Mixed mode failure criteria for brittle elastic V-notched structures

Priel, Esther; Bussiba, A.; Gilad, Ilan; Yosibash, Zohar

doi:10.1007/s10704-007-9098-x

Cited by 40 publications

(34 citation statements)

References 24 publications

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“…It has been demonstrated that the sharp V-notch criterion presented in Yosibash et al (2006) is the limiting case where the V-notch tip radius a → 0. Using mixed mode experimental data reported in Priel et al (2007) on PMMA we demonstrate that the correction brings the predicted sharp V-notch values closer to the experimental observations (Fig. 18).…”

Section: Discussionsupporting

confidence: 80%

“…To the best of our knowledge, mixed mode loading on V-notch specimens with different notch radii are reported only in Yosibash et al (2006), Priel et al (2007). There three point bending (3PB) experiments conducted on PMMA blunt V-notched specimens are detailed.…”

Section: Comparison With Experimental Resultsmentioning

confidence: 99%

“…The specimens considered are sets b1 and b2 having a V-notch opening angle of ω = 315 • and notch tip radii of a = 0.03 and a = 0.25 mm respectively with K I c = 1.12 MPa √ m (averaged value), E = 3100 MPa, ν = 0.36 and σ c = 111.8 MPa. In Yosibash et al (2006), Priel et al (2007) the failure load and failure initiation angle were predicted by the assumption Table 3 Mixed mode loading: H i j (µ) for ω = 315 • , E = 1, ν = 0.3, α 1 = 0.5050097, α 2 = 0.6597016, a = 0.03, ρ 1 = 80, ρ 2 = 110, ρ ∞ = 250 of a sharp V-notch, being corrected herein to include the influence of the notch tip radius. Table 7 summarizes the experimental data and the failure loads predicted by the assumption of a sharp V-notch and these predicted including the influence of the notch tip radius.…”

Section: Comparison With Experimental Resultsmentioning

confidence: 99%

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Failure initiation at a blunt V-notch tip under mixed mode loading

2008

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A criterion to predict crack onset at a sharp V-notch tip in homogeneous brittle materials under a mixed-mode loading was presented and validated by experimental observations in a previous paper by the authors. This criterion slightly underestimates the experimental loads causing failure which is attributed to a small notch tip radius that blunts the sharp corner. This discrepancy is rigorously analyzed mathematically in this paper by means of matched asymptotics involving 2 small parameters: a micro-crack increment length and the notch tip radius. A correction is brought to the initial prediction and a better agreement is obtained with experiments on PMMA notched specimens.Keywords Failure initiation · Mixed-mode fracture · Generalized stress intensity factors · V-notch · U-notchGeneralized stress intensity factors (GSIFs), mode I and mode II, associated with the sharp V-notch A 1c , A blunt 1c Critical mode I GSIF for sharp/blunt V-notch α 1 , α 2 Sharp V-notch singularity exponents λ, GThe two Lamé constants E, ν Young modulus and Poisson ratio G c , σ c , K I c Fracture toughness, stress at brittle failure and plane-strain critical SIF , 0 Crack length and critical crack length at the V-notch tip

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Section: Discussionsupporting

confidence: 80%

Section: Comparison With Experimental Resultsmentioning

confidence: 99%

Section: Comparison With Experimental Resultsmentioning

confidence: 99%

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Failure initiation at a blunt V-notch tip under mixed mode loading

2008

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“…In those papers the SED was given in terms of generalized NSIF. Worth mentioning is also the proposal by Priel et al (2007) dealing with sharp notches under a mixed mode.…”

Section: Introductionmentioning

confidence: 99%

Generalised stress intensity factors for rounded notches in plates under in-plane shear loading

2011

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The Notch Stress Intensity Factors (NSIFs) quantify the intensities of the asymptotic linear elastic stress distributions of sharp (zero radius) V-shaped notches. When the notch tip radius is different from zero, the singular sharp-notch field diverges from the rounded-notch solution in the close neighborhood of the notch tip. Nevertheless the NSIFs might continue to be parameters governing fracture if the notch root radius is small enough. Otherwise they can be seen simply as stress field parameters useful in quantifying the stress distributions ahead of the specific notch. Taking advantage of some analytical formulations which are able to describe stress distributions ahead of parabolic, hyperbolic and V-shaped notches with end holes, the paper discusses the form and the significance of the NSIFs with reference to in-plane shear loading, considering explicitly the role played by the notch opening angle and the notch tip radius. These parameters quantify the stress redistribution due to the root radius with respect to the sharp notch case to which they should naturally tend for decreasing values of the notch radius

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“…In general case, for notched bodies under mixed mode loading only several fracture criteria have been proposed (Papadopoulos and Poniridis 1988;Seweryn and Mróz 1995;Dunn et al 1997b;Hallström and Grenestedt 1997;Seweryn and Łukaszewicz 2002;Yosibash et al 2006;Tovo et al 2006;Berto et al 2007;Gómez et al 2007;Priel et al 2007;Susmel and Taylor 2008;Gómez et al 2008).…”

Section: Fracture Criterion For Notched Solidsmentioning

confidence: 99%

Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches

Savruk

Kazberuk

2009

Int J Fract

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The survey of research on the problems of fracture mechanics of solids with V-shaped notches is discussed. The methods of solution of plane problems of the elasticity theory for domains with angular points on boundary contours are considered. Special attention is paid to the results of the research which authors obtained applying the unified approach to the solution of stress concentration problems in the neighborhood of the vertices of sharp and rounded V-notches. The solutions of elastostatics problems for domains with rounded V-shaped notches were obtained by singular integral equation method. Based on the relation between stress intensity factor at the sharp notch vertex and the stress concentration factor at the vertex of rounded V-notch (notch with straight edges and vertex rounded with circular arc), the stress intensity factors for V-notches in various domains were obtained. The presented examples include notch stress intensity factors for periodically placed notches in the edge of halfplane, diamond and lens-like holes in infinite plane. Through limit transition from the system of periodically placed diamond-shaped ovals to infinite doublesided notch, the stress concentration factors for rounded deep V-notch and the notch stress intensity factors for sharp notch were obtained. The comparison between calculated data and known solutions for the hyperbolic notch documents strong influence of the notch shape in the neighborhood of the rounded vertex on the stress concentration values for small vertex radii. The numerical results are presented not only in graphical form but also the numerous approximation formulas are given. Based on the solution of the nonlinear problem of rounded V-notch with plastic strip at the vertex, the new deformation fracture criterion is proposed. This criterion contains only standard strength parameters and it is intended to determine fracture toughness of the elements with rounded notches made of quasibrittle materials.

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Mixed mode failure criteria for brittle elastic V-notched structures

Cited by 40 publications

References 24 publications

Failure initiation at a blunt V-notch tip under mixed mode loading

Failure initiation at a blunt V-notch tip under mixed mode loading

Generalised stress intensity factors for rounded notches in plates under in-plane shear loading

Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches

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