Importance of the surface roughness of a steel fibre pulled out from cement paste by slowly increasing load cycles

Pull-out tests of fibres were conducted using slow cyclic tension to evaluate the behaviour of the bond between cement paste and steel fibres with different types of surface roughness. Even though the load amplitude increases in small steps between the cycles, the development of the residual slip increment proves the absence of a complete bond at the beginning of loading. During the load steps, the residual slip evolves in the deceleration, steady, and acceleration stages. The bond stiffness during the ascending and descending parts of the load-slip curve increases up to the last load cycles, indicating that loading compacts the matrix near the fibre surface. The growth of the roughness of the fibre surface increases the amount of cement paste adhered to the surface of fibres pulled out, explaining the changes in the behaviour of the bond and the increase in the pull-out capacity of these fibres.


Introduction
In fibre reinforced cementitious composites (FRCC), the performance of fibres depends on their attachment or bond to a cementitious matrix and the ability of this bond to transfer stresses.Many studies considered the bond between fibres and the surrounding cementitious matrix on the micro-level and characterised the cementitious matrix near the fibres as highly porous with precipitation of calcium hydroxide compared to the bulk matrix [1][2][3][4].A similar microstructure of the cement paste was observed around the aggregates and was called the interfacial transition zone (ITZ), which was reported to affect the overall performance of concrete as cracks initiate in the ITZ [5][6][7][8].Bond has usually been evaluated by a pull-out test, where the load affecting the bond can be measured as a function of slip.Slip is the displacement between the fibre and the matrix and indicates the loss of complete contact between them.During the pull-out test, the response of the bond is divided into three stages that describe the nature of the fibre-matrix interaction: linear elastic, debonding, and frictional sliding [1,[9][10][11].In the linear elastic stage, fully bonded fibre moves together with the matrix.However, this assumption has not been clearly proved experimentally.The cementitious matrix around the fibres has a porous and heterogeneous microstructure [4,[12][13][14] that may develop discontinuous contact between fibre and matrix and result in non-linear behaviour of the bond under uni-axial tensile loading due to local stress concentrations [15,16].The possibility of microcrack development at the first stage of the fibre pull-out process, when adhesion prevails, has * Corresponding author.E-mail addresses: anna.antonova@aalto.fi(A.Antonova), marika.eik@eek.ee(M.Eik), jari.puttonen@aalto.fi(J.Puttonen).also been discussed by studies reported in [17,18].Therefore, the bond may not be linear elastic at the beginning of loading.
The capacity of the bond studied by conventional single fibre pullout tests does not directly explain the micro-scale characteristics of stress transfer between the fibre and the matrix, as was also noted in [16].When a monotonically increasing load is applied to the fibre during the pull-out test, only the development of load as a function of slip, which may include fibre elastic elongation and elastic and plastic deformation of the fibre-matrix bond, can be observed.If the bond between the steel fibre and the cementitious matrix is complete, their strains are compatible, meaning that the slip measured could be attributed to the elastic elongation of fibre.However, the elastic elongation of steel fibre was assumed to be neglected in [19][20][21], which considered the slip as the pure performance of the fibre-matrix bond from the beginning of loading.This assumption may lead to the conclusion that the fibre-matrix bond was not complete and that the fibre had already moved relative to the matrix from the beginning of loading.However, the micro-scale changes in the fibre-matrix bond cannot be easily distinguished.A different experimental approach would be useful to improve the monitoring of these changes.Most of the materials in construction, including FRCC, are subjected to load cycles or alternating loading during their lifetimes [22].Therefore, some previous studies evaluated the changes in the behaviour of brittle materials, such as sandstone and basalt, by measuring the response under cyclic https://doi.org/10.1016/j.cemconcomp.2022.104799Received 15 November 2021; Received in revised form 28 September 2022; Accepted 2 October 2022 loading [23,24].Wang et al. [25] studied the damage evolution and strain-stress relationship of concrete with recycled aggregate and the addition of steel and polypropylene (PP) fibres under compressive load cycles with a load rate of 0.025 mm/s.The authors derived the damage evaluation model for concrete based on the residual strain development considering the content of both types of fibres in concrete.In [26], the residual slip and average reversible stiffness of concrete with the addition of corrugated steel fibres were investigated under cyclic compression.The evaluation of residual slip and reversible stiffness per cycle enabled the estimation of the accumulation of damage and degradation of material for each loading step.The cyclic tension of the fibre-matrix bond resembles the repetitive life load experienced by the concrete elements more than the monotonic load, which is traditionally used in fibre pull-out tests.The application of load cycles allows to follow and quantify the deterioration of fibre-matrix bond by analysing the evolution of residual slip and stiffness of the bond and discover novel explanations for the resistance mechanisms and capacity development of the bond.For the bond between the fibre and the cementitious matrix, these parameters have not previously been measured using slow tension cycles with gradually growing amplitudes, as done in the present study.
