Elastic T-Stress Solutions of Embedded Elliptical Cracks Subjected to Uniaxial and Biaxial Loadings

Abstract The elastic T-stress has been found to be an important parameter in characterizing the near crack tip elastic-plastic stress states of 2-D and 3-D crack problems. In addition to the J-integral, the T-stress provides an effective two-parameter characterization of 2-D and 3-D elastic-plastic crack tip fields in a variety of crack configurations under small scale yielding conditions. Embedded elliptical crack in an infinite solid subjected to uniaxial or biaxial tension conditions represents an excellent model for many engineering components with embedded cracks. Although extensive analyses are available for stress intensity factors (SIFs) for embedded elliptical cracks, to date no analytical T-stress solutions are available. This paper presents the exact close form solutions for elastic T-stress of an embedded elliptical crack in an infinite body under remote uniaxial or biaxial tension. The foundation of the derivation is based on the potential method for three-dimensional elasticity. Solutions of stress components parallel to and perpendicular to the cracked plane are derived first. T-stress is then obtained from the asymptotic stress field near the crack front. Complete solutions of T-stress along the crack front are established. Further, three-dimensional finite element analyses are conducted to verify the derived solutions; excellent agreements are achieved. When combined with the corresponding K or J solutions, these T-stress solutions are suitable for the analysis of constraint effects for embedded elliptical shaped cracks in engineering components.