characterize the crack tip stress states. In addition to K in elastic analysis, or the J-integral in elastic–plastic analysis, T-stresses provide an effective two-parameter characterization of the constraint levels in the vicinity of a crack. A quarter-elliptical corner crack in a finite thickness plate is a representative model for many cracks in engineering components, such as corner cracks found in weld toes, rivet holes or the nozzle areas of pressure vessels. In this paper, three-dimensional finite element analyses are conducted to calculate the T-stresses for a quarter-elliptical corner crack in a finite thickness plate with a wide range of crack aspect ratios and relative depths. Both remote tension and bending loads are considered. For engineering applications, empirical equations for T-stresses at two points near the free surfaces are also presented. When combined with the solutions for stress intensity factor K or J, these T-stresses solutions are suitable for constraint-based fracture and fatigue analysis for quarter-elliptical corner cracks in engineering components.