Strength or toughness? A criterion for crack onset at a notch

By D. Leguillon. 2002

921 citations recorded by the source corpus.

Both energy and stress criteria are necessary conditions for fracture but neither one nor the other are sufficient. Experiments by Parvizi et al. on transverse cracking in cross-ply laminates corroborate this assumption. Thanks to the singularity at the tip of the notch, the incremental form of the energy criterion gives a lower bound of admissible crack lengths. On the contrary, the stress criterion leads to an upper bound. The consistency between these two conditions provides a general form of a criterion for crack nucleation. It enjoys the desirable property of coinciding with the usual Griffith criterion to study the crack growth and with the stress criterion for the uniform traction along a straight edge. Comparisons with experiments carried out on homogeneous notched materials and on bimaterial structures show a good agreement.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/29110c4969b2c101faae87c9f5d2412ec4b5b438

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

1. A. Kazberuk
2. M. Savruk
3. Pedro P. Camanho
4. F. J. Gómez
5. M. Elices
6. P. Lazzarin
7. G. Catalanotti
8. V. Mantič 

Citations in the corpus

• A failure criterion for brittle elastic materials under mixed-mode loading (2006, methodology): “Therefore, we herein extend the failure criterion presented by Leguillon (2002), based on finite fracture mechanics concept, to mixed mode loading.”
• Finite fracture mechanics: A coupled stress and energy failure criterion (2006, methodology): “The present criterion is close to the one proposed in Leguillon [22,23], where it was applied successfully to the prediction of the failure load of a three point bending beam with re-entrant corners of different amplitude.”
• Failure criteria for brittle elastic materials (2004, methodology): “Leguillon (2001, 2002) proposed a criterion for failure initiation at a sharp V-notch based on a combination of the Griffith energy criterion for a crack, and the strength criterion for a straight edge.”
• Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches (2010, background): “For symmetrically loaded notches (mode I), likewise as for the cracks (Irwin 1957), the following local stress criterion is used most often (Cherepanov 1979; Ibragimov and Romanchak 1984; Berkun and Protsenko 1985; Carpinteri 1987; Seweryn 1994; Dunn et al. 1997a,b; Leguillon 2002; Leguillon and Yos”
• Toughness or strength? Regularization in phase-field fracture explained by the coupled criterion (2020, background): “We draw a comparison between the variational approach and the so-called coupled criterion (Leguillon, 2002).”
• Crack onset at a v-notch. Influence of the notch tip radius (2003, methodology): “…(Leguillon, 2002) with a comparison with experiments (Reedy and Guess, 1993, 1997, 1999; Qian and Akisanya, 1998), failure of a bimaterial wedge (Leguillon and Siruguet, 2002) again with a comparison with experiments (Mohammed and Liechti, 2000), prove the generality of the criterion although…”
• A finite fracture mechanics approach to structures with sharp V-notches (2008, methodology): “Finally, among recent advances in the analysis of V-notched structures, we want to cite: the failure criterion proposed by Lazzarin and Zambardi [17], which assumes as a critical parameter the strain energy in a small region around the notch tip; the fracture criterion proposed by Leguillon [18,19],”
• Failure Models and Criteria for Frp Under In-Plane or Three-Dimensional Stress States Including Shear Non-Linearity (2013, neutral): “Geometry of slit crack in a thin embedded ply been observed by Dvorak and Laws [9] and Leguillon [51], and as was shown in Fig.”
• Modelling large crack propagation: from gradient damage to cohesive zone models (2012, background): “For instance, it is unable to predict crack initiation without additional ingredients such as stress thresholds (Leguillon 2002) or variational interpretations of cracking (Francfort and Marigo 1998).”
• Failure Criteria for FRP Laminates (2005, methodology): “Therefore, the in situ strengths for thick plies are independent of the ply thickness, as has been observed by Dvorak and Laws [19] and Leguillon [25], and as was shown in Figure 4.”
• Failure criteria for linear elastic materials with U-notches (2006, background): “This criterion was proposed by Leguillon (2002) and states that fracture occurs when the maximum circumferential stress at a critical distance from the notch tip and when the energy release rate at the virtual crack tip placed at the same point both reach their critical values, i.e.:”
• Characteristics of the process zone at sharp notch roots (2011, methodology): “…long way, the practical use of notch-tip intensity factors as characterizes of crack nucleation has been less popular (Cornetti et al., 2006, 2010; Leguillon, 2002), partly, perhaps, because sharp features are normally avoided in engineering design, but partly, also, because the characteristic…”
• Injection-Sensitive Mechanics of Hydraulic Fracture Interaction with Discontinuities (2014, background): “This condition can be written in terms of the energy release rate (ERR) Ginc due to incremental creation of a crack with length dl as (Jaeger et al. 2007; Janssen et al. 2004; Leguillon 2002) GincðdlÞ 1⁄4 dWn dl [ GIC; ð31Þ”
• Failure Criteria for Frp Laminates in Plane Stress (2013, neutral): “ϕσ ϕσ τ τ ϕ ( 33 ) where the absolute value of the”