A. Vervuurt

Lattice model evaluation of progressive failure in disordered particle composites

Abstract Results from experimental and numerical investigation on the fractal properties of particle composites are presented. Splitting tests on concrete were carried out and the fractal dimension of the crack patterns detected on microscope images was measured. Numerical simulations of the tests were performed by means of a lattice model, and non-integer dimensions were measured on the predicted lattice damage patterns. The ability of the model to reproduce realistic statistical interactions and self-organization in the propagation of the cracks is discussed. In particular, an increasing Hausdorff dimension was measured during damage development in the lattice network. It is concluded that, next to the stable crack growth provided by fractality in disordered materials, an optimal choice of the percentages of weak and strong microstructural elements, together with their particle-like distribution, may lead to improved mechanical performance of the considered materials.

Crack growth mechanisms in four different concretes : Microscopic observations and fractal analysis

Splitting tests have been carried out for evaluating damage in four types of concrete. The concretes contained either river gravel with maximum aggregate size equal to 2 and 16 mm, phosphorous-slag aggregates, and Lytag aggregates. Different failure behaviours have been revealed, mainly depending on the aggregate and interface characteristics. The microscopic cracking mechanisms strongly affect strength, toughness, and ductility. In addition to mechanical measurements, a high resolution optical microscope was adopted for detecting the crack growth. Fractal dimensions of the crack lips and of the complex damage patterns were computed. No simple relation exists between fracture energy and fractal dimension, but relative differences in the material structure affect the value of the fractal dimension. This confirmed the peculiar different behaviours encountered in the tests.

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.

Numerical Analysis of Interface Fracture in Concrete Using a Lattice-Type Fracture Model

A key parameter in (numerical) models for simulating fracture of concrete at the meso-level is the behaviour of the interfacial transition zone between aggregate and matrix. In normal concrete the interface is a very porous thin layer with relatively low strength and stiffness. However, more dense interfaces can be obtained when different types of aggregates are used, or by means of selected additives to the cement matrix. Using a lattice-type fracture model of concrete, the effect of the interface properties on the global stress-strain behaviour is studied. To this end, splitting type tests on single particle specimens are conducted. Different types of aggregates are included. From the analyses, the sensitivity of the crack patterns to variations in interface strength and stiffness was obtained. Comparison with experimental observations is quite favourable. Next to the single particle specimens, concrete plates were tested, containing broken aggregates of the same material as used in the single particle plates. The effect of the type and size of the aggregates on the fracture geometry (fractal dimension) is analyzed. The results indicate that improved mechanical performance of composites may be obtained by carefully engineering the interface, taking care that an optimal ratio of weak to strong microstructural elements is present.

Lattice model for analysing steel-concrete interface behaviour

Publisher Summary This chapter presents the application of a newly developed lattice model to the bond between steel and concrete. In the model, the concrete is modeled as a triangular framework. The heterogeneity of the concrete is implemented by projecting the lattice on top of a generated particle structure, and by assigning different properties to the lattice beams appearing in the various phases of the particle structure. Fracture is simulated by removing in each load-step the beam element with the highest stress over strength ratio. The model is applied to bond of steel to concrete. Three different examples are shown: the effect of ribs on cracking in the bond zone, a detailed analysis of a miniature bond-slip test, and the pull-out of a steel anchor from concrete. All problems are treated as plane stress problems; this implies that longitudinal cracking is omitted. In all the analyses, adhesion between the steel and the concrete is modeled through a very low tensile strength of the beam elements in the lattice.

A LATTICE APPROACH FOR ANALYZING STEEL-CONCRETE BOND-SLIP-LAYER FRACTURE

In this paper steel-concrete interface fracture is modelled at the meso level. At this level a simple linear elastic fracture law seems to suffice to explain global fracture mechanisms of composite materials. Interfaces between aggregate and matrix and between matrix and reinforcing bars are simulated using a lattice model. In the model the material is discretized as a lattice of brittle breaking beam elements. Disorder of the material is implemented by assigning different strength and stiffness properties to the beam elements. Cracking is simulated by removing in each load step the element with the highest stress over strength ratio. The model is applied to uniaxial tensile fracture of plain concrete specimens and to bond of steel to concrete.

CRACK GROWTH SIMULATIONS IN CONCRETE AND ROCK

In the paper the lattice model developed in the Stevin Laboratory is outlined. In the model, the material is discretised as a network of brittle breaking beam elements. For simulating fracture in highly disordered materials like concrete and rock, the material structure is mimiced in great detail. The generated (two-dimensional) structure of the material is projected on top of a regular triangular lattice, or on top of a lattice with beams of random length. The amount of detail included in the material structure determines the size of the beam elements used in the lattice. Obviously the computer time will increase with the size of the lattice, and the available computer capacity mainly determines the size of the lattices that can be analysed. Fracture is simulated by removing in each load step the beam with the highest stress over strength ratio. This implies that fracture is completely brittle, and the results obtained so far indicate a close relationship between the amount of detail included in the projected material structure and the computed softening behaviour of concrete in tension. In the laboratory the model is used for assessing the response of fracture tests, for example for determining the correct response parameter in a displacement controlled experiment. Some examples of analyses are included in the paper.

Experimental And Numerical Analysis OfBoundary Effects In Uniaxial Tensile Tests

Results are presented of experiments and simulations of cylindrical specimens loaded in tension under different boundary conditions. It is shown that the global softening behaviour of a specimen is affected substantially by changing the boundary conditions. Experiments were performed using four different geometries and two different boundary conditions. One set-up was already available in which the loading platens were not allowed to rotate. A new testing machine was build for loading the specimens between freely rotating boundaries. Next to the experiments on sandstone and concrete, simulations were carried out with a numerical lattice model. The effects on the crack patterns when changing the boundary conditions are simulated quite realistically with the lattice model.

Experiments and Simulations of Interface Fracture in Concrete

At the aggregate level of concrete the fracture processes in the material are dominated by failure of the individual composites. A numerical lattice model has been applied which uses this knowledge for simulating fracture of concrete. In the model concrete is treated as a three phase material consisting of aggregates, matrix and the interfacial transition zone between the matrix and the aggregates. In order to determine the model’s fracture properties with respect to the interfacial transition zone, experiments and simulations have been carried out simultaneously. Two dimensional tensile splitting tests have been performed in which a cylindrical aggregate particle was embedded in a matrix of cement paste or mortar. In the simulations a variation was applied to the properties of the beams in the lattice model. It was concluded that the fracture behaviour is dominated by the strength of the beams in the interfacial transition zone, whereas the beam stiffness seems to have a minor effect on the fracture mechanism.

Experimental and Numerical Analysis of Cracking in Concrete and Sandstone

In the paper an experimental and numerical analysis of fracture of cement-based composites and sandstone is given. Tensile fracture in this class of brittle disordered materials is a complicated growth process from distributed tensile cracking to crack face bridging. Experimental evidence for crack face bridging is shown, using different crack detection techniques. The fracture process is simulated using a simple lattice model. In the model the material is schematised at the meso-level as a network of brittle breaking beam elements. Heterogeneity is introduced following different concepts. A simple fracture law suffices to simulate the complex crack geometries that have been observed in the experiments.