The efficiency of the fibre-matrix bond depends on the properties of the fibre surface and the cementitious matrix around the fibre [12,13,27].Modification of fibre surface roughness can influence the contact between the fibre and the cement paste on a micro-scale.The bond strength between straight steel or PP fibres and the fly ash-based geopolymer paste examined in [28] was greater with the steel fibres that had higher surface roughness and a more hydrophilic surface than the PP fibres.The effect of roughness of steel fibre surface on the water mobility along the fibre and the microstructure of cement paste near the straight steel fibres was studied in [13].The authors observed that the spreading and sticking of the water on the fibre surface improved with the increase in their roughness, decreasing the porosity of the cementitious matrix near the fibre surface.Pinchin et al. [3] observed growth in the maximum pull-out capacity of steel wires with a diameter of 0.27 mm pulled out from both cement mortar and paste due to the increased roughness of their surface.The study results indicated that a large number of cement hydrates were left on a rough wire surface after the wire was pulled out.The phenomenon was explained by the increase in force required to overcome the asperity of the wire surface, which compressed the cement matrix near the fibre.The effect of the roughness of the steel fibre surface on the maximum pull-out load and post-peak behaviour of the bond was studied in [19,29].The diameter and length of the straight steel fibres used were 0.3 mm and 30 mm, respectively, and ultra-high performance concrete (UHPC) with silica fume and the addition of siliceous fine aggregates (sand and flour) was used as a matrix material in both studies mentioned.The authors in [19] observed that the maximum pull-out load of the steel fibres improved by 31%-66% with the parallel and by 15%-95% with the perpendicular sanding direction of fibre to its length.Yoo et al. [29] measured the bond strength between steel fibre and UHPC by applying monotonic uni-axial tension to the dog-bone specimen with loading rates of 4800 and 0.018 mm/s.Their results indicated that the bond strength grew with the increased roughness of fibre surface regardless of the rate of loading.Apart from sanding, the straight steel fibres with a diameter and a length of 0.3 mm and 30 mm, respectively, were roughened with a ethylenediaminetetraacetic (EDTA) solution as reported in [30].The authors observed that the pull-out resistance of the steel fibres roughened in the EDTA solution was more than 80% greater than the resistance of unmodified fibres when both fibre types were monotonically pulled out from UHPC at a loading rate of 0.018 mm/s.The effect of fibre treatment with EDTA solution on the pull-out capacity of the steel fibres with different cross-section geometry from UHPC was examined in [31].The authors identified that the roughening of steel fibres with circular and triangular cross-sections increased the pull-out energy by 26% and 39%, respectively.The increase in tensile strength was 17%-25% for circular cross-sections and 20%-36% for triangular cross-sections.UHPC in the two latter studies had the same constituents as in [19,29].As dog-bone shaped specimens were used in [19,[29][30][31], the results included the effect of stress concentrations due to the gripping of the samples during the testing [32].The effect of roughness of fibre surface on the microstructure of the surrounding cement paste and/or bond behaviour before the peak pull-out load was not addressed in these studies.The application of a coating on the steel fibre surface by chemical treatment has also been studied in recent years [33][34][35].Suolioti et al. [35] applied the ZnPh coating on the surfaces of straight, hooked-end and undulated steel fibres to study the changes in the capacity of the fibre-matrix bond by pulling these fibres out of the cement mortar.The results indicated the increase in shear strength and energy required to debond the fibre from the matrix due to the increase in fibre roughness provided by the ZnPh precipitation.Pi et al. [34] modified the surface of pretreated straight steel fibres by coating them with a film of nano-SiO 2 particles in an alkaline reaction environment, providing a better bond between the fibre surface and the applied coating.The authors studied the reactivity of the resulted SiO 2film and the bond strength between the coated fibres and the cement mortar prepared with 20% cement substitution by silica fume.SiO 2coated fibres exhibited a dense and rough film on their surface that remained rough after immersion in Ca(OH) 2 solution, resulting in the formation of calcium-silicate-hydrates on the film surface.The energy required to pull modified fibres from the cement mortar increased by 60.5%, 62.2% and 67.4% at the ages of 3, 7 and 28 days, respectively.Carmo et al. [33] also tested the effect of coating of steel fibre on the fibre-matrix bond by soaking fibre in adhesive liquid with SiO 2 particles.The result indicated that the SiO 2 coating was completely removed during the pull-out test, giving lower strength values for the fibre-matrix bond than the non-coated fibres.Accordingly, the reactivity of fibre coatings can be insufficient if their bonding to the fibre surface is poor.Therefore, the properties of the fibre surface, such as surface roughness, which can ensure the sticking of the coating to the fibre surface, should be investigated.
The main aims of this research work are listed below: • Define the nature of the degradation of fibre-matrix bond by analysing the development of residual slip and stiffness of the bond during the ascending and descending parts of the load-slip curve measured during the slow tension cycles.• Investigate the existence of a complete fibre-matrix bond using a direct fibre pull-out test with uni-axial tensile load cycles by a load increment of 10 N and a rate of loading of 1 μm∕min.
In the scope of the present study, objectives that related to the fibre roughness and the arrangement of the pull-put setup were also investigated: • Analyse the effect of fibre surface roughness on the behaviour of fibre-matrix bond prior to the peak pull-out load.• Examine the cement paste left on the fibre surface after pull-out with the secondary electron (SE) images to explain the effect of fibre surface roughness on the degradation of fibre-matrix bond and pull-out capacity.• Develop the experimental arrangement for a direct single fibre pull-out test to eliminate external compressive forces that could affect the interaction between the steel fibre and cement paste.

