Numerical Calculation And Experimental Investigation On3D Mixed Mode Brittle Fracture Behavior

Due to the complexity of three dimensional (3D) mixed mode fracture problem, thecorresponding issue is not yet well understood and needs further investigation. Based onprevious relative studies, the3D mixed mode brittle fracture was investigated on modified allfracture modes (AFM) specimen by numerical calculation, experimental study, and theoreticaldiscussion. The corresponding theoretical meaning and engineering application value isdistinct.The compact tension shear (CTS) specimen and the AFM specimen in combination withtheir special loading devices were introduced. Based on their advantages, the modified AFMspecimen and its special loading device were proposed, and the corresponding principle of3Dfracture experiment was discussed.By suppressing corresponding boundary conditions (BCs), the plane strain conditionswere enforced on3D-model of the single edge notched tension (SENT) specimen.Non-dimensional stress intensity factors (SIFs) were calculated by virtual crack closure (VCC)method and equivalent domain integral (EDI) method respectively along the crack front. Bycomparing the numerical results with the corresponding2D reference analytical value, theVCC method was found to be so numerically accurate and handy that it can be fitful fornumerically analyzing3D mixed mode fracture problem.The fracture behavior was computationally investigated by the VCC method on AFMspecimens with three thickness ratios, under mode I, mode II, and mode III loading conditionsrespectively. The influence of thickness ratio was investigated on the distribution ofnon-dimensional SIFs along the crack front. It was obtained that although the specimen isglobally subjected to the mode II loading, the mode III fracture behavior is induced locallyalong the crack front, and vice versa. In particular, it is strong coupling effect that mode IIstresses are induced by mode III loading along the crack front. In order to reduce this couplingeffect as far as possible, the specimen with appropriate thickness was proposed in this paper.For the AFM model with the given thickness, the non-dimensional SIFs along the crackfront were calculated by the VCC method, under mixed mode I+II, mixed mode I+III, mixedmode II+III, and mixed mode I+II+III loading conditions. Based on the previous non-dimensional SIFs data, a series of non-dimensional equivalent SIFs and initial breakpointsalong the crack front were calculated by employing the Richard criterion, for pure mode I, puremode II, pure mode III, mixed mode I+II, mixed mode I+III, mixed mode II+III, and mixedmode I+II+III.Based on the proposed AFM specimen made of transparent material–PMMA and therelated loading device, a series of3D experimental investigations were performed under modeI, mode II, mode III, mixed mode I+II, mixed mode I+III, mixed mode II+III, and mixed modeI+II+III loading conditions. Correspondingly, the complete process was observed from crackinitial break, unstable propagate to final fracture. It was shown that the initial breakpointassessments by the VCC method and the Richard criterion were in agreement withcorresponding experimental findings, and the validity of the computational results wasdemonstrated.Critical loads and initiation angles, which were gained by different mixed mode loadingexperiment, were compared with three classical criterion––the maximum tangential stresscriterion (or MTS criterion), the strain energy density criterion (S criterion), and themaximum energy release rate criterion (G criterion), and recently developed3D fracturecriteria––Pook criterion and Richard criterion. It was found that the prediction by Richardcriterion agrees well with the results by fracture experiment. Therefore, Richard criterion isapplicable for predicting3D brittle fracture behavior.In this paper, with the proposed AFM specimen,3D numerical calculations andexperimental investigation were achieved for mode I, mode II, mode III, mixed mode I+II,mixed mode I+III, mixed mode II+III, and mixed mode I+II+III loading conditions. Thepromising3D fracture results can make contribution to3D brittle fracture investigation.