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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]

A dynamic mode-I energy release rate (ERR) of a double cantilever beam (DCB) under impact from a striker is derived for the first time for isotropic and orthotropic composite materials, accounting for DCB properties, a striker mass and an initial impact velocity. This is achieved in the context of structural vibration analysis by employing beam dynamics. It is found that the initial impact velocity determines the magnitude of the ERR, which is proportional to the velocity squared, while the delamination length ratio and the mass ratio between the striker and the DCB defines the time response. To understand the transient effect, a dynamic factor is defined as a function of the mass ratio. This factor decreases with an increasing striker mass, indicating a transition in the dynamic response from flexural-wave dominant to quasi-static-motion dominant, allowing an attunable dynamic effect. The developed theory is verified against the finite-element simulations for isotropic and orthotropic materials as well as experimental verification using published data. This work allows the measurements of fracture toughness under the impact load with the derived analytical solution. In addition, the developed theory can guide a design of impact tests and provide a fundamental understanding of impact-induced fracture for carbon-fiber-reinforced plastics. [Display omitted] [ABSTRACT FROM AUTHOR]

The dynamic mode-II energy release rate of the end-notched flexure (ENF) test with applied time-dependent displacement is derived for the first time with the effect of vibration included. A dynamic Euler-Bernoulli beam theory is employed together with a deflection condition to simulate contact. To investigate the dynamic effect and the relative dynamic contribution from each vibration mode, a dynamic factor and a spatial factor are defined. It is found that the contribution of the i th vibration mode is dependent on the spatial factor (which is a function of the delamination length and the total length of the ENF specimen) and that certain vibration modes are dominant (depending on the delamination-length ratio). In addition, for a given spatial factor, there may be a certain vibration mode with a zero contribution to the ERR. The developed theory is verified against results from finite-element-method simulation for two cases of ENF tests and they are in excellent agreement. This work now allows the loading rate-dependent mode-II delamination toughness of layered materials to be determined using ENF tests. In addition, it provides understanding of the structural dynamic response in the presence of mode-II delamination and can guide the design of structures to mitigate the vibration-driven 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]

• Analytical theory for energy release rate with account for dynamics and vibration. • Double cantilever beam (DCB) modeled with Euler-Bernoulli beams. • Derived expressions are short, mathematically-elegant and convenient-to-use. • Dynamic factor is defined and proven to be an intrinsic property of the DCB structure. • Finite-element method simulations verify the analytical theory with good agreement. Assessment of the energy release rate (ERR) of layered material structures with account for dynamic and vibration effects is important for understanding and predicting fracture behavior in various engineering applications. In this work, the pure-mode-I interfacial fracture behavior of a symmetric double cantilever beam (DCB) under constant-rate opening displacement is studied using a dynamics and vibration analysis of Euler-Bernoulli beams, and the ERR is derived. Furthermore, a 'dynamic factor' that quantifies the dynamic effect in relation to the static component of ERR is defined. The resulting expressions are relatively short, mathematically elegant and convenient-to-use by engineers and researchers, which increases their usefulness. It is found that the dynamic factor is a function of the characteristic time only, and that this is an intrinsic property of DCB structures. An approximate method is also proposed to predict the crack extension. Predictions of ERR and crack extension are in good agreement with results from numerical results with finite-element method (FEM) simulations. Using only the first vibration mode is sufficient to capture the amplitude and frequency of ERR variation predicted by the FEM. Using higher-order vibration modes causes divergence in the amplitude of ERR oscillation; this is due to the limitation of Euler-Bernoulli beams in vibration analysis. [ABSTRACT FROM AUTHOR]

The theory of dynamic three-point bending tests under high-loading rates is developed for the first time with account for structural vibration. Analytical solutions for dynamic normal (flexural) and shear stresses are derived. To study the dynamic effect, dynamic factors for both types of stresses are defined and investigated by employing a dimensionless characteristic time and a strain rate. It is found that both dynamic factors attenuate with respect to the characteristic time and, therefore, the quasi-static time thresholds and loading conditions are obtained. In addition, the dominant failure mode is studied for potential application in brittle materials in terms of normal-to-shear stress ratio, which is oscillatory in contrast to the quasi-static case. The developed theory is verified with a split Hopkinson bar test together combined with digital image correlation as well as finite-element simulations. The findings of this study can provide a guideline for test design, such as selection of specimen geometry and loading rate. As the theory provides a modal decomposition of dynamic normal and shear stresses, it can also be used in the field of structural health monitoring. • Development of theory for dynamic three-point bending under high loading rates accounting for structural vibration. • Evolution of dynamic factors to derive classification of dynamic and quasi-static condition and loading rates. • Investigation of the dominant failure mode with respect to the normal-to-shear stress ratio. • Verification of the developed theory against Hopkinson bar test with digital image correlation method. [ABSTRACT FROM AUTHOR]