Size Effect Tests Research Articles

Identification of Stress-Slip Law for Bar or Fiber Pullout by Size Effect Tests

Test results on the size effect in the pullout strength of reinforcing bars embedded in concrete are presented. Attention is focused on failures due solely to interface slip, with no cracking in the surrounding concrete. This type of failure is achieved by using smooth round bars and a sufficiently large ratio of bar diameter to embedment length. Elimination of cracking in the surrounding concrete makes it possible to study the characteristics of the interfacial shear fracture between steel and concrete. The results of tests of geometrically similar specimens show that interfacial shear fracture causes a size effect on the nominal strength in pullout. The size effect is found to be transitional between plastic failure (the current approach of concrete design codes, for which there is no size effect) and linear elastic fracture mechanics (for which the size effect is the maximum possible). This transitional size effect can be approximately described by the size effect law proposed by Bažant in 1984 for qua...

Eigenvalue analysis of size effect for cohesive crack model

The paper analyses the effect of structure size on the nominal strength of the structure that is implied by the cohesive (or fictitious) crack model proposed for concrete by Hillerborg et al. A new method to calculate the maximum load of geometrically similar structures of different sizes without calculating the entire load-deflection curves is presented. The problem is reduced to a matrix eigenvalue problem, in which the structure size for which the maximum load occurs at the given (relative) length of the cohesive crack is obtained as the smallest eigenvalue. Subsequently, the maximum load, nominal strength and load-point displacement are calculated from the matrix equilibrium equation. The nonlinearity of the softening stress-displacement law is handled by iteration. For a linear softening law, the eigenvalue problem is linear and independent of the matrix equilibrium equation, and the peak load can then be obtained without solving the equilibrium equation. The effect of the shape of the softening law is studied, and it is found that the size effect curve is not very sensitive to it. The generalized size effect law proposed earlier by Bažant, which describes a transition between the horizontal and inclined asymptotes of strength theory and linear elastic fracture mechanics, is found to fit the numerical results very well. Finally some implications for the determination of fracture energy from the size effect tests are discussed. The results are of interest for quasibrittle materials such as concrete, rocks, sea ice and modern tough ceramics.

Identification of nonlinear fracture properties from size effect test and structural analysis based on geometry-dependent R-curves : Bazant, Z P; Gettu, R; Kazemi, M T Int J Rock Mech Min SciV28, N1, Jan 1991, P43–51

Identification of nonlinear fracture properties from size effect test and structural analysis based on geometry-dependent R-curves : Bazant, Z P; Gettu, R; Kazemi, M T Int J Rock Mech Min SciV28, N1, Jan 1991, P43–51

Determination of r‐curves of steel fiber reinforced concrete from size effect tests

Abstract A developed size effect law for blunt fracture is used to determine the R‐Curves and related parameters of steel fiber reinforced concrete. Geometrically similar single‐edge notched beams of different sizes made of cementitious mixes at various fiber volume fractions and different maximum aggregate sizes were used for the tests. Fracture energy of concrete is identified by linear regression using the size effect law. From the experimentally calibrated size effect law, the R‐curve is obtained as the envelope of the family of fracture equilibrium curves for different specimen sizes.

Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curves

The size effect method, previously developed for concrete and mortar, is demonstrated for rock. Geometrically similar fracture specimens of limestone are tested and the measured maximum load values are used to obtain fracture energy, fracture toughness and effective size of the fracture process zone. Further, it is shown how to determine, from these results, other nonlinear fracture parameters including the critical effective crack-tip opening displacement. R-curves, dependent on specimen geometry, are calculated and used to predict load-deflection curves, which are found to agree very well with measurements. A modification of the R-curves for post-peak response is proposed.

Size effect tests of torsional failure of plain and reinforced concrete beams

The current design code formulae for the torsional failure of plain or longitudinally reinforced beams exhibit no size effect, i.e. the failure of geometrically similar beams of different sizes is supposed to occur at the same nominal stress. Experiments on reduced-scale beams were carried out, and the results confirm that there is a significant size effect, such that the nominal stress at failure decreases as the beam size increases. This is found for both plain and longitudinally reinforced beams. The results are consistent with the recently proposed Bažant's size-effect law. However, the scatter of the results and the scope, and range limitations prevent it from being concluded that the applicability of this law is proven.

Size effect tests and fracture characteristics of aluminum

The recently established approximate size effect law for blunt fracture is shown to agree with test data for aluminum. The data are obtained with three-point bent fracture specimens of depths ranging from 0.25 to 4 in. Non-linear fracture parameters can be obtained by a linear regression based on the size effect law. Thus, the fracture energy can be determined using only the maximum load values from fracture tests, and the R- curve can be obtained as an envelope of fracture equilibrium curves. No measurements of crack length or specimen compliance are needed.

Nonlinear Fracture Properties from Size Effect Tests

The previously derived size effect law for blunt fracture is exploited for determining the parameters of the R-curve of the crack band model, and of Hillerborg’s fictitious crack model. No measurements of the crack length or of the unloading compliance are needed. It suffices to measure only the maximum load values for a set of geometrically similar specimens of different sizes. The parameters of the size effect law can then be identified by linear regression. The inverse slope of the regression line yields the fracture energy. The regression also has a twofold benefit: it smoothes statistically scattered data, and it extends the range of the data, so that one can do with fewer tests. From the experimentally calibrated size effect law, the R-curve may then be obtained as the envelope of the family of fracture equilibrium curves for different specimen sizes. A simple algebraic formula for this envelope is presented. The size effect regression plot makes it also possible to determine crack band model parameters, particularly the fracture energy, the crack band width, and the strait-softening modulus. The same is made possible for Hillerborg’s model.

Size effect in tests of commercial devitrified glasses in uniaxial compression

1. A method and test facilities were developed for studying the effect of size in short-time compression tests of glass and ceramic glasses with a force up to 2000 tons. Such tests require specimens the dimensions of which must be comparable to certain parameters of prospective products made of glass and ceramic glasses, such as the thickness of a cylinder wall. 2. The elastic properties of cast ceramic glasses are nearly independent of the size effect, and strength and character of failure in compression for large specimens depends largely on the method of their production, rather than on size. 3. With increasing diameter of specimens of ceramic glasses A-1 and STL-10 from 10 to 80 mm, strength in compression tests is cut in half. 4. In the case of axial compression, ground specimens of brittle materials fail primarily from the surface due to the growth of cracks along the specimen axis, regardless of their original orientation. Noticeable damages in the form of surface cleavage steps are present in large specimens much earlier than in standard specimens at a level of stresses 30–60% of the breaking stress.