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The dynamic mode-I energy release rate of cracks propagating along elastic interfaces in double cantilever beams under high loading rates is derived analytically for the first time by accounting for structural vibration, wave propagation, and the Doppler effect along with the assumption of crack tip energy conservation. The developed theory can be used to study the "stick-slip" crack propagation behavior commonly observed in experiments, a progression of crack initiation, propagation, arrest, and reinitiation. In addition, the developed theory can be applied to measure crack initiation toughness as well as crack arrest toughness. The developed theory is verified against results from finite-element-method simulations of two experimental cases under high loading rates, demonstrating the excellent ability of the developed theory in capturing the crack propagation behavior as well as the ability in assessing dynamic mode-I energy release rate. [ABSTRACT FROM AUTHOR]

• Analytical theory for dynamic energy release rate of a double cantilever beam. • Consideration of dynamics, including vibration, and dispersive wave propagation. • Stationary and propagating delamination under high loading rate are both considered. • Theory predicts dynamic energy release rate, and initiation, propagation and arrest. • Finite-element-method simulations and experimental results validate the theory. Analytical theory for the dynamic delamination behavior of a double cantilever beam (DCB) under high loading rate is developed. Structural vibration and wave dispersion are considered in the context of Euler-Bernoulli beam theory. The theory is developed for both initiation and propagation of delamination in mode I. Two solutions for the energy release rate (ERR) are given for a stationary delamination: an accurate one and a simplified one. The former is based on global energy balance, structural vibration and wave dispersion; the latter is 'local' since it is based on the crack-tip bending moment. For the simplified solution to be accurate, sufficient time is needed to allow the establishment of all the standing waves. For a propagating delamination, a solution for the ERR is derived using the same simplification with the crack-tip bending moment. The obtained ERR solutions are verified against experimental data and results from finite-element simulations, showing excellent agreement. One valuable application of the developed theory is to determine a material's dynamic loading-rate-dependent delamination toughness by providing the analytical theory to post-process test results of dynamic DCB delamination. [ABSTRACT FROM AUTHOR]

• Analytical theory for dynamic energy release rate of a double cantilever beam. • Consideration of dynamics, including vibration, and dispersive wave propagation. • Dynamic factor due to vibration quantifies contribution from each vibration mode. • Finite-element-method simulations verify the analytical theory with good agreement. The dynamic energy release rate (ERR) is derived for a delamination on the interface between a partially supported vibrating beam and an elastic foundation, with a time-dependent displacement applied to the beam's free end. The configuration may represent, for example, the dynamic delamination of a laminated composite, or the cracking of a typical adhesively bonded composite joint. The developed theory is completely analytical and applicable to both symmetric double cantilever beams (DCBs) and thin layers on thick substrates. It was discovered that the dispersive propagation of flexural waves should be considered in order to capture contributions to the ERR from higher-order vibration modes. The developed theory is verified using finite-element-method (FEM) simulations and they are found to be in excellent agreement. This work will be useful to characterize the dynamic fracture toughness of layered materials in DCB tests, and to determine the fracture behavior of engineering structures under dynamic loads. Furthermore, the partially supported beam's elastic foundation is relevant for the study of crack process zones, which are usually analyzed using the FEM and the cohesive-zone model. The potential applications of this study include determining the dynamic fracture toughness for crack initiation in laminated composite DCBs and adhesively bonded structures. [ABSTRACT FROM AUTHOR]