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 fourpoint 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 semianalytically 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.).
Highlights
I t is well known that the classical fracture mechanics concept is based on the existence of the stress intensity factor that expresses the amplitude of the singular term describing the stress distribution in a cracked specimen
The results are presented in the form of dependences of the initial crack propagation direction angle γ on the relative crack length ( = a/W = 0.1 0.9)
The semi-analytical results, denoted as "N = M = 1, 2, 4, 7 and 10": crack propagation direction angle γ is determined from the multi-parameter/generalized form of the fracture criteria, i.e. the maximum of the tangential stress and minimum of the strain energy density, respectively is being sought iteratively from Eq 3 and 6 when the stress tensor components are expressed by means of the Williams expansion (WE) considering various numbers of the initial terms of the series
Summary
I t is well known that the classical (one-parameter) fracture mechanics concept is based on the existence of the stress intensity factor that expresses the amplitude of the singular term describing the stress distribution in a cracked specimen. The specimen was meshed with PLANE82 elements, only the vicinity of the crack tip was specially refined: one row of special crack elements with shifted mid-side nodes was used around the crack tip and six more regular rings of nodes were modelled at the distances of rc = 0.2, 0.4, 1.0, 1.5, 1.8 and 3.2 mm from the crack tip These rings were utilized for the analyzes performed, : the displacements and coordinates of the nodes at the defined rings were used for the evaluation of the initial 10 terms of the WE by means of the ODM, as it is described in the text above; the corresponding stress tensor components in the nodes at the defined rings were used for the direct evaluation of the fracture criteria. It is assumed that this value should be a material property, i.e. it should be constant for the particular material and should be related to material characteristics, see several suggestions in [22,23,24]
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