Measuring the fracture toughness of cement paste and mortar

Brown, J. H.

doi:10.1680/macr.1972.24.81.185

Cited by 82 publications

(19 citation statements)

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“…Thus: ( 13) in which We is the effective width of the fracture process zone (or crack band) over which the microcracks are assumed to be uniformly spread, and f; is the direct tensile strength. If rI f' f; and We are known from measurements, then the basic parameters of our stressstrain relation may be calculated as: ( 14) It is interesting to note that Equation 4 allows us to link the area W under the complete uniaxial stressstrain diagram with the fracture energy.…”

Section: Fracture Characteristicsmentioning

confidence: 99%

“…The relative bending strength is here defined as the ratio between the bending strength at the various beam depths and the bending strength at the largest beam depth. Figure 9 shows comparisons with the recent data on the so-called R-curves (resistance curves) [13,17,45,50], which represent the dependence of fracture energy on the crack length in slow stable crack growth. The test specimens of Sok, Baron and Franc;ois ( fig.…”

Section: R--~~l~lrem~----------------------------~~~mentioning

confidence: 99%

“…The length of a fully developed fracture process zone is about 12-times the maximum aggregate size. 13. For very large structures (compared to aggregate size), the present theory assures that the energy consumed per unit crack band advancement equals the critical value of the energy release rate, and so the theory is, in the limit, equivalent to linear fracture ----------------------------------------------.…”

Section: \72mentioning

confidence: 99%

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Crack band theory for fracture of concrete

Bažant¹,

Oh²

1983

Mat. Constr.

2,130

1,371

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INTRODucnONThe structural size effect is the central problem in predictions of fltacture. Fracture tests are normally conducted on relatively small specimens, and fracture theories are usual~y verified in the laboratory by testing relatively small ,*ams or panels. In practice, we then dare to extrapola~e this information to structures which are often far larger than anything tested. This, of course, cannot be done I reliably without a sound, realistic fracture theory. 'For the initiation of cracks in a body without,cks and stress concentrations, the concept of stfi:,' :1 is acceptable. Not so, however when a sharp crack, .:ady exists. The elastic analysis then yields infinite strf'~S at the crack front, and the strength criterion inc,' c~ctly predicts the crack to extend at an infinitely sma) ,oad. When a finite element mesh is refined, the load '1i.:edc!d to reach the strength limit strongly depends u: the choice of element size and incorrectly converges tc le:-o. Thus, the elastic finite element analysis of cracking based on the strength criterion, as currently used in 0025-5432/1983/155/$ 5,00/ ~ BORDAS-DUNOD 155 Materials and Structures 16: 155-177, 1983

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Section: Fracture Characteristicsmentioning

confidence: 99%

Section: R--~~l~lrem~----------------------------~~~mentioning

confidence: 99%

Section: \72mentioning

confidence: 99%

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Crack band theory for fracture of concrete

Bažant¹,

Oh²

1983

Mat. Constr.

2,130

1,371

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“…There is considerable evidence [from fracture properties (Brown, 1972); frcm acoustic emission (Evans et al, 1976); and fran direct observation (Hsu et al, 1963)] that the fracture of mortar and concrete occurs by the coalescence of microcracks to form a macrocrack. The microcracks are generally nucleated at the aggregate/matrix bond in a zone ahead of the crack, which increases in size to a limiting value with increasing crack extension (see section 2B.III.ii).…”

Section: Bii the Applicability Of Fracture Mechanics To Hcp Mortarmentioning

confidence: 99%

Crack Growth in Hardened Cement Paste

Baldie

Pratt

1985

MRS Proc.

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This thesis describes the examination of the microstructure of hardened cement paste [HCP], in particular, cracking in HCP, and the measurement of subcritical crack growth in HCP.A scanning electron microscope has been used to examine, fracture surfaces, complementary fracture surfaces, polished surfaces, and polished surfaces containing introduced cracks. This examination has provided information about fracture paths in HCP, which shows that the main hydration products [C-S-H gel and calcium hydroxide] form the majority of crack path elements. The interpenetration of these products during hydration, and the expected variations in strength of these hydration products suggest that both must be recognised as significant contributors to the mechanical properties of HCP. The examination of cracks in polished surfaces appears to be a very useful way of determining the microstructural aspects of cracking, and its possible future applications are discussed.Two methods of determining the subcritical crack growth parameter [n] were performed, the first, load-relaxation in double torsion plates yielded a value of 64, while the second, the variation in the critical stress intensity of single edge notched beams with loading rate yielded a value of 27. The much higher value determined by load relaxation is thought to be due to both, the effect of crack resistant inhcmogeneities in the microstructure which have a more marked effect on load relaxation measurements, and a susceptibility to creep in the double torsion plates which reduced the amount of crack growth. The susceptibility to creep was identified by a shift of the crack velocity-stress intensity [V-K] curves to higher stress intensities with repeated loading. The value of subcritical crack growth parameter of 27, determined by the variation of critical stress intensity with loading rate, is therefore regarded as the more valid.

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“…7-8, ... Q- From extensive statistical computer calculations and data plotting it appears that the presently available fracture data for the maximum load can be roughly equally well approximated by both the exponential and parabolic formulas (Eqs. [7][8], and that a relatively wide range of pa-…”

Section: Calculation Of Failure Load and Analysis Of Fracture Datamentioning

confidence: 99%

Approximate Linear Analysis of Concrete Fracture by R‐Curves

̆ant¹,

Cedolin

1984

J. Struct. Eng.

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Using linear elastic fracture analysis, the energy consumed per unit length of fracture (fracture energy) varies with the crack length, as described by the resistance curve (R-curve). This concept, originally proposed for metals, is developed here into a practical, applicable form for concrete. The energy release rate is determined by an approximate linear elastic fracture analysis based on a certain equivalent crack length, which differs from the actual crack length, and is solved as part of structural analysis. It is shown that such an analysis, coupled with the R-curve concept, allows achieving satisfactory fits of the presently existing fracture data obtained with three-point and four-point bent specimens. Without the R-curve, the use of an equivalent crack length in linear analysis is not sufficient to achieve a satisfactory agreement with these data. The existing data can be described equally well with various formulas for the R-curve, and the material parameters in the formula can vary over a relatively broad range without impairing the representation of test data. Only the overall slope of the R-curve, the initial value, and the fina1 value ,are important. A parabola seems to be the most convenient shape of R-curve because the failure load may then be solved from a quadratic equation. For the general case, a simple algorithm to calculate the failure load is given. Deviations from test data are analyzed statistically, and an approximate relationship of the length parameter of the R-curve to the maximum aggregate size is found.

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Measuring the fracture toughness of cement paste and mortar

Cited by 82 publications

References 0 publications

Crack band theory for fracture of concrete

Crack band theory for fracture of concrete

Crack Growth in Hardened Cement Paste

Approximate Linear Analysis of Concrete Fracture by R‐Curves

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