steel fiber engineered cementitious composite

Materials and Design 105 (2016) 179–189

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Electrochemical immittance spectroscopy applied to a hybrid PVA/steel fiber engineered cementitious composite B. Suryanto ⁎, W.J. McCarter, G. Starrs, G.V. Ludford-Jones School of Energy, Geoscience, Infrastructure and Society, Institute for Infrastructure and Environment, Heriot Watt University, Edinburgh EH14 4AS, Scotland, UK

a r t i c l e

i n f o

Article history: Received 9 December 2015 Received in revised form 23 April 2016 Accepted 11 May 2016 Available online 16 May 2016 Keywords: Electrical properties Immittance spectroscopy Cement composite Multifunctional material Effective medium theory

a b s t r a c t Alternating current (a.c.) electrical property measurements are presented on an Engineered Cementitious Composite (ECC) reinforced with a hybrid mix of polyvinyl alcohol fibers (fixed dosage) and straight steel fibers of varying dosages (0.15–1.0% by volume), with the aim at elucidating the influence of conductive inclusions on the nature of conduction and polarization processes within the composite. Measurements were undertaken over the frequency range 1 Hz–10 MHz at 7, 14 and 28 days after casting and the data presented in a range of formalisms to aid interpretation. When plotted in the frequency domain, the work shows that steel fibers enhance the polarizability of the material, particularly within the frequency range ~10 Hz–10 kHz. When presented in Nyquist format, this feature manifests itself as an intermediate arc forming between a high frequency arc (N 10 kHz) and a low frequency arc (b 10 Hz), the latter resulting from polarization processes at the sample/electrode interface. The prominence of the intermediate arc was found to be dependent upon steel fiber dosage and curing time. It is shown that the bulk electrical conductivity conforms to the equivalent inclusion theory which is a variant on the effective medium theory. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction Since its first application to cementitious systems [1], considerable advances have now been made in the use of a.c. impedance spectroscopy (ACIS) to study this group of important construction materials. Impedance measurements can be interpreted in terms of the mechanisms of hydration, reaction kinetics and pore-structure development from initial mixing through setting [2–14] and long-term hardening [15–17]. The influence of both chemical admixtures, such as accelerators and retarders [18], and supplementary cementitious materials, such as blast-furnace slag, fly-ash and silica fume [19–22], on the various stages of hydration has also been investigated using ACIS techniques. These studies have also shown that the impedance response can be linked to a number of material properties including pore-water content, pore-water chemistry, and the porosity, connectivity and tortuosity of the capillary pore network. Studies on the electrical properties of fiber-reinforced cements are more limited and work tends to be confined to d.c. or fixed-frequency, a.c. conductivity/resistivity measurements [23–28]. In the main, these studies have explored the piezo-resistive properties of cementitious materials containing short conductive fibers (i.e. carbon) and it is through these properties the materials have self-monitoring capabilities with respect to deformation and damage under static and dynamic ⁎ Corresponding author. E-mail address: [email protected] (B. Suryanto).

http://dx.doi.org/10.1016/j.matdes.2016.05.037 0264-1275/© 2016 Elsevier Ltd. All rights reserved.

loading. This has initiated the development of fiber-reinforced cements as potentially smart materials. A multi-frequency impedance approach to study cement-fiber composites is a relatively recent development [29–32] and has been used to study the dispersion and orientation of steel fibers [33,34] and plant fibers [35] within cement paste, with measurements obtained over the frequency range 0.1 Hz–30 MHz. When plotted in Nyquist format, a dual-arc behavior has been observed for steel fibers and a frequency-switching fiber coating model has been proposed to explain the electrical impedance spectrum. The dual arc behavior was absent for the plant fiber composite. This current paper presents, for the first time, a detailed study on the a.c. electrical properties of an advanced cement-based material termed an Engineered Cementitious Composite (ECC), with a focus on the influence of conductive fibers, viz. steel, on conduction and polarization processes. The distinctive engineering properties of an ECC are its high tensile strain capacity, typically in excess of 3%, and a controllable crack width, typically less than 0.1 mm under service load [36,37]. It is these unique properties of ECC that have attracted widespread interest from the engineering community, particularly for applications where cracking, toughness and long-term durability are critical. Apart from being viable as a durable construction material, the inclusion of conductive fibers could also allow ECC to be further developed and exploited as a multi-functional material thereby simultaneously fulfilling both structural and non-structural roles. Regarding the latter, research to-date has primarily focused on developing a suitable ECC mixture for damagesensing applications [38–41].

