Comparison of predictions by mode II or mode III criteria on crack front twisting in three or four point bending experiments

Abstract

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

Development of fracture facets from a crack loaded in mode I+III: Solution and application of a model 2D problem

“…The fact that similar phenomena are observed in such diverse materials as glass (Sommer, 1969), alumina (Suresh and Tschegg, 1987), steels (Hourlier and Pineau, 1979;Yates and Miller, 1989;Lazarus, 1997), rocks (Pollard et al, 1982;Pollard and Aydin, 1988;Cooke and Pollard, 1996), PMMA (Lazarus et al, 2008), gypsum and cheese (Goldstein and Osipenko, 2012) strongly suggests that the microstructure of these materials plays little or no role and that the standard tools of macroscopic Linear Elastic Fracture Mechanics (LEFM) should be able to explain the observations made.…”

Recent developments in dynamic fracture: some perspectives

“…There are several other basic phenomena that necessitate a 3D framework of fracture dynamics. In the quasi-static regime, simulations coupled with analytic work [111][112][113][114][115] has shed light on a crack front instability under mixed-mode I+III conditions.Recently, helical perturbations have been shown, in 3D simulations, to develop into segmented crack fronts [116][117][118].Related segmented crack front structures have been observed in mode I [106,119] and mixedmode I+III fracture of of both "standard" [120][121][122][123][124][125] and soft materials [108].…”

Criterion for initiation of cracks under mixed-mode I + III loading

“…Lazarus and Leblond (2001a,b) performed a detailed analysis of the stress intensity factors for cracks loaded under arbitrary K ∞ I , K ∞ II , K ∞ III with the crack front perturbed locally; their main focus was on the determination of the stress intensity factors, energy release rates and their implication primarily on the rate of rotation of crack planes as the crack front extended; comparison of their predictions to experimental observations on the rate of rotation were found to be satisfactory. In more recent work Lazarus et al (2008) used finite element analysis to calculate the stress intensity factors and compare the rate of rotation of the crack front with four-point bend experiments and found better correlation. However, neither work addresses the problem of spacing of the crack front fragmentation.…”