Effect of loading rate on the tensile behaviour of concrete: description of the physical mechanisms

Founded upon several works carried out by the Laboratoire Central des Ponts et Chaussées on the dynamic behaviour of concrete (already published), and upon new ideas about this subject, this article attempts to further develop the analysis of the physical mechanisms. In particular to investigate how the Stéfan effect, the cracking process, and the inertia forces participate together in the dynamic behaviour of a specimen subjected to a uniaxial tensile test. These mechanisms can be summed up as follows:

1. At strain rates smaller than approximately 1 s^?1, the main physical mechanism is a viscous mechanism that may be regarded as similar to the Stéfan effect. This mechanism counters both a microcracking localization, leading to an increase of concrete tensile strength, and the macrocrack propagation that leads to failure of the specimen.
2. At strain rates greater than or equal to approximately 10s^?1, the forces of inertia become preponderant. They counter microcracking localization and in particular macrocrack propagation.

     

Mode I fracture behaviour of concrete under biaxial loading

Most concrete structures are biaxially loaded when cracking occurs and propagates. A test equipment was developed to evaluate fracture mechanic parameters of concrete, based on the principle of wedge splitting. Notched cubic specimens are tested under stable crack propagation. An additional compressive load application device simulates a homogeneous biaxial state of stress. A force-crack opening displacement diagram is obtained from which the specific fracture energy is calculated. The strain softening behaviour is then evaluated by means of numerical modelling. The approach was applied for biaxially loaded concrete samples with 8, 16 and 32 mm maximum size aggregate (MSA). Based on the experimental data a model is developed and discussed. It is found that the fracture energy changes non-uniformly with increasing compressive stress level, and that interaction of microcracking and aggregate interlocking influences the fracture mechanism.     

Strength of concrete subjected to high temperature and biaxial stress: Experiments and modelling

The mechanical behaviour of normal weight concrete subjected to high temperature and biaxial stress is not well understood. The investigation reported is twofold. The strength is studied of unsealed concrete and mortar incorporating quarzitic aggregate and bound by Portland cement and subjected to high temperature and biaxial stresses. This involves short-term tests and includes the influence of the composition. Additionally a mechanical model is developed for the failure of concrete subjected to these stresses which incorporates not only the main variable temperature, but also compositional variables which have a significant influence on the strength of concrete at high temperatures.

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Resume Le but de cette recherche était d'améliorer nos connaissances sur la résistance du béton soumis à de hautes températures ainsi qu'à des contraintes biaxiales. De nombreux essais ont été menés sur des éprouvettes non scellées de béton et de mortier à base de CPA. On a aussi étudié, outre le type de sollicitations, l'influence des paramètres de composition les plus importants. Les essais ont révélé que, dans tout le domaine des sollicitations biaxiales en compression, la composition influence directement la diminution de la résistance du béton en fonction de l'augmentation de la température. Le diamètre maximal des granulats s'avère être un facteur déterminant alors que la nature de ces derniers et le rapport eau/ciment n'ont en général que des effects secondaires. L'amplitude de ces influences diffère. Comme le montrent les essais à température normale, les valeurs de la résistance du béton sont affectées par sa composition avant la désintégration de la portlandite entre 450°C et 550°C. Afin de généraliser le comportement observé, on a modélisé la résistance du béton soumis à des contraintes biaxiales à haute température; pour ce faire, le critère de defaillance de Podgorski a été modifié afin de prendre en compte les paramètres suivants: haute température, rapports eau/ciment et granulats/ciment. Avec quelques simples essais de résistance à température normale et élevée, le modèle peut être facilement ajusté pour décrire le comportement d'un béton possédant une composition spécifique. La théorie ainsi développée est bien vérifiée par les résultats des essais.

     

Size effects in polyurethane bonds: experiments, modelling and parameter identification

In this study we examine polyurethane bonds of varying thickness between anodised aluminium substrates. The performed shear tests showed an intriguing size effect of the kind “thinner equals softer”. This size effect occurs not only in the basic elasticity (relaxed state), but also in the viscoelastic behaviour of the tested material. The cause of such size effects is supposed to be found in the existence of so-called interphases or boundary layers, which may differ considerably from the bulk in terms of mechanical behaviour, thus having an enormous impact on thin bonds. In thick bonds, however, these interphases or boundary layers have a minor effect on the overall mechanical behaviour. To account for these experimental results in bond modelling, an extended phenomenological continuum mechanics-based model, which explicitly includes such size effects in its calculation, is developed and presented. For this purpose, an abstract structure parameter with its corresponding balance equation is established describing the formation of the interphases by means of a phase transition. This makes it possible to define the bond stiffness at a macroscopic level, without entering into the microstructure. The extended model brings up a set of model parameters, which are determined efficiently by an ES (evolution strategy). The study concludes with a summary and an outlook on our further research work.

