Cohesive crack analysis of size effect

Cusatis, Gianluca; Schauffert, Edward A.

doi:10.1016/j.engfracmech.2009.06.008

Cited by 93 publications

(68 citation statements)

References 23 publications

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“…where g 0 5 gða 0 Þ; g 0 9 5 g9ða 0 Þ; a 5 a=D 5 relative crack length; a 0 5 a 0 =D 5 initial value of a; gðaÞ 5 k 2 ðaÞ 5 dimensionless energy release rate function gðaÞ of LEFM; kðaÞ 5 b ffiffi ð p DÞK I =P where K I 5 stress intensity factor, P 5 load; g9ðaÞ 5 dgðaÞ=da; E9 5 E 5 Young's modulus for plane stress and E9 5 E=ð1 2 n 2 Þ for plane strain (where n 5 Poisson ratio); G f 5 initial fracture energy 5 area under the initial tangent of the cohesive softening stress-separation curve; c f 5 characteristic length, which represents about a half of the FPZ length and may be expressed as c f 5 g s l 0 , where g s 5 material-dependent coefficient, for the present specimens equal to 0.29 (Bazant and Yu 2011;Cusatis and Schauffert 2009); and l 0 5 EG f =f 9 2 t 5 Irwin's material characteristic length (Irwin 1958). G f , c f , and l 0 are all considered to be independent of structure size, i.e., as constants, because they are the characteristics of the cohesive crack softening law, which itself is a material property (note the difference of G f from the total fracture energy, which represents the total area under the cohesive softening stress-separation law, and the fact that G f is not equal to the energy release rate, which can vary with the size and distance from notch tip; on the other hand, G F is equal to the energy release rate in an infinitely large specimen).…”

Section: Review Of Size Effect and Crack Length Effectmentioning

confidence: 99%

Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests

2014

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The universal size-shape effect law is a law that describes the dependence of nominal strength of specimen or structure on both its size and the crack (or notch) length, over the entire range of interest, and exhibits the correct small-size and large-size asymptotic properties as required by the cohesive crack model (or crack band model). The main difficulty has been the transition of crack length from 0, in which case the size effect is Type 1, to deep cracks (or notches), in which case the size effect is Type 2 and is fundamentally different from Type 1, with different asymptotes. In this transition, the problem is not linearizable because the notch is not much larger than the fracture process zone. The previously proposed universal law could not be verified experimentally for the Type 1-Type 2 transition because sufficient test data were lacking. The current study is based on recently obtained comprehensive fracture test data for three-point bend beams cast from one batch of the same concrete and cured and tested under identical conditions. The test data reveal that the Type 1-Type 2 transition in the previous universal law has insufficient accuracy and cannot be captured by Taylor series expansion of the energy release rate function of linear elastic fracture mechanics. Instead, the size effect for a zero notch and for the transitional range is now characterized in terms of the strain gradient at the specimen surface, which is the main variable determining the degree of stress redistribution by the boundary layer of cracking. The new universal law is shown to fit the comprehensive data quite well, with a coefficient of variation of only 2.3%.

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Section: Review Of Size Effect and Crack Length Effectmentioning

confidence: 99%

Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests

2014

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“…As already proven by previous analytical and numerical studies [21,48,46], the SEL is equivalent to the asymptotic behavior of the CSEC, namely the CSEC tends asymptotically to a straight line for large sizes that corresponds to the SEL. For a nonlinear softening law and for realistic structural sizes, it can be shown that Eq.…”

Section: Literature Review On Size Effectmentioning

confidence: 76%

“…Following Cusatis and Schauffert [21], size effect relationships represented symbolically by Eq. 2, and all other similar relationships involving normalized ultimate nominal stress as a function of normalized structural size, will be termed cohesive size effect curves and abbreviated "CSEC".…”

Section: Literature Review On Size Effectmentioning

confidence: 99%

“…where G(α) = energy release rate, α 0 = a 0 /D is the initial dimensionless notch depth, a 0 = initial notch depth, g(α) = dimensionless energy release rate, and c F = effective fracture process zone length, assumed to be a material property [38,21]. By approximating g(α 0 + c F /D) with its Taylor series expansion at α 0 and retaining only up to the linear term of the expansion, the classical form of Bažant's SEL 6 can be obtained:…”

Section: Literature Review On Size Effectmentioning

confidence: 99%

“…After confirming the model's ability to correctly predict the size effect at a given age as well as the aging effect of a given size, predictions are carried out for all early ages and scaled specimen sizes. The nominal flexural strengths obtained from experiments as well as predictive simulations are then analyzed by various methods including the size effect law (SEL) [49] and the cohesive size effect curve (CSEC) method [21]. The tensile strength and tensile characteristic length can be directly obtained through data fitting by SEL and CSEC.…”

Section: Introductionmentioning

confidence: 99%

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Age-dependent size effect and fracture characteristics of ultra-high performance concrete

Wan-Wendner

Wan‐Wendner

Cusatis

2018

Cement and Concrete Composites

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Abstract:This paper presents an investigation of the age-dependent size effect and fracture characteristics of an ultra high performance concrete (UHPC). The study is based on a unique set of experimental data connecting aging tests for two curing protocols of one size and scaled size effect tests of one age. Both aging and size effect studies are performed on notched three point bending tests. Experimental data is augmented by state of the art simulations employing a recently developed discrete element based early-age computational framework.

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Fracture propagation in Indiana Limestone interpreted via linear softening cohesive fracture model

2015

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We examine the use of a linear softening cohesive fracture model (LCFM) to predict single-trace fracture growth in short-rod (SR) and notched 3-point-bend (N3PB) test configurations in Indiana Limestone. The broad goal of this work is to (a) understand the underlying assumptions of LCFM and (b) use experimental similarities and deviations from the LCFM to understand the role of loading paths of tensile fracture propagation. Cohesive fracture models are being applied in prediction of structural and subsurface fracture propagation in geomaterials. They lump the inelastic processes occurring during fracture propagation into a thin zone between elastic subdomains. LCFM assumes that the cohesive zone initially deforms elastically to a maximum tensile stress (σ max ) and then softens linearly from the crack opening width at σ max to zero stress at a critical crack opening width w 1 . Using commercial finite element software, we developed LCFMs for the SR and N3PB configurations. After fixing σ max with results from cylinder splitting tests and finding an initial Young's modulus (E) with unconfined compressive strength tests, we manually calibrate E and w 1 in the SR model against an envelope of experimental data. We apply the calibrated LCFM parameters in the N3PB geometry and compare the model against an envelope of N3PB experiments. For accurate simulation of fracture propagation, simulated off-crack stresses are high enough to require inclusion of damage. Different elastic moduli are needed in tension and compression. We hypothesize that the timing and location of shear versus extensional micromechanical failures control the qualitative macroscopic force-versus-displacement response in different tests. For accurate prediction, the LCFM requires a constant style of failure, which the SR configuration maintains until very late in deformation. The N3PB configuration does not maintain this constancy. To be broadly applicable between geometries and failure styles, the LCFM would require additional physics, possibly including elastoplastic damage in the bulk material and more complicated cohesive softening models.

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Cohesive crack analysis of size effect

Cited by 93 publications

References 23 publications

Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests

Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests

Age-dependent size effect and fracture characteristics of ultra-high performance concrete

Fracture propagation in Indiana Limestone interpreted via linear softening cohesive fracture model

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