Experimental investigations of internal energy dissipation during fracture of fiber-reinforced ultra-high-performance concrete

Abstract

Split-cylinder fracture of fiber-reinforced ultra-high-performance concrete (UHPC) was examined using two complementary techniques: X-ray computed tomography (CT) and acoustic emission (AE). Fifty-mm-diameter specimens of two different fiber types were scanned both before and after load testing. From the CT images, fiber orientation was evaluated to establish optimum and pessimum specimen orientations, at which fibers would have maximum and minimum effect, respectively. As expected, fiber orientation affected both the peak load and the toughness of the specimen, with the optimum toughness being between 20% and 30% higher than the pessimum. Cumulative AE energy was also affected commensurately. Posttest CT scans of the specimens were used to measure internal damage. Damage was quantified in terms of internal energy dissipation due to both matrix cracking and fiber pullout by using calibration measurements for each. The results showed that fiber pullout was the dominant energy dissipation mechanism; however, the sum of the internal energy dissipation measured amounted to only 60% of the total energy dissipated by the specimens as measured by the net work of load. It is postulated that localized compaction of the UHPC matrix as well as internal friction between fractured fragments makes up the balance of internal energy dissipation.

Keywords

ultra-high-performance concrete / concrete fracture / X-ray computed tomography / acoustic emission

Introduction

Damage and fracture of ultra-high-performance concrete (UHPC) features a complex set of micromechanical processes that dissipate energy and lead to enhanced toughness. UHPC matrices are generally categorized by high compressive strengths (>150 MPa), and the addition of different types of steel fibers gives the system very high toughness [¹]. The applications of UHPC are many and range from primary structural members to niche applications [²].

Of interest in this work is the evolution of damage that occurs during mechanical loading. Various toughening mechanisms in fiber-reinforced cement-based composites have been identified and are well documented [³,⁴] and have been applied to understanding UHPC materials [⁵]. However, quantitative experimental assessment of individual toughening mechanisms is limited. True quantitative information on internal damage mechanisms is necessary for proper validation of high-fidelity predictive models as well as proper implementation of “materials by design” frameworks.

The goal of this work was to concurrently apply two complementary experimental techniques, X-ray computed tomography (CT) and acoustic emission (AE), to quantify the energy released during fracture of steel fiber reinforced UHPC specimens. By combining these two techniques, we are exploiting the best of what each offers. X-ray CT provides high-resolution 3D measurements of internal damage, but the information is available for only a limited number of fixed points during loading. Alternatively, AE monitoring does not provide the level of internal detail, but the information it provides is real time, and the measurements can be tied to specific features of load-deformation curves.

The specific objective of this work was to characterize and quantify internal damage during split-cylinder fracture and to connect the damage mechanisms to overall load-deformation response. A split-cylinder configuration was chosen as a more complex stress state than three-point bending, which was the focus of previous work [⁶]. Two energy dissipation mechanisms were examined: Matrix cracking and fiber pullout. Other mechanisms, such as fiber bending and fiber rupture, were previously found not to be significant. We hypothesize that, as with three-point bending, we should be able to account for most of the total energy dissipated by the specimen during loading. However, in a split-cylinder configuration, there are additional mechanisms not directly associated with matrix cracking or fiber pullout. The influences of these additional mechanisms should manifest themselves in the differences between internal dissipation measurements and total external energy dissipation.

Materials and methods

Ultra-high-performance concrete mix

The UHPC matrix used in this study was “Cor-Tuf,” developed by the U.S. Army Engineer Research and Development Center. The mix constituents are listed in Table 1, while details of the material and processing methods are presented in Refs. [⁷,⁸]. The cube strength of the unreinforced UHPC matrix was 170 MPa.

In this work, two different fibers were investigated: Dramix 30-mm-long 0.55-mm-diameter hooked-end steel fibers (ZP 305) and Bekaert 12-mm-long 0.20-mm-diameter straight brass-coated steel fibers (OL 13/.20). Both are of interest: The larger hooked-end fibers require a higher pullout force, but the smaller straight fibers can be better distributed through the matrix and are more likely to bridge cracks [⁹].