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Fatigue behaviour of a box-welded joint under biaxial cyclic loading: effects of biaxial load range ratio and cyclic compressive loads in the lateral direction

ABSTRACT The biaxial fatigue of a steel plate (JIS SM400B) having a box‐welded (wrap‐around) joint was experimentally studied. Special concerns were focused on the effects of the biaxial load range ratio and compressive cyclic loading in the lateral direction. The direction of fatigue crack propagation under biaxial cyclic tensile loading, which has a phase difference of π, changed according to the biaxial load range ratio, R_xy = ΔP_x/ΔP_y. When R_xy was less than 0.56, fatigue cracks propagated along the toe of the weld in the x‐direction because the principal tensile stress range Δσ_y at that location exceeded the orthogonal value Δσ_x at the box‐weld toe. The fatigue lives in biaxial tests related well to the data from uniaxial tests when invoking the Δσ₅ criterion. However, the location and direction of Δσ₅ should be chosen according to the R_xy value and the failure crack direction. An increase in Δσ₅, as induced by the Poisson's ratio effect from either the out‐of‐phase tensile loading or the in‐phase compressive loading in the y‐direction, leads to an increase in fatigue damage (decrease in fatigue resistance or specifically a faster crack propagation rate), and this effect can be successfully estimated from uniaxial fatigue test data.     

Bleeding: Evaluation of its effects on concrete behaviour

In many existing structures strength variations of about 20–30% between upper and lower levels have been registered. These differences are attributed to bleeding and segregation of concrete. In the present work standard specimens and structural elements (2.00 m high) were molded with concretes of different bleeding capacity and velocity. The influence of bleeding on hardened concrete characteristics was studied: visual appreciation of localized defects, determination of absorption, specific gravity, compressive and tensile strength, and strain measurements. With a high bleeding velocity the formation of vertically-oriented channels was observed. With a high bleeding capacity water accumulated under coarse aggregates causing on drying approximately horizontally-oriented fissures. These localized defects are responsible for concrete anisotropic behaviour. The presence of defects was not detected in standard specimens owing to their small volume and height. According to the measured bleeding parameters a decrease of strength of up to 30% in the upper levels and a difference of about 25% according to the loading direction were registered. From the evaluations realized it comes out that when the bleeding of concrete is high the results of tests made on molded specimens are not representative of the real state of the structure.

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Résumé Plusieurs structures existantes présentent des variations de résistance pouvant atteindre 20 à 30% selon la hauteur considérée. Ces différences sont attribuées au ressuage et à la ségrégation du béton. Dans ce travail on a préparé des éprouvettes normalisées ainsi que des éléments de structure (hauteur 2 mètres) avec des bétons dont la vitesse et la capacité de ressuage étaient différentes. On a étudié l’influence du ressuage sur le béton durci: appréciation visuelle des défauts localisés, détermination de l’absorption, masse volumique apparente, résistance à la compression et à la traction ainsi que déformabilité. Avec une vitesse de ressuage élevée on a observé la formation de canaux orientés verticalement. Lorsque la capacité de ressuage est élevée, on constate une accumulation d’eau sous les granulats grossiers, qui lors du séchage, provoquent des fissures à peu près horizontales. Ces défauts localisés sont les causes de l’anisotropie du béton. Ces défauts, par contre, n’ont pas été décelés dans les éprouvettes normalisées à cause de leur petite taille (hauteur et volume). On a observé une baisse de résistance pouvant atteindre plus de 30% à la partie supérieure et une variation de cette résistance, en fonction de la direction de la charge, de l’ordre de 25%. De ce qui a été réalisé, on déduit que lorsque le béton a un ressuage important, les résultats des essais faits sur de petites éprouvettes ne représentent pas l’état réel d’une structure.

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This research was realized in the Laboratories of LEMIT-CIC (Commission of Scientific Research) and Engineering Faculty of the National University of La Plata (UNLP), Argentina     

Analytical modelling of plastic behaviour of uniformly FRP confined concrete members

A method is presented for the assessment and calibration of the elastoplastic behaviour of FRP confined concrete. The method is based on the evaluation of permanent deformations from observed experimental deformations and theoretical elastic response of confined concrete. The inelastic response of concrete and the parameters of its mathematical modelling are investigated. Closed form expressions are produced to relate the model parameters to the mechanical properties of the material. A strain-hardening Drucker–Prager model is developed which simulates both the hardening and softening material response with reasonable agreement to the experimental observations. The predictive ability of the model is verified through comparisons to numerous published experimental data and analytical models.     

