Analytical solution of T-stresses for an inclined crack in compression

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It is widely accepted that T-stress near crack tip has a considerably effect on crack behavior. In the classic fracture mechanics, only Tx (T-stress component in x-direction) was addressed, and recently one researcher pointed out that both Tx and Ty exist for a crack in compression. In order to theoretically study the T-stress for an inclined crack under compression, analytical solution of stresses near crack tip was derived from the complex stress functions which were obtained according to the crack surfaces stress conditions and boundary conditions. The analytical solution of stresses consists of two parts: one is singular term which is the same as the classical stress expressed in terms of stress intensity factor, and the other is non-singularity term which can be expressed in terms of three components of T-stress, i.e. Tx, Ty and Txy, which indicates that the T-stress should have three components. In order to validate the result of T-stress, the crack initiation angle was calculated by the MTS criterion for four cases: (1) without T-stress, (2) Tx only, (3) Tx and Ty, and (4) Tx, Ty and Txy. The prediction results of the crack initiation angles by MTS criterion were compared to the previous test results of PMMA and the test results conducted in this study by using sandstone specimens with an inclined crack under uniaxial compression. The results show that the prediction results by considering the three components Tx, Ty and Txy can better fit both test results of PMMA and sandstone, which indicates that the T-stress near crack tip should have three components Tx, Ty and Txy, and all of them have effect on crack initiation behavior.