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As yet, there has been no systematic study on the electrical properties of ECCs. Research findings from the present investigation into the influence of conductive steel fibers on the nature of conduction and polarization processes will therefore be of considerable importance in aiding the design of mixture compositions that give ECC multi-functional capabilities (e.g. through the use of electrically conductive inclusions). Areas where conductive ECC could find practical application in non-structural roles include, for example: electrically conductive cementitious overlays for cathodic protection systems thereby providing a more uniform current distribution; in structures where electromagnetic shielding or screening is required; in civil/military aviation applications where background static can cause problems; or self-sensing applications in the detection and (real-time) monitoring of cracking, vibration or fatigue in concrete structures (e.g. bridges, pressure vessels). Different applications may require different mixture compositions, but the flexibility in ECC material design [36] would allow the material to be tailored to suit the needs of any particular application. It must be emphasized that the presentation of impedance in the Nyquist format noted previously, which has been generally used in a.c. electrical property measurements, is only one of four connected parameters within the more general field of immittance spectroscopy. These levels are impedance Z(ω) and its reciprocal admittance Y(ω); relative permittivity εr(ω) and its reciprocal electric modulus M(ω) [42]. The work presented focuses on both the impedance and permittivity levels.

Table 2 Oxide analysis and physical properties of fly-ash and silica sand (wt.%).

2. Experimental program

2.2. Test specimens: preparation, casting and curing

2.1. Materials

A 10-litre Hobart planetary motion mixer was used for preparing all the mixtures with a total of six specimens cast for each ECC presented in Table 1: two, 40 × 40 × 160 mm prisms for electrical measurements, two, 20 × 40 × 170 mm prisms for flexural strength testing, and two, 50 mm cubes for compressive strength tests. Specimens for each mixture were cast from the same batch. With reference to Fig. 1(a), specimens for electrical measurements were cast in polystyrene molds, each mold having two 45 × 65 × 2 mm (thick) perforated stainless steel electrodes placed 140 mm apart. The perforations on the electrodes were 10 mm in diameter with a 15 mm pitch, which ensured both intimate bonding between the electrode and the specimen and that the ECC mixture flowed easily through the perforations. After casting, all samples were covered with polythene sheeting and placed in a temperature controlled laboratory (20 ± 1 °C, 55 ± 5% RH). The samples were demolded after 24 h and placed in a small curing tank in the same laboratory environment until required for testing. The electrical measurements were conducted on the 7th, 14th and 28th days of curing. The mean 28-day compressive strengths of the mixtures are presented in Table 1.

Table 1 presents the mix proportions of the ECCs used in the current study. The binder comprised CEM I 52.5N cement to BS EN197-1:2011 [43] and a fine fly-ash (Superpozz SV80 from ScotAsh), with a fly-ashto-cement (FA/C) ratio of 1.7. The water/binder (w/b) ratio was 0.28. A fine silica sand (RH110 from Minerals Marketing Ltd.) with an average particle size of 120 μm was used in all mixes at a constant sand-to-cement ratio of 0.6 by mass. The oxide analysis of the FA and silica sand is presented in Table 2. A polycarboxylate high-range water-reducing admixture (Glenium C315 from BASF) was added to the mix at a fixed dosage rate of 1% by weight of cement. Standard 12 mm (long) polyvinyl alcohol (PVA) fibers (REC15 from Kuraray) were used at a fixed dosage of 1.75% by volume. The PVA fibers had an average diameter of 39 μm and a tensile strength of 1.60 GPa. The surface of the PVA fibers was coated with a proprietary oiling agent (1.2% by weight) to reduce any excessive fiber–matrix chemical bond strength due to their hydrophilic nature. In addition to the PVA fibers which, as a polymeric material is considered non-conductive, 6 mm steel fibers (Dramix OL6/.16 from Bekaert) were used at dosages in the range 0.15–1.0% by volume. The steel fibers had a diameter of 160 μm (aspect ratio = 37.5) and a tensile strength of 2.60 GPa.

