Methodology for calculating J-integral range ΔJ under cyclic loading

• Published in: The International journal of pressure vessels and piping 2021-06, Vol.191, p.104343, Article 104343
• Main Authors: Hagihara, Seiya, Shishido, Nobuyuki, Hayama, Yutaka, Miyazaki, Noriyuki
• Format: Article
• Language: English
• Subjects: Cyclic J-integral; Error estimation; Fatigue crack growth; HRR singular Fields; J-integral range; Large scale yielding
• ISSN: 0308-0161; 1879-3541
• DOI: 10.1016/j.ijpvp.2021.104343

The J-integral range or the cyclic J-integral, ΔJ, is frequently utilized to deal with the fatigue crack growth of ductile materials with large scale yielding. ΔJ 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 ΔJ defined by Jmax−Jmin. Although it is theoretically shown that the latter definition of ΔJ, that is, ΔJ=Jmax−Jmin, is not equivalent to the former defined by a line integral, why is the latter definition of ΔJ utilized so frequently? This question is main concern of the present paper. To answer this question, we derive the expression of ΔJ 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 ΔJ represented by a line integral and ΔJ=Jmax−Jmin. We perform the error estimation for three-point bending specimens to clarify how accurately (Jmax−Jmin) predicts the ΔJ-value, compared with the ΔJ represented by a line integral, which is supposed to provide the exact ΔJ-value. As a result, theΔJ-value calculated from (Jmax−Jmin) is identical to the ΔJ-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 ΔJ defined by (Jmax−Jmin) should be limited to the cases where near zero-tension and large cyclic loading amplitude conditions are satisfied. •The expression of ΔJ is represented by a line integral for the HRR singular fields near a crack tip under large scale yielding.•ΔJ are derived in order to formulate the difference between the exact expression of ΔJ and that given by (Jmax−Jmin).•We perform the error estimation of ΔJ=(Jmax−Jmin) and the exact ΔJ-value for three-point bending specimens.•The ΔJ=(Jmax−Jmin) value is identical to the exact ΔJ-value in the case of the zero-tension cyclic loading conditions.•The deviation between the two kinds of ΔJ values is small under near zero-tension and large cyclic loading amplitude conditions.•As the minimum load goes away from zero, the deviation between the value (Jmax−Jmin) and the exact value of ΔJ becomes large.