A B S T R A C T In many practical cases, the crack growth leads to abrupt failure of components and structures. For reasons of a reliable quantification of the endangerment due to sudden fracture of a component, therefore, it is of enormous importance to know the threshold values, the crack paths and the growth rates for the fatigue crack growth as well as the limiting values for the beginning of unstable crack growth (fracture toughness). This contribution deals with the complex problem of a-however initiated-crack, that is subjected to a mixed-mode loading. It will present the hypotheses and concepts, which describe the superposition of Mode I and Mode II (plane mixed mode) as well as the superposition of all three modes (Mode I, II and III) for spatial loading conditions. Those concepts admit a quantitative appraisal of such crack situations and a characterization of possible crack paths.
Whatever the external loading, a crack front in a solid tries to reach mode I loading conditions after propagation. In mode I + II, the crack kinks to annihilate mode II, kinking angle being well predicted by the principle of local symmetry (PLS) or by the maximum tangential stress criterion (MTS). In presence of mode III, the problem becomes three-dimensional and the proposed propagation criterion are not yet well proved and established. In particular in three point bending experiments (3PB) with an initially inclined crack, the crack twists around the direction of propagation to finally reach a situation of pure mode I. The aim of the paper is to compare the propagation paths predicted by two different criteria for 3PB fatigue experiments performed on PMMA. The first criterion developed by Schollmann et al. (Int J Fract 117(2):129-141, 2002), is a three-dimensional extension of the MTS criterion and predicts the local angles that annihilates mode II and III at each point of the front. The second one developed by Lazarus et al. (J Mech Phys Solids 49 (7): 1421-1443, 2001b), predicts an abrupt and then progressive twisting of the front to annihilate mode III. Due to presence of sign changing mode II and almost uniform mode III in the experiments, both criteria give good results. However, since mode III is predominant over mode II in the case under consideration, the global criterion gives better results. Nevertheless, the local type criterion seems to be of greater universality for practical engineering applications.Keywords Brittle fracture · Mode II · Mode III · Maximum tangential stress criterion · 3D crack propagation path · 3D fracture criteria · LEFM
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