1. Introduction
The degradation phenomena of fiber-reinforced concrete during fatigue loading is a complex mechanism framed by a combination of the destructive processes fiber rupture, matrix rupture and fiber pull out. Being part of the priority program SPP 2020, this project examines the materials fatigue behavior and crack development of a high strength carbon short fiber reinforced concrete (CSFRC) in an experimental-virtual lab. As preparation for the analysis of complex fatigue tests, this paper describes the investigation of static flexural and tensile tests with multiple sensor types to capture the degradation process and presents convergence studies of accompanying numerical algorithms.
The usage of discontinuous chopped fibers as reinforcement in cementitious composite materials can yield materials with interesting properties but requires careful attention to mixture design and sample preparation. Parameters such as fiber length and aspect ratio, dispersion and wetting behavior of the fibers as well as fiber orientation in the hardened sample have a tremendous impact on the final mechanical properties of the material [
1]. Especially fiber length plays an important role, as fibers that are too short cannot effectively transfer tensile loads out of the matrix and thus only contribute to post-cracking toughness by being pulled out of the fiber canal [
2].
In contrast, composites in which the (micro-)mechanical behavior of fiber and matrix are tailored to each other show a noticeable increase in tensile strength and a capacity for deformation beyond their linear-elastic limit [
3,
4]. Stress–strain diagrams for loading scenarios under tension for such composites appear bilinear, with the typical linear-elastic behavior occurring until a first crack is introduced. After this point, deformation behavior known as ‘strain-hardening’ starts to set in. The composite is able to withstand a further increasing load, albeit with noticeably decreased stiffness. This strain-hardening behavior is linked to multiple microcracking appearing in the specimen, as the fibers bridging the cracks thus allow for further transmission of the load. Final failure will only occur once this bridging capacity is eventually exhausted [
5,
6].
The small and very well controlled width of these microcracks leads to several advantages of these materials when considering durability. The small crack width hinders diffusion of aggressive substances into the material [
7] and has even been linked to self-healing capabilities [
8,
9]. Materials exhibiting such behavior have been described by the umbrella terms ‘strain-hardening cementitious composites’ (SHCC) or ‘engineered cementitious composites’ (ECC). Prior research nearly universally focuses on the use of polymer fibers in their systems. While these fibers provide the composite with an impressive capacity for deformation, the achievable tensile strength is limiting when considering structural use. Prior research by our group shows that composites with enticing strength values (flexural strength above 100 N/mm
2) can be achieved when using carbon fibers [
10,
11]. In addition, carbon fibers provide additional benefits in the field of structural health monitoring due to their electric conductivity [
12] or fire protection due to better mechanical behavior when exposed to heat [
13].
We use a CSFRC with a specifically designed mixture and a fiber content of 1 to 3 vol%. With the help of an additive manufacturing process, in which the admixed carbon fibers are oriented in an almost uniaxial direction, this material gains extremely high flexural and tensile strength and shows a strain-hardening effect [
11,
14,
15]. The use of a 3D concrete printer makes it possible to establish the alignment because of the homogenous material flow inside the printer’s nozzle. The aligned fibers strengthen the concrete extremely in comparison to non-reinforced concrete or a sample with statistically oriented fibers.
The virtual and numerical part of this study consists of a multiscale simulation method. Using X-ray computed tomography (CT) data, the location and orientation of carbon fibers are the basis for structural-oriented modeling in micro-scale. Small representative volume elements (RVE) depict fibers and the cementitious matrix in high definition. Homogenizing these elements for macro-scale simulation leads to global material properties. The question, how changes in structure in micro-scale such as local fiber rupture, fiber–matrix debonding and matrix failure affect macroscopic behavior of fatigue degradation, is one main goal of this research project. Part of this paper is a convergence study of different RVE sizes and numbers of elements.
The data of meso- and macro-scaled experiments delineate the calibration of these calculations. The basic CT data originate from miniature specimens in order to attain images capable of resolving the meso scale. Next to fiber detection, this method helps to discover micro matrix cracks and their development during fatigue testing, as shown in [
16]. Here, we especially examine miniature specimens under flexural loading combined with sound wave-based non-destructive testing methods giving an insight into the load-bearing behavior.
On a macroscopic level, locally detached measurement methods accompanied uniaxial tensile tests. Digital image correlation (DIC), in particular, makes a significant contribution to identifying the development of cracks and damage by covering a large measurement range of the specimen’s surface. A new method based on the electrical conductivity of the carbon fibers was also developed and successfully applied to show fiber destruction as a main cause of failure. Furthermore, acoustic emission analysis provides additional insight into the specimen degradation on macro-scale experiments as well. Both sound-based analysis and electrical resistivity measurement enable the detection of damage in the specimen’s inside while DIC gives high-resolution information about microcrack evolution on the surface.
2. Raw Material and Sample Preparation
The use of fibers as reinforcement for concrete connects the tensional stress capabilities of the fibers with the compression resistivity of concrete to form a composite material, which can withstand high loads. Most often, fiber reinforcement is either admixed to the fresh concrete as chopped fibers or textile layers consisting of continuous fiber strands are embedded into the molded concrete [
17]. The latter has the advantage that most of the fibers are directed uniformly, which reinforces a uniaxial stressed construction in the best way. The arbitrary orientation of short fibers leads to extreme inefficiency, as statistically only 6% of the fibers face in the loading direction within an angle of 20°. If all fibers point in parallel along a beam, they all contribute to the absorption of tensile forces, allowing for a resource-saving and efficient use of short-fiber reinforcement. Studies describing the possibility of achieving an orientation of polymer fibers suggest an extrusion of concrete as a viable way to control fiber alignment [
18,
19,
20,
21,
22]. The concrete moves uniformly inside the nozzle, which rectifies the admixed fibers along the printed strand’s longitudinal axis. Similarly, an orientation can be achieved by pouring concrete into an oblong mold at one end, letting the concrete flow to the other. Hereby the unidirectional movement leads to fiber alignment parallel to the direction of movement as well [
23]. By positioning several extruded strands next to each other, structures build up. This procedure is a 3D printing method called liquid deposition modeling (LDM). It leads to concrete with a high amount of aligned fibers in the direction of nozzle movement [
10,
14]. By choosing engineered extrusion paths, the possibility to align the fibers according to the principal tensional stresses within the structure exists [
24].
Ref. [
14] examined the possibility of enhancing the fiber–matrix bond by pretreating the carbon fibers in different ways. This research proposes a thermal de-sizing process under oxidizing conditions that leads to hydrophilization of the fiber surface as oxygen is introduced into the inorganic carbon structure. We adopt this process by heating the carbon fibers to 425 °C and holding the temperature for three hours. Under these conditions, the sizing burns and the fibers’ surface starts to oxidize, increasing its roughness. The positive side effect of increasing the fiber’s hydrophilicity enables the addition and effective dispersion of high fiber amounts of up to 3% by volume to the concrete. This high fiber content requires a high amount of plasticizer to make the mixture suitable for pumping and printing.
Table 1 shows the concrete recipe used in this study. Due to the small nozzle of 2 to 4 mm in diameter used for 3D printing, the maximum grain size is 0.5 mm. The water–cement ration is 0.41, including the water in the plasticizer. Carbon fibers are added additionally to the amounts specified.
After production, the specimens are cured at room temperature for one day at 100% RH, set under water for six days and stored for another 21 days with 60% RH.
2.1. Preparation of Miniature Bending Beams for Three-Point Bending Tests
Small-sized specimens with dimensions of 60 × 12 × 3 mm were manufactured as described in [
16] and subjected to the static three-point bending tests on the universal testing machine Wolpert 10 kN, Ludwigshafen, Germany with a 500 N load cell. The test was conducted in displacement-controlled mode with a constant rate of 0.11 mm/min. For flexural testing, specimens are reinforced with 3 vol.-% carbon fibers (Tenax-J HT C261, Teijin Ltd., Tokyo, Japan).
