An Approximate Solution of Compact Test Specimen for Mode I Fracture Test by Variational Approach: Applied to Fibrous Composite

Yuling Bian, Baolu Sheng, Aiping Zhou


The present work presented an approximate solution for a compact test (CT) specimen that was employed as a standard test provided by ASTM E399-19 (2019). The variational method was employed to obtain the solution. The method used a two-step strategy to approximate the displacement response of the CT specimen. The first step was to obtain the general form of displacement solution, and then, the Rayleigh-Ritz approach was employed to modify the solution of the first step. A compliance equation of the CT specimen was obtained, and furthermore, the formula to calculate the stress intensity factor was obtained. The solution was validated by finite element (FE) model and the formula specified in ASTM E399-19 (2019). It was concluded that the calculation results of the proposed solution agreed well with the results of the FE model prediction for the ratio of initial crack length-to-ligament length, which was in the range of 0.25 to 0.35. Furthermore, compared to the results predicted by using the formula addressed in ASTM E399-19 (2019), the method proposed in the present study can achieve closer results than that of the FE model.


Mode I fracture; Fracture toughness; Variational approach; Compact specimen

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