Four different UHPC specimen types were used for this work. All were nominal 50-mm-diameter cylinders. Three were cast as 50-mm diameter by 100-mm long, while one was cored from a larger UHPC block. The cored specimens were included to test an assumption that larger specimens (in this case the blocks from which the specimens were cored) are more likely to have a more uniform fiber alignment than specimens that are cast in a mold with dimensions only slightly larger than the fiber length. The assumption here is that fibers in cast specimens are more susceptible to the boundary effects of the specimen molds. In larger specimens, these effects are not as significant.

A summary of specimens tested, along with the naming nomenclature, is presented in Table 2. Among the four cylinders was one specimen that had no fibers. This specimen was used for baseline UHPC matrix fracture analysis. All specimens with fibers were prepared with a nominal fiber volume fraction of 3.5%.

X-ray CT imaging

Each of these specimens was scanned with a Northstar Imaging X-ray CT scanner at an acceleration voltage of 168 kV and a current of 230 µA. The geometry of the scanning setup produced images with nominally 36-µm voxels. True resolution is closer to perhaps 50‒70 µm, depending on relative contrast of phases. Tomographic reconstruction volumes were nominally 1600×1600×3000 voxels for a volume domain of 58 mm×58 mm×108 mm. Renderings of these specimens are shown in Fig. 1. The renderings qualitatively illustrate the distribution of fibers in the specimens.

Once scanning was complete, each of the four cylinders was cut in half with a diamond wet saw, resulting in two cylindrical specimens nominally 50 mm in diameter by 50 mm in length. The cut specimens provided a matched set for mechanical testing. Scanning was conducted on the uncut specimens to optimize X-ray time. The resulting 3D images of the undamaged specimens were electronically cut into two separate images to match the saw-cut specimens.

Optimum & pessimum orientations

Prior to mechanical testing, image data from each 50-mm by 50-mm specimen were analyzed to evaluate what we are defining here as the optimum and pessimum orientations for resistance to split-cylinder fracture. Qualitatively, the concept is easy to visualize. The plane of failure in a split cylinder is defined by the intersection of the specimen’s cylindrical axis and its load axis. In the optimum orientation, fibers tend to have a larger component in a direction normal to this plane; while in the pessimum orientation, fibers tend to have larger components that are parallel to the failure plane. Fiber orientations were evaluated by using a 3D fiber orientation algorithm developed by Trainor et al. [⁶], which uses Hessian eigenvalue analysis at each fiber point to find the fiber orientation angle with respect to the axis of interest. Optimum and pessimum specimen orientations were evaluated by electronically rotating the specimen over a range of orientations, Q, relative to the load axis. At each Q, all relevant fibers were projected (direction cosine) onto an axis perpendicular to the plane of the load axis. These direction cosines were then summed for all relevant fibers. Specifically,

(1){{\displaystyle \mathbf{\Omega }}}_{\mathrm{\Theta }}={\displaystyle \sum _{i=\mathrm{1}}^N\cos {{\displaystyle \mathit{\varphi }}}_i},

where {{\displaystyle \varphi }}_i is the angle of deviation of fiber i from the axis perpendicular to the plane of the load (the x-axis of Fig. 2), and N is the number of fibers evaluated. We can then define the optimum orientation, Q_opt, as

(2){{\displaystyle \mathbf{\Theta }}}_{\mathrm{opt}}=\max ({{\displaystyle \mathbf{\Omega }}}_{\mathrm{\Theta }}),

and the pessimum orientation, Q_pess, as

(3){{\displaystyle \mathbf{\Theta }}}_{\mathrm{pess}}=\min ({{\displaystyle \mathbf{\Omega }}}_{\mathrm{\Theta }}).

There are several items of note about this analysis. First, only the fibers in the middle vertical third of the specimen are considered for this analysis, which is illustrated in Fig. 2. The reason for this is that we can assume the fibers will have their greatest effect where the tension field is the highest. We expect fibers to play little role outside this region. The second thing to note is that because we limit our analysis to the middle third, we do not find that the optimum and pessimum orientations are necessarily orthogonal, as one might intuitively presume.

An illustration of the outcome of the analysis is presented in Fig. 3. Note that these images show only a small subset of fibers and are for illustrative purposes only. The full array of fibers is too dense to check by visual inspection.

