Experimental Analysis of Fracture Processes in Concrete

Experimental Analysis of Fracture Processes in Concrete

José Luiz Antunes de Oliveira e Sousa

Universidade Estadual de Campinas

Faculdade de Engenharia Civil

Caixa Postal 6021

13084-971 Campinas, SP. Brazil

[e-mail]

Túlio Nogueira Bittencourt

Universidade de São Paulo, Escola Politécnica

Av Prof. Almeida Prado, Trav. 2

05508-900 São Paulo, SP. Brazil

[e-mail]

This paper draws on the basic problems related to the determination of parameters to characterize the structural behavior of concretes using Fracture Mechanics concepts. Experimental procedures and results are discussed.

Keywords: Concrete, crack, fracture energy, fracture mechanics, fracture toughness

Introduction

Engineering materials are full of cracks. Although structures can be safely built with these materials, this fact is relevant for the design of a wide class of structures. Most of the design procedures currently in use are based on Strength of Materials concepts, i. e., stresses have yielding or rupture limits. However, the presence of stress concentrations in notches, around holes, in connections, etc. require that more sophisticated design procedures be used as the safety factors are lowered due to the preoccupation with conservation of materials and energy.

The presence of cracks, apparently a sign that something is wrong with the component or structure, does not mean that the structure reached the limit of its useful life. With the development of Fracture Mechanics the question now is not whether a crack exists or not, but whether the cracks are stable or not. In the case of reinforced concrete, cracks are tolerated since the earlier design procedures, which consider that concrete resists to compression while steel is responsible for tensile stresses required for equilibrium. Using Fracture Mechanics concepts, one would say that the reinforcement role is to arrest the cracks, thus making them stable.

The state-of-the-art in Fracture Mechanics applied to concrete indicates a great variety of models to simulate concrete behavior. These models require that parameters be obtained from concrete samples to characterize, basically, resistance to crack propagation. This paper focus on the determination of fracture parameters for concrete, describing experimental procedures developed by the authors and others, and experimental results.

Nomenclature

G_f = fracture energy, kN mm
K_Ic = fracture toughness
K_SR = fracture toughness from short rod specimens, MPa
CMOD = crack mouth opening displacement, mm
p = inelastic correction factor, dimensionless
= average load, kN D = specimen diameter; mm
C_K = correction factor to account for the specimen size variation, dimensionless

Greek Symbols

Dx, Dx₀= CMOD interval, according to Figure 3a, mm

DW = variation in specimen height, mm
Da₀ = initial position of notch apex, mm
Dq = chevron notch angle, dimensionless

Theoretical Background

The basic theory of Fracture Mechanics developed from the studies of Inglis (1913), Griffith (1921), Westergaard (1939) and others, based on concepts of linear elasticity. Westergaard (1939) developed a linear elastic description for the stress field around the crack tip, using stress functions in the complex domain. The introduction of the concept of stress intensity factors became straightforward from Westergaard's solution, which, associated to the concept of fracture toughness, form the basis for the Linear Elastic Fracture Mechanics (LEFM). The earliest engineering applications emerged in the end of the fourties, with Irwin's work (1948).

The fact that the elastic solution presents infinite stresses at the crack tip suggested that some sort of inelastic stress redistribution close to the crack tip would occur. The size of this region, called inelastic process zone, is a measure to evaluate the applicability of LEFM, when compared to crack and ligament sizes, and component thickness.

Dugdale (1960) and Barenblatt (1962), developed, independently and for different applications, a solution for the stress redistribution along a strip ahead of the crack tip, valid for elastic-perfectly plastic materials. Later, these basic concepts were used to model the cohesive crack model for quasi-brittle materials, applicable to concrete (Hillerborg, 1976; Bazant, 1983; Bittencourt, 1995). This solution, although suitable to model a single or a few cracks, is not sufficient to model any fracture process in concrete. Other models are still necessary to simulate processes in which microcracks and microvoids propagate and coalesce to a group of macrocracks. However, the development of such sophisticated models for the concrete is meaningless if the appropriate parameters are not available for Engineering applications. In this paper, the development and application of experimental procedures for the determination of fracture parameters in concrete is described, using two different types of specimens.

