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.
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