Estimation of the crack propagation direction in a mixed-mode geometry via multi-parameter fracture criteria

摘要

The presented work introduces a numerical parametric study on the crack propagation directionunder mixed-mode conditions (mode I + II). It is conducted for the geometry of an eccentric asymmetric fourpointbending of a single edge notched beam specimen; various levels of mode-mixity are ensured bymodifications in the crack length and crack eccentricity. The direction of crack propagation is estimated semianalyticallyusing both the maximum tangential stress criterion and the strain energy density criterion(implemented as a procedure within the used finite element computational code) as well as numerically (fromverification reasons). Multi-parameter fracture mechanics is employed in the presented work for preciseanalytical evaluation of the stress field in the cracked specimen. This theory is based on description of the stressand deformation fields in the cracked body by means of their approximation using several initial terms of theWilliams power series. Recent studies show that utilization of only first term of the series, which corresponds tothe stress intensity factor (SIF), the single controlling parameter for the crack initiation and propagationassessment in brittle materials, is insufficient in many crack problems. It appears also in this study that thehigher-order terms of the asymptotic crack-tip field are of great relevance for the conducted analysis, similarlyto a number of other fracture phenomena (near-crack-tip stress field approximation, non-linear zone extentestimation, etc.).