Characterization of the fracture toughness of the concrete mortars exposed to elevated temperatures

INTRODUCTION

The elastic linear mechanics of fracture (MLER) is a usual theory for analysing the fracture of metals or brittle materials such as glass or ceramics (1). All the phenomena of damage are supposed to be concentrated at the tip crack. As for the nonlinear mechanics of fracture (MNLR), it is supposed the existence of [much less than]fracture process zone[much less than] (FPZ) (2). Indeed, the damage mechanics and the MNLR were developed to solve the fracture problems within materials having a softening behaviour. However, the concepts of the MNLR and MLER can be used to solve the problem of the crack initiation.

Although concrete is a composite material, its mechanical performance did not reflect the simple theory of composites. This is expressed by the typical stress-strain curve of concrete and its constituent materials (cement paste and aggregates) as shown in Fig. 1. While both the cement paste and the aggregates have linear elastic behaviour up to 80% of their ultimate strength, concrete begins to deviate to nonlinear behaviour when the applied stresses reach 40-50% of its ultimate capacity. The non-linear (inelastic) behaviour of concrete under stress can be explained by defining concrete as a three phase heterogeneous material, the cement paste, the aggregates and the transition zone (TZ). The TZ represents the interfacial region between the cement paste and the aggregates. The transition zone is 10-50 [micro]m thick around the aggregates particles and has less resistance than the other two phases. Because of its high porosity and low strength, microcracks can easily propagate in the transition zone while the other two phases are not Cracked. This result is the non-linear behaviour of the concrete composite. The microcraks development and propagation determines the shape of stress-strain curve of concrete under uniaxial compression. The total amount of mortar crac[K.sub.I]ng is considerably less than the transition zone crac[K.sub.I]ng. While the ascending part of the concrete stress-strain curve is only dependent on crac[K.sub.I]ng extent in concrete, the descending part is highly influenced by the testing machine characteristics especially its stiffness.

[FIGURE 1 OMITTED]

Crac[K.sub.I]ng of concrete: It is also reported that some cracks are initiated at cement paste voids and then crack away of the transition zone. In the mean time, it is well established that even before the application of external stresses, microcracks already exist in the TZ as a result of shrinkage and thermal stresses. The number and width of these microcracks in the transition zone depend mainly on bleeding characteristics, wall effect, curing history of concrete and thermal and carbonation shrinkage extent.

FRACTURE MECHANICS MODELS APPLIED TO CONCRETE

It is well established that two basic criteria govern fracture of materials in either tension or compression. These are the stress and the energy criteria(4-6). Although these two criteria can explain the fracture behaviour of any material, the complexity is how to determine accurately the amount of energy consumed and the stress developed during the fracture process under specific boundary conditions (7). In brittle materials, elastic energies are consumed in the form of surface energy with no "fracture process zone" FPZ (8). In ductile materials the FPZ is known as the plastic zone which can consume a considerable amount of energy, much more than the surface energy (9). For quasi-brittle materials, a large FPZ which consumes a large amount of energy prior to failure is usually formed ahead of the crack tip. This FPZ, schematically represented in Fig.2, provides concrete with its quasi-brittle response.

[FIGURE 2 OMITTED]

Linear elastic fracture mechanics (LEFM): The applicability of LEFM models to concrete behaviour was made experimentally and it was concluded that the Griffith concept of a critical strain-energy release is convenient. Some observations on concrete behaviour that allow the use of LEFM:

* Fracture of concrete tends to be brittle.

* The strength of concrete depends on the loading rate (10).

* The tensile strength of concrete is about 1/10 of its compressive strength (7).

* Concrete and mortar are notch-sensitive.

The compliance approach: One of the useful LEFM models developed for concrete is the compliance approach. This approach relates the displacement of the concrete element to the load applied through a linear relation using the cracked body stiffness or Compliance as shown in Eq. (1).

P = C.[delta] (1)

Where [delta] is the displacement, P is the applied load and C is the compliance which is a function of geometrical parameters and the crack depth.

Evaluation of [K.sub.IC] and [G.sub.IC] for concrete: The critical stress intensity factor [K.sub.IC] is used to express the fracture toughness of concrete. [K.sub.IC] represents a measure of how much and how far the local stress field is altered. Equation (2) shows the mathematical expression of [K.sub.IC].