Table 1 Materials mix proportions and mechanical property. FA Silica sand w/b Mix CEM I (kg/m3) (kg/m3) (kg/m3)

HRWR (kg/m3)

PVA Steel F28 (kg/m3) (kg/m3) (MPa)

M1 M2 M3 M4 M5 M6

4.7 4.7 4.7 4.7 4.7 4.7

22.8 22.8 22.8 22.8 22.8 22.8

471 471 470 469 468 467

801 800 799 797 796 793

284 283 283 282 281 280

0.28 0.28 0.28 0.28 0.28 0.28

– 11.8 19.6 39.3 58.9 78.5

44.6 + 48.4 + 49.7 49.0

Notes: binder includes cement and fly-ash; + means not available; F28: 28-day compressive strength determined on 50 mm cubes.

Chemical analysis SiO2 Al2O3 Fe2O3 K2O CaO MgO Na2O equivalent SO3 Free CaO Total phosphate Loss on Ignition (LOI) Physical properties Specific gravity Surface area (m2/kg) Fineness (% retained on 25 μm) Size distribution (μm) and cumulative retained (%) 500 355 250 180 125 90 63

Fly-ash

Silica sand

52.7 26.6 5.6 – 2.4 1.2 1.7 0.33 0.03 0.5 b2.0

98.8 0.21 0.09 0.03 – – – – – – 0.14

2.20 1300 b25

2.65 – –

– – – – – – –

0.1 0.5 1.5 6.0 46.0 83.0 96.5

2.3. Test equipment and procedures Electrical measurements were taken using a Solartron 1260 Frequency Response Analyser connected in two-point mode, with the current-generator and potential-high leads coupled to one electrode, and the current-input and potential-low leads to the other. A logarithmic sweep at 20 points per decade was made over the frequency range 1 Hz–10 MHz at a voltage of 350 mV rms (matching the signal amplitude of previous studies, including field tests [15–17,48]). The flexural properties for each mixture were determined using a 100 kN Instron 4206 testing machine under a cross head rate of 0.5 mm/min. The samples were loaded under a 4-point bending configuration with central and shear spans of 40 mm and 55 mm, respectively (see Fig. 1(b)). The load-deflection profiles of individual samples were recorded to failure. The peak load and the corresponding deflection were then converted to tensile strength, ftu, and tensile strain, εtu, by assuming a uniform tensile stress distribution [44] and relating the

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Fig. 1. Schematic diagram of test samples for: (a) electrical property measurements; and (b) flexural tests (all dimensions in mm).

curvature and the average deflection at the two load points [45]. Axial compression tests were carried out using a 3000 kN Avery–Denison testing machine under a loading rate of 38 kN/min. 3. Results and discussion 3.1. Preliminaries The impedance, Z(ω), of a cementitious system subjected to a sinusoidal electric field at an angular frequency, ω, can be written in rectangular form as, 0

00

Z ðωÞ ¼ Z ðωÞ−iZ ðωÞ

with notable fluctuations in load with increasing vertical deflection. These fluctuations can be attributed primarily to progressive development of micro-cracks on the tension face of each sample. Fig. 2(b) presents the tensile strength, ftu, and tensile strain capacity, εtu, determined using the procedure described in Section 2.3, with the error bars on the markers representing the spread of results from the mean value presented. It is evident that, within the scatter of the results, the tensile strength and tensile strain capacity remain virtually unchanged, although the tensile strain capacity appears to decrease slightly with increasing steel fiber dosage. The minor influence of the steel fibers can be associated with the relatively low interfacial bond between the fibers and the matrix. The values of the tensile strength and tensile

ð1Þ

where the real component Z'(ω) is the resistance and the imaginary component Z''(ω) is the reactance. At any frequency, the electrical response of such a system will result from the superposed phenomena of conduction and polarization. These are quantified, respectively, by the bulk conductivity, σ(ω), and the real part of relative permittivity, ε'r(ω), which are de-embedded from the resistance and reactance by 0

σ ðωÞ ¼

Z ðωÞ

L A Z ðωÞ þ Z ðωÞ 0

2

2

00

ð2Þ

00

0

ε r ðωÞ ¼

1 Z ðωÞ L εo ω Z 0 ðωÞ2 þ Z 0 0 ðωÞ2 A

ð3Þ

where εo is the permittivity of a vacuum (8.854 × 10−12 Farads/m); L/A is a factor which is related to the electrode geometry and sample configuration. This was determined by electrical measurements on solutions of known conductivity placed within the test-cell and for the cell shown in Fig. 1(a), the L/A factor was determined as 94.7/m. 3.2. Flexural tests Although the focus of this paper is the a.c. electrical properties of ECC, for completeness, it was considered appropriate to include the mechanical properties of the composite. The mean 28-day compressive strengths are presented in Table 1, whereas Fig. 2(a) presents the flexural response under monotonically increasing displacement to failure. It is evident that all samples displayed a deflection hardening response

Fig. 2. Results of flexural tests: (a) load-deflection response for all samples; and (b) computed tensile stress and strain capacity (error bars indicate the spread of measurements from the mean value presented).

