A Size and Boundary Effects Model for Quasi-Brittle Fracture

The fracture behaviors of quasi-brittle materials are commonly specimen size (size effect) and crack size (boundary effect) dependent. In this study, a new failure model is developed for characterizing the size and boundary effects. The derivative of the energy release rate is firstly introduced to predict the nominal strength dominated by the strength mechanism. Combined with the energy criterion for the energy mechanism, an asymptotic model is developed to capture the effect of any crack size on the nominal strength, and its expression for geometrically similar specimens is also established, which is able to characterize the size effect. Detailed comparisons of the proposed model with the size effect law and the boundary effect model are performed, respectively. The nominal strength predictions based on the proposed model are validated with the experimental results of cracked three-point bending beam specimens made of concrete, of limestone and of hardened cement paste and compared with the model predictions given by the size effect law and the boundary effect model.

[1]  Z. Bažant,et al.  Size dependence of concrete fracture energy determined by RILEM work-of-fracture method , 1991, International Journal of Fracture.

[2]  J. Eisenmann,et al.  Macroscopic Fracture Mechanics of Advanced Composite Materials , 1971 .

[3]  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 .

[4]  N. Gascons,et al.  Size Effect Law and Critical Distance Theories to Predict the Nominal Strength of Quasibrittle Structures , 2013 .

[5]  Z. Bažant,et al.  Scaling of quasibrittle fracture: asymptotic analysis , 1997 .

[6]  H. Neuber.  Theory of notch stresses : principles for exact calculation of strength with reference to structural form and material , 1958 .

[7]  David Taylor,et al.  The Theory of Critical Distances: A New Perspective in Fracture Mechanics , 2010 .

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

[9]  Zdeněk P. Bažant,et al.  Problems with Hu-Duan Boundary Effect Model and Its Comparison to Size-Shape Effect Law for Quasi-Brittle Fracture , 2010 .

[10]  Xiaozhi Hu,et al.  Size effect on toughness induced by crack close to free surface , 2000 .

[11]  R. A. Schmidt,et al.  Fracture-toughness testing of limestone , 1976 .

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

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

[14]  Hiroshi Tada,et al.  The stress analysis of cracks handbook , 2000 .

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

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

[17]  Zdeněk P. Bažant,et al.  Comparison of the Hu-Duan Boundary Effect Model with the Size-Shape Effect Law for Quasi-Brittle Fracture Based on New Comprehensive Fracture Tests , 2014 .

[18]  L. Napolitano.  Materials , 1984, Science.

[19]  Alberto Carpinteri,et al.  Size effects on concrete fracture energy: dimensional transition from order to disorder , 1996 .

[20]  Xiaozhi Hu,et al.  Size effect: Influence of proximity of fracture process zone to specimen boundary , 2007 .

[21]  Xiaozhi Hu,et al.  An asymptotic approach to size effect on fracture toughness and fracture energy of composites , 2002 .

[22]  Alberto Carpinteri,et al.  Size effects on nominal tensile strength of concrete structures: multifractality of material ligaments and dimensional transition from order to disorder , 1995 .

[23]  Z. Bažant,et al.  Scaling theory for quasibrittle structural failure. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[24]  G. Irwin.  ANALYSIS OF STRESS AND STRAINS NEAR THE END OF A CRACK TRAVERSING A PLATE , 1957 .

[25]  Alberto Carpinteri,et al.  Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy , 1995 .

[26]  M. E. Haddad,et al.  Fatigue Crack Propagation of Short Cracks , 1979 .

[27]  Surendra P. Shah,et al.  Nonlinear Fracture Parameters for Cement Based Composites: Theory and Experiments , 1985 .

[28]  Xiaozhi Hu,et al.  Scaling of quasi-brittle fracture: Boundary and size effect , 2006 .

[29]  Filippo Berto,et al.  Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches , 2014 .

[30]  Z. Bažant,et al.  Scaling of structural strength , 2003 .

[31]  Bhushan Lal Karihaloo,et al.  Size effect in concrete beams , 2003 .

[32]  Zdenek P. Bazant,et al.  Zero-Brittleness Size-Effect Method for One-Size Fracture Test of Concrete , 1996 .

[33]  Z.,et al.  Identification of Nonlinear Fracture Properties From Size Effect Tests and Structural Analysis Based on Geometry-dependent R-curves , 2005 .

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

[35]  Qiang Yu,et al.  Universal Size Effect Law and Effect of Crack Depth on Quasi-Brittle Structure Strength , 2009 .

[36]  Zdenek P. Bazant,et al.  Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests , 2014 .

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