2.2. Macro Scaled Specimen for Uniaxial Tension Tests
Similar to the description in [
16], the dry concrete components are admixed in a BECKEL bucket mixer (Schwallungen, Germany), water and plasticizer are added and mixing is continued until nearly all agglomerates are dispersed. Finally, 1 vol.-% carbon fibers (PX35, Zoltek Corporation, Bridgeton, MO, USA) are added and the mixing process is continued shortly for 40 s twice, while in between the bucket’s walls are cleared from dry fibers.
For the production of larger specimens, we developed a 3D concrete printer with a possible working zone of 1.00 × 1.00 × 0.50 m [
15]. It consists of three separately controllable axes, which are arranged spatially, to move the printing unit. It is a speed-controlled pneumatic piston pump, which compresses a foil cartridge filled with fresh CSFRC. The nozzle has a quadratic aperture with a lateral length of 4 mm.
The macroscopic specimens are bone-shaped and tested under uniaxial tensional load. Their outermost dimensions are 450 × 100 × 50 mm with a tallied region of a constant width of 50 mm in length in the specimen’s center, leading to a cross section of 50 × 50 mm (Figure 11). In the reducing part, the specimen has a circular outline. Ref. [
25] examined the influence of different bone shapes concerning minimum stress peaks due to the specimen’s outline resulting in the aforementioned dimensions. The printing path is parallel to the bone-shaped outline, i.e., circular with increasing radiuses to the vertical centerline to establish the tapering area. Consequently, the carbon fibers, which are oriented in the printed strand’s direction, are aligned to the principal stresses of the specimen under a uniaxial load.
After the printing process has finished, the specimen is molded to gain a more definite surface. This is only necessary to flatten the specimen’s surface to be able to apply measuring equipment. Therefore, the specimen’s prior outline is slightly bigger than desired, as molding compresses the wet concrete. Concomitantly, the specimen’s top is pushed upwards and needs to be cut off after curing with a stone saw Norton CM 501, Wesseling, Germany.
The specimen is glued via connecting steel plates to the machine using a duromer adhesive, MC-DUR 1280 (MC-Bauchemie Müller GmbH & Co. KG, Bottrop, Germany), to establish a stressless clamping at the specimen’s end (Figure 11). Additional steel plates are mounted to the sides in the clamping region to increase friction and to enlarge the area of load transmission. Clamping is preferred to a jointed connection as it leads to a uniaxial loading independent of the distribution of microcracks. The static tests are performed displacement-controlled on a universal testing machine, Roell+Korthaus 100 kN, Ulm, Germany.
4. Flexural Testing of Miniature Bending Beams Combined with AE
Acoustic emission (AE) can be defined as transient elastic waves caused by the release of stored energy due to structural alteration in the material [
36]. Compared to other non-destructive monitoring techniques which were developed to examine the structural condition of materials, the AE method has higher sensitivity. Besides detection of the instant of the damage initiation, AE analysis provides particularly an idea of different damage mechanisms, such as matrix cracking, fiber pull-out, or fiber breakage [
37,
38,
39]. Correlating between certain AE features, such as the emitted energy of the AE signal and the cumulative number of AE events, it is feasible to monitor the main stages of crack development with the AE technique [
40,
41,
42,
43]. Recently, the AE method has proven to be a meaningful tool for damage evaluation in fiber-reinforced high-performance materials in experimental studies under different loading regimes [
44,
45,
46].