Split-cylinder tests

An Instron 5900R-4485 with the maximum capacity of 200 kN was used to perform split-cylinder tests. Tests were performed under displacement control with a crosshead displacement rate set to 0.15 mm/min. A pair of linear variable differential transformers (LVDTs) was used to measure platen-to-platen displacement. Loading continued until the platen-to-platen displacement was approximately 3 mm. Figure 4 shows the test setup.

Acoustic emission activity was monitored with a Digital Wave six-channel system. Full waveforms were recorded at 1-MHz sampling rate. Waveform length was 1024 points, or 1.024 ms. Signals were detected with broadband transducers attached to the specimen with screw-based mounting fixtures. The sensors were coupled to the specimens with vacuum grease. Care was made to make consistent sensor mounting so that measurements from different tests would be comparable. Prior to acquisition, signals were amplified 20 dB and subjected to a 20-kHz to 1.5-MHz band-pass filter.

Experimental results

Load-deformation results

Eight specimens were tested, two each of specimens designated as Z, Zc, B, and U. For the fiber-reinforced specimens (all but U), one specimen was tested in the optimum orientation, and one specimen was tested in the pessimum orientation. Figure 5 shows the influence of fiber orientation on load-deformation response. In all cases, the optimum orientation produced both a higher peak load as well as a higher work of load (defined here as the area under the plot from zero to maximum deformation, less the elastic recovery). A summary of these results is presented in Table 3.

The B series specimens showed the highest overall net work of load, although the Z specimens both showed higher peak loads than the pessimum B specimen. We can likely attribute the higher energy absorption performance of the B specimens to the more uniform distribution of fibers. While hooked fibers require greater work for pullout of the UHPC matrix, the much larger number of the smaller means there are more fibers to bridge the cracks. The net result is higher overall toughness.

Additionally, the plots show differences that perhaps can be related to the differences in the optimum and pessimum orientation. If we consider the definitions of optimum and pessimum orientations defined by Eqs. (2) and (3), we could show that, if the fiber orientations were perfectly random, there would then be no optimum or pessimum orientation, and Eqs. (2) and (3) would result in the same values. In this sense, we could take the difference between the optimum and pessimum of Eqs. (2) and (3) as a measure of a degree of alignment. The more aligned the fibers, the bigger the differences we would expect to see between load-deformation responses of optimum and pessimum specimens. Looking at the Z and Zc series, we see that, as expected, the Zc pairs had greater differences between optimum and pessimum. This would explain the greater differences in both peak load and energy dissipation in the Zc pair compared to the Z pair.

Acoustic emission

AE activity was high with between 28000 and nearly 65000 individual events recorded per test. A number of parameters were extracted from the recorded waveforms, but because of the relevance to fracture energy, we were particularly interested in the energy released by each AE event. For this work, AE energy, E_AE, was evaluated by using the simple method of Harris and Bell [¹⁰]. Specifically,

(4)E_{\mathrm{AE}}={\displaystyle \sum _i{\displaystyle \underset{\mathrm{0}}{\overset{T}{\int }}{V}_i{(t)}^{\mathrm{2}}\mathrm{d}t}},

where V_i(t) is the recorded AE waveform for channel _i. Formally, the units of E_AE are V²∙s. However, since we are performing only relative comparisons, we simply denoted “arbitrary units” for AE energy.

Table 4 presents a summary of AE measurements for all reinforced specimens. Additional results for the “B” and “Z” series are presented in Figs. 6(a) and 6(b). Figures 6(a) and 6(b) illustrate several important phenomena. First, they show when a majority of the AE energy is released. In all tests, the rate of energy release (slope of plot) is highest before the peak load is reached. Indeed, in each of these cases, the rate of AE energy release has already dropped by the time peak load is reached. We suggest this high rate of AE energy release corresponds to both high rates of matrix cracking and high rates of initial fiber debonding. Second, the plots show the differences in total energy release between the optimum and pessimum orientations. The total AE energy released is shown as the right-most values on the plots. As seen in Figs. 6(a) and 6(b), the greater the difference in specimen net work of load, the greater the difference in total AE energy measured. The relationship between specimen energy dissipation and AE energy release is plotted for all specimens in Fig. 6(c). This relationship is not surprising, based on results for plain concrete [¹¹], but it confirms existence for fiber-reinforced UHPC and will be useful for additional analysis.

