Question

Why do we need methods in addition to tensile testing?

Answer 1

Tensile Testing

Tensile testing is a way of determining how something will react when it is pulled apart - when a force is applied to it in tension.

Tensile testing is one of the simplest and most widely used mechanical tests. By measuring the force required to elongate a specimen to breaking point, material properties can be determined that will allow designers and quality managers to predict how materials and products will behave in their intended applications.

Tensile test can be used in many ways including:

• To determine batch quality
• To determine consistency in manufacture
• To aid in the design process
• To reduce material costs and achieve lean manufacturing goals
• To ensure compliance with international and industry standards

Tensile testing is the most suitable to assess the influence of fibre reinforcement in cement-based materials. From these tests, the values of the parameters of the constitutive models used to simulate the crack initiation and crack propagation, under the framework of the fracture mechanics, can be determined. Fracture mechanics has begun to assume its importance as the theoretical basis for the majority of simulation models implemented into finite element method (FEM)-based computer programs (Bazant and Oh 1983, de Borst 1986, Rots 1988, Barros and Figueiras 2001) and the physical comprehension of fracture processes in concrete (Hillerborg et al. 1976).

There are a few parameters that seem to have the most influence in the fracture behaviour of concrete, and are common to many theoretical models. In the fictitious crack model (FCM), one of the most important models in the progress of understanding tensile fracture in concrete, introduced by Hillerborg et al.(1976), the material parameters are the tensile strength fct, the Young’s modulus, Ec, the shape of the descending branch of the stress-crack opening diagram, and the fracture energy Gf, which is defined as the area under the stress-crack opening diagram. The stress-crack opening relationship can be obtained from a direct tensile test, as schematized in Fig. 4.9.

The test equipment is absolutely essential when stable softening behaviour is required. In fact, the tests must be carried out in closed-loop control of very stiff testing rigs, like the one shown in Fig. 4.10 (Barros et al. 1994). It is well known that the shape of the softening branch depends on the boundary conditions of the testing specimen, which influences the fracture energy values derived from the tests, see Fig. 4.11. In case of pin-ended boundary conditions, the specimens are free to rotate when the onset of the macrocrack takes place and no additional restraint is introduced. In case of fixed-end platens, the eccentricity originated by the crack opening has to be balanced by the introduction of bending moments that contributes to the generation of multiple cracks. This behaviour influences, to certain extent, the softening behaviour, where a horizontal plateau can occur when a second macrocrack opens. The higher cracking density found in fixed boundary conditions leads generally to larger values of fracture energy relative to the ones achieved in uniaxial tensile tests conducted using pin-ended platens (van Vliet 2000; van Mier et al. 1996).

To assure tensile stable tests under the assumption that a three-dimensional (3D) non-uniform crack opening process can occur in the critical crack, the control signal of a servo testing unit should result from the average signal of the LVDTs placed in the corners of prismatic specimens, near the notched controlled fracture surface, see Fig. 4.12 (Hordijk 1991, Barros et al. 1994). In cylindrical specimens, three LVDTs should be placed around the specimen, forming 120 degrees between consecutive LVDTs (Barragán 2002) (Fig. 4.12).

The FCM assumes a linear stress–strain law for the pre-peak stage and a stress-crack opening diagram for the post-peak stage, agreeing with the idea that the deformation localization phenomenon invalidates the use of the concept of strain as a state variable. This approach is the basis of the discrete crack models for modelling crack initiation and crack propagation under the framework of finite element analysis (Rots 1998; Sena 2004). If cracks can be diffusively distributed into concrete, as in highly reinforced concrete and concrete reinforced with high content of fibres, smeared crack models can be used for modelling the concrete post-crack behaviour. In this case, the crack strain is the crack opening divided by the crack bandwidth, which is a parameter depending on the characteristics of the finite element (Rots 1988; Oliver 1990).

The characteristic length, Lch, physically related to the concept of the width of the damage zone, may be derived from the fracture parameters:

[4.1]Lch=EcGffct2

Many other expressions for computing the characteristic length are suggested by other authors, in the context of different assumptions and models, but it seems fair to assume that the characteristic length measures the brittleness of the material and is intimately related with factors like the size of the aggregates present in the concrete structural skeleton, the presence of another toughening mechanisms (like the addition of fibres), the properties of the cementitious matrix, and the behaviour of the interfacial transition zones (Taha and Shrive 2002).

When a concrete specimen is tested under uniaxial tension, the stress–deformation diagram obtained typically assumes the shape shown in Fig. 4.13. The example shows a typical strain softening behaviour after peak, but also strain hardening may be found for higher fibre contents. The measurement of the deformation depends on the positioning chosen for the measuring devices, since after reaching the peak load, deformations rapidly concentrate in the failure zone, and a strong discontinuity appears in the strain field. As shown in Fig. 4.13, distinct load–deformation curves may be obtained, depending on the localization of the deformation measuring device. After the peak load is reached, unloading (curve c), slow softening (curve b) or rapid softening (curve a) behaviours may be simultaneously found at the same specimen. The failure process of concrete in tension is clearly a localized phenomenon. The cracked material, where energy is dissipated during failure, is limited by a band of a certain width. The width of the damaged zone depends on the structure of concrete, with coarser grained concretes showing a wider damage zone than the finer grained ones. This is physically explained by bridging and branching mechanisms that become more important in coarse-grained materials. Also, fibre reinforcement contributes positively to increase the fracture energy, acting as additional bridging mechanisms and spreading cracking over a wider volume of the concrete specimen. When the crack opening reaches significant values and aggregates bridging at the crack surface fails, stress transfer over the crack is possible through the fibres crossing it. The maximum bridging stress that can be reached depends on the shape and deformability of the fibres, the number and inclination of the fibres with respect to the crack faces, and the pull-out behaviour (related to interfacial properties and matrix structure of concrete). It is reasonable to accept that small microcracks are present in concrete matrix before any mechanical tensile loading has been applied. These microcracks will extend under loading since the very beginning of loading procedure, and the load–deformation curve will tend to diverge, although very slightly at the beginning, from the ideal linear elastic behaviour, at a tangent to the initial part of the curve. Propagation of microcracks will be very dependent on the interaction of microcracks with each other, or between microcracks and aggregates, and the confining effect given by the presence of fibres.

A nonlinear branch before peak load can occur in fibrous specimens, being the amplitude of this branch as larger as higher is the content of fibres.