This study considers the concurrent application of the AE technique, stress-time curve analysis and dye penetrant inspection (DP) to assess the damage evolution and fracture behavior in CSFRC during flexural loading. To monitor AE activity, four small-sized passive piezoelectric AE sensors VS700-D (150–800 kHz) were coupled to the edges of the miniature beam specimen (see
Figure 8 and
Section 2.1) using a hot adhesive. Sensors were connected to the eight-channel acquisition system Elsys, where signals were recorded and digitalized at a 20 MHz sampling rate.
Figure 8 provides an overview of the experimental setup.
Analysis of the AE activity is based on three aspects: the interpretation of the time domain features of the signal, the
RMSAE value of the signal and the cumulative number of events. The root-mean-square level of a raw acoustic emission signal,
RMSAE, represents the power of an acoustic signal and can be considered a proxy for the AE energy magnitude [
47,
48].
AE signals were localized in linear geometry by comparing the time delay of the elastic wave between the different sensors. An onset time of AE signal is determined using an automatic picking algorithm based on the Akaike Information Criterion (AIC) [
49].
Figure 9 compares the applied stress with the AE signal’s characteristics
RMSAE and normalized cumulative sum of AE events.
The stress development during static, displacement-controlled loading can be characterized by two successive states: an elastic state, where it increases linearly, and a more extended strain-hardening state, where stress continues to rise with a reduced rate relative to the previous period. Failure is very brittle and is characterized by a sudden drop in stress.
Based on the analysis of the RMSAE and cumulative sum of AE events, two periods of different AE activity which correlate with the specimen’s mechanical behavior are roughly distinguishable. The first one, 0–1.2 min, does not have any AE activity matching the linear elastic behavior in the stress curve, while the second phase, 1.2–7.2 min, has significant, increasing AE activity. During the initial stage, AE activity was absent, suggesting that no damage has yet occurred in the specimen. The first acoustic signals become evident, and the change of the slope of the stress curve marks the onset of microcracking in the concrete matrix, as 40% of the failure load has been reached. At the beginning of the second stage, the recorded AE signal is dominated by low and medium amplitude acoustic emissions, and the normalized cumulative sum of AE events curve increases slowly. With a further increase of the load, the acoustic signals become more pronounced, and higher RMSAE peaks start to occur. This stage represents the gradual damage accumulation resulting from the stable growth of microcracks in the matrix. This is also visible in the normalized cumulative AE event’s plot as an increase in the gradient of the cumulative events curve. The high activity of AE in the last stage reflects the critical crack growth in the localized zone of maximal stress, ultimately causing the failure of the specimen.
Figure 10 shows the specimen after failure and the spatial distribution of the AE events. It is evident that the specimen underwent an extensive cracking process before the final failure occurred. Multiple thin cracks opened up in the central area of the specimen on the tensile side (bottom). The eventual failure was initiated by the expansion of the crack located near the centerline of the specimen, slightly closer to the right support region. This conclusion is based on the agreement between the visual inspection of the damage zone and the plot of cumulated locations of the AE events. Most of the AE events originate from the region within 20–40 mm, with the maximum of the events generated near the midpoint of the specimen in the location of the main crack. The spatial AE event distribution reflects the damage zone width and the distinct crack’s actual positions.
5. Tensional Testing of Large Bone-Shaped Specimen Combined with DIC, AE and Electrical Resistivity Measurement
As flexural testing is a combination of local compression and tension, it is necessary to investigate the material’s uniaxial behavior as well. In a static flexural analysis, our team found out that using rectangular cross sections, failure occurs not because of collapse in compression zone but due to fiber pull-out or rupture which is shown as a loss of strength in the tensile zone [
24]. The fibers in the compression zone are oriented in the direction of stress, meaning they barely influence the material’s compression strength: in compression tests, transverse tension is mostly decisive for the specimen’s failure. However, the fibers are not oriented perpendicular to the transverse tension, so they do not increase the load transfer for this stress direction. Therefore, the compressive behavior is similar to unreinforced concrete and is not part of this paper.