Internal damage analysis

In order to quantify energy dissipation mechanisms, the eight damaged cylinder specimens were re-scanned with the same CT system. Care was taken to align the specimens in the same orientation as the original scans, and the scan parameters were set to record images with the same spatial resolution. It should be noted that, for the first set of scans (undamaged), the specimens were nominally 50-mm-diameter by 100-mm-long cylinders. For the second set of scans, (after saw cutting and testing), the specimens were nominally 50-mm-diameter by 50-mm-long cylinders. Eight scans were made, all at a 36-µm voxel size. In order to capture the entire specimen, the scan volumes were typically about 1600×1600×1600 voxels, for a total volume domain of about 58 mm×58 mm×58 mm.

Three-dimensional renderings of several specimens are shown in Fig. 7. Figure 7 illustrate both the internal crack networks that develop and the bridging of fibers across those crack networks. Figure 7(a) further illustrates the damage pattern typically observed in these tests. Specifically, a large crack network forms along the axis of split-cylinder loading as would be expected from the known stress distribution. However, because the fibers bridge the cracks, keeping them from expanding further, a triangular “plug” forms at one of the load points on the specimen. This plug features considerable compaction or plastic deformation such that the specimen flattens out.

The energy dissipation of matrix cracking

By using techniques developed by Trainor et al. [⁶] combined with newly developed techniques, the 3D image data collected before and after testing were analyzed to assess the influence of individual energy dissipation mechanisms. Specifically, energy dissipation was divided between the energy dissipated by matrix cracking and the energy dissipated by fiber pullout.

A preliminary step in our analysis was to evaluate fracture energy of unreinforced specimens. The approach was to measure the specific fracture energy of the UHPC matrix in such a way that we could use the result to analyze matrix cracking in reinforced specimens. Two 50-mm-diameter by 50-mm-long unreinforced specimens were prepared by halving a single 50-mm × 100-mm cylinder. Figure 8 illustrates the remaining analysis steps. Specimens were subjected to split-cylinder loading. The net work of load is evaluated by taking the total area under the load-deformation curve and subtracting the residual elastic energy. For the two specimens tested, the net work of load was 3.25 J for the top-half specimen and 1.09 J for the bottom-half specimen. Figure 8(b) and 8(c) show that, although the net work of load was quite different, so were the corresponding fracture patterns. Then, an evaluation of the crack area was performed by applying a simple 3D edge detection algorithm to scans of each specimen before and after fracture. The difference between the total surface area in the two scans is taken as the crack area. Finally, the specific fracture energy, G_f, is taken as simply the net work of load, U, divided by the crack area, A

(5)G_{\mathrm{f}}={\displaystyle \frac{U}{A}}.

The specific fracture energy is simply the work required to grow a unit crack area. We note here that this fracture energy is based on a crack surface area that includes all parts of a tortuous crack network. That is, it includes branches and non-planar surfaces, not just an assumed planer crack area [¹²]. For the two unreinforced specimens evaluated here, measured crack surface areas were 38800 and 11300 mm², leading to G_f values of 84 and 96 J/m² for the top and bottom specimen halves, respectively.

For reinforced specimens, the total energy dissipated by matrix cracking was determined by analyzing the total crack area created during the test and then multiplying that area by the specific fracture energy of the matrix material determined in the tests of unreinforced specimens described above. A technique similar to that used on the unreinforced specimens was applied to the reinforced specimens. That is, a simple 3D edge detection algorithm was applied to measure total surface area of specimens before and after testing. The difference in surface area measurements was then attributed to crack growth. Measured crack area ranged from 323000 to 144000 mm². Note that these crack areas are more than an order of magnitude greater than those found in the unreinforced specimens, illustrating the effect fibers have on inducing additional matrix cracking. Final estimates of energy dissipated by matrix cracking were made by multiplying the measured crack areas by the previously determined average specific fracture energy of 90 J/m². That is

(6)W_{\mathrm{f}}=G_{\mathrm{f}}A,

where A is the measured crack surface area and W_f is the total energy dissipated by matrix cracking.

