Abstract
Double-cantilever beams (DCBs) are widely used to study mode-I fracture behavior and to measure mode-I fracture toughness under quasi-static loads. Recently, the authors have developed analytical solutions for DCBs under dynamic loads with consideration of structural vibration and wave propagation. There are two methods of beam-theory-based data reduction to determine the energy release rate: (i) using an effective built-in boundary condition at the crack tip, and (ii) employing an elastic foundation to model the uncracked interface of the DCB. In this letter, analytical corrections for a crack-tip rotation of DCBs under quasi-static and dynamic loads are presented, afforded by combining both these data-reduction methods and the authors’ recent analytical solutions for each. Convenient and easy-to-use analytical corrections for DCB tests are obtained, which avoid the complexity and difficulty of the elastic foundation approach, and the need for multiple experimental measurements of DCB compliance and crack length. The corrections are, to the best of the authors’ knowledge, completely new. Verification cases based on numerical simulation are presented to demonstrate the utility of the corrections.
Highlights
Double cantilever beams (DCBs) (Fig. 1a) are widely used to study mode-I fracture behavior and to measure mode-I fracture toughness
The beam-theory-based data-reduction method in these standards assumes an effective boundary condition to calculate the energy release rate (ERR), whereby each DCB arm is perfectly built-in at the crack tip (Fig. 1b)
Results from Eq (1) for ERR based on the effective boundary condition without any correction for cracktip rotation are shown in Fig. 3 alongside FEM simulation results
Summary
Double cantilever beams (DCBs) (Fig. 1a) are widely used to study mode-I fracture behavior and to measure mode-I fracture toughness. This is sometimes called the modified beam theory (MBT) method (ASTM D5528 2014) Another data-reduction method is to introduce an elastic foundation to model the uncracked region of the DCB (Fig. 1c) (Kanninen 1973). Cabello et al (2016) reported a general analytical model for the relationship between the Young’s modulus of the adhesive Eadhesive and the foundation stiffness k under plane-strain conditions. It is worth noting the difference between the foundation modulus k0 (with SI units of N m−3) seen in some works, and the foundation stiffness k (with SI units of N m−2) used by Kanninen (1973) and in this letter. DCB arm with effective boundary condition; c DCB arm with uncracked region resting on elastic foundation
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