Misconception on variability of fracture energy, its uniaxial definition by work of fracture, and its presumed dependence on crack length and specimen size

Recent polemics on fracture testing of concrete and mathematical modeling of the size effect impede the efforts to introduce of fracture mechanics into the design practice, and especially into the design codes. To overcome this barrier to progress, this paper compares the Hu-Duan Boundary Effect Model (BEM) promulgated during the last decade to the Size-Shape Effect Law (SEL) proposed at Northwestern University in 1984 and extended to the geometry (or shape) effects in 1990. The comparison shows that within a rather limited part of the range of sizes and shapes, the fracture energy values identified by BEM and SEL from maximum load data are nearly the same. But in other parts of the range the BEM is found to be either inferior or inapplicable. Several hypotheses of BEM are shown to be unrealistic. The material tensile strength values identified by BEM are found to be inconsistent with the cohesive crack model and have a much larger error than those obtained from the SEL. As a related problem, it is shown that without testing at various specimen sizes, the cohesive softening stress-separation law determined from the work-of-fracture method or from the two-parameter model is non-unique. Especially, the same data can be fitted with very different values of the initial fracture energy (area under the initial tangent) and of the tensile strength limit, which give very different size and shape effects on the nominal strength of structure. Finally it must be emphasized that formulation of a coherent fracture theory for a quasibrittle material such a concrete is impossible without capturing the size effect. Misconceptions on Variability of Fracture Energy, Its Uniaxial Definition by Work of Fracture, and Its Presumed Dependence on Crack Length and Specimen Size Z. P. Bažant 1 , Qiang Yu 1 , Gianluca usatis 2 , Luigi C dolin 3 , Mila Jirásek 4 1 Northwestern University, Department of Civil and Environmental Engineering, Illinois 60208, USA. 2 Rensselaer Polytechnic Institute, Troy, New York, USA. 3 Politecnico di Milano, Milan, Italy. Czech Technical University, Prague. ABSTRACT: Recent polemics n fracture t sting of concrete and mathematic l mod ling of the size ffect impede the efforts to introduce of f acture mechanics into the design practice, and especially int the design codes. To overcome this barrier to progr ss, this p r compares the Hu-Duan Boundary Eff c Model (BEM) promulg ted during the last decad to the Size-Shap Effect Law (SEL) proposed at Northwestern University in 1984 and extended to the geometry (or shape) e fe s in 1990. The comparison shows that within a rather limited part of the r nge of sizes and shapes, the fracture energy values identif ed by BEM and SEL f om maximum load data are nearly th same. But in ot er parts of the r nge the BEM is found to be either inferior or inapplicable. Several hypo hes s of BEM are shown to be unrealistic. The material t nsile strength values ide tified by BEM a e found to be inconsis nt with the cohe ive crack model and have a much larg r error than those bta n d from the SEL. As related problem, t is sh wn that with ut tes ing at various specimen sizes, the cohesive softe ing stress-separat on law determined from the work-of-fracture method or from t two-pa met r model is non-unique. Especially, the same data ca be fi t d with very different values o the i itial fr cture energy (area under the initial tangent) and of the tensile strength li it, which give very different size and shape effects n the nominal strength of structure. Finally it must be emphasized that formulation of a coherent fracture theory for a quasibrittle material such a concrete is impossible without capturing the size effect. Fracture Mechanics of Concrete and Concrete Structures Recent Advances in Fracture Mechanics of Concrete B. H. Oh, et al.(eds) c 2010 Korea Concrete Institute, Seoul, ISBN 978-89-5708-180-8 Recent polemics n fracture t sting of concrete and mathematic l mod ling of the size ffect impede the efforts to introduce of f acture mechanics into the design practice, and especially int the design codes. To overcome this barrier to progr ss, this p r compares the Hu-Duan Boundary Eff c Model (BEM) promulg ted during the last decad to the Size-Shap Effect Law (SEL) proposed at Northwestern University in 1984 and extended to the geometry (or shape) e fe s in 1990. The comparison shows that within a rather limited part of the r nge of sizes and shapes, the fracture energy values identif ed by BEM and SEL f om maximum load data are nearly th same. But in ot er parts of the r nge the BEM is found to be either inferior or inapplicable. Several hypo hes s of BEM are shown to be unrealistic. The material t nsile strength values ide tified by BEM a e found to be inconsis nt with the cohe ive crack model and have a much larg r error than those bta n d from the SEL. As related problem, t is sh wn that with ut tes ing at various specimen sizes, the cohesive softe ing stress-separat on law determined from the work-of-fracture method or from t two-pa met r model is non-unique. Especially, the same data ca be fi t d with very different values o the i itial fr cture energy (area under the initial tangent) and of the tensile strength li it, which give very different size and shape effects n the nominal strength of structure. Finally it must be emphasized that formulation of a coherent fracture theory for a quasibrittle material such a concrete is impossible without capturing the size effect. Fracture Mechanics of Concrete and Concrete Structures Recent Advances in Fracture Mechanics of Concrete B. H. Oh, et al.(eds) c 2010 Korea Concrete Institute, Seoul, ISBN 978-89-5708-180-8