Size effects on fracture toughness of quasi-brittle materials – A new approach

Abstract A new approach called the modified maximum tangential stress criterion has been developed for investigating size effects on mode I fracture toughness of quasi-brittle materials. This approach employs the maximum tangential stress criterion while accounting for the higher order term of Williams expansion A3. Having assumed that the FPZ length changes with the specimen size, a formulation was suggested for expressing the variation of FPZ length versus the specimen size. Some experimental results reported for concrete and limestone were employed to assess the proposed criterion. It is shown that the proposed approach provides good estimates for the experimental data.

[1]  R. A. Schmidt,et al.  A Microcrack Model And Its Significance to Hydraulic Fracturing And Fracture Toughness Testing , 1980 .

[2]  M.R.M. Aliha,et al.  Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading , 2010 .

[3]  M.R.M. Aliha,et al.  Mode I and Mode II Fracture Toughness Testing for a Coarse Grain Marble , 2006 .

[4]  X. Zhang,et al.  A criterion study for non-singular stress concentrations with size effect , 2005 .

[5]  A. Carpinteri Decrease of apparent tensile and bending strength with specimen size: two different explanations based on fracture mechanics , 1989 .

[6]  B. N. Whittaker,et al.  Rock Fracture Mechanics: Principles, Design and Applications , 1992 .

[7]  M. A. Gutiérrez,et al.  Deterministic and stochastic analysis of size effects and damage evolution in quasi-brittle materials , 1999 .

[8]  Zdenek P. Bazant,et al.  CRACK BAND MODEL FOR FRACTURE OF GEOMATERIALS. , 1982 .

[9]  Hirozo Mihashi,et al.  Size effect on fracture energy of concrete , 1990 .

[10]  X. Hu,et al.  Size Effect on Fracture of MEMS Materials , 2009 .

[11]  Abdussamet Arslan,et al.  The neural network approximation to the size effect in fracture of cementitious materials , 1996 .

[12]  Naser A. Al-Shayea,et al.  Crack propagation trajectories for rocks under mixed mode I–II fracture , 2005 .

[13]  M. Ayatollahi,et al.  Fracture Analysis of Some Ceramics Under Mixed Mode Loading , 2011 .

[14]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[15]  J. Mier,et al.  Experimental investigation of size effect in concrete and sandstone under uniaxial tension , 2000 .

[16]  Bhushan Lal Karihaloo,et al.  Higher order terms of the crack tip asymptotic field for a wedge-splitting specimen , 2001 .

[17]  F. Erdogan,et al.  On the Crack Extension in Plates Under Plane Loading and Transverse Shear , 1963 .

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

[19]  G. I. Barenblatt Self-similarity: Dimensional analysis, and intermediate asymptotics , 1980 .

[20]  M. Williams,et al.  On the Stress Distribution at the Base of a Stationary Crack , 1956 .

[21]  Alberto Carpinteri,et al.  Finite fracture mechanics: A coupled stress and energy failure criterion , 2006 .

[22]  A. A. Griffith The Phenomena of Rupture and Flow in Solids , 1921 .

[23]  S. Morel Size effect in quasibrittle fracture: derivation of the energetic Size Effect Law from equivalent LEFM and asymptotic analysis , 2008 .

[24]  Z. Bažant Size Effect in Blunt Fracture: Concrete, Rock, Metal , 1984 .

[25]  Bhushan Lal Karihaloo,et al.  Higher order terms of the crack tip asymptotic field for a notched three-point bend beam , 2001 .

[26]  Surendra P. Shah,et al.  Two Parameter Fracture Model for Concrete , 1985 .

[27]  Jin-Keun Kim,et al.  Size Effect on Compressive Strength of Plain and Spirally Reinforced Concrete Cylinders , 1999 .

[28]  Bhushan Lal Karihaloo,et al.  Size effect in shallow and deep notched quasi-brittle structures , 1999 .

[29]  Z. Bažant,et al.  IDENTIFICATION OF NONLINEAR FRACTURE PROPERTIES FROM SIZE EFFECT TESTS AND STRUCTURAL ANALYSIS BASED ON GEOMETRY-DEPENDENT R-CURVES , 1991 .

[30]  Xiaozhi Hu,et al.  Size effect on specific fracture energy of concrete , 2007 .

[31]  D. S. Dugdale Yielding of steel sheets containing slits , 1960 .

[32]  M. Elices,et al.  GENERALIZED SIZE EFFECT EQUATION FOR QUASIBRITTLE MATERIALS , 1997 .

[33]  Z. Bažant,et al.  Nonlinear Fracture Properties from Size Effect Tests , 1986 .

[34]  Soo-Ho Chang,et al.  Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens , 2002 .

[35]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .