Reinforcement Behaviour under Static Loading

Steel may be considered as isotropic for most design calculations in civil engineering.

A high tensile strength together with a high ductility – both greatly dependent on the chemical composition, the heat treatment, production technique, and service temperature – are the principal properties which may be used to complement the negligible tensile strength of concrete. Reinforced concrete is a very effective composite material that exhibits sufficient ductility if a reasonable structural design is provided.

An important simplification is the assumption of homogeneously distributed stresses at the cross section of reinforcing bars. In fact, stress concentrations, which are located espe-cially at the rib roots, are not accounted for. A further essential assumption corresponds to the stress direction. Accordingly, steel reinforcement experiences only uniaxial stresses in the longitudinal axis. Multiaxial stress states, like those present in the dowel effect in cracked slab structures, are practically disregarded.

Pull-out tests of reinforcement steel are mostly strain-controlled with minor strain rates of approximately 0.02 ‰/s.

Steel belongs to the crystalline materials, being an alloy of iron and carbon, whereas the carbon content is limited by definition up to 2.06%. Higher carbon contents produce another microstructure and the final material is known as cast iron. The idealised internal structure of steel is composed by crystals where iron and carbon atoms, present as an interstitial solid solution, are arranged in geometric defined units called elementary cells.

Similar to other metals, iron and steel exhibit a so called polymorphism – a property that describes the change of the elementary cell depending on temperature, surrounding pressure, and concentration. The most important polymorph transformation is that of face-centred cubic iron (austenite) into body-centred cubic iron (ferrite) [169]. Based on the idealised structure of steel and the currently accepted physical material models, the theoretical steel strength may reach a value of 21,000 MPa. Real materials, though, have a considerably lower strength with values which are lower by a factor of 10²[172].

The presence of multidimensional lattice defects is considered responsible for the difference between real and idealised material behaviour. Among others, principally dislo-cations (one-dimensional), and crystal boundaries (two-dimensional) affect the theoretical steel strength [172]. Dislocations may be present in form of edge or screw dislocations.

According to [89], the normal dislocation density in metal materials after solidification

33

34 Chapter 3 Material Behaviour

Figure 3.1:Phase diagram of iron and carbon [89]

amounts 10⁷/cm². This value may increase up to 10¹²/cm²due to the development of plastic deformations.

Materials experience deformations under the action of forces. In principle, forces activate inner bonding attractive or repulsive stresses between atoms and deviate them from their equilibrium position, enlarging or reducing their corresponding distances. As long as the acting forces do not exceed a critical local value, a local material rupture or the induction of sliding motions (plastic deformations) is not expected. The atoms return to their original equilibrium position and the induced material deformation reverts fully (elastic deformation) [89]. In case of unalloyed steel under one-dimensional stress states and ambient temperature, tensile forces that exceed a certain critical value cause a sliding of crystals along crystallographic planes (sliding planes) in determined crystallographic directions (slip directions) [169]. A crystallographic plane with its corresponding slip direction defines a crystal system. Shear stresses are, therefore, the principal slip parameter [12]. The sliding capacity of crystals is a function of the elementary cells which exhibit various lattice planes depending on the plane direction. Hence, the plasticity of steel is locally a rather anisotropic property [12]. Following the sphere model of atoms, sliding motions are generally activated along those lattice planes which posses the highest packing density of atoms since the required shear stresses in this direction are a minimum. Face-centred cubic elementary cells (e.g. austenite steel) have 12 crystal systems while a hexagonal closed packed elementary cell (e.g. graphite) has only one – a reason for

3.1 Reinforcement 35

the poor plasticity of materials with hexagonal closed packed elementary cells. Body-centred cubic elementary cells (e.g. ferrite steel) have, in contrast, theoretically 48 crystal systems. However, not every one may be considered as equivalent to the others. Hence, the plasticity of body-centred cubic materials resides between face-centred cubic and hexagonal closed packed materials [89].

τ

τ τ

τ

(a) (b)

Figure 3.2:(a) Sphere model of dislocation slips [12], (b) Model for an edge dislocation (left) and a screw dislocation, redrawn from [12]

Dislocations inside the crystal lattice structure are described as carrier of plastic defor-mations [22]. Their formation is induced mainly by diverse crystallographic restrains during crystallisation and the presence of other phases. Dislocations are one-dimensional lattice defects, show interaction effects with other dislocations, and may experience slip motions under the action of forces or temperature. In [22], the elementary processes for dislocation motions are extensive described:

• Slip of edge and screw dislocations,

• reciprocal slicing of edge and screw dislocations,

• cross slipping of screw dislocations, and

• climbing of edge dislocations.

An important phenomenon is the creation of further lattice defects like dipoles, lattice vacancies, and new dislocations owing to plastic deformations. As a consequence, an increasing number of obstacles for the additional dislocation motion emerges and further forces are required for overcoming them. Thus, the material exhibits a strain hardening which is also a function of the deformation rate. A higher deformation rate causes the material to have a lower time lapse to activate the necessary mechanisms for inducing inner slip motions [22]. This leads to a higher material strength.

Reinforcement steel is classified under the unalloyed steel class [33]. In accordance with [38], the percental amount of accompanying elements like manganese, nickel, chrome, molybdenum, silicon, aluminium, and others is strictly limited to comparably low values.

Carbon does not exceed a 0.22% content. These elements generally lead to a strength increase in different degrees, however, with a simultaneous loss of ductility (exception:

36 Chapter 3 Material Behaviour

nickel). Therefore, the reduction or restriction of other metallic, or non-metallic elements causes reinforcement steel to be (more) adequate for welding, possessing also an acceptable ductility capacity [89]. Moreover, alloy elements lead in many cases to a creation of mixed crystals, and for instance, of further obstacles for the dislocation motion (strength increase).

This process is usually subjected to a ductility decrease, though. In compliance with [36]

and [33], the adopted manufacturing processes are listed below:

• Hot-rolled steel without post-treatment. The molten steel flows into a rising per-manent mould, being moulded to a slab [89]. Following this step, the ribbed bar shape is achieved by hot rolling the still hot or reheatet steel slab (approx. 1100°C) into the desired shape [91]. The steel properties depend only on the steel chemical composition. In many cases, carbide-forming alloy elements with an overall content percentage of <0.12% like vanadium, titan, and boron, are added to the steel melt, leading to the formation of a fine-grained microstructure which results from the presence of nucleus-inducing carbides [33].

• Hot-rolled steel with a post-heat-treatment. The heat treatment consists on hard-ening and tempering the steel during the rolling process [33]. High strength and hardness values are obtained first due a rapid cooling of the austenite steel (γ-steel) generally in water, resulting in a difussionless microstructural transformation where carbon atoms are forced-dissolved in a body-centred cubic ferrite steel (α-steel). The obtained microstructure is a highly strained body-centred tetragonal one, known as martensite, which exhibits significant strength and hardness values, yet a very brittle bahaviour. The martensite distribution over the steel is, depending on the hardening process and the temperature gradient, not uniform and is especially concentrated on the ribbed surface area of the reinforcement (surface-hardening). In a further step, the steel is tempered, i.e. it is subjected to a heat treatment beneath the so called A₁-temperature [89], which lets, depending on temperature and time, to a certain diffusion of carbon atoms and a partial reduction of hardness combined with an increase of ductility. The reinforcement presents, thus, a normal-strength ductile core and a comparatively hard surface. This has the clear advantage of an increased resistance against wear resulting from the friction with the surrounding concrete under fatigue loading, yet with a more susceptible behaviour against notches [199], and a consequently lower fatigue strength. Also the induced surface-hardening leads to residual stresses inside the reinforcement bars – a fact that may further reduce the fatigue strength.

• Hot-rolled steel, then cold-hammered. After the hot-rolling process the steel bar is subsequently subjected to a stretch forming with up to 10% plastic strains [154]

without any heat addition. As a consequence, the crystal dislocation intensity is considerably increased, which leads to a more abundant mutual impediment between crystal dislocations and to an aggravation of the crystal sliding motion [89].

Finally, a so called strain hardening occurs, revealed in form of an strength increase with an undesired ductility loss.

• Cold-formed steel. The reinforcement bars are manufactured by cold-rolling the

3.1 Reinforcement 37

steel slab.

It is worth mentioning that rolling processes cause a stretching of the steel grains whereby the steel loses its isotropic properties [89].

1000

800

600

400

200

10!² 10!¹ 1 10 10² 10³

T [°C]

cooling time in [s]

R = 10 9.5 9 8.5 8 7 6 5 0 [mm]

martensite

ferrite + perlite

bainite

(a) (b)

Figure 3.3:(a) Time-temperature-transformation (TTT) diagram of hot-rolled reinforcement steel with a post-heat-treatment, redrawn from [154]; (b) Reinforcement cross section: Hard surface and ductile core, redrawn from [33]

A detailed description of the mechanical behaviour of reinforcement steel under static, monotonically increasing, practically one-axial loading is given in [2]. Until reaching the so called yield strength fsythe reinforcement steel behaves linear-elastically. Reinforcement steel that has been subject of hot-rolling or heat treatment processes presents a yield plateau immediate after exceeding the yield strength. At this stage, which begins as soon as the steel strain achieves a value of ca. _sy = 2.5‰ and that corresponds nowadays to an average stress of ca. fsy =550 MPa, several dislocation motions are induced and the reinforcement steel exhibits under strain-controlled load conditions a nearly constant strain increment by a virtually constant nominal stress (yield strength). The yield plateau is completed after yielding is distributed over the entire bar length [178], which occurs by average steel strains of 15...25‰. The steel deformations are already irreversible; after unloading only the elastic part may be reversed. Following the yield plateau, a so called strain hardening occurs under increasing strains, i.e. a nonlinear stress increment is required in order to increase the average strains until reaching the nominal ultimate tension strength f_su. A volume variation does not take place; consequently, a transverse bar contraction is observed, and the sectional area decreases [116]. By determining the nominal stresses by means of the coefficient of force and initial section area, a material softening may be noticed. By further increasing strains the steel stress declines until failure.

Hereby, an intense local lateral bar contraction takes place which extends over a length twice the bar diameter [116]. If the real stress in this contraction region is calculated, it may be observed that the stress increases locally until finally a material failure happens.

38 Chapter 3 Material Behaviour

Other than hot-rolled steel, cold-formed reinforcement steel does not present such a yield plateau since dislocation motions have already been activated during manufacturing and the transition from elastic to plastic deformations is steady. According to a general agreement, the yield strength is defined as the strength which corresponds to a remaining strain of_sy=2.0‰ after unloading [178].

σ!

Figure 3.4: (a) Idealised bilinear stress-strain curve of reinforcement steel according to [2];

(b) Idealised stress-strain curve of reinforcement steel with nonlinear hardening according to [2]; (c) Stress-strain curve of reinforcement steel with technical softening and real stress in constriction zone

The (ductile) failure of reinforcement steel in the material plane proceeds in 3 stages [89]:

1. Tensile stresses lead initially to elastic strains without producing any damage.

2. By greater becoming stresses, manganese sulphide are segregated from the steel mi-crostructure, forming local defects where microcontractions originate as consequence of raised stresses.

3. Microcavities result from the above mentioned defects, weakening the inner structure and leading to stress concentrations which ultimately cause a material separation.