Size effects in concrete fracture: Part I, experimental setup and observations

This paper presents an experimental investigation on the influence of microstructural parameters, such as aggregate size, and macroscopic parameters, such as specimen dimensions, on brittle fracture. Maximum aggregate size was used as a representative parameter of aggregate distribution in agreement with ASTM C136 standards. Six groups of geometrically similar concrete specimens with various dimensions and aggregate sizes were prepared. Similarity of the specimens was strictly maintained by scaling the specimen dimensions from one group to another by a factor of two starting from a specimen size of (width × total depth × thickness) 105×105×12.5mm to 1680×1680×200mm. Two separate sets of removable pre-cast notches were designed to determine the effect of initial notch size. A considerable effort was devoted to the design of the loading fixture to have a reproducible crack initiation and controlled crack growth. Several loading fixtures were evaluated prior to selection of the one used in the experimental program. Quasi-static splitting cyclic loading in edge cleavage configuration was applied. A servo-hydraulic Instron machine was used for testing. The fracture process was monitored by optical and acoustic imaging techniques. Three forms of comparisons of the test results with respect to the specimen and aggregate sizes were adopted. The first corresponded to the various specimen sizes cast with the same maximum aggregate size. The second comparison was based on the geometrically identical specimens cast with various maximum aggregate sizes. The third form of comparison dealt with complete geometrical similarity, i.e., all dimensionless geometrical characteristics including specimen thickness to maximum aggregate size ratio were identical. Results from this study indicated that as the specimen size decreases, the envelope becomes larger within the first and third forms of comparison. In the second form of comparison, i.e., geometrically identical specimens cast with various maximum aggregate sizes, the area under the envelope was greater as the maximum aggregate size increased. The existence of a trend in dimensionless critical load-CMOD envelopes despite the apparent geometrical and physical similarity of the test conditions is the direct indication of a scale effect, i.e., the modified fracture energy, indicates the existence of a strong scale effect: increases with the specimen dimensions as well as maximum aggregate size.     

CDM based modelling of damage and fracture mechanisms in concrete under tension and compression

Anisotropic damage evolution and crack propagation in the elastic–brittle materials is analysed by the concepts of continuum damage mechanics (CDM) and finite element method (FEM). The modified Murakami–Kamiya (MMK) model of elastic-damage material is used to describe damage anisotropy in concrete. The Helmholtz free energy representation is discussed. The unilateral crack opening/closure effect is incorporated in such a way that the continuity requirement during unloading holds. The incremental form of the stress–strain equations is developed. The general failure criterion is proposed by checking the positive definiteness of the Hessian matrix of the free energy function. The local approach to fracture (LAF) by FEM is applied to the pre-critical damage evolution that precedes the crack initiation, and the post-critical damage/fracture interaction. Crack is modelled as the assembly of failed finite elements in the mesh, the stiffness of which is reduced to zero when the critical points at stress–strain curves are reached. A concrete specimen with the pre-load, inclined crack is analysed in order to simulate different fracture mechanisms in tension or compression. The constitutive model is capable of predicting the kinked-type crack under tension and the wing-type crack under compression.     

Identification of the physical mechanisms underlying acoustic emissions during the cracking of concrete

The investigation presented concerns the use of acoustic emission as a tool for the interpretation and explanation of crtain physical mechanisms involved in mechanical damage to concrete. From assumptions made concerning the existence, for a given acoustic emission test and appratus, of ‘critical’ inclusion sizes that lead to irreversible mechanisms that can be detected by acoustic emission, it is shown that it is possible to distinguish cracks at the matrix-inclusion interface and cracks propagating in the matrix during mechanical tests.     

Uniaxial and biaxial fracture behaviour of refractory materials

Mechanical fracture properties of specimens taken from refractory materials of different brittleness are described using the wedge splitting method according to Tschegg in uniaxial and biaxial load cases. Notch-tensile strength, fracture energy and the characteristic length were determined. Fracture energy under a uniaxial load is more or less the same for all materials; if a load becomes biaxial, values fall to approx. 70% in materials with reduced brittleness and to 40% in brittle materials, compared to uniaxial values. The sensitivity against crack propagation (l_ch) changes insignificantly under both uniaxial and biaxial loading of brittle and brittleness-reduced materials.     

Self-similarity in concrete fracture: size-scale effects and transition between different collapse mechanisms

Since the pioneering paper by Mandelbrot (Nature, 308:721–722, 1984) on the fractal character of the fracture surfaces in metals, the fractal aspects in the deformation and failure of materials have been investigated by several Researchers (see the reviews by Bouchaud (J Phys Condens Matter, 9:4319–4344) and Carpinteri et al. (Appl Mech Rev, 59:283–305, 2006)) and the attempts to apply fractals to fracture have grown exponentially. Aim of this paper is 2-fold: on one hand, it summarizes in a detailed yet concise fashion the major results of the fractal approach to the scaling of mechanical properties in solid mechanics; on the other hand, it reports some recent results concerning the size effect in the failure of reinforced concrete (RC) beams. These recent findings clearly show that the picture of the size-scale effects is much more complex when interaction among different collapse mechanisms occurs. The consequences on the size-scale effects are discussed in detail.     

