Methodology for calculating J-integral range ΔJ under cyclic loading

Abstract The J-integral range or the cyclic J-integral, Δ J , is frequently utilized to deal with the fatigue crack growth of ductile materials with large scale yielding. Δ J was originally defined as a line integral similar to the J-integral proposed by Rice. Many researchers correlated fatigue crack growth rate of ductile materials with Δ J defined by J m a x − J m i n . Although it is theoretically shown that the latter definition of Δ J, that is, Δ J = J m a x − J m i n , is not equivalent to the former defined by a line integral, why is the latter definition of Δ J utilized so frequently? This question is main concern of the present paper. To answer this question, we derive the expression of Δ J represented by a line integral for HRR singular fields, which govern the vicinity of a crack tip under large scale yielding, then formulate the difference between the Δ J represented by a line integral and Δ J = J m a x − J m i n . We perform the error estimation for three-point bending specimens to clarify how accurately ( J m a x − J m i n ) predicts the Δ J -value, compared with the Δ J represented by a line integral, which is supposed to provide the exact Δ J -value. As a result, the Δ J -value calculated from ( J m a x − J m i n ) is identical to the Δ J -value calculated from a line integral in the case of the zero-tension cyclic loading conditions, and the deviation between the former and latter values is small under near zero-tension and large cyclic loading amplitude conditions. The use of the Δ J defined by ( J m a x − J m i n ) should be limited to the cases where near zero-tension and large cyclic loading amplitude conditions are satisfied.