Materials
Steel fibres (Arcelor Mittal HE 1/60) with a diameter of 1 mm and a length of 60 mm are the most commonly used fibres in the construction industry of Finland and were used in this study.The surface treatments of fibres were carried out as was done in the study [13].The fibres are  further denoted in the text according to the method for processing the surface: electrolytically polished -R1; non-processed -R2; sanded -R3.Atomic force microscope (AFM) was used to measure the surface roughness of R1 and R2 fibres.A stylus profilometer was applied to measure the roughness of R3 fibres since the magnitude of the roughness of R3 fibres exceeded the measuring limits of AFM.The measuring procedures for both methods are described in [13].The roughness parameters of the fibres are given in Table 1 and schematically represented in Fig. 1.The root mean square roughness (  ) was also calculated and described the standard deviation of the height of surface roughness from the mean line.The average inclination angle () of the irregularities of fibre roughness that can contribute to the friction was estimated with l av and h av (Table 1) as follows: tan  = h av ∕ (l av ∕ 2).
To study the response of the bond between steel fibres and cement paste under load cycles, the cement paste was prepared with ordinary Portland cement CEM I 52,5 N and a water-to-cement ratio of 0.5.The cement paste was mixed with water in a Hobart mixer for 4 min and then poured into the mold.The mold consisted of 2 parts that were fixed together with screws and were designed for casting 2 cement paste cylinders with a diameter of 45 mm and a height of 60 mm all at once (Fig. 2).The mold had 2 fixation beams with grooves in the middle to ensure the vertical and centralised mounting of the fibres with an embedment of 30 mm (Fig. 2(a)).One hooked end of the fibre was bent at an angle of 90 • to provide additional fixation of the fibre on the beam and was also cut off on the day of testing (Fig. 2(b)).The opposite hooked end was cut off, and the straight part of the fibre was embedded for 30 mm into the middle of the cement paste cylinder (Fig. 2(a)).The actual length of each hook varied between 5-7 mm for all fibres measured.Cutting the hooks off, the total length of fibre resulted in around 47 mm, including the 17 mm outside the cement paste (Fig. 2(b)).

