An analytical solution for determining crack length correction of double cantilever beam tests

The double cantilever beam (DCB) specimen has been standardized by ASTM standard for measuring the mode I interlaminar fracture toughness of composite laminates. Modified beam theory (MBT) is one of the three data reduction schemes in ASTM standard, where the crack length correction term Δ is usually determined by fitting the experimental data. It is effective when the interface failure is a linear elastic fracture. However, some non-linear elastic fracture phenomena caused by fiber bridging often occur. Although the delamination initiation can still be regarded as linear elastic fracture, the critical strain energy release rate (SERR) may not be correctly calculated by MBT if Δ is determined by fitting the compliance data influenced by fiber bridging. Thus, in this study, two new analytical expressions of Δ are proposed by using Timoshenko beam based on cohesive zone model (TB-CZM) and based on infinite rigid interface (TB-IRI). Experimental results of unidirectional and multidirectional laminates with different material systems are used to verify the effectiveness of the analytical solutions. And for comparisons, three classical beam theories including Euler-Bernoulli beam based on clamped crack tip (EB-CCT), Euler-Bernoulli beam based on Elastic Foundation (EB-EF) and Timoshenko beam based on Elastic Foundation (TB-EF) are also used to calculate Δ. It is found that the results of TB-CZM have the highest accuracy, the results of TB-IRI show the same precision as those of TB-EF, but the equations based on TB-IRI are more concise. This work provides insights to accurately calculate the critical SERR of DCB tests.