Abstract
The existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. Despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important. The purpose of the present investigation is to study by means of accurate 3D finite element (FE) models a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic plates. An extended version of the present work has recently been published in the literature. The results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked components under anti-plane loading. The influence of plate bending is increasingly important as the thickness decreases. It appears that a new field parameter, probably a singularity, is needed to describe the stresses at the free surfaces. Discussion on whether KIII tends to zero or infinity as a corner point is approached is futile because KIII is meaningless at a corner point. The intensity of the local stress and strain state through the thickness of the cracked components has been evaluated by using the strain energy density (SED) averaged over a control volume embracing the crack tip. The SED has been considered as a parameter able to control fracture in some previous contributions and can easily take into account also coupled three-dimensional effects. Calculation of the SED shows that the position of the maximum SED is independent of plate thickness. Both for thin plates and for thick ones the maximum SED is close to the lateral surface, where the maximum intensity of the coupled mode II takes place.
Highlights
Crack tip surface displacements in the vicinity of a corner point in which a crack front intersects a surface are often of practical interest
There has been a lot of discussion on whether KIII tends to zero or infinity as a corner point is approached [3]
When apparent KIII values are calculated from stresses at a constant distance from the crack tip KIII appears to tend to zero as the model surface is approached (Fig. 7), in accordance with the linear elastic prediction
Summary
Crack tip surface displacements in the vicinity of a corner point in which a crack front intersects a surface are often of practical interest. There do not appear to be any exact analytic solutions for corner point singularities In their analysis Bažant and Estenssoro [5] assumed that all three modes of crack tip surface displacement are of the form rλρpF(θ, ), where ρ is distance from the crack tip, and p is a given constant. The implication is that the non linearities cannot be regarded as being in a core region within a corner point singularity dominated region and that Bažant and Estenssoro’s prediction that KIII tends to infinity as a corner point is correct. The SED, once the control volume is properly modeled through the thickness of the plate, is able to quantify the 3D effects in comparison with the sensitivity of the specific material so providing precious information for the fracture assessment
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