For uniaxial tensional tests, macro scaled, bone-shaped specimens (see
Figure 11 and
Section 2.2) are equipped with various non-destructive measurement methods for the locally differentiated recording of deformations. This enables the detection of the damage process in high precision. In addition to the use of displacement transducers (LVDT) and strain gauges, digital image correlation (DIC) detects strain over a wide area of the specimen’s surface. A single camera (DALSA Genie Nano M4040) is used for a 2D measurement. With its high resolution of 12 MPx, the observation of small deformations and growth of microcracks is possible. The specimens are prepared with white painting and either a randomly black dot pattern or trembling black lines using a rubber stamp.
The degree of damage is also visible by using the non-destructive measurement of electrical resistivity. The high proportion of electrically conductive carbon fibers leads to a well-measurable change in voltage resulting from the connectivity losses of the fibers. This procedure, which is already well established for carbon fiber-reinforced plastics (e.g., [
50]), has so far only rarely been applied to concrete specimens [
12,
51,
52]. With the help of a DC voltage source and a series resistor, acquiring the voltage drop at different locations of the test specimen is well suited as a damage detection tool showing qualitative relationships to damaged sections. Depending on the test specimen, the measured resistance values are in the range of a few hundred ohms to a few kilo-ohms.
Furthermore, eight acoustic emission (AE) sensors, V103-RB Olympus (680–1630 kHz), were mounted on the specimen, as shown in
Figure 11.
As described above for flexural testing, strain hardening occurs. This effect is also visible in tensional testing, as
Figure 12 shows. The strain gauges show linear elastic behavior for a large range of tension. Once a critical point is reached, the strain significantly increases while only little further stress can be applied (point
d). This point describes the emergence of microcracks at the end of the linear elastic region. Looking at the integral-measuring LVDT sensors, they show similar results; however, the two phases of elastic and plastic deformation cannot be made out as clearly as with strain gauges.
DIC helps to understand the material’s load-bearing behavior: Not only did several microcracks evolve during the test, but they also extended continuously. Reaching the maximum stress level at points
f and
g,
Figure 13 reveals a series of densely spaced cracks across the entire width of the specimen. Therefore, the observed increase in strain capacity for the specimen during tension is ensured through the pronounced multiple cracking, which permits the excessive strain energy to be released at failure. One crack spreads out further than the others, resulting in brittle failure. The widening and lengthening of the existing cracks can be observed rather than forming new ones.
The strain gauges measure over a length of 3 mm, which is a lot smaller than the distance between the two cracks visible in
Figure 13. They measure at a very specific point in a region of high stress values. In contrast, the LVDTs span over the specimen’s total length measuring also parts with lower stress due to the bone shape leading to a smeared stress–strain relation with smaller overall strain values. The plastic deformations are visible as the gradient decreases continuously starting between points
c and
d, concluding that microcracks already appear in a region next to the area where the strain gauges are positioned.
Point
g marks an instable point where stress decreases while strain still augments.
Figure 13 reveals that the final crack already interpenetrates the whole width of the observed specimen’s side, implying that only the failure-causing crack enlarges. It might be possible that the non-observed sides of the specimen are not fully departed yet, and fibers break or are pulled out of the matrix in a zipper principle starting at one point in the cross section. Rupture occurs when the fibers cannot overstretch the crack and withstand the load anymore.
Looking at the results of the acoustic emission analysis in
Figure 14, it is evident that the acoustic emission characteristics significantly varied in CSFRC specimens subjected to different loading conditions. Unlike the three-point bending test, where no acoustic activity was recorded in the linear-elastic stage, the AE signals started appearing at the beginning of monitoring at a low level of stress in the tensile test. As can be seen from the analysis of the
RMSAE, signals do not differ significantly in amplitude throughout the test. In fact, low-amplitude signals dominated the whole loading process, while strong AE signals appeared only in the final phase, in the proximity of the ultimate strength.
