For performing the testing and following the standards UNE 36065:2011 and UNE 36068:2011 about ribbed steels for concrete (21, 22), ribbed bars made of special characteristics of ductility were used. The bars deployed were hot-rolled steel bars fabricated with continuous casting billet. They had solid circular sections, with at least two ribbed transversal rows equally distributed over its whole length. 12 and 16 mm diameter high ductility steel weldable bars, type B500SD, were cut at 500 mm of length for tensile stress tests.

Table 1 shows the required minimum mechanical characteristics for B500SD steel according to standard UNE 36065.2011.

The B500SD steel has specific chemical characteristics referred to the analysis of the chemical composition of casting and the admissible values in the analysis of the product, as shown in Table 2.

The equivalent carbon is calculated as follows (Equation [1]):

where the symbols of chemical elements indicate its content in percentage in mass.

At the microstructural level, the B500SD steel is composed by a ferrite matrix with a substantial volume fraction of the pearlite micro-constituent (formed by a ferrite-cementite lamellar composite). The crystal structure of cementite is orthorhombic and ferrite in body-centred cubic, which are related with the magnetic domain structure on magnetization of the steel (23).

It is intended to show the variation of magnetic properties of concrete steels under mechanical stress. For such a purpose, it was necessary to design a coil capable of generating a strong enough magnetic field to delimit the test to the breaking zone in the ferromagnetic material.

The relation in which flow density can be calculated in any point of space where the electric current circulates is given by Biot-Savart law (Equation [2]):

where d B → is a differential element of the magnetic field generated in a plane perpendicular to the plane formed by longitudinal element d l → separated at a → distance from the point of application, where I is the intensity of the current circulating through the conduct; and μ 0 is the magnetic susceptibility in a vacuum.

The configuration of the current corresponds to the Helmholtz coil, that is, two circular coils of equal radius, with a common axis, separated at such distance that the second derivative of B → is cancelled in a point of the axis situated in the center of two coils (24).

The magnetic induction at a point P indicated in Figure 1b is given by the expression (Equation [3]):

where factor N is included to take into account the situation in which every coil has N turns; a is the radius of the coil; 2 b indicates the separation between coils; and z the distance to the point P .

The first derivative of B z   with respect to z is (Equation [4]):

As it can be observed, it is cancelled for z = b . The second derivative with respect to z is (Equation [5]):

for z = b it is reduced to (Equation [6]):

Which is cancelled if a 2 − 4 b 2 = 0 . Thus, a proper choice for b is 2 b = a , being the separation between coils equal to the radius.

With the separation mentioned above, a magnetic induction is obtained in the midpoint of (Equation [7]):

Nevertheless, it is convenient to know the value of the magnetic field at any point along the coil axis that is near the midpoint of the two coils and where the steel bar will be situated. In this way, the field B z ( z ) can be developed in Taylor series around the point z =   1 2 a in order to know its intensity variations with respect to the midpoint according to the following expression (Equation [8]):

As the first three derivatives are cancelled, the fourth derivative B z ( z ) can be expressed as follows (Equation [9]):

so for the region where | z − a 2 | is less than a 10 , B z ( z ) presents a deviation with respect to B z ( a 2 ) that is really small (less than 1/5 in 10000).

Thus, the configuration of the Helmholtz coil is presented as an ideal solution for establishing a specific area of a known and uniform magnetic field. In this research, this area corresponds to the breaking section of test specimens. The objective of that was to determine the influence of this mechanical stress in its magnetic properties.

For the convenience of analysis, for each bar of B500SD steel, instructions established by the standard UNE EN ISO 6892-1:2017 were followed. To define this model, it is necessary to use unit deflection in z direction (longitudinal direction of the bar), that is given by the expression (Equation [10]):

and the elastic tension defined as (Equation [11]):

where F defines the tensile force in kN through a bar section, and S is the section of the bar that, for this study, varies according to the diameters of 12 mm or 16 mm.

Moreover, it is known that for unidimensional tensile states in which deflections are small, both expressions are related by the Hooke law (Equation [12]):

where E is the Young modulus of steel.

Before the test, each bar was marked over its whole length with lines separated from each other by one centimetre distance. This will allow us to measure the last elongation after the tensile strength, elongation that was determined over the initial length of the specimen that was around 5 diameters (Equation [13]):

where L f and L 0 are the initial and final length of the specimen.

These tests were performed using a hydraulic machine of IBERTEST series, with a testing capacity of 100 kN, according to the standard UNE-EN ISO 6892-1:2017. This mechanism was equipped with a extensometer of 50 mm of length that allows obtaining the stress-strain diagram.

Elasticity was controlled by the load, removing the extensometer when the deformation reached 2%. Once elasticity limit was reached, control was made by deflection. In this way, diagrams in which load was indicated in the Y-axis and elongation in the X-axis were obtained. Results also show the hydraulic press piston.

In addition, B500SD is classified as a ferromagnetic material. In these materials, the atomic magnetic moments can be ordered under the action of a magnetic field that is below its Curie temperature. This is due to the spins orientation of unpaired internal electrons.

As it can be observed in Figure 2, the pattern resistance of 1 Ω is connected in series with the primary coils in order to measure the tension and the current (25). In the secondary reel, that is formed by the number of turns ( N S ) , the induced electromotive force ( U i n d ) is given as (Equation [14]):

where B is a magnetic induction over the transversal section of the material; H is the magnetic induction; μ 0 is the magnetic permeability in a vacuum; S f is the area of transversal section of a steel bar; and S 0 is a transversal area of the detection coil (26).

This induced tension is collected by the integrating fluxmeter. In this way, the magnetic induction B ( t ) is obtained by the integration of the U i n d ( t )   signal . An analogue integrator, with an RC time constant, will provide the output voltage (Equation [15]):

where Δ H ( r ) and Δ B ( r ) correspond to the variation of the intensity of magnetic field and induction respectively within the time frame ( t 1 ,    t 2 ) .

If we consider as uniform the magnetization field in the transversal area of detection coil S 0 , its intensity H will depend only on the intensity of the tension I that circulates in the magnetizing coil. The output tension of the analogue integrator can be expressed according to the known magnetization field Δ H and to the magnetic induction Δ B of the sample using the following expression (Equation [16]):

where S f is a transversal section area of the steel bar.

In order to obtain the magnetic amplitude permeability μ = − B μ 0 H of the material, the following equation can be used (Equation [17]):

where U 0 represents the tension obtained in the secondary circuit in a vacuum, without the steel bar.

Moreover, the magnetic induction B is not a linear function of the magnetic induction H , that is, the magnetic permeability μ is not constant. This means that there can be a flow in the steel even without the existence of an exterior field. This is caused by the ferromagnetic properties of this material. In this way, it is possible to build curves that allow studying the behaviour of μ according to H when the material is under a specific tensile stress.

Figure 3 shows the installation of the measuring equipment used in this research. The hydraulic traction machine used for standardized steel tests can be observed in the figure, as well as the scheme devices in Figure 2. It also includes a Teslameter, a device that is able to measure a magnetic field.

Figure 4 and Figure 5 show the graphics obtained after the tensile test for the steel bars with the two studied diameters: 12 and 16 mm. The test was performed at ambient temperature, so it has no influence on the results. The sample was placed in such a way that its longitudinal axis was parallel to the direction of the tensile axis force.

The break of the steel bars is cup-shaped on the furthest end from the break and truncated cone-shaped on the side corresponding to the point of rupture. This is related to the 45° plans theory of break with relation to the force direction, with the particular feature of the specimen having rotational symmetry.

At the atomic level, there are differences between the behaviour in the elastic zone and the plastic zone (Figure 6). In the first instance, the atoms are maintained unified in their original structure, even though they get slightly separated. However, when the force ceases, the atoms regain their balance properties and their crystalline structure remains unchanged as it was at the beginning. On the contrary, during the plastic stage, a lot of atoms break their original connection even though they will rejoin nearby atoms. This will generate a new crystalline structure that has similar properties to the initial one, with the difference that when the force decreases, the resulting deflection is permanent and the crystalline structure gets altered, as well as the external physical form of the material (27, 28).

Thus, this defT produced during the test causes a variation of the induced electromotive force that is registered by the measuring equipment. The results corresponding to each bar are shown in Figure 7 and Figure 8, where colour code is maintained to facilitate the interpretation.

In Figure 7 and Figure 8, it can be observed how the induced electromotive force varies according to the time since the tensile force began to be applied to each bar. These curves show several well-defined areas that have their interpretation in the force-strain diagram.

In the first area, there is an increase of the induced electromotive force, that corresponds to the rise of the magnetic permeability due to the tensile force. In the second area, there is a decline of the induced electromotive force until a change in the slope of the curve is produced. This change corresponds to the unit load in the point where the deflections of the sample are not proportional to the applied force, in other words until the yielding limit. This is the real yielding limit that can be defined as the maximum load with a momentary application that does not produce significant modifications in the dimensions of the bar nor in the physical or chemical properties of the steel.

The third area corresponds to the beginning of the plastic deflection, when the phenomenon of yield strength starts. In this area, a gradual decline of the induced electromotive force can be observed, what is related to the decline of the steel bar section. Finally, in the last part of the graphics, there is a rapid increase of the slope of the curve corresponding to the moment of the break. That finishes with the sample divided into two parts.

This study also determines the variation of the magnetic permeability of B500-SD steel specimens, for different tensile states under different magnetic induction states. For the measuring of magnetization field H, a Hall probe was used. It was also examined the effects of uniaxial tensile strength in the cycles of hysteresis of 12 mm and 16 mm diameter steel bars.

As illustrated in Figure 9 and Figure 10, we see the behaviour within a tension range from 0 to 60 kN in intervals of 15 kN for 12 mm diameter bars, and within a tension range from 0 to 120 kN in steps of 20 kN for 16 mm diameter bars. Two similar behaviours can be observed, as on the one hand, the maximum permeability decreases when the applied tensile force increases, and on the other, the maximum point of permeability shifts to the right for higher magnetic fields. Moreover, it can be also observed how the permeability is higher for bars with a larger diameter.

The measuring equipment and the described method allow ascertaining effectively the elastic limit of a steel bar as well as its tensile state under a specific load. The latter is of particular relevance concerning bars that are embedded into reinforced concrete structures and it is impossible to reach them without destroying the containing surface.

Finally, as it can be seen in Figure 11a, figure that was obtained from an infrared thermography using a FLIR E50 bx camera, during the tensile test, there is an overheating of the bar. This overheating is enhanced as we approach the point of rupture. This thermographic inspection allows regulating the position of the coils during the test, placing their centre into the point of rupture where the variation of the magnetization is studied. Moreover, Figure 11b and 11c shows the final state of a bar of B500SD steel and diameter 16 mm after the rupture. The analysis of its final temperature shows that even though this final temperature is higher than the ambient temperature, it is lower than the temperature of the change on its magnetic properties (normally about 230°C for carbon steels) (29).