4.1. Test Specimen and Test Configuration
The experimental investigations in this research part (“bare” steel fibre,
Figure 1) included monotonic and cyclic loaded tensile tests of high-strength micro steel fibres suitable for UHPFRC. Two types of micro steel fibres were investigated under monotonic loading: one with a diameter of 0.19 mm (VFS-A) and another with a diameter of 0.13 mm (VFS-B).
According to the manufacturer’s specifications, both fibres show similar properties like a brass coating, a young’s modulus of 200,000 N/mm
2, and a tensile strength of more than 2200 N/mm
2. The only mechanical difference between the fibres is the diameter. The authors of [
15] give further detailed information regarding the high-strength micro steel fibre.
Due to the steel’s fibre filigree character (0.19 mm and 0.13 mm) and the short length (13 mm and 6 mm), it was challenging to perform the tensile tests, especially for cyclic loading. In terms of pilot tests, clamping the bare steel fibre directly into the jaws of a testing machine led to high transverse pressure on the fibre’s surface. The clamping jaws damaged the fibre considerably, and a following examination of the surface near the crack area was no longer possible. Therefore, gluing the uncut (raw) material of the steel fibre with a length of 300 mm into the (medical) cannulas at both ends was performed.
Figure 2 shows the raw material of the steel fibre (a) and the test specimen for the monotonic and cyclic loaded tensile tests (b). The length between the cannulas (test length) was 100 mm. A precision testing machine with a 500 N load cell ran the test execution of all tests and its transducer measured the displacement of the fibre.
4.2. Monotonic Loading
Nine (VFS-A) and six (VFS-B) specimens were subjected to monotonically increasing tensile loading. The loading rate was 0.01 mm/s for each test. The measured loads of the testing machine were converted into the tensile stress of the fibre by
. The diameter of the fibres was assumed to be in good order to 0.19 and 0.13 mm.
Figure 3 shows the tensile stress–strain curves for VFS-A and VFS-B (black lines) and the mean curves (red lines) of the test series.
The curves of VFS-A
in
Figure 3a show an approximately linear elastic behaviour up to 90% of the failure load. After that, the curves are slightly curved until fibre rupture occurs abruptly. The failure occurs at an elongation of about 22 to 27‰ and an average ultimate tensile strength of approximately 3576 N/mm
2.
The curves of VFS-B show slightly uneven characteristics. The curves increase nonlinearly, and the curve’s curvature does not change upon failure load. The failure also occurs without preannouncement. The strain at the failure point of about 22 to 27‰ is nearly equal to the micro steel fibres of test series VFS-A. However, the ultimate tensile strength of VFS-B is approximately 15% higher.
Table 1 lists the detailed results of the tensile tests of the high-strength micro steel fibres under monotonic loading. The value’s exponent is its standard deviation.
Due to the unexpected high deviation of the tensile strengths between the manufacturer’s specification and the test results in
Table 1, scanning electron microscopy (SEM) images were obtained in order to confirm the “true” diameter of the fibre. In this connection, removal of the brass coating from the steel surface of the fibre was inevitable. No chemical removal was possible because it might have affected the steel of the fibre. Removing the brass coating with sandpaper was also unrewarding because it also damaged the steel’s material.
The third possibility was an embedment of the steel fibre in UHPC and a careful pullout with a precision testing machine. The embedment in concrete seemed to be a good solution, which is why the pulled out fibre was prepared for SEM images.
Figure 4 shows the steel fibre’s surface with brass coating (a) and without brass coating (b) in SEM.
The steel fibre’s surface (VFS-A) with brass coating in
Figure 4a is quite smooth. Only some faults are noticeable on the surface with a very slight depth. In contrast to that, the fibre’s surface without brass coating in
Figure 4b shows many gouges located mostly in the longitudinal direction of the fibre. The production process might have caused these gouges and the brass coating hides them underneath.
As the cross-sectional area is very important for the calculation of the tensile strength of the micro steel fibre, accurate determination of the gouge’s depth was attempted in additional SEM investigations. Instead of the micro steel fibre’s surface, the cross-sectional area should reveal the depth of the gouges. The fibre had to be located parallel to the electron beam for visualization. Nevertheless, a steel fibre located in the electron beam’s direction works like an antenna. The detector might not collect all electrons and provide blurry pictures. This is why the steel fibre was orientated at an angle of approximately 45° to the electron beam.
Figure 5 shows the image of the SEM with the cross-section of the fibre.
The SEM image shows quite a high resolution of the cross-sectional area of the fibre. The image shows a slight shadow, starting at the top edge of the fibre and moving towards its centre. The electron beam might have caused the shadow because of the (nearly) parallel location of the fibre. The gouges of the surface (
Figure 4) are not visible in the cross-section, so that it is assumed that they are probably not deeper than 1.0 μm. Thus, the calculation of the tensile strength with the “bare” diameter of approximately 0.19 and 0.13 mm is feasible.
Based on this finding, the theoretical tensile stress–strain values for high-strength micro steel fibres were calculated with a diameter of 0.19 (VFS-A) and 0.13 mm (VFS-B). Besides the theoretical relationship, the characteristic material values are also required. Characteristic values are usually 5% quantiles of mean values assuming that the measured data is normally distributed.
Table 2 gives the parameters for the statistical evaluation of the theoretical tensile stress–stain curve.
4.3. Cyclic Loading
The test configuration for cyclic loading was the same compared to monotonic loading. Each test series contained three test specimens for gathering possible scatter. The load amplitudes
varied between 5% and 80% of the reference tensile strength
, according to
Table 1. The testing machine’s electromechanical drive limited the frequency to approximately 0.85 Hz.
Table 3 lists the most critical parameters of the experimental program for cyclic tensile loading. Besides general test parameters,
Table 3 also contains basic results (load cycles leading to failure
) of the cyclic loaded fibre tests.
Except for the test series VFZ-7 and VFZ-8, all fibres fractured within the test area, i.e., between the cannulas. However, in one test of VFZ-7 and VFZ-8, the fibre crack occurred in the cannulas. This crack location could indicate higher scatter of ultimate load cycles
. The specimen’s manufacturing process might have caused additional damage while pressing and gluing the filigree steel fibre into the cannulas. The additional damage might be responsible for the lesser fatigue resistance of the steel fibres. Nevertheless, the test results and the number of load cycles lie within the usual scatter range for fatigue tests [
17,
18].
The load cycles
and load amplitudes
were plotted on an S/N-diagram, and the corresponding regression curve was determined. Equation (1) gives the formulae of the regression curve:
where
is the load amplitude and
is the number of load cycles.
Figure 6 shows the S/N curve of the high-strength micro steel fibre and the plotted test results. For load amplitudes smaller than
, the regression curve (red dashed line) equals the short-term strength. The red arrows pointing to the right
Figure 6 mark so-called “run-outs”.
Furthermore,
Figure 6 shows the S/N curve for prestressing steel according to Model Code 2010 [
19] (dashed black line). In comparison, prestressing steel shows no good agreement with the fatigue behaviour of high-strength micro steel fibres in “low-cycle fatigue”
and “high-cycle fatigue”
. The non-agreement could be the reason for comparing the characteristic values (for prestressing steel) and mean values (high-strength steel fibre) with each other. This is why modification of the steel fibre S/N curve (conversion of the mean values into characteristic values) is necessary.
Additionally, the typical ranges of the fatigue life in S/N curves for conventional reinforcing bars and prestressing steel are not transferable to high-strength micro steel fibres and need adjustment. While fatigue loads in reinforcing bars and prestressing steel strands are precisely calculable, the stresses in randomly distributed fibres of UHPFRC components might differ vastly from each other. Some fibres in UHPFRC components obtain higher stresses than others, although they lie right next to each other. Therefore, the beginning of the fatigue endurance limit starts earlier at
load cycles (instead of
). The other limits of the S/N curve remain equal to conventional reinforcing bars and prestressing steel (
Table 4).
The calculation goal is a bilinear S/N curve for the high-strength steel fibre under consideration of the 5% quantile values. Therefore, the S/N curve of finite-life fatigue strength between
and
load cycles needs a conversion of the mean values into the characteristic values. This conversion requires the test series results with the highest scattering in terms of ultimate load cycles. All the other test series remain disregarded for the calculation at first. The 5% quantile of the test series with the highest scattering (VFZ-7) is:
The 5% quantile of the test series VFZ-7 belongs to a load amplitude of 715.2 N/mm2. Two points ( and ) are added to the S/N diagram: Point (7986/715.2) is equal to the load cycles and load amplitude of the mean S/N curve. Point (5615/715.2) corresponds to the 5% quantile of the test series VFZ-7.
If the mean S/N curve (red line) is moved parallel until it intersects point
(5615/715.2), the characteristic S/N-curve is formed and is shown in
Figure 6 by the blue line. Equation (3) expresses the characteristic S/N curve determined by regression with:
Equation (3) is consequently only valid for ultimate load cycles between and , i.e., the finite-life fatigue strength. For higher ultimate load cycles, Equation (3) shows no good accordance, and modification would be useful.
The test series VFZ-9 has not been included in the calculation so far. It shows three run-outs at a load amplitude of
(cf.
Table 3). Thus, the characteristic S/N curve (blue line in
Figure 6) changes its direction and obtaines a reduced inclination and crosses the “run-outs”. The redirection of the S/N curve requires another regression to assign an equation. Equation (4) gives the formulae of the carried on S/N-curve for
:
Comparing the 5% quantile values, Equation (4) shows very good accordance with the behaviour of prestressing steel strands. Only at higher load cycles (), high-strength steel fibres may have a slightly better fatigue resistance. However, Equation (4) is not applicable for global data because it only rests upon one type of high-strength micro steel fibre. A general validated S/N cure for steel fibre requires more fatigue of other fibre types, especially in terms of high cycle fatigue.