A small number of AE signals were recorded during the initial linear elastic stage of the loading between points
a and
c, causing a relatively flat growth of the curve of the normalized cumulative sum of AE events. As can be seen in
Figure 13, the AE signals in the initial stage are associated with the formation of isolated micro-cracks in the gauge area of the specimen. The acoustic emission method does not discern the formation of the initial crack at the time of transition from the elastic to the plastic deformation stage after point
d, although it could give some indication of this, namely, a slight increase in the amplitude and density of the AE signal. With the further increase in the stress, the formation of new cracks, their coalescence and propagation are continued, accompanied by moderate acoustic emission activity.
A distinctive feature of the last stage was the strong acoustic emission activity, marked by the appearance of the high-energy AE signals and a sudden increase in the number of cumulative AE events at point f. The highest RMSAE peak amplitude is one order larger than that in previous stages, which coincides with the time of the failure.
Comparable results can also be obtained from electrical resistivity measurement (
Figure 15). The initial specimen’s resistance is about 1070 Ω. While strain grows, the resistivity barely changes until the end of linear elastic behavior is reached at point
d. From there on, continuous material degradation is detected as resistivity increases exponentially. Especially after reaching the unstable point
g, the gradient becomes extremely high. The carbon fibers are mainly responsible for good conductivity, concluding that the increase in resistivity is an indication for fiber destruction. This can either be fiber rupture or fiber pullout, although it is not possible to distinguish between either one.
6. Conclusions
Carbon short fiber reinforced concrete shows great promise as a material for use in civil engineering structures due to its outstanding performance under tensile load. Results seem very promising regarding both static and dynamic loading. The large amount of oriented fibers in the direction of principal tensile stresses leads to high tensile and flexural capabilities. Hereby, the orientation of the fibers can be achieved by processing the concrete with a 3D printer.
Fiber alignment could successfully be examined using X-ray CT analysis. Several difficulties had to be overcome to be able to separate fibers from the surrounding concrete matrix. This could be achieved by employing various filtering techniques developed for digital image processing and iterating on the result using shape identification algorithms. After segmentation, the retrieved data was analyzed and quantified in view of the fiber’s orientation. Approximately 68% of the fibers are oriented within an angle of ±10° to the desired direction, leading to an economic use of carbon fibers and considerable improvement of tensile and flexural strength. The success of this process poses as a promising starting point for further automation of the as-now still user input-reliant analysis. Further research into alternative segmentation methods (such as those based on deep learning methods) seem especially fruitful for the reliable segmentation of carbon fibers with even smaller diameters.
The CT data are further used for numerical simulation with representative volume elements. For most realistic calculations, fibers and the surrounding matrix are transferred to a small FEM-model. A convergence study using different sizes of the RVE itself and also different mesh sizes shows that in linear-elastic ranges, the material can be represented very well with reasonable calculation efforts.
The performed static tests are a preliminary stage to the analysis of CSFRC under fatigue loading to compare multiple measuring techniques. Both flexural and tensile tests were performed, while the successful combination of acoustic emission analysis, digital image correlation and electrical resistivity measurement as well as conventional displacement and strain measurement lead to a very concise description of the material’s load-bearing behavior. The material shows strain-hardening behavior, which results from multiple, yet locally restricted and distributed, microcracks arising in combination with plastic deformation. Unlike conventional steel fiber reinforced concrete, CSFRC is able to withstand even higher stresses after leaving the linear elastic stage, which classifies the material as a strain-hardening cement-based composite (SHCC). The starting point of matrix degradation was detected comparably by all sensors, though with different intensities and accuracies. While the processes on the macroscale seem relatively clear, we aim to obtain a more complete picture of the CSFRC system by further researching behavior on the single fiber scale. The usage of frequency analyses of acoustic emission datasets is likely to lead to a better understanding of the processes governing final failure, especially the question of whether it is governed by fiber rupture or fiber pullout.