Pull-out test setup
The direct uni-axial pull-out test of the fibre was implemented with a universal testing machine Roell+Korthaus.The maximum capacity of the load cell used was 500 N.If the maximum capacity of the fibrematrix bond was not reached within 500 N, a load cell with a maximum capacity of 50 kN was used.As shown in Fig. 3, one side of the sample was glued with epoxy resin to the metal holder.The visible part of the steel fibre was fixed inside the metal rod by three screws.The fibre gripping system was designed to tightly fix the fibre inside the metal rod by pressing and bending it with 3 screws of a diameter of 2 mm against the groove wall, as illustrated in Fig. 3.The screw tip has a concave middle part and a protruding convex on the outer part that deforms fibre surface and penetrates into it (Fig. 4(a)).The tightening of screws prestresses them against the fibre and the surface of the groove behind the screws, creating constant static friction forces on the contacting surfaces at the location of each screw that prevent the movement of the fibre in the direction of the loading exerted.Similar fibre gripping systems were used in [36].
Preliminary tests were performed to validate the reliability of the fibre fixation with screws under cyclic load.Based on Fig. 4(b), the measured increment of residual slip decreased with the first steps of load increase.This observation indicates that the residual slip was not related to the sliding of the fibre between the screw tip and groove wall.The increment of residual slip development was non-linear and finally the fibre was debonded from the cement paste.Preliminary tests with fibres of different types demonstrated a similar pattern of the increments of residual slip, confirming the repeatability of the tests.
The length of the fibre part between the surface of the cement cylinder and the first screw in the metal rod was kept at 6 mm so that the elastic elongation of the fibre part in sight could be calculated (Fig. 3).The concave and convex washers enabled rotation between the metal rod and the bottom grip, eliminating the force effects that a slight tilting of the sample during the test may have had on the results.This setup ensured that only uni-axial tensile forces affected the sample during the pull-out.Thus, the vertical movements of the fibre grip were assumed to be the same as the slip between the fibre and the cement paste and were measured with two linear variable differential transformers (LVDTs) with a measuring range of 15 mm each.The LVDTs were fixed with 2 plates on the sides of the sample and were touching the metal plate fixed to the bottom grip (Fig. 3).
To study the development of the bond degradation between the cement paste and the steel fibres with different types of surface roughness, two sorts of tensile loading were used: monotonically increased loading and loading in which the maximum load of the consecutive loading cycles was increased step-wise by a load increment of 10 N. Three monotonic tests were performed for each fibre surface type to estimate the maximum peak pull-out load and to recognise any changes in the slope of the ascending part of the load-slip curve, or the proportional limit, which can be an indicator of gradual debonding, as stated in [1].The number of loading cycles per samples with each fibre type was estimated using the load level corresponding to the proportional limit defined by the load-slip curve that had the largest maximum capacity.The cyclic loading was not continued until the failure of the bond, since the maximum capacity of the fibre-matrix bond may vary among the samples with the same fibre type, thus complicating the comparison of fibre-matrix bond response as a function of fibre surface roughness.Six pull-out tests using the load cycles were performed per fibre type.The load increment of 10 N between sequential cycles was chosen by the preliminary tests in which various loading steps were used.All pullout tests were performed at a loading rate of 1 μm∕min, which was confirmed to be short enough by preliminary tests.

SE image analysis
The fibres with different surface types were studied with a scanning electron microscope (SEM) using SE detector before and after the pull-out test.These results allowed to explain the gradual failure development of the fibre-matrix bond under the tension cycles considering the fibre surface roughness.SE images with a resolution of 1 mm and magnification of 200x were taken from the middle of the embedded part of the fibres.The SE images with a magnification of 1000x or 2000x were also taken to better observe the topology of the fibre surface after the pull-out test.

