Size-independent Specific Fracture Energy Research Articles

Modified Disk-Shaped Compact Tension Test for Measuring Concrete Fracture Properties

A new approach for measuring the specific fracture energy of concrete denoted modified disk-shaped compact tension (MDCT) test is presented. The procedure is based on previous ideas regarding the use of compact tension specimens for studying the fracture behavior of concrete but implies significant modifications of the specimen morphology in order to avoid premature failures (such as the breakage of concrete around the pulling load holes). The manufacturing and test performance is improved and simplified, enhancing the reliability of the material characterization. MDCT specimens are particularly suitable when fracture properties of already casted concrete structures are required. To evaluate the applicability of the MDCT test to estimate the size-independent specific fracture energy of concrete (GF), the interaction between the fracture process zone of concrete and the boundary of the MDCT specimens at the end of the test is properly analyzed. Further, the experimental results of GF obtained by MDCT tests for normal- and high-strength self-compacting concrete mixes are compared with those obtained using the well-established three-point bending test. The procedure proposed furnishes promising results, and the GF values obtained are reliable enough for the specimen size range studied in this work.

Fitting the fracture curve of concrete as a density function pertaining to the generalized extreme value family

The load-displacement (P-δ) curve, recorded during the fracture process of concrete in three-point bending tests, is supposed to depict a fracture phenomenon of statistical character that can be suitably described by a density function pertaining to the generalized extreme value family, which proves to be maximal Fréchet, as a particular case of heavy tail distributions. Since the proposed analytical function fits the test record throughout, the non-measured fracture work, corresponding to the upper asymptotic tail of the fracture curve P-δ, is expected to be measured in a more reliable and accurate way than using other methods currently recommended to evaluate the total fracture energy of concrete. The general scale parameter Ω, identified as the area under the fracture curve, and the three parameters of the Fréchet density function are estimated by fitting the recorded data to the experimental P-δ curve using a specific Matlab program. The model is applied to fit experimental fracture curves from an ample 3-PB test program on notched specimens for different self-compacting concrete mixes. The results obtained for the size-independent specific fracture energy are compared with those provided by other well-established conventional approaches. In both instances, the suitability of the proposal is confirmed.

Size and boundary effects on notch tensile strength and fracture properties of PMMA bone cement

Poly (methyl methacrylate) bone cement is widely used for anchoring total joint replacements. In such an application, tensile and fracture properties of the cement are particularly important as they have strong implications for the stability of the implant in the bone bed and, hence, its life. Being a quasi-brittle material, it is to be expected that any mechanical property of bone cement would be size-dependent. This issue has not been addressed in the literature. In the present work, tests using modified wedge-splitting specimens were carried out to determine the size and boundary effects on the notch tensile strength (σNT) and on two fracture parameters, namely, specific fracture energy (Gf), and characteristic length based on the notch tensile strength (lchspl) of a widely used approved brand, Palacos® R. Size and boundary effects, of varying magnitudes, on each of these properties were found. For example, 1) for geometrically-similar specimens (specimen height (W) was varied from 15 mm to 36 mm but ratio of length of the starter crack (a) to W was fixed), the general trend was marked decrease in σNT with increase in W for a given a/W; and 2) for identical-sized specimens (W was fixed but a/W was varied from 0.06 to 0.81), the general trend was moderate decrease in Gf with increase in a/W for a given W. A validated boundary effect model presented in the literature and results from some of the specimens used in the present experimental work were used to compute the size-independent specific fracture energy and transition ligament length of the cement brand to be 2096 N m−1 and 4 mm, respectively.

Determination of size-independent specific fracture energy of normal- and high-strength self-compacting concrete from wedge splitting tests

Wedge splitting tests have been conducted on two different self-compacting concretes (normal- and high-strength) and the size-dependent fracture energy Gf determined from the measured RILEM work of fracture. Then the specific size-independent fracture energy, GF, has been determined using the boundary effect (BE) method of Hu and Wittmann and the simplified boundary effect (SBE) method proposed by Abdalla and Karihaloo. Tests on specimens of three different sizes and four different relative notch depths have shown that a unique value of GF can be obtained irrespective of the specimen size and relative notch depth. The results by both the BE and SBE methods are in very good agreement. A comparison with previous results from Abdalla and Karihaloo for normal- and high-strength vibrated concretes tested under the same conditions in the same laboratory shows that the SCC has a lower specific size-independent fracture energy than the vibrated concrete of the same strength.

Bilinear tension softening diagrams of concrete mixes corresponding to their size-independent specific fracture energy

The study of the fracture behaviour of concrete structures using the fictitious crack model requires two fracture properties of the concrete mix, namely, the size-independent specific fracture energy GF, and the corresponding tension softening relation σ(w) between the residual stress carrying capacity σ and the crack opening w in the fracture process zone ahead of a real crack. In this paper, bi-linear tension softening diagrams of three different concrete mixes, ranging in compressive strength from 57 to 122MPa whose size-independent specific fracture energy has been previously determined, have been constructed in an inverse manner based on the concept of a non-linear hinge from the load-crack mouth opening plots of notched three-point bend beams.

Influence of the properties of polypropylene fibres on the fracture behaviour of low-, normal- and high-strength FRC

This paper describes a comprehensive experimental study of the influence of the geometrical and mechanical properties of polypropylene fibres on the fracture parameters and ductility of low, normal, and high-strength fibre-reinforced concrete. Three-point bending tests were carried out on 88 notched beams using the simplified boundary effect method of Abdalla and Karihaloo. The influence of the fibre reinforcement was especially felt on the tail of the load–displacement curve, and its effect on the size-independent specific fracture energy of concrete has been subsequently analysed. An analysis of the ductility of the concrete has also been carried out based on the Hillerborg’s brittleness number. The increase in ductility due to the influence of the fibre reinforcement was conveniently analysed for the different mixes. From results, an analysis of the likeliest mechanisms of failure of the fibres reliant on their properties and the strength of concrete was completed. The results showed the most suitable fibres that were used to get the best fracture behaviour for a particular strength of concrete.

Determination of size-independent specific fracture energy of concrete mixes by two methods

The RILEM work-of-fracture method for measuring the specific fracture energy of concrete from notched three-point bend specimens is still the most common method used throughout the world, despite the fact that the specific fracture energy so measured is known to vary with the size and shape of the test specimen. The reasons for this variation have also been known for nearly two decades, and two methods have been proposed in the literature to correct the measured size-dependent specific fracture energy (Gf) in order to obtain a size-independent value (GF). It has also been proved recently, on the basis of a limited set of results on a single concrete mix with a compressive strength of 37 MPa, that when the size-dependent Gf measured by the RILEM method is corrected following either of these two methods, the resulting specific fracture energy GF is very nearly the same and independent of the size of the specimen. In this paper, we will provide further evidence in support of this important conclusion using extensive independent test results of three different concrete mixes ranging in compressive strength from 57 to 122 MPa.

Determination of size-independent specific fracture energy of concrete mixes by the tri-linear model

The methods proposed by Elices and co-workers [1–3] and by Hu and Wittmann [4] are commonly used to determine the size-independent specific fracture energy (GF) of concrete by correcting the size-dependent specific fracture energy (Gf) measured by the RILEM work-of-fracture method. In the boundary effect model of Hu and Wittmann [4], the change in the local fracture energy (gf) is approximated by a bilinear function, whereas the method of Elices et al. [1] consists in determining the non-measured work-of-fracture by adjusting the tail of the P-δ curve that corresponds to the final part of the test. Acoustic emission (AE) experiments on notched specimens (Muralidhara et al. [5,6]) have revealed that under loading the AE events follow approximately a tri-linear distribution; initially the number of events increases almost linearly reaching an extended plateau when the number of events remains nearly constant and eventually the number reduces as the crack approaches the back stress free boundary of the specimen, reminiscent of the development of R-curve in a finite size specimen. This paper exploits this observation and proposes a tri-linear model for the determination of the size-independent specific fracture energy for three different concrete mixes ranging in compressive strength from 57 to 122MPa. Remarkably, it is found that the resulting size-independent specific fracture energy GF determined by this tri-linear model and by the bi-linear model of Hu and Wittmann [4] is very nearly the same and independent of the size of the specimen.

An experimental study on acoustic emission energy as a quantitative measure of size independent specific fracture energy of concrete beams

Notched three point bend specimens (TPB) were tested under crack mouth opening displacement (CMOD) control at a rate of 0.0004 mm/s and during the fracture process acoustic emissions (AE) were simultaneously monitored. It was observed that AE energy could be related to fracture energy. An experimental study was done to understand the behavior of AE energy with parameters of concrete like its strength and size. In this study, AE energy was used as a quantitative measure of size independent specific fracture energy of concrete beams and the concepts of boundary effect and local fracture energy were used to obtain size independent AE energy from which size independent fracture energy was obtained.

Size effect on tensile softening relation

Tensile softening essential to the well-known fictitious crack model should be independent of specimen size and test methods. Commonly observed size effect (SE) on tensile softening relations measured from direct tensile specimens with smooth surface needs to be explained in order to determine the size independent tensile softening behaviour. In this paper, SE on tensile softening from direct tensile tests is elucidated by considering a boundary region where the key tensile softening mechanisms such as aggregate interlocking and frictional pull-out activities are limited in comparison with the inner region where those crack-bridging activities can be fully developed. SE on the tensile softening relation and the closely related specific fracture energy Gf is inevitable if the boundary and inner regions are comparable. The same SE is gradually diminished with the increasing specimen size simply because the relative contribution from the boundary region is reduced in comparison with that from the increasing inner region. In principle, the size independent tensile softening relation and the size independent specific fracture energy GF in the inner region can be obtained by separating the influence of the boundary region from the test results.

Deterministic size effect in the strength of cracked concrete structures

This paper is concerned with identifying and quantifying the deterministic (as opposed to statistical) size effect in the strength of cracked concrete structures that is believed to be a result of stress discontinuities introduced by the cracks. For this, the strength of geometrically similar pre-cracked specimens of varying sizes made from three concrete mixes is measured in three-point bend and wedge splitting geometries. The true, size-independent specific fracture energy and the corresponding tension softening diagram of each of the three mixes are independently established in order to exclude their influence on the strength size effect. The test results show that the deterministic strength size effect weakens as the size of the crack reduces. This is confirmed by theoretical/computational studies based on the fictitious crack model in the range of sizes tested in the laboratory. The theoretical/computational model has been extended beyond this limited range to include cracked concrete structures in the size range 1 : 80. The computational results have been fitted by a simple strength size effect formula with appropriate asymptotic behaviour at both size extremes. The three unknown coefficients in this formula depend only on the size of the crack and they can be obtained by conducting tests on geometrically similar specimens of any shape but of varying sizes that can be conveniently handled in a laboratory. The three material properties of the concrete mix appearing in this formula, namely the Young modulus E, the direct tensile strength f t and the size-independent specific fracture energy G F must be independently measured.

A simple method for determining the true specific fracture energy of concrete

In a recent paper, Abdalla and Karihaloo confirmed the boundary effect hypothesis of Hu and Wittmann and observed that a size-independent specific fracture energy GF of concrete could be obtained by testing three point bend (TPB) or wedge splitting (WS) specimens containing either a very shallow or a deep starter notch. This observation was based on TPB and WS tests on limited number of specimens. In this paper, we have re-evaluated 26 test data sets on specific fracture energy of concrete published in the literature to assess the validity of this observation. The re-evaluation is found to support this observation. The determination of the true specific fracture energy GF of concrete thus becomes a simple and straightforward task requiring very few specimens of the same dimensions and shape. This re-evaluation also provides guidance for the selection of the specimen dimensions depending on the maximum size of aggregate used in the concrete mix in order to obtain its true GF.

A simple method for determining the true specific fracture energy of concrete

In a recent paper, Abdalla and Karihaloo confirmed the boundary effect hypothesis of Hu and Wittmann and observed that a size-independent specific fracture energy GF of concrete could be obtained by testing three point bend (TPB) or wedge splitting (WS) specimens containing either a very shallow or a deep starter notch. This observation was based on TPB and WS tests on limited number of specimens. In this paper, we have re-evaluated 26 test data sets on specific fracture energy of concrete published in the literature to assess the validity of this observation. The re-evaluation is found to support this observation. The determination of the true specific fracture energy GF of concrete thus becomes a simple and straightforward task requiring very few specimens of the same dimensions and shape. This re-evaluation also provides guidance for the selection of the specimen dimensions depending on the maximum size of aggregate used in the concrete mix in order to obtain its true GF.

Determination of size-independent specific fracture energy of concrete from three-point bend and wedge splitting tests

Three-point bend (TPB) and wedge splitting (WS) tests have been conducted on three different concretes and the specific fracture energy GF determined on the basis of the concept of local fracture energy. The latter is influenced by the free back surface of a notched test specimen, as explained by Hu and Wittmann. Tests on three or four specimen sizes with four notch to depth ratios confirm the idea of Hu and Wittmann that the size-independent specific fracture energy GF can be determined from measured fracture energy values that vary with the size of the specimen, W, and notch to depth ratio, a/W. More importantly, it is shown that the same size-independent GF can also be obtained by testing a single size specimen with only two notch to depth ratios, provided they are well separated (a/W = 0·05 and 0·50 in TPB, and 0·2 and 0·5 in WS), thus greatly simplifying the determination of the size-dependent fracture energy GF.

Determination of size-independent specific fracture energy of concrete from three-point bend and wedge splitting tests

Three-point bend (TPB) and wedge splitting (WS) tests have been conducted on three different concretes and the specific fracture energy GF determined on the basis of the concept of local fracture energy. The latter is influenced by the free back surface of a notched test specimen, as explained by Hu and Wittmann. Tests on three or four specimen sizes with four notch to depth ratios confirm the idea of Hu and Wittmann that the size-independent specific fracture energy GF can be determined from measured fracture energy values that vary with the size of the specimen, W, and notch to depth ratio, a/W. More importantly, it is shown that the same size-independent GF can also be obtained by testing a single size specimen with only two notch to depth ratios, provided they are well separated (a/W = 0·05 and 0·50 in TPB, and 0·2 and 0·5 in WS), thus greatly simplifying the determination of the size-dependent fracture energy GF.