T-stresses solution and out-of-plane constraint for central cracked plate (CCP) with I-II mixed mode crack under uniaxial compression

Abstract

The crack tip constraint effect should be considered in the fracture assessment of structures with cracks, and the in-plane constraint and out-of-plane constraint should be illustrated simultaneously for the three-dimensional cracks in practical engineering structures. The constraint effect of central cracked plate (CCP) specimens with I-II mixed mode crack under uniaxial compression has been investigated quantitatively in present work. The relationship between T-stress components (Tx, Ty, Txy) and in-plane constraint parameter T11 has been established. The effects of a wide range of in-plane and out-of-plane geometrical configurations (including relative crack length a/W and thickness to width ratio t/W), material parameters (including elastic modulus E and Poisson's ratio ν), crack inclination angle β and friction coefficient μ corresponding to stress intensity factors (K), in-plane constraint parameter T11 and out-of-plane constraint parameters T33 and Tz at the crack tip have been calculated and discussed theoretically and numerically. It demonstrates that the constraint parameters can effectively express the stress-strain field at the crack tip. The relative crack length a/W has an influence on the in-plane and out-of-plane constraint parameters, and the thickness to width ratio t/W mainly affects the out-of-plane constraint parameters T33 and Tz. The out-of-plane constraint parameters should be considered for long cracks. There is a loss of out-of-plane constraint under compression when t/W less than or equal to 0.9, which can be much more directly and evidently investigated through the analysis of Tz than T33. The empirical equations for KII, T11 and Tz have been obtained according to theoretical analysis and simulation results, which are convenient and effective for application.