Behaviour of fibres with different types of surface roughness during pull-out
The results of monotonic pull-out tests of fibres with different types of surface roughness are represented in Fig. 5(a).The proportional limits were observed to be around load levels of 160, 200, and 340 N with the fibres R1, R2, and R3, respectively, or around 75% of the maximum capacity of the fibre-matrix bond.Based on the tests with monotonically increasing loading, the numbers of cycles with load increments of 10 N were assumed to be 16, 20, and 34 for R1, R2, and R3 fibres, respectively.However, in the case of R2 fibres, the progressive increase in residual slip increments was not observed after 20 cycles; therefore, the number of loading cycles was increased to 24.The stress that occurred in the fibres with each load increment of 10 N increased by 13 MPa.The maximum stress in fibre at the maximum measured load of 520 N reached 676 MPa, which did not exceed the yield capacity of the fibre, which was equal to 1100 MPa according to the manufacturer.Therefore, only elastic elongation of the fibre was considered in this study.The load-slip curves illustrated in Fig. 5 were corrected by subtracting the elastic elongation of the exposed fibre part (ΔL), which was calculated with the following equation, which was also used in [17]: where s ′ is the measured slip, L 0 is the length of the exposed fibre part (6 mm), A f is the cross-section area of the fibre, E f is the elasticity modulus of fibre (200 GPa).The average elastic elongations of different steel fibres at their maximum loads and at their peak loads during their last loading cycles are reported in Table 2.According to Table 2, ΔL was around 17, 13, and 12 times smaller than the total slip at the maximum capacity (s tot max ) and 8, 7, and 7 times smaller than the reversible slip increment at the last load cycle (s rev last cycle ) for the respective R1, R2, and R3 fibres, indicating a small contribution of ΔL to the measured slip.
The schematic interpretation of load-slip curves that illustrate the response of the fibre-matrix bond to slow load cycles in Figs.5(b)-5(d) is represented in Fig. 6.The descending part of the load-slip curve of each cycle was concave and represented the reversible deformation of the fibre-matrix bond.The stiffness of the bond during the descending part of the load-slip curve decreased from the beginning of the curve to its end, complicating its quantification; thus, its average stiffness (k des i ) was estimated (Fig. 6(a)).The ascending part of the load-slip curve of each cycle, on the contrary, was almost linear, which can be attributed to the mechanisms between the fibre and the cement paste that produced the residual deformation.According to a study reported in [37], the concave and linear shapes of the descending and ascending parts of the load-slip curve were typical for the response of concrete to cyclic compression.The authors also pointed out that the degradation of stiffness of the material during the ascending parts of the load-slip curve was rarely considered.However, it was also observed in the present study that the ascending curve did not reach the slip of the previous cycle at the same level of loading, indicating bond degradation (Fig. 6).Since the descending part of the load-slip curve of each cycle did not return to the starting point of the cycle, the increment of the residual slip (s res i ) was developed.This means that the strains of fibre and cement matrix are not compatible, even at low loads at the beginning of the tests.Therefore, the behaviour of the fibre-matrix bond at the beginning of the tensile loading was analysed in terms of the change in the increments of residual slip and the average stiffness of the bond during the ascending (k asc i ) and descending parts of the loadslip curve of each cycle, as demonstrated in Fig. 6.At the beginning of the load-slip curve, the initial change in slope was attributed to the adjustment of the measuring equipment, such as the aliment of the washers, which have a rubber band with a thickness of 1 mm in between.The setup adjustment was included in the curve as it might be useful information for the development and interpretation of similar kinds of measurements in the future.
The development of the residual slip increments is demonstrated in Table 3 and Fig. 7 According to Fig. 7(a), the development of the residual slip increment can be divided into three stages: deceleration of increment, steady increment and acceleration of increment.However, the transition points between these stages may not be easy to identify in Fig. 7 only.Therefore, the difference between the successive residual slip increments (|s res i − s res i+1 |) was calculated and divided by the largest residual slip increment (s res max ) measured under the cyclic loading of the fibre-matrix bond.For all fibre types, the largest s res i developed at the second loading cycle and was around 4.5 μm ( Table 3).In Fig. 8, a difference of less than 5% between successive s res i relative to s res max was considered to indicate steady development of the residual slip increment.
Therefore, the initial decrease of s res i continued up to 5, 6, and 7 cycles, which also represented 26%, 21%, and 16% of maximum bond capacity in the respective cases of R1, R2, and R3 fibres.Then, s res i had a fluctuating and almost constant development for the following 8, 14, and 24 cycles in the respective cases of R1, R2, and R3 fibres.The progressive increase in the residual slip increment started at 13, 20, and 31 cycles, which were also 67%, 69%, and 69% of the maximum bond capacity of the respective R1, R2, and R3 fibres (Table 4).As the load cycles covered 83%, 83%, and 76% of the maximum bond capacity of the respective R1, R2, and R3 fibres, the beginning of the acceleration stage, which was assumed to continue until 100% of maximum bond capacity, was covered by the reported tests.The values of cumulative s res i with R1, R2, and R3 fibres were, respectively, 9, 10, and 11 μm  at the transition point between the deceleration and stable stages and 18, 21, and 28 μm at the beginning of the acceleration stage.
Despite the development of s res i with each cycle, the stiffness of the bond during the ascending part of the load-slip curve increased at the beginning of loading and started to decrease only at the last cycles that corresponded to the acceleration of the residual slip increment (Fig. 7(a)).The rate of k asc i growth correlated with the roughness of the fibre surface.In the case of R1 fibres, k asc i was the lowest among all fibre types, reaching a maximum value of 3028 N∕μm.k asc i for samples with R2 and R3 fibres coincided up to the seventh cycle, after which k asc i for samples with R2 fibres fell behind that of R3 fibres.The maximum values of k asc i with R3 and R2 fibres were 3779 N∕μm and 3474 N∕μm, respectively.The stiffness of the bond during the descending part of the load-slip curve with R1 and R2 fibres increased with each cycle up to the values of 3138 N∕μm and 3630 N∕μm, respectively.In the case of R3 fibres, k des i increased from the beginning of loading up to the value of 3875 N∕μm and started to decrease in the last cycles.k des i was, on average, 9%, 6%, and 5% larger than k asc i for R1, R2, and R3 fibres, respectively.The largest difference between k des i and k asc i of more than 5% was observed during the first five cycles with all the fibre types.