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strain capacity obtained are in general agreement with those obtained from direct tensile tests [46].

3.3. Impedance response of ECC The complex impedance spectra for Mix M1 specimens (no steel fibers) are presented in Fig. 3(a) as a Nyquist plot (i.e. Z'(ω) vs −iZ''(ω)), with frequency increasing from right-to-left across the curve. Although measurements were obtained at 140 spot frequencies, for clarity, only selected frequencies are highlighted with data markers. The results indicate good repeatability and, at any stage during the hydration process, the impedance response can be divided into three regions comprising, (i) a spur at the low-frequency (right-hand) side of the curve; (ii) a weakly developed intermediate plateau giving a U-shaped valley region; and,

(iii) a semicircular arc on the high-frequency (left-hand) side whose center is depressed below the Z'(ω) axis.

The low-frequency spur is associated with the polarization at the sample–electrode interface [1,47,48] and would form part of a much larger arc that only develops at frequencies lower than 1 Hz. The intermediate U-shaped valley feature is more evident at longer hydration times and has been reported as a feature typical of cementitious systems containing fly-ash [20,21]. The prominence of this feature is dictated by the proportion of unburnt carbon in the fly-ash which is quantified by the loss on ignition (LOI), with the feature becoming more discernible as the LOI increases [21]. The fly-ash used in this work has a relatively low LOI (b2%; Table 2) and would explain the U-shape rather than a more distinctive plateau region. The high-frequency semi-circular arc represents the bulk response from the sample, with the intercept of the low-frequency end of the arc with the real axis (i.e. Z'(ω)) representing the bulk resistance of the ECC. It is evident from Fig. 3(a) that as curing age increases, the sample impedance increases which results in a progressive displacement of the response to the right-handside of the plot. This is due to the on-going hydration process and resulting pore structure refinement which is well documented. Fig. 3(b)–(d) presents the complex impedance spectra for all mixes in Table 1. These Figures show that the addition of steel fibers results in a marked transformation of the impedance spectra which can now be separated into three, well-defined regions: (i) a low-frequency spur on the right-hand-side of the plot representing electrode polarization at the specimen/electrode interface. This arc would become more pronounced at frequencies lower than those used in the current experimental program; (ii) a mid-frequency arc which arises as a direct result of the inclusion of the steel fibers; and, (iii) a high-frequency arc on the left hand side of the response.

The mid- and high-frequency arcs constitute the bulk response and it is apparent that the relative contributions of these two arcs on the overall impedance are directly influenced by steel fiber dosage. The double-arc feature has also been identified in a limited study using carbon and steel fibers [29–31]. In general terms, at any stage in the hydration process, as the fiber dosage increases, (i) the radius of the high-frequency arc decreases and the high-frequency cusp point (i.e. the junction between the high- and midfrequency arcs) is progressively displaced towards the origin; (ii) the radius of the mid-frequency arc increases and the low-frequency cusp point (i.e. the junction between the right-hand electrode spur and the mid-frequency arc) is progressively displaced away from the real impedance axis (Z'(ω)) and merges into the electrode spur.

Fig. 3. (a) Impedance response for Mix 1 at 7, 14 and 28-days curing, with the arrows indicating the minimum point within the U-shaped valley region. Impedance response for all mixes after (b) 7-days curing; (c) 14-days curing and (d) 28-days curing.

