Energy Release Rate of Double Beam-Plates with Repairing Elements

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An engineering analysis for determining the strain energy release rate of symmetrically loaded double beam-plates with repairing or reinforcing elements in the transverse direction which are densely distributed across the width in the disbond regions is presented. The concept of strain energy release rate evaluated by computing the rate of energy released from the disbond front has been verified to be exactly the same and simpler to use than the most referenced work of Kanninen by differentiation of the total strain energy of the entire system with respect to the disbond length. Due to the simplicity of the new concept for determining the strain energy release rate, it allows one to derive the exact analytical solutions for double beam-plates containing repair or reinforce elements and satisfying continuity at the delamination front as well as boundary conditions at both ends of the system. Some comparisons of the strain energy release rate for double beam-plates without repair elements to other approximations are also made. Each side of a double beam-plate system in the perfect segment is modeled as a beam-plate on an elastic foundation, while disbond segments are treated as beam-plates under transverse loading and constrained by repairing or reinforcing elements as axially loaded members at discrete points. Some numerical results for a double cantilever beam-plate with one and two rows of reinforcing elements under end loads are presented for illustrating the procedure as well as for future reference. The general concept and analysis procedure should be applicable to other structural systems and for mixed-mode delaminations.