Experimental Methodology

Fracture toughness tests were performed on short-rod and three-point-bend specimens of concrete, at room temperature and at ages 14, 28 and 56 days. Crack mouth opening displacement (CMOD) controlled the load application in a MTS Model 810 closed-loop testing machine. The load was applied at a rate between 2 and 3 N/s. During the test, a plot of CMOD versus applied load is produced. Based on this plot, the system is unloaded down to 10-20% of the maximum observed load, and reloaded subsequently. These unloading-reloading cycles are performed, at least twice, to provide information for the computation of a correction factor to account for the nonlinear behavior of the concrete. This correction factor should be applied to the fracture toughness computed directly by LEFM formulae to result the actual fracture toughness of the concrete.

Short-rod Specimens

Short-rod specimens were built with loading bars bolted at the notch mouth face, perpendicular to the chevron notch plane, as shown in Fig. 1. Alternative systems for load application (Fig. 2) were developed by other researchers and are currently being tested by USP/UNICAMP research group. Crack mouth opening displacement (CMOD) was measured with a MTS Model 632.03C.20 clip on gauge.

According to ISRM (1988), fracture toughness can be obtained by Eq. (1).

where:

Dx, Dx₀: according to Fig. 3a;

: average load (points A and B in Fig. 3a);

D specimen diameter

C_K correction factor to account for the specimen size variation, Eq. (2);

DW: variation in specimen height;

Da₀: initial position of chevron notch apex;

Dq: chevron notch angle

Three-point-bend Specimens

Size effect on fracture energy G_f and fracture toughness K_Ic is investigated for plain concrete, using three-point-bend tests on specimens with initial through notches (Fig. 4). The investigation is conducted using similar beams, with depth varying from 3 cm to 12 cm. Fracture toughness is determined the two-parameter crack model and the effective crack model suggested by RILEM (International Union of Testing and Research Laboratories for Materials and Structures), and the linearization procedure proposed by ISRM (International Society for Rock Mechanics). Fracture energy is determined using the size effect model, also proposed by RILEM.

Experimental Results for Short Rod Specimens

The short rod specimen is very simple to test. The test setup developed lead to significant results, with only a few specimen lost during testing. The rupture mode was uniform (mode I). Low values of standard deviation were observed in the experimental results, showing the reliability of the test procedures. Results indicated that fracture toughness is inversely influenced by the increase in the water/cement ratio and by the increase in the agregate size. The ratio between the fracture toughness in level II and in level I (factor ) increases as the agregate size increases.

Experimental Results for Three-point-bend Specimens

Fracture Toughness values obtained from the laboratory tests appear to be strongly influenced by the size effect, within the range of sizes investigated. The phenomenon of relaxation, observed at peak load under a constant CMOD condition, was investigated and associated to a possible break down of the cohesive interface (Ferreira, 1998). Under these circumstances, the length of the cohesive interface at peak load was modelled. Fracture toughness values originated from these lengths appear to be almost constant, independently of specimen size.

Conclusions

A brief description of the first attempts performed by researchers towards the application Fracture Mechanics concepts to concrete and reinforced concrete was presented. Results obtained by two co-workers are briefly presented (Santos, 1998, and Ferreira, 1998). Although results are not exaustive, an important area of research was initiated and is currently active in the research groups of USP and Unicamp, in collaboration with Ingraffea's Cornell Fracture Group and other researchers.

Acknowledgments

The authors would like to acknowledge the support provided by CNPq–Conselho Nacional de Desenvolvimento Científico e Tecnológico and FAPESP–Fundação de Amparo à Pesquisa do Estado de São Paulo, Brazilian sponsorship agencies.

Bittencourt, T. N., 1999, Material Modelling Group, www site: http://www.lmc.ep.usp.br/people/tbitten/frat/

Hanson, J., Ingraffea, A. R., 1999, Measurement of Fracture Toughness of Concrete Using the Short-Rod Procedure, www site: http://www.cfg.cornell.edu/projects/ConcreteShortRod.html

Paper originally presented at the 15^th Brazilian Congress of Mechanical Engineering (XV COBEM), São Paulo, November 22-26, 1999.

COBEM Editors: R. G. dos Santos, M. H. Robert, A. C. Dannwart, J. R. B. Cruz.

Associate Editor: J. R. F. Arruda.

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Publication Dates

• Publication in this collection
  24 Sept 2002
• Date of issue
  2001