Vol.13, No1, 2013, pp.39–44
UDC  539.42

The amplitudes of the second order terms in the three-dimensional expansion of the crack front stress field are the terms T_xx and T_zz which describe in-plane and out-of-plane constraint, respectively. All previous analyses of the crack tip plastic zone have ignored the effect of T_zz-stress. At the same time, the effect of T_zz-stress on crack tip plastic zones is not revealed heretofore. It is therefore very important to obtain solutions for crack tip plastic zone size taking into account two components of the T-stresses. The present study focuses on theoretical and numerical analysis of the joint effect of the non-singular T_xx and T_zz-stress on sizes of the plastic zone in the vicinity of the crack tip under mode I loading conditions. The three-dimensional crack tip stresses including T_xx and T_zz stresses are incorporated into the von Mises yield criteria to develop an expression that models the crack tip plastic zone. Calculations are performed for three thicknesses of the CT specimen. The predicted sizes of the plastic zone in the vicinity of the crack tip of the analysed CT specimens are bounded by sizes of the plastic zones corresponding to two special conditions, namely, plane stress and plane strain. The theoretical results are compared with the results computed by FEM. Theoretical estimations of the plastic deformation zone size with provision for T-stress components as a whole shows satisfactory results, especially in the line of crack continuation.

Keywords: plastic zone, T_zz-stress, mode I crack