Steel-fibre-reinforcement and hydration coupled effects on concrete tensile behaviour

This paper presents the effect of hydration development on the tensile behaviour of steel-fibre-reinforced concrete. Tensile tests were performed on plain and fibre-reinforced concretes at 2, 7 and 28 days in order to determine the response of the composites, in particular to establish the post-peak behaviour and the evolution of the residual post-peak strength with hydration development and the associated improvement in the fibre–matrix bond.From the laws governing the tensile behaviour of plain concrete on the one hand and the residual strength capacity due to fibre reinforcement on the other, parameters fitting an analytical model of the uniaxial tensile response of fibre-reinforced concrete were determined. The proposed model takes into account the tensile damage to the concrete and the development of hydration. An original aspect of the model is that it also integrates the damage to the fibre–matrix bond.     

On modelling cracks in orthotropic plates under biaxial loading: synthesis and summary

The model of a crack with a process zone is considered and generalized to orthotropic materials. It is assumed that a material in the process zone satisfies a strength condition of arbitrary form. Based on the crack model, the fracture of an orthotropic cracked plate under biaxial loading is studied. The crack is directed along one of the anisotropy axes with external loads being applied in parallel and perpendicularly to it. The influence of the biaxiality of external loading on the critical state of the cracked plate is analysed within the framework of the critical crack opening displacement and critical J ‐integral criteria. Numerical solution is obtained using the Mises‐Hill and Gol’denblat‐Kopnov strength criteria. Theoretical results are compared with experimental data obtained by testing specimens made of structural metals.     

Influence of aggregate deformation and contact behaviour on discrete particle modelling of fracture of concrete

The discrete element method, DEM, has been used in fracture studies of non-homogeneous continuous media adopting circular or spherical particles. A 2D circular rigid DEM formulation developed with the purpose of modelling concrete is described and evaluated in uniaxial tensile and compression tests. According to this model, the aggregate can be modelled either as a rigid macro-particle or as a deformable group of particles. The inter-particle contacts can either be assumed as brittle or follow a given bilinear softening curve. It is shown that aggregate deformability, together with the consideration of pure friction contacts working under compression, increases the fracture energy in compression, leading to a better agreement with concrete tests. The softening contact model, by adding a higher capability of load redistribution, is shown to give a better agreement than the brittle model under tensile loading. The recognized crack mechanisms of the brittle model (tensile splitting, branching, bridging) are also present with softening.     

Size and geometry effects on ductile rupture of notched bars in a C-Mn steel: experiments and modelling

The aim of this work was to investigate the effect of specimen size and geometry on ductile fracture of a C-Mn steel with high sulphur content. Uniaxial tensile tests were conducted at 300°C on axisymmetric notched specimens having different sizes and geometries. Geometry effects were studied using specimens with various notch radii, thus inducing different stress triaxiality levels. Size effects were evidenced using homothetic samples having the same geometry. Results show that ductility is reduced on specimens with sharp notches (which is a common observation). As specimen size increases, mean ductility as well as scatter are reduced (showing a clear size effect). In order to predict rupture, locally coupled (post-processing type) and fully coupled (continuum damage mechanics) Finite Element models were used. They are based on the plastic criteria introduced by Gurson and Rousselier. In order to model size effect (decrease of ductility and scatter), initial distribution of inclusion volume fractions, measured by quantitative metallography, was accounted for in the simulations. Comparison of experiments with simulations showed that both model types could predict mean values of ductility and scatter. This revised version was published online in August 2006 with corrections to the Cover Date.     

Size effects on concrete fracture energy: dimensional transition from order to disorder

The nominal fracture energy of concrete structures is constant for relatively large structures, whereas it increases with size for relatively small structures. If the energy dissipation space is modeled as a monofractal domain, with a non-integer dimension comprised between 2 and 3, a unique slope in the bilogarithmic fracture energy versus size diagram is found, as was stated in a previous paper [1]. On the other hand, when the scale range extends over more than one order of magnitude, a continuous transition from slope+1/2 to zero slope may appear, according to the hypothesis of multifractality of the fracture surface [1]. This means that, at small scales, a Brownian microscopic disorder is prevalent whereas, at large scales, the effect of disorder vanishes, yielding a macroscopical homogeneous behavior. The dimensional transition from disorder to order may be synthesized by a Multifractal Scaling Law (MFSL) valid for toughness, in perfect correspondence with the MFSL valid for strength, which has been described in a previous paper [2]. The MFSL for fracture energy is applied, as a bestfitting method, to relevant experimental results in the literature, allowing for the extrapolation of fracture energy values valid for real-sized structures.