Theoretical Study on J-integral Subjected to T-stress.

T-stress is one of the necessary physical quantities to characterize the stress field at the crack tip, and the properties of J-integral under its action remain to be investigated. The expression of J-integral considering T-stress was derived in this paper. The numerical simulation method was used to verify the expression under mode I, mode II and mixed mode I+II loading conditions, and a calculation method of crack tip stress field parameters based on J-integral was given. The theoretical derivation proves that the path conservation of the J₁-integral is not affected by T-stress, but the value of the J₂-integral meets the linear relationship with the square root of the distance from the start and end point of the integral path to the crack tip, and the coefficient of J₂-r curve is related to T-stress. The finite element simulation results show that the crack length of the specimen has a significant effect on the J-integral, while the mesh size has a small effect on the J-integral calculation results. Under the same loading condition, J-integral values of different sizes specimens are different, but the trend of J₂-r curve change is consistent with the expression derived from theory. Under mode II and mixed mode I+II loading conditions, the solving accuracy of T-stress is high, while under mode I loading conditions, J₂ ≈ 0, the solving accuracy is reduced due to factors such as rounding error. [ABSTRACT FROM AUTHOR]