Application of J-Integral in the Case of a Single Crack in Cantilever Beam

In the present study the J-integral approach has been applied to investigate a single crack in two cantilever beams made of unidirectional fiber reinforced composite. The crack is situated in the middle of the beam's cross-section and is parallel to the reinforcing fibers. The two beams are loaded in different manner, but both loading configurations are asymmetric with respect to the crack. Closed form analytical solutions of the J-integral have been obtained using the linear-elastic beam theory. It was established that in the cases under consideration the term containing the strain energy density is not equal to zero and exerts a great influence on the J-integral value. Comparisons between the J-integral expressions and the formulas for the strain energy release rate are performed and a very good agreement is obtained. The dependence of the J-integral magnitude on the crack length has been also examined and the results obtained are presented graphically. The present paper is a part of an investigation in the field of fracture behaviour of fiber reinforced composite beams.