Abstract
A mixed-mode geometry has been chosen to investigate a crack propagation using the multi-parameter fracture mechanics concept. The so-called Williams’ series expansion is used for the crack-tip stress field approximation. It has been shown that application of the generalized fracture mechanics concept can be crucial for materials with specific fracture behaviour, such as elastic-plastic or quasi-brittle one, when fracture occurs not only in the very vicinity of the crack tip, but also in a more distant surrounding. Then, considering the higher-order terms of the Williams’ expansion in fracture criteria (describing the crack stability and/or crack propagation direction) can bring more precise results. The coefficients of the Williams’ expansion must be calculated numerically (for instance by means of the over-deterministic method in this work) for each cracked configuration, which is very time-consuming, and the analysis is very extensive even for a few basic cracked specimen configurations. On the other hand, a suitable choice of the geometrical configuration of the cracked disc enables performing experiments only on the specimens that could prove the theory about the importance of using the higher-order terms.
Highlights
A lthough fracture mechanics has been studied for approximately one century, proper assessment of crack behaviour is still under investigation of many researchers
A) Maximum Tangential Stress criterion (MTS), = a/R = 0.2, rc = 0.1 mm b) MTS, = a/R = 0.2, rc = 1.0 mm c) Strain Energy Density (SED), = a/R = 0.2, rc = 0.1 mm d) SED, = a/R = 0.2, rc = 1.0 mm criterion applied at critical distances of 0.1 mm and 1.0 mm for various crack inclination angles ( = 10, 20, 30, 40 and 50°) and considering various numbers of initial terms of Williams’s expansion (N, M = 1, 2, 3, 6 and 10)
If the suggested approach is not able to describe the crack path in the fine-grained composite based on the alkali-activated slag as a quasi-brittle material, other fracture criteria should be applied, such as maximum average tangential stress (MATS) criterion [29] or others
Summary
A lthough fracture mechanics has been studied for approximately one century, proper assessment of crack behaviour is still under investigation of many researchers. Crack-tip field; Multi-parameter fracture mechanics; Finite element analysis; Mixed-mode; Williams’ expansion.
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