Fibre surface after pull-out from cement paste
Examples of SE images of the fibres with different surface roughness before and after the pullout test are illustrated in Figs. 9 and 10.The surface of the R1 fibre was clearly visible with slight precipitation of the cement hydrates, indicating the failure of the fibre-matrix bond at the interface between two contacting materials (Figs.9(d) and 10(d)).The deposits of cement hydrates inside the valleys of the surface roughness of R2 fibre were clearly observed in Figs.9(e) and 10(e), revealing the ability of cement hydrates to fill the valleys on the fibre surface.However, the amount of cement paste that precipitated on the surface of R2 fibre outside the valleys was still low, suggesting the failure of the fibre-matrix bond close to the fibre surface.The surface of the R3 fibres was almost entirely covered by the cement paste left on the fibre surface after pullout test (Figs.9(f) and 10(f)).According to Fig. 10(f), thick cement paste patches were left on the surface of R3 fibre, indicating that the fibre-matrix bond failed in the matrix surrounding the fibre.

Discussion
The continuous development of the residual slip and the difference between the stiffness of the bond during the ascending and descending  parts of the load-slip curves with each loading cycle indicated the existence of inelastic deformation of the fibre-matrix bond from the beginning of loading, which proved the absence of a complete bond between two materials.The analysis of the bond response between the steel fibre and the cement paste to slow tensile cycles with growing amplitudes identified the non-linear propagation of residual slip and stiffness of the bond during the ascending and descending parts of the load-slip curve with the increase in the load (Fig. 7).The three stages  of the behaviour of the bond degradation in terms of the residual slip or displacement increments between the fibre and the cement paste were observed: deceleration, steady, and acceleration.The generalised division of these stages is represented in Fig. 11.A similar type of development of residual deformation was observed between coarse mineral grains and the binding clay or calcite fine-grained material in the rocks with the initial porosity subjected to cyclic compression [22][23][24]38,39].The cumulative curves of residual slip increments in Fig. 7(b) are also similar to the ones reported in [40,41] for plain and steel fibre reinforced concrete under cyclic compression.The deceleration of the residual slip can be attributed to the heterogeneous and porous micro-structure of the cement paste near the fibre surface .Since the adhesion between the fibre and the cement paste still existed at the low levels of loading, the residual slip could have developed due to the closure of pores and compaction of the cement matrix near the fibre, which did not recover completely after the load release.The obvious difference between the stiffness of the bond at the ascending and descending parts of the load-slip curve during the   deceleration stage indicated that the movement of the fibre-matrix interface at the beginning of loading produced compaction of the surrounding matrix that could not be reversed entirely during unloading.
The assumption of cement paste compaction near the steel wires due to the pressure created by asperities of the wire surface during the pullout was also made in [3].Based on Table 4, the deceleration stage was only slightly extended in cycles along with the increased roughness of fibres.However, during the first five cycles, the roughness of the fibre surface did not affect the cumulative residual slip, which was about 9 μm after the fifth cycle.This can be explained by the small size of the cement hydrates and pores close to the fibre that were crushed and compacted or closed during the first loading cycles.The authors in [13] studied straight steel fibres, surface of which was treated similarly as in the present study.The results indicated that the large pores with a thickness of several hundred micrometres formed in the cement paste only around polished and non-processed fibres.The porosity formed around fibres embedded into cement paste was studied by SEM [42] and micro-computed tomography [14].The large voids with a thickness of several times larger than 10 μm were found and considered as a weak link that could initiate the degradation of bond.Therefore, the large pores present at the fibre-matrix interface cannot be closed within the deceleration stage but can trigger early microcracking and a more rapid start of the steady stage.The steady stage of the residual slip development can be attributed to the stable fracture propagation and explained by the formation of disconnected microcracks in the matrix.The difference between the stiffness values of the bond during the ascending and descending parts of the load-slip curves at steady stage was low, supporting the assumption of low irreversible damage produced during this stage.The microcracking could develop randomly due to the heterogeneous and porous nature of the cement paste formed around the fibre, which was also reflected by a larger coefficient of variation during