Jan G. M. van Mier

Multiaxial strain-softening of concrete

The present paper deals with an experimental investigation of the strain-softening behaviour of concrete subjected to multiaxial loading conditions. A multiaxial apparatus for testing cubical specimens was developed and built at Eindhoven University of Technology. Servocontrols in combination with stiff loading frames allowed for measuring stable post-peak response. Loading was applied to the specimens using brush bearing platens.The failure modes of uni- and triaxially loaded specimens are discussed in the first part of this paper. Important in this context were the results of uniaxial compression tests on prisms with varying height. The experiments revealed a localised fracture mode in uniaxial compression. A constant fracture energy was measured, irrespective of the specimen’s size. Furthermore, from the multiaxial tests it was found that the slope of the descending branch is dependent on the applied symmetric or non-symmetric confinement. It was concluded that strain-softening is the response of the structure formed by the specimen and the complete loading system. In Part II [15] attention will be paid to the behaviour of this “structure” subjected to multiaxial load histories.RésuméOn expose ici une étude expérimentale du phénomène d’adoucissement pour un béton soumis à une sollicitation pluriaxiale. Un équipement d’essai pluriaxial pour éprouvettes cubiques a été mis au point et construit à l’Université de Technologie d’Eindhoven. Un système de servo-commandes et de bâtis de chargement rigide a rendu possible la mesure de réponses post-crêtes stables. Les charges ont été appliquées aux éprouvettes avec utilisation de balais montés sur les plateaux.On considère dans la première partie de cet article les modes de rupture sous charge uni- et tri-axiale. En regard de cette étude, les résultats d’essais de contrainte uniaxiale sur prismes de différentes hauteurs ont pris de l’importance. On a mis en évidence un mode de rupture localisée sous compression uniaxiale. Quelle que soit la dimension de l’éprouvette, on mesure une énergie de rupture constante. En outre, les essais pluriaxiaux montrent que la pente décroissante de la courbe dépend du choix du confinement symétrique ou pas. La conclusion est que l’adoucissement est la réponse de la structure que composent l’éprouvette et l’ensemble du système de chargement.

Fracture mechanisms in particle composites: statistical aspects in lattice type analysis

Abstract The effect of material microstructure on crack growth and force–deformation behaviour under uniaxial tension has been investigated in an extensive numerical study. A simple beam lattice model has been used to estimate the effect of strength and stiffness contrast, and particle density in a three-phase particle composite as found in concrete. The results from these explicit three-phase analyses have been compared to the outcome of simulations where the effects of microstructure were mimicked by assigning random strength values drawn from a Weibull or Gauss distribution to a regular triangular lattice. The results indicate that strength contrast is more important than stiffness contrast, and that global behaviour is largely governed by percolation of the weakest material phase. This behaviour was obvious from the three-phase analyses. The results from the different Weibull simulations resemble the mode of failure observed in the more realistic three-phase particle overlay. Bridging is a salient phenomenon observed in these analyses. In contrast the (symmetric) Gauss distribution is not appropriate. Although a large variety in force–deformation diagrams can be simulated, depending on the two parameters in the Gauss distribution and the lattice geometry, the failure mode along a single straight crack does not resemble the real fracture behaviour of three-phase composites like concrete. It is not recommended to use statistical strength distributions for simulating the behaviour of three-phase particle composites. Furthermore, the results clearly indicate that the force–deformation diagram cannot be used as a single indicator for judging the accuracy of a model for the fracture behaviour of materials. The crack mechanisms and the ensuing crack patterns are considered a salient element in such judgements. The model simulations can be applied as a guideline to design real three-phase composites. In particular optimization of tensile strength of the composite by selecting the correct amount of particles seems possible.

Experimental investigation of size effect in concrete and sandstone under uniaxial tension

Abstract A series of uniaxial tension experiments has been conducted to investigate the size effect on strength and fracture energy of concrete and sandstone. This paper specifically deals with the variation of the nominal strength for specimens of six different sizes in a scale range of 1:32. Depending on the material and the curing conditions a stronger or weaker size effect on the nominal strength occurred in the tests. The observed size effect has to be attributed to a combination of statistical size effect and strain gradients in the cross section of the specimens, which were caused by the specimen shape, load eccentricity and material inhomogeneity.

Joint investigation of concrete at high rates of loading

Uniaxial tensile tests have been carried out on a micro-concrete with strain rates between 0.5 and 1.25 s−1. The investigation is described and the results are discussed with respect to the influence of water content on the strain-rate sensitivity.

Experimental and numerical study on the behavior of concrete subjected to biaxial tension and shear

Abstract In this article an experimental and numerical study on the behavior of concrete subjected to biaxial loading is outlined. For this purpose the unique biaxial machine available at the Stevin Laboratory was used. Two load-paths were pursued, namely axial tension at constant shear and proportional tension/shear. The recently developed lattice model was used to simulate the two load-paths. The remarkable feature of the lattice model is its ability to simulate curved overlapping cracks which resemble the experimental findings.

