The theoretical basis of a method to determine the fracture energyG F of concrete

Hillerborg, Arne

doi:10.1007/bf02472919

Cited by 563 publications

(246 citation statements)

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“…As a result of many important studies, including Humphreys (1957), Rusch et al (1962), Leonhardt and Walter (1962), Kani (1967), Bhal (1968), Hsu (1968), McMullen and Daniel (1972), Taylor (1972), Hillerborg et al (1976), Walsh (1976), Walraven (1978Walraven ( ,1990, Chana (1981), Petersson (1981), Reinhardt (1981a,b), Hawkins (1985), Iguro et al (1985), Hillerborg (1985Hillerborg ( , 1989, Ingraffea (1985), Rots (1988Rots ( , 1992 and others, it has been known that failure of concrete structures exhibits a size effect. For a long time the size effect has been explained statistically as a consequence of the randomness of material strength, particularly by the fact that in a larger structure it is more likely to encounter a material point of smaller strength.…”

Section: Nature Of Problemmentioning

confidence: 99%

Fracture Size Effect: Review of Evidence for Concrete Structures

Bažant

Ožbolt²,

Eligehausen³

1994

J. Struct. Eng.

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The paper reviews experimental evidence on the size effect caused by energy release due to fracture growth during brittle failures of concrete structures. The experimental evidence has by now become quite extensive. The size effect is verified for diagonal shear failure and torsional failure of longitudinally reinforced beams without stirrups, punching shear failure of slabs, pull-out failures of deformed bars and of headed anchors, failure of short and slender tied columns, double-punch compression failure and for part of the range also the splitting failure of concrete cylinders in the Brazilian test. Although much of this experimental evidence has been obtained with smaller laboratory specimens and concrete of reduced aggregate size, some significant evidence now also exists for normal-size structures made with normal-size aggregate. There is also extensive and multifaceted theoretical support. A non local finite element code based on the microplane model is shown to be capable of correctly simulating the existing experimental data on the size effect. More experimental data for large structures with normal-size aggregate are needed to strengthen the existing verification and improve the calibration of the theory. NATURE OF PROBLEMAs a result of many important studies, including Humphreys (1957), Rusch et al. (1962), Leonhardt and Walter (1962), Kani (1967), Bhal (1968, Hsu (1968), McMullen and Daniel (1972), Taylor (1972), Hillerborg et al. (1976), Walsh (1976), Walraven (1978,1990), Chana (1981, Petersson (1981), Reinhardt (1981a,b), Hawkins (1985), Iguro et al. (1985), Hillerborg (1985), Ingraffea (1985, Rots (1988Rots ( , 1992 and others, it has been known that failure of concrete structures exhibits a size effect. For a long time the size effect has been explained statistically as a consequence of the randomness of material strength, particularly by the fact that in a larger structure it is more likely to encounter a material point of smaller strength. Various existing test data on the size effect were interpreted in terms of Weibull weakest-link theory [e.g. Mihashi and Zaitsev (1981) and Mihashi (1983)]. Later, however, it was proposed (Bazant 1984(Bazant , 1986) that whenever the failure does not occur at the initiation of cracking, which represents most situations, the size effect should properly be explained by energy release caused by macrocrack growth, and that the randomness of strength plays only a negligible role [in detail see Bazant and Xi (1991)].The size effect, however, does not follow the classical, linear form of fracture mechanics, in which all the fracture process is presumed to be happening at one point-the crack tip. Rather, the size effect in concrete structures must be explained by a nonlinear form of fracture mechanics that takes into account the localization of damage into a fracture process zone lWalter P. Murphy Prof. of Civ. Engrg. and Mat. Sci., Northwestern Univ., Evanston, IL 6020S.2Res. Engr., Institut fUr Werkstoffe im Bauwesen, Stuttgart Univ., Germany. 3Prof., ...

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Section: Nature Of Problemmentioning

confidence: 99%

Fracture Size Effect: Review of Evidence for Concrete Structures

Bažant

Ožbolt²,

Eligehausen³

1994

J. Struct. Eng.

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“…Most of experimental investigations of fracture energy follow the recommendation of Hillerborg model [5] by using the three-point bending test. Based on this model, fracture energy can be determined using the following equation:…”

Section: Determination Of Fracture Energymentioning

confidence: 99%

Fracture Energy of Foamed Concrete: Numerical Modelling Using the Combined Finite-Discrete Element Method

et al. 2017

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Abstract. Foamed concrete is known as lightweight concrete that proven in the low range of densities with good strength. Numerous studies were conducted to investigate its performance in term of mechanical properties. However, these investigations are still not adequate in the requirement of failure and damage mechanisms. This is due to the lack of knowledge on fracture energy that governs the crack resistance of foamed concrete. Therefore, this paper presents the numerical prediction of fracture energy of foamed concrete using the combined finite-discrete element method. The notched beam was modelled in the two-dimensional with unstructured mesh elements and a simple material model of Rotating Crack. The results of numerical prediction signify that various notch depths have an apparent impact toward fracture energy of foamed concrete.

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“…where l ch is the characteristic length of the material, first introduced by Hillerborg [72], E is elastic stiffness, and h is the slab thickness. It is also observed from Figure 19 (c) that β is inversely proportional to B, and that it may be postulated that a unique relationship exists that would allow one to determine the peak load for a particular value of B, given the corresponding peak load for different brittleness number [48].…”

Section: Effect Of Tensile Strength and Fracture Energymentioning

confidence: 99%