On the evaluation of energy release rate and mode mixity for ductile asymmetric four point bend specimens

A method for evaluating the contributions from mode I and II components of loading to the energy release rate J in ductile asymmetric four-point bend (4-PB) specimens is proposed. The validity of the method is established by conducting elastic-plastic finite element analysis of several asymmetric 4-PB specimens exhibiting a range of mode mixities from pure mode I to II and having different crack length to width (a / W) ratios. Further, a definition of plastic mode mixity is introduced based on the near-tip opening and sliding displacements. This definition and the proposed method to evaluate J are easy to apply since the required crack opening and sliding displacements can be determined from in-situ optical imaging coupled with Digital Image Correlation (DIC) technique. The application of the proposed methodology is demonstrated by analyzing mixed-mode fracture experiments being conducted with a magnesium alloy. It is found that the critical value of J at crack initiation reduces as loading changes from mode I to II.