A J-integral approach in characterizing the mechanics of a horizontal crack embedded in a cantilever beam under an end transverse force

•J-integral estimates are developed for a beam containing a fully embedded horizontal crack.•The J-integral is evaluated with the aid of a mechanics of material model developed elsewhere.•Compliance method energy release rates are also developed.•The analytical J-integral estimates are compared favorably to 2D finite element results.•A maximum in the J-integral is shown to exist for cracks located at the beam mid-plane.

For a cantilever beam with an embedded sharp crack and subjected to an end transverse force, the J-integral approach was employed in developing analytical estimates of the energy release rate made available to the left and right crack tip. Finite element studies also revealed that mode II conditions dominate the tip regions of such a crack (Fang and Charalambides, 2015). Thus, analytical estimates of the mode II stress intensity factor dominating each of the crack tip regions are also obtained. The analytical energy release rate predictions are compared to 2-D finite elements for a broad range of crack depths and crack center location along the beam axis. Using energy considerations, rotary spring stiffness estimates employed in Charalambides and Fang (2016a,b) in the development of a four-beam model obtained. The outcomes of the methodology used in this work provide strong encouragement in extending the method to heterogeneous composite laminates containing delamination cracks and subjected to a combination of applied loadings. Given the predominately mode II nature of the crack considered, the solutions developed herein may be used in characterizing mode II interface fracture for bonded homogeneous layered beams.