The energy dissipation of fiber pullout

Our estimation of the energy dissipated by fiber pullout required a multi-step analysis. First, the length of fiber pulled out of the concrete matrix was measured, then the work required to pull that length of fiber out of the matrix was determined from individual fiber pullout calibration data. In order to measure the length of fiber pullout, a technique was developed based on the kinematic assumption that a fiber pulled out of the cement matrix must cross a crack. Furthermore, the total length of pullout must be the same as the sum of all cracks that the fiber crosses. Hence, the technique focuses on locations where fibers cross cracks.

The analysis can be illustrated by a series of images, presented in Fig. 9. Note that the images shown in Fig. 9 are 2D, but the analysis is done in 3D. First, the grayscale image is segmented into voids and solids. Next, the grayscale image is segmented to isolate fibers. These two operations can be conducted independently due to the significant differences in X-ray absorption between the steel fibers and the cement matrix. The two segmented images are combined such that the solids (Fig. 9(b)) provides a mask that can be applied to the fiber image (Fig. 9(c)). The result is an image of fibers that cross cracks, as shown in Fig. 9(d), and illustrated in the 3D rendering of Fig. 9(e). Once the crack-crossing fiber segments are isolated, their lengths can be measured.

The next step is to take the isolated fiber segments and use them to estimate the work of fiber pullout. A model fiber pullout curve was developed for each fiber type, based on fiber pullout experiments [¹³,¹⁴]. Pullout experiments were done on specimens in which a fiber was partially embedded in a cast unreinforced UHPC matrix. Tests were conducted for both fiber types used in the split-cylinder tests, and in the case of the ZP 305 fibers, the tests were conducted on fibers with hooks. An example measured pull out curve is shown in Fig. 10 along with an idealized curve based on many such measurements. This particular curve illustrates characteristics of hooked fibers, with its descending branch showing several bumps that occur as the fiber straightens out. The smaller, straight brass-coated fibers show a more linear descending branch.

For each fiber that bridges a crack, the work to pullout that fiber is estimated by integrating the model pullout curve over the distance the fiber has pulled out, that is,

(7){{\displaystyle w}}_{\mathrm{p}}={\displaystyle \underset{\mathrm{0}}{\overset{l}{\int }}P(v)}\mathrm{d}v,

where w_p is the work required to pull out the fiber, P(v) is the model pullout function, and l is the length of pullout. This is repeated for all fibers so that the total energy dissipated by fiber pullout, W_p, is simply

(8){{\displaystyle W}}_{\mathrm{p}}={{\displaystyle \sum _{i=\mathrm{1}}^N({{\displaystyle w}}_{\mathrm{p}})}}_i,

where i indicates a particular fiber, and N is the total number of fibers pulled out (68 separate fiber segments for the specimen illustrated in Fig. 9).

It should be noted that the magnitude of the force-pullout curves was found to be dependent on the lateral stress in the concrete matrix [¹⁴]. To account for this effect, the work of fiber pullout was increased by 60% based on the estimated magnitude of confining stresses that result from the compression field in loaded specimen. It should be further noted that while nonuniform elastic stresses exist in the fiber during the pullout process, the CT scan of the damaged specimen was made in an unloaded state, thus most of these stresses have been relaxed, and as such they do not factor into this analysis.

Total energy dissipation

An initial assumption in this work is that the primary mechanisms for energy dissipation in UHPC are matrix cracking and fiber pullout. If this is true, we can simply add the quantities determined through Eqs. (6) and (8)

(9)W_{\mathrm{int}}=W_{\mathrm{f}}+W_{\mathrm{p}},

where W_int is the total internal energy dissipation. We define W_int as distinct from the net work of load, W_ext, which is presented in Table 3 for each specimen. Since the two need to be equal, a comparison of W_int with W_ext provides us with a convenient check of our measurements.

The results of this energy accounting are presented in Table 5 for all specimens. The table presents the matrix cracking component, W_f, the fiber pullout component, W_p, the total internal dissipation, W_int, and the external work of load, W_ext. In addition, the table shows the relative contribution of matrix cracking and fiber pullout to the total internally dissipated energy. Finally, the table shows the measured internal energy dissipation as a fraction of the total energy dissipated by the specimen (net work of load). This last value is a measure of how well we are able to account for all energy dissipation in the specimen.

The first general observation from the results of Table 5 is that (with all but one exception) fiber pullout dissipates between three and four times more energy than matrix cracking. There does not seem to be a distinction in this distribution between optimum and pessimum orientations, but we would not necessarily expect there to be. We would only expect the total amounts to vary commensurately, which they do.

The second general observation is that the total internal energy dissipation is typically less than two thirds of the external net work of load work, indicating that a significant amount of internal energy dissipation is not accounted for in this analysis.

Discussion

The results show that, on average, we are able to capture about 60% of the internal energy dissipation in UHPC specimens subject to split-cylinder loading. This is quite low compared to the nearly 90% that is captured using a similar approach for specimens subjected to three-point bending [⁶]. That said, our hypothesis all along has been that there are other mechanisms that manifest themselves in the split-cylinder configuration.

With respect to these additional energy dissipation mechanisms, we submit two we can easily identify that are not accounted for in our analysis. Both can be qualitatively understood by an examination of the cross-sectional rendering of Fig. 7(a). In this specimen, we see the main crack network along the axis of the load. In addition, we see two things at the top of the (upper left-hand side of image) specimen that are relevant. The first is the flattened region where the specimen was in contact with the platen. This flattening cannot occur unless there is another mechanism introduced (e.g., plastic deformation). In a traditional quasi-brittle material, plastic deformation is typically not considered significant, but the observation here is unquestionable. It may not be plastic deformation in the traditional sense in that there is not necessarily a “flow” of continuous material. More than likely it reflects a localized pulverizing and re-compaction of the material. This pulverization phenomenon would not necessarily be visible through traditional X-ray CT image analysis, although we are considering ways in which such phenomenon may be reflected in the images. Regardless, if the analysis reported here is of similar accuracy as the beam tests of Trainor et al. [⁶], then the results here suggest that the combination of matrix compaction and crack friction add up to about 30% of total energy dissipation, which is comparable to the energy dissipated by fiber pullout.

The second mechanism that can be qualitatively observed in Fig. 7(a) is the wedge that appears below the previously mentioned flattened section. If a wedge is moving through the damaged split-cylinder, there must be friction associated with that movement. Indeed, it is likely these friction forces could be high, given the degree of confinement that the bridging fibers produce in the specimen. Unfortunately, there is no way to directly measure friction forces with the CT images, although Mondoringin and Ohtsu [¹⁵] were able to monitor sliding energy to a limited extent by using quantitative acoustic emission.

With respect to our own acoustic emission analysis, at this point all that it adds to the CT analysis is an estimate of when the most energy is released relative to the loading history. Current work is focused on classification schemes by which the AE signals may be categorized by the particular energy dissipation mechanism that led to the AE event.

Finally, we acknowledge that the measurement techniques employed in this work have limitations. With respect to matrix cracking, CT image resolution restricts our measurements to crack apertures greater than about 50 µm. Undoubtedly, microcracks that are not visible in the CT images exist in the specimens. Current work-in-progress is aimed at solving this problem in two ways. First, through digital volume correlation techniques that can track specimen motion, we hope to use kinematic-based methods that do not rely so explicitly on direct crack observation. Second, through the above-mentioned AE event classification schemes, we may be able to infer the amount of matrix cracking distinct from fiber debonding and pullout. At this point, however, we suggest that the error associated with our crack measurements is likely somewhat larger than the error associated with fiber pullout.

Summary and conclusions

In this work, two different experimental techniques were exploited in a quantitative study of internal energy dissipation mechanisms in ultra-high-performance concrete reinforced with different types of steel fibers. Split-cylinder fracture was investigated, as it produces slightly more complex stress states for damage propagation compared, for example, to three-point bending. X-ray CT scans were made of specimens before and after loading so that detailed changes in internal structure could be measured. In addition, the pretest scan allowed us to examine the fiber alignment in the specimen and set up different loading orientations relative to fiber alignment. Although the specimens were prepared without concern for preferential fiber alignment, casting procedures led to small but measurable preferences. Optimum and pessimum orientations were established based on the degree for which fibers would resist principal tensile stress. For otherwise matched specimens, the load-deformation differences between optimum and pessimum specimen orientations ranged from modest to significant, with between 20%–30% higher net work of load for the optimum. The greatest difference was seen in the cored specimens, where we would expect fiber alignment to be somewhat more homogeneous than cast specimens. Acoustic emission monitoring showed that the highest degree of energy dissipation occurs as the specimen approaches peak load. Presumably, this is due to the high degree of matrix cracking and initial fiber debonding that occurs during this time. Separate analysis of internal matrix cracking and fiber pullout in the specimens showed that fiber pullout dissipates between three and four times more energy than matrix cracking.

When compared to the net work of load (a measure of the total energy dissipated by the specimen), our internal energy measurements accounted for less than 60% of the total on average. This reveals analysis limitations that can be attributed to two primary causes. First, the limitations of CT image resolution limit the direct measurement of matrix cracking in particular. Second, the analysis does not consider the energy dissipated by separate mechanisms such as matrix compaction or crack friction. Both of these are likely to be significant. In previous work with three-point bending specimens that do not exhibit such matrix compaction or crack friction, the measured internal dissipation mechanisms approached 90% of the external work. This leads us to suggest that these unaccounted for mechanisms add an additional 30%.

As a final note, we recognize that any conclusions drawn from this work are somewhat tenuous due to the limited sample size. We anticipate that as CT acquisition and data analysis throughput improve, sample sizes will grow accordingly. Additionally, current work in progress is focused on ways to integrate our measurements with computational models that can accommodate such information. It is suggested here that the best path for quantifying the missing energy dissipation mechanisms is to continue the iterations with computational models in such a way that models can be used to develop new experiments to isolate these different mechanisms.

References

[1] FHWA. Ultra-High Performance Concrete. Tech Note FHWA-HRT-11-038. 2011

[2] Fehling E, Middendorf B, Thiemicke J. Ultra-High Performance Concrete and High Performance Construction Materials. Kassel: Kassel University Press, 2016

[3] Balaguru P, Shah S. Fiber-Reinforced Cement Composites. New York: McGraw-Hill, 1992

[4] Bentur A, Mindess S. Fiber Reinforced Cementitious Composites. London: Elsevier, 1990

[5] Yoo D Y, Banthia N. Mechanical properties of ultra-high-performance fiber-reinforced concrete: A review. Cement and Concrete Composites, 2016, 73(C): 267–280

[6] Trainor K J, Foust B W, Landis E N. Measurement of energy dissipation mechanisms in fracture of fiber-reinforced ultrahigh-strength cement-based composites. Journal of Engineering Mechanics, 2013, 139(7): 771–779

[7] Williams E M, Graham S S, Reed P A, Rushing T S. Laboratory Characterization of Cor-Tuf Concrete With and Without Steel Fibers. Technical Report ERDC/GSL TR-09-22. 2009

[8] Roth M J, Rushing T S, Flores O G, Sham D K, Stevens J W. Laboratory Investigation of the Characterization of Cor-Tuf Flexural and Splitting Tensile Properties. Technical Report ERDC/GSL TR-10-46. 2010

[9] Wille K, Naaman A. Pullout behavior of high-strength steel fibers embedded in ultra-high-performance concrete. ACI Materials Journal, 2012, 109(4): 479–487

[10] Harris D O, Bell R L. The measurement and significance of energy in acoustic emission testing. Experimental Mechanics, 1977, 17(9): 347–353

[11] Landis E N, Baillon L. Experiments to relate acoustic emission energy to fracture energy of concrete. Journal of Engineering Mechanics, 2002, 128(6): 698–702

[12] de Wolski S C, Bolander J E, Landis E N. An in-situ X-ray microtomography study of split cylinder fracture in cement-based materials. Experimental Mechanics, 2014, 54(7): 1227–1235

[13] Flanders L S. A 3D image analysis of energy dissipation mechanisms in ultra high performance concrete subject to high strain rates. Thesis of the Master’s Degree. Orono: University of Maine, 2014

[14] McSwain A C, Berube K A, Cusatis G, Landis E N. Confinement effects on fiber pullout forces for ultra-high-performance concrete. Cement and Concrete Composites, 2018, 91: 53–58

[15] Mondoringin M R I A J, Ohtsu M. Kinematics on split-tensile test of fiber-reinforced concrete by AE. Journal of Advanced Concrete Technology, 2013, 11(8): 196–205

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