the steady stage of residual slip growth in Table 3 than that during the deceleration and acceleration stages.Since the porosity in the cement paste near the steel fibres decreased with the increased roughness of fibre surface, as was reported in [13], where same fibres and matrix as in the present study were used, fewer pores were available for the initiation of the microcracking.According to Table 4, the length of the steady stage increased along with the roughness of fibre surface due to the increase in the energy required to create microcracks in the cement paste around rougher fibres.Bentur et al. [43] studied the movements of the straight steel fibre during its pull out from the cement paste with SEM.The fibre was cast longitudinally with cement paste for about half of its diameter and then ground to expose the fibre-matrix bond.The authors described the development of damage along the length of the steel fibre during its pull-out as a microcracking of the surrounding cement paste rather than the growth of one continuous crack.Similar microcracking along the interface of corrugated steel fibres and concrete under cyclic compression was reported in [26] and between the tooth bone and dental cement in [44].Therefore, the reversible slip identified in Figs.5(b), 5(c), 5(d) and 6 can be attributed to the relaxation of the fibre-matrix bond due to the reopening of closed pores and the formation of microcracks.However, these reversed movements of the bond were restricted by the matrix still bonded to the fibre.
The acceleration of the residual slip can be connected to the merging of microcracks into the debonding crack within the region of porous cement matrix formed around the fibre (Fig. 11), as was also explained in [26] for FRCC.Since the formation and merging of the microcracks depend on micro-structure of cement paste near the fibre surface, the debonding crack can propagate simultaneously at the fibre-matrix interface and at some distance from the fibre (Fig. 11).As was noted in [43], the failure of the steel fibre-matrix bond can occur at the fibrematrix interface, in the case of a weak bond, and in UHPC matrix at a distance of several micrometres from the surface of steel fibres simultaneously, resulting in a complex pattern of the debonding crack.
Easley et al. [18] studied the surface of the steel fibres pulled out from the cement paste and mortar and concluded that the greater amount of the cement hydrates left on the fibre surface was a result of porosity of cement matrix near the fibre, which defined the pattern of the debonding crack.A similar observation was made by Pinchin et al. [3], who studied the resistance of steel wires to the pull-out from the cement paste and mortar under monotonically increasing loading.The increased roughness of the fibre surface decreased the porosity of cement matrix near these fibres, as was similarly assumed in [18] and proved in [13] with SEM investigations, which could have affected the development of the debonding crack and the pattern of its propagation.Based on Figs. 9 and 10, the amount of cement paste left on the studied areas of fibre surface grew with the increased surface roughness of the corresponding fibres.This indicated an increase in the strength of fibre-matrix bond and shifted the bond failure into the matrix along with the increased roughness of the fibres.According to [13], where same matrix and fibres as in the present study were used, the porosity decreased with the distance from the fibre surface.The latter results in a larger amount of energy required for development of a debonding crack in the matrix rather than at the fibre surface, which can also lead to an increase in the bond capacity.In the present study, the maximum capacity of the fibre-matrix bond (Table 2) and the amount of cement paste that covered the fibre surface after the pull-out test (Figs.9 and 10) increased along with the roughness of the fibre surface.Park et al. [45] studied the sensitivity of the fibre-matrix interface under pull out load to the rate of loading.The authors also indicated that the complexity of the debonding crack and the pull-out resistance of the steel fibres of several geometries increased with the density of the fibrematrix interface.The stiffness of the bond during the ascending part of the load-slip curve stopped growing and started to decrease cycle by cycle at the acceleration stage, whereas the stiffness of the bond during the descending part of the load-slip curve continued its growth.This development of stiffness also supported the initiation of progressive debonding, when adhesion disappeared and friction was activated.The growth of the maximum bond capacity observed in Figs.5(b)-5(d) was obviously connected to increased friction at the acceleration stage.Bentur et al. [46] found that irregularities of steel fibre surface could interlock with the surrounding cement hydrates and contribute to pullout resistance after the initiation of debonding.In the case of R3 fibres (Fig. 1(b)), the interlocking resulted in the development of compressive stress in front of the inclined plane of fibre irregularities like the ribs in the case of the reinforcement bars [47,48].

