J integral solution for beam-like fracture specimens with arbitrary symmetric cross-sectional geometry and material properties

A closed form J integral solution is derived for beam-like specimens loaded with axial forces and bending moments, including residual stresses, for functionally graded materials with elastic and thermal properties varying both in the thickness and the width direction. The cross-sections may be of any shape but must be symmetric (in terms of geometry and material properties) with respect to a plane perpendicular to the cross-section and the crack plane. A J integral solution can thus be obtained for important cases of fracture mechanics test specimens such as the double cantilever beam with symmetrical side grooves.