Increasing hydration/curing time results in an overall increase in impedance over the test period and in a displacement of the entire response to the right; in addition, over the frequency range of the investigation, increasing the curing time results in a diminution in the prominence of the right-hand spur. With reference to Fig. 4(a), (b)–(f) provide the summary of the frequency values at which the two bulk arcs maximize (fp,m and fp,h on Fig. 4(a)) and at which the cusp-points occurs (fc,l and fc,h on Fig. 4(a)). For Mix M1 (see Fig. 4(b)), the frequency, fp , at which the bulk arc maximizes is 6.3 MHz at 7-days decreasing to 5.3 MHz at 14-days and 3.5 MHz at 28days hydration (these frequencies are also highlighted on Fig. 4(c)); the cusp-point frequency, fc , is 1.4 kHz at 7-days, decreasing to 700 Hz at 14-days and 400 Hz at 28 days. Increasing curing time results in an overall reduction of all salient frequencies reflecting on-going hydration and microstructural changes within the cement paste. It is also interesting to

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Fig. 4. (a) Schematic showing salient frequencies on Nyquist plot for ECC with and without steel fibers; (b) observed peak, fp, and cusp, fc, frequencies for Mix 1. Influence of steel fiber dosage and curing time on (c) fp,h — peak on high frequency arc; (d) fp,m — peak on mid-frequency arc; (e), fc,h — cusp on high frequency arc, and (f), fc,l — cusp on low-frequency arc.

note that the frequency at which the high frequency arc maximizes, fp,h (Fig. 4(c)), is virtually insensitive to fiber dosage, particularly at early curing times, as the values are similar to those obtained for Mix M1 at the same stage of hydration (fp on Fig. 4(c)) suggesting that this parameter is related to the cement paste component and not the inclusion of the steel fibers. As steel fiber dosage increases, both fp,m (Fig. 4(d)) and fc,l (Fig. 4(f)) decrease whereas fc,h (Fig. 4(e)) increases although it is evident that fp,m and fc,l are more sensitive to changes in fiber dosage than fc,h. With reference to Fig. 4(a), the bulk resistance of the ECC (no fibers) can be obtained at the cusp-point frequency, fc, whereas when steel fibers are added to the composite, at the frequency fc,h. Regarding the Nyquist formalism, it is evident from Fig. 3 that the plots are dominated by a single circular arc (Mix M1) or two circular arcs (Mixes M2–M6) whose centre is depressed below the real (Z'(ω)) axis. This feature results from dielectric dispersion within the system and is discussed in Section 3.4 below. In modelling the response in terms of resistive and capacitive circuit elements, the capacitance is replaced by a pseudo-capacitance or constant phase element (CPE) to account for the dispersive behaviour of the medium. The CPE is a complex, frequency-dependent parameter defined by the relationship, 00

Z CPE ðωÞ ¼

1 C o ðiωÞp

ð4Þ

where i = √ − 1, Co is a coefficient and the exponent, p, has a value such

that 0 b p b 1; if p equals 1, then the equation is identical to the reactive component of a pure capacitor of value Co with units in farads (F). When a CPE with value of p b 1 is placed in parallel with a resistor, a circular arc is produced with its centre depressed below the real axis, with Co having units Fs(p − 1). The arc depression angle, α (see Fig. 5(a)), is related to the exponent, p, in Eq. (4) through the relationship, α¼

π ð1−pÞradians 2

ð5Þ

The responses presented in Fig. 3 can be represented by a number of parallel and/or series connected circuit elements. With reference to Fig. 5(b), when the ECC is placed between a pair of electrodes, it can be considered as comprising three electrical pathways: (i) the continuous capillary pore network; (ii) the solid matrix comprising sand particles, products of hydration, unhydrated cement, isolated water-filled capillary cavities and ‘dead-end’ capillary pores; and (iii) the fiber/fiber–matrix interface/solid matrix and continuous capillary pores between the fibers. These can now be represented by the following circuit elements (see Fig. 5(c)): (1) a circuit comprising a resistor, Rcp, in parallel with a constant phase element, CPEsm. Rcp represents ionic conduction through the continuous, interstitial pore solution within the capillary network and CPEsm represents the response from the solid matrix; (2) a circuit comprising a resistor, Rf, and two, series connected, parallel elements Rfi/CPEfi and Rf-cp/CPEf-sm. This pathway represents

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Fig. 6. Measured and simulated impedance responses for Mixes 1, 3 and 6 at 7-days curing.

3.4. Relative permittivity and conductivity of ECC

Fig. 5. (a) Schematic diagram of Nyquist plot showing arc depression angle, α, with centre, O; (b) diagrammatic representation of electrical pathways in the cementitious composite placed between a pair of electrodes, and, (c) electrical model for the cementitious composite represented in (b). Refer to text for circuit element notation.

that fraction of the composite whereby the fibers and cement matrix are considered to be in series with each other as the fiