Identification of concrete fracture parameters through size effect experiments

This paper deals with the identification of concrete fracture parameters through indirect methods based on size effect experiments. These methods utilize the size effect curve (structural strength versus structural size), associated with a certain specimen geometry, to identify the tensile strength and the initial fracture energy. These two parameters, in turn, are typically used to characterize the peak and the initial post-peak slope of the cohesive crack law. In the literature, two different approaches can be found for the calculation of the size effect curve: (a) an approach based on the polynomial interpolation of numerically calculated structural strengths of geometrically similar specimens of different sizes, and (b) the classical approach based on equivalent elastic fracture mechanics, which gives rise to the well-known Bažant’s size effect law (SEL). In this paper, the two approaches are first reviewed, the relationship between them is investigated, and a new procedure to identify the tensile strength using the SEL is proposed. Then several sets of experimental results, recently performed at the Politecnico di Milano, are analyzed with both approaches in order to assess their range of applicability and accuracy in the identification of the two fracture parameters specified above.     

Determination of concrete fracture parameters based on two-parameter and size effect models using split-tension cubes

The notched beam specimens have been commonly used in concrete fracture. In this study, the splitting-cube specimens, which have some advantages - compactness and lightness - compared to the beams, were analyzed for the effective crack models: two-parameter model and size effect model. The linear elastic fracture mechanics formulas of the cube specimens namely the stress intensity factor, the crack mouth opening displacement, and the crack opening displacement profile were first determined for different load-distributed widths using the finite element method. Subsequently, four series of experimental studies on cubic, cylindrical, and beam specimens were performed. The statistical investigations indicated that the results of the split-cube tests look viable and very promising.     

真空发生器结构参数与性能参数关系研究

简要介绍了真空发生器的工作原理及应用,探讨了真空发生器的结构参数与性能参数之间的联系.     

Correlation between stretched zone size and fracture toughness

The topography of the stretched zone was measured from stereo electron micrographs. The stretched zone reflects crack tip blunting preceding fracture. The depth of the stretched zone of fourteen fracture toughness specimens of some Al-Zn-Mg alloys appeared to correlate reasonably with the critical crack tip opening displacement. The width of the stretched zone appeared to be in the order of magnitude of the ligament spacing in Krafft's model.     

Relationships between fracture parameters and fracture surface roughness of brittle polymers

Fracture parameters such as crack velocity à, stress intensity factor K _d and a specific crack extension resistance R ^* were measured for Homalite-100, PMMA and epoxy in the course of fast crack propagation using a Cranz-Schardin type high speed camera. Fracture surface roughness was evaluated as a function of crack length a so that it could be correlated with the fracture parameters above. The results showed that none of those parameters could be uniquely related to . Instead, there was a good correlation between and a product R ^* à.     

Relationship between strength variability and size effect in unidirectional carbon fibre/epoxy

Unidirectional carbon fibre/epoxy exhibits a size effect which is not necessarily consistent with the variability of specimen strengths predicted on the basis of classical Weibull theory. In some cases the variability is higher than expected and this may be due to other sources of variability in the tests apart from the material. However, in bending tests consistently lower variability than expected has been measured. This is explained qualitatively in terms of the splitting that occurs during failure which means that the composite behaves between the extremes of a brittle solid and a loose fibre bundle. This also implies that the size effect should be more strongly dependent on specimen length than indicated by Weibull theory. Three-point bending tests on specimens of different lengths but the same cross-section have been carried out which support this.     

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

This paper presents an investigation of the age-dependent size effect and fracture characteristics of 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 size effect tests of one age. Both aging and size effect studies are performed on notched three-point bending tests. Experimental data are augmented by state-of-the-art simulations employing a recently developed discrete early-age computational framework. The framework is constructed by coupling a hygro-thermo-chemical (HTC) model and the Lattice Discrete Particle Model (LDPM) through a set of aging functions. The HTC component allows taking into account variable curing conditions and predicts the maturity of concrete. The mechanical component, LDPM, simulates the failure behavior of concrete at the length scale of major heterogeneities. After careful calibration and validation, the mesoscale HTC-LDPM model is uniquely posed to perform predictive simulations. The ultimate flexural strengths from experiments and simulations are analyzed by the cohesive size effect curves (CSEC) method, and the classical size effect law (SEL). The fracture energies obtained by LDPM, CSEC, SEL, and cohesive crack analyses are compared, and an aging formulation for fracture properties is proposed. Based on experiments, simulations, and size-effect analyses, the age-dependence of size effect and the robustness of analytical-size effect methods are evaluated.     

An asymptotic approach to size effect on fracture toughness and fracture energy of composites

Size effect on fracture toughness and fracture energy of composites is investigated by a simple asymptotic approach. This asymptotic analysis based on the elastic/plastic fracture transition of a large plate with a small edge crack is extended to study fracture of composite. A reference crack length, a^*, is used in the model, which indicates an ideal elastic/plastic fracture transition defined by the yield strength and plane strain fracture toughness criteria. Experimental results of cementitious materials available in literature are analyzed and compared. It is shown that the common K_R-curves can also be obtained by the current asymptotic model. Furthermore, a local fracture energy distribution concept is also discussed and compared with the present asymptotic approach.     

Self-affinity of fracture surfaces and implications on a possible size effect on fracture energy

As demonstrated within the last 15 years by numerous experimental studies, tensile fracture surfaces exhibit a self-affine fractal geometry in many different materials and loading conditions. In the last few years, some authors proposed to explain an observed size effect on fracture energy by this fractality. However, because they did not consider a lower bound to this scale invariance (which necessarily exists, at least at the atomic scale), they had to introduce a new definition of fracture energy with unconventional physical dimensions. Moreover, they were unable to reproduce the observed asymptotic behavior of the apparent fracture energy at large specimen sizes. Here, we show that this is because they considered self-similar fracture surfaces (not observed in nature) instead of self-affine. It is demonstrated that the ignorance of the self-affine roughness of fracture surfaces when estimating the fracture energy from the work spent to crack a specimen necessarily leads, if the work of fracture is proportional to the fracture area created, to a size effect on this fracture energy. Because of the self-affine (instead of self-similar) character of fracture surfaces, this size effect follows an asymptotic behavior towards large scales. It is therefore rather limited and not likely detectable for relatively large sample sizes (10^–1 m). Consequently, significant and rapid increases of the apparent fracture energy are more likely to be explained mainly by other sources of size effect.     

The effect of void size and distribution on ductile fracture

The ductility of materials with different distributions of voids is examined theoretically. The theory of Thomason [7] is used which assumes that the material deforms homogeneously until localized deformation between the voids intervenes. The fracture is expected to occur so rapidly after the onset of localized deformation that the transition from homogeneous to inhomogeneous deformation is used as a criterion for ductility. Upper bound solutions are used to derive a criterion for the fracture strain.Void size distributions with equal numbers of voids of two sizes are examined. It is also investigated how a distribution of inter void distances influences the ductility. The importance of small secondary voids in a distribution of large primary voids is studied. The effect of the shape of the voids is also considered. In all cases analytical expressions are derived for the fracture strain. The void distributions are centered on a plane orthogonal to the tensile axis and all voids are of rectangular shape.

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Résumé On examine sur le plant théorique la ductilité de matériaux présentant différentes distributions de cavités. On recours à la théorie de Thomason, qui suppose qu'un matériau se déforme de manière homogène jusqu'à ce que suive une déformation locale entre deux cavités. Le processus de rupture doit se produire tellement vite après l'apparition de cette déformation locale, que la transition entre déformation homogène et déformation hétérogène sert de critère de ductilité. L'enveloppe supérieure des solutions obtenues permet de déduire un critère de dilatation de rupture.On examine des distributions des dimensions de cavités où se présentent, en nombre égal, des cavités de deux dimensions. On étudie également comment une distribution donnée de ligaments entre deux cavités influence la valeur de la ductilité et quelle est l'importance de petits trous secondaires dans une distribution de cavités primaires d'une certaine taille. L'effet de la forme des cavités est également analysé. Dans tous les cas envisagés, des expressions analytiques sont données pour la dilatation de rupture. Les distributions des cavités sont toutes concentrées sur un plant orthogonal à l'axe de la mise en charge, et les cavités sont supposées être de forme rectangulaire.

     

Relationship between fracture topography and fracture toughness of a high strength steel

The relationship between fracture topography and the plane strain fracture toughness of Comsteel En25 tempered at nine different temperatures and with crack planes in the R-L, R-C and L-R orientations has been studied. The results show that fracture toughness is qualitatively relatable to the fracture morphology. Due to the shape and alignment of the elongated MnS inclusions, fracture toughness in the L-R orientation was found to be 1.8 times those in the other two orientations. Terrace-type fracture prevailed in the R-L orientation, but this frequently was observed to change to zigzag type fracture in the R-C orientation. However, both these fracture mechanisms were absent in the L-R orientation.     

A comparative study on five approaches to evaluate double-K fracture toughness parameters of concrete and size effect analysis

The current paper presents a comprehensive comparison of double-K fracture toughness parameters of concrete evaluated using experimental method and four existing analytical methods. Fracture tests were carried out on compact tension wedge splitting specimens with various depths varying from 200 mm up to 1000 mm. In the analytical calculation, depending on the relationship between critical crack tip opening displacement and the abscissa value of turning point on bilinear softening curve, two different distributions of cohesive stress are considered along crack extension. Results show that four available analytical calculations yield almost the same values of double-K fracture toughness parameters and agree well with those obtained from the experiment, which confirms the consistency of five approaches. Size effect was discussed, including unstable fracture toughness, initiation fracture toughness, critical effective crack length, the length of critical fracture process zone and critical crack tip opening displacement.     

Probability distribution of energetic-statistical size effect in quasibrittle fracture

The physical sources of randomness in quasibrittle fracture described by the cohesive crack model are discussed and theoretical arguments for the basic form of the probability distribution are presented. The probability distribution of the size effect on the nominal strength of structures made of heterogeneous quasibrittle materials is derived, under certain simplifying assumptions, from the nonlocal generalization of Weibull theory. Attention is limited to structures of positive geometry failing at the initiation of macroscopic crack growth from a zone of distributed cracking. It is shown that, for small structures, which do not dwarf the fracture process zone (FPZ), the mean size effect is deterministic, agreeing with the energetic size effect theory, which describes the size effect due to stress redistribution and the associated energy release caused by finite size of the FPZ formed before failure. Material randomness governs the statistical distribution of the nominal strength of structure and, for very large structure sizes, also the mean. The large-size and small-size asymptotic properties of size effect are determined, and the reasons for the existence of intermediate asymptotics are pointed out. Asymptotic matching is then used to obtain an approximate closed-form analytical expression for the probability distribution of failure load for any structure size. For large sizes, the probability distribution converges to the Weibull distribution for the weakest link model, and for small sizes, it converges to the Gaussian distribution justified by Daniels' fiber bundle model. Comparisons with experimental data on the size-dependence of the modulus of rupture of concrete and laminates are shown. Monte Carlo simulations with finite elements are the subject of ongoing studies by Pang at Northwestern University to be reported later.