Geometrical and structural aspects of concrete fracture

Abstract Results are presented of uniaxial and biaxial tensile experiments. Relatively large specimens were chosen to study the fracture mechanism of concrete. Essentially the material experiments were regarded as structural tests, from which material properties must be derived, by either varying the boundary conditions or the specimen geometry. In the present paper the specimen shape was varied: SEN and DEN geometries were studied under uniform boundary displacement. Structural changes were determined utilizing detailed surface deformation measurements and a photoelastic technique. The results suggest that two basic mechanisms take place in the softening regime of concrete. Firstly, the development of discrete perimeter cracks along the circumference of the specimen leading to a steep stress-drop in the softening regime just beyond peak, and secondly bending of intact ligaments between the perimeter cracks leading to large deformations in the softening zone. The first mechanism is largely influenced by possible stress-redistributions that may occur within the specimen. The mechanism is used for explaining the response of DEN specimens under biaxial tensile loads.

Numerical simulation of chaotic and self-organizing damage in brittle disordered materials

Abstract The results of a numerical investigation on the fracture properties of heterogeneous materials are presented. Numerical simulations of tensile, compressive and splitting tests have been performed by means of the Delft lattice model, and fractal dimensions have been measured on the lattice damage patterns. The ability of the model to reproduce statistical interactions and self-organization in the propagation of the cracks is discussed. In particular, the global fractal dimension of the microcracks network increases with a progressively decreasing rate during damage propagation in the lattice. Useful indications are provided by the discrete model that can be inserted in a continuum formulation. An optimal choice of the percentages of weak and strong microstructural elements, together with their particle distribution, may lead to improved mechanical performances.

Multiaxial strain-softening of concrete: Part II: Load-histories

The paper describes the behaviour of concrete specimens (cubes, d=100mm) subjected to multiaxial cyclic and rotation load paths. The specimens were loaded in a recently developed multiaxial apparatus which was described shortly in Part I. A cyclic load path corresponds to a series of loading-unloading cycles to the envelope curve, for which the major compressive stress-strain curve was used for defining the unloading conditions. The rotation paths implied a simple exchange of major and minor compressive stress, after some damage was sustained to a specimen. The observed stress-strain behaviour of the different loading paths was discussed in relation to the “final structure” of a specimen subjected to multiaxial compression. The “final structure” consists of a number of more or less intact rest pieces, separated by localised shear zones. The movement of the blocks with respect to each other and into the shear localisations seems to determine the complete observed response. By using cyclic and rotation load paths, the geometry and frictional characteristics of the shear fractures may be determined.RésuméOn décrit le comportement d’éprouvettes de béton (cubes,d=100 mm) soumises à des modes de chargement pluriaxials cycliques et en rotation. L’équipement utilisé est celui décrit dans la première partie. Ce chargement cyclique se traduit par une série de cycles de chargement/déchargement à la limite élastique (courbe intrinsèque), les conditions de déchargement ayant été définies à l’aide de la composante majeure de contrainte/déformation en compression. La rotation implique un simple passage de l’une à l’autre des composantes majeure et mineure après un certain endommagement de l’éprouvette. on a considéré le comportement contrainte/déformation suivant les différents modes de chargement en relation avec la ‘structure finale’ d’une éprouvette chargée en compression pluriaxiale. La “structure finale” consiste en un certain nombre de “blocs” séparés par des zones de cisaillement localisé. Ce sont les mouvements de ces ‘blocs” les uns par rapport aux autres et leur pénétration dans les zones de cisaillement qui semblent déterminer la réponse complète fournie par l’observation. Au moyen des modes de chargement, cycles et rotations, les caractéristiques géométriques et tribologiques des fractures par cisaillement peuvent être déterminées.

Microstructural Effects on Fracture Scaling in Concrete, Rock and Ice

Concrete, rock and ice are brittle disordered materials. Materials belonging to either of these classes display small-scale heterogeneity at the level of the material micro- and/or meso-structure, but also a large-scale heterogeneity at the level of the structure in which the material appears. The interplay between crack growth at the small-scale and large-scale heterogeneity leads to distinct size/scale effects in fracture. The determination of the two transition scales at which the macro-scale heterogeneity takes over from the micro-scale heterogeneity and where the macro-scale heterogeneity loses its importance is crucial for an understanding of size/scale effects. Both transitions are important to decide where continuum models could be applied to come to predictive extrapolation from laboratory scale experiments. Furthermore such knowledge is essential to design a reliable standard test for the determination of fracture parameters. Issues related to fracture of geo-materials are debated in the paper for mode I fracture only.

Size effect in tensile strength caused by stress fluctuations

The randomness of microstructure heterogeneous materials leads to creation of microscopic random stress fields within the bulk of the material under loading. Although in average the microscopic stresses coincide with the macroscopic (e.g., externally applied) stress, the local differences (stress fluctuations) can be high, the magnitude increasing with the volume of the heterogeneous material. In the case of uniform macroscopic loading, Gaussian stress fluctuations lead to a size effect in which the tensile strength reduces as square root of logarithm of the sample size. In practice, however, the macroscopic tensile stress fields are usually nonuniform. In this case, failure is determined by the maximum value of the macroscopic stress with the scale effect controlled by the minimum degree of the macroscopic stress decrease from its maximum. Therefore, a second model is proposed which accounts for a linear stress variation. Comparison of both models with the experimental data on macroscopic strength and stress variations in dog-bone shaped samples (scale range of 1:32), shows that the model based on the assumption of uniform macroscopic stresses can only explain part of the experimental data with unrealistic values of the fitting parameters. The model which takes into account the linear part of the macroscopic stress distribution offers reasonably good accuracy. This serves as another indication that macroscopic stress nonuniformity plays a crucial role in the mechanism of size effect.