Failure criteria for linear elastic materials with U-notches

This paper provides a simple, albeit accurate, criterion for prediction of the rupture loads of brittle, or quasi-brittle, U-notched samples, where linear elastic fracture mechanics is not applicable because blunted notches do not exhibit stress singularities. Good agreement is found between numerical predictions and experimental results. The results of fracture tests from 18 different ceramic materials and a polymer (at  − 60°C) are summarized and are used as a reference for checking the fracture criterion. Seven fracture criteria are reviewed and it is shown that all can be recast into the proposed criterion.

[1]  G. Sih.  Strain-energy-density factor applied to mixed mode crack problems , 1974 .

[2]  W. M. Rainforth,et al.  The effects of notch width on the SENB toughness for oxide ceramics , 1992 .

[3]  David Taylor,et al.  The fracture mechanics of finite crack extension , 2005 .

[4]  F. Berto,et al.  Some Expressions for the Strain Energy in a Finite Volume Surrounding the Root of Blunt V-notches , 2005 .

[5]  V. V. Novozhilov,et al.  On a necessary and sufficient criterion for brittle strength: PMM vol. 33, n≗2, 1969, pp. 212–222 , 1969 .

[6]  Paul C. Paris,et al.  Elastic field equations for blunt cracks with reference to stress corrosion cracking , 1967 .

[7]  Jaime Planas,et al.  The cohesive crack concept: application to PMMA at −60 °C , 2005 .

[8]  Kotoji Ando,et al.  EFFECTS OF CRACK LENGTH, NOTCH ROOT RADIUS AND GRAIN SIZE ON FRACTURE TOUGHNESS OF FINE CERAMICS , 1993 .

[9]  Paolo Lazzarin,et al.  A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V-shaped notches , 2001 .

[10]  Andrzej Seweryn,et al.  Brittle fracture criterion for structures with sharp notches , 1994 .

[11]  D. Munz,et al.  Fracture Toughness Determination of A12O3 Using Four‐Point‐Bend Specimens with Straight‐Through and Chevron Notches , 1980 .

[12]  Z. Bažant,et al.  Fracture and Size Effect in Concrete and Other Quasibrittle Materials , 1997 .

[13]  Ando,et al.  An investigation into the location of crack initiation sites in alumina, polycarbonate and mild steel , 1999 .

[14]  M. Elices,et al.  The cohesive zone model: advantages, limitations and challenges , 2002 .

[15]  Roberto Tovo,et al.  Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates , 2002 .

[16]  M. Elices,et al.  A fracture criterion for blunted V-notched samples , 2004 .

[17]  P. Lukas,et al.  Stress intensity factor for small notch-emanated cracks , 1987 .

[18]  Paolo Lazzarin,et al.  A generalized stress intensity factor to be applied to rounded V-shaped notches , 2006 .

[19]  Dominique Leguillon,et al.  Strength or toughness? A criterion for crack onset at a notch , 2002 .

[20]  Zohar Yosibash,et al.  Crack onset at a v-notch. Influence of the notch tip radius , 2003 .

[21]  F. J. Gómez,et al.  Fracture loads for ceramic samples with rounded notches , 2006 .

[22]  Zohar Yosibash,et al.  Failure criteria for brittle elastic materials , 2004 .

[23]  R. Bertolotti.  Fracture Toughness of Polycrystalline Al2O3 , 1973 .

[24]  Grzegorz Glinka,et al.  Energy density approach to calculation of inelastic strain-stress near notches and cracks , 1985 .

[25]  George A. Gogotsi,et al.  Fracture toughness of ceramics and ceramic composites , 2003 .

[26]  Ioannis Chasiotis,et al.  The mechanical strength of polysilicon films: Part 2. Size effects associated with elliptical and circular perforations , 2003 .

[27]  M. Elices,et al.  Assessment of defect size in brittle fibers , 2002 .

[28]  John R. Rice,et al.  ON THE RELATIONSHIP BETWEEN CRITICAL TENSILE STRESS AND FRACTURE TOUGHNESS IN MILD STEEL , 1973 .