Conclusion
The non-linear change in the development of the residual slip and the stiffness of the bond during the ascending and descending parts of the load-slip curve per loading cycle indicates that bond degradation occurs in several stages that are connected to the microstructure of the fibre-matrix interface.The SE images obtained from the surface of the pulled-out fibres supported the interpretation of the results of the pull-out tests and provided additional physical reasoning for the development of debonding cracks.Based on the study results, the following conclusions were made.
• The non-linear development of the residual slip increment with each loading cycle indicated the absence of a complete fibrematrix bond from the beginning of loading.Three stages of the development of the residual slip increment were recognised: deceleration stage, steady stage and acceleration stage.The lengths of the deceleration and steady stages were affected by fibre surface roughness, whereas, the beginning of the acceleration stage started at around 70% of the maximum bond capacity for all fibre types.• The stiffness of the bond during the ascending and descending parts of the load-slip curve grew with each cycle, but the rate of its growth decreased along with the number of cycles.The stiffness of the bond during the ascending part of the load-slip curve also increased by about 16% and 26% in the respective cases of the non-processed and sanded fibres relative to the polished fibres.The stiffness of the bond during the descending part of the load-slip curve increased by about 16% and 23% in the respective cases of the non-processed and sanded fibres compared to the polished fibres.The stiffness of the descending part of the load-slip curve was larger than that of the ascending part, also indicating the existence of residual deformation.• The SE images indicated the greater amount of the cement paste left on the studied surface of sanded fibres compared to the nonprocessed and polished fibres, which supported the increase in strength of fibre-matrix bond and the shift of the bond failure into the matrix.• Increased fibre surface roughness correlated with increased maximum loading capacity of the fibre-matrix bond.The maximum capacity of the samples with non-processed fibres was 48% greater than with polished fibres, and that of sanded fibres was 55% larger than that of non-processed fibres.
The present study highlighted the importance of the investigation of the fibre-matrix bond under repeated loading, since it describes the effect of the life load on the fibre-matrix bond and provides information about the behaviour of the bond degradation that cannot be observed under monotonic loading.

Declaration of competing interest
No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work.For full disclosure statements refer to https://doi.org/10.1016/j.cemconcomp.2022.104799.

Fig. 1 .
Fig. 1.Schematic interpretation of fibre roughness.(a) Profile element of fibre surface.(b) Average inclination of surface profile.

Fig. 2 .
Fig. 2. (a) The part of the casting mold.(b) The final sample tested with the scheme of cutting the hooked ends.

Fig. 3 .
Fig. 3. Scheme and photo of the pull-out setup.

Fig. 4 .
Fig. 4. (a) Cross-sectional scheme of a fixation between the fibre surface and a gripping screw.The shapes of fibre and screw were drawn according to the corresponding images obtained with a scanning electron microscope.(b) Residual slip development measured in the preliminary tests.
(a) with the stiffness of the bond during the ascending part of the load-slip curve per cycle.Fig. 7(b) represents the change of the stiffness of the bond during the descending part of the load-slip curve per cycle and the cumulative development of the residual slip increment as it describes the degradation of the bond.Figs.7(a) and 7(b) were calculated from the load-slip curves measured for fibres with different surface roughness (Figs.5(b)-5(d)).

Fig. 5 .
Fig. 5.The pull-out responses of the fibres with different surface roughness to (a) the monotonic and (b)-(d) the cyclic tension.

Fig. 6 .
Fig. 6.Schematic notation of (a) the residual (s res i ) and the reversible (s rev i ) slip increments, (b) stiffness of the bond during the ascending part (k asc i ) and average stiffness of the bond during the descending part of the load-slip curve with its graphical indication at the beginning (k des start i

Fig. 7 .
Fig. 7. Development of (a) the residual slip increments (black curves) and the stiffness of the bond during the ascending part of the load-slip curve (grey curves) and (b) the cumulative increment of residual slip (black curves) and the stiffness of the bond during the descending part of the load-slip curve (grey curves) per each cycle influenced by different roughness of fibre surface.

Fig. 8 .
Fig. 8. Difference between the successive increments of the residual slip relative to the largest slip increment measured under the cyclic loading of the fibre-matrix bond.

A
.Antonova et al.

Fig. 11 .
Fig. 11.Interpretation of the detected degradation of the fibre-matrix bond under cyclic loading.

Table 1
Roughness parameters of different fibre surfaces.

Table 2
L with s tot max at maximum capacity or with s rev last cycle at the last load cycle affected by the roughness of fibre surface (standard deviation in brackets).

Table 3
Evaluation of the residual slip increment as a function of loading.
i = average increment of residual slip per cycle i; COV = coefficient of variation.

Table 4
Changes in the development of residual slip increment influenced by fibre surface roughness.