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

Abstract

The presented work introduces a numerical parametric study on the crack propagation direction under mixed-mode conditions (mode I + II). It is conducted for the geometry of an eccentric asymmetric four-point bending of a single edge notched beam specimen; various levels of mode-mixity are ensured by modifications in the crack length and crack eccentricity. The direction of crack propagation is estimated semi-analytically using 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 (from verification reasons). Multi-parameter fracture mechanics is employed in the presented work for precise analytical evaluation of the stress field in the cracked specimen. This theory is based on description of the stress and deformation fields in the cracked body by means of their approximation using several initial terms of the Williams power series. Recent studies show that utilization of only first term of the series, which corresponds to the stress intensity factor (SIF), the single controlling parameter for the crack initiation and propagation assessment in brittle materials, is insufficient in many crack problems. It appears also in this study that the higher-order terms of the asymptotic crack-tip field are of great relevance for the conducted analysis, similarly to a number of other fracture phenomena (near-crack-tip stress field approximation, non-linear zone extent estimation, etc.).The presented work introduces a numerical parametric study on the crack propagation direction under mixed-mode conditions (mode I + II). It is conducted for the geometry of an eccentric asymmetric four-point bending of a single edge notched beam specimen; various levels of mode-mixity are ensured by modifications in the crack length and crack eccentricity. The direction of crack propagation is estimated semi-analytically using 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 (from verification reasons). Multi-parameter fracture mechanics is employed in the presented work for precise analytical evaluation of the stress field in the cracked specimen. This theory is based on description of the stress and deformation fields in the cracked body by means of their approximation using several initial terms of the Williams power series. Recent studies show that utilization of only first term of the series, which corresponds to the stress intensity factor (SIF), the single controlling parameter for the crack initiation and propagation assessment in brittle materials, is insufficient in many crack problems. It appears also in this study that the higher-order terms of the asymptotic crack-tip field are of great relevance for the conducted analysis, similarly to a number of other fracture phenomena (near-crack-tip stress field approximation, non-linear zone extent estimation, etc.).