Closed form second order energy release rate in a cracked elastic beam

This study presents a closed form, second order, Mode-I fracture mechanics solution for a cracked elastic beam subject to axial compressive load. The solution considers a crack with a symmetric parabolic geometric imperfection in the beam and provides the strain energy release rate (SERR) as a continuous function of the axial load level. The effect of the elastic interface is considered by means of an additional equivalent beam length determined from a Winkler beam model. The closed form solution is corroborated through numerical non-linear fracture analyses for different geometries with isotropic and transverse isotropic material properties. The results show that the analytical models provide accurate predictions with an accuracy ranging between 2% and 4%. It is analytically adduced that the second order SERR in a cracked beam subject to axial loading is stable inasmuch the SERR decreases with increasing crack length. Moreover, the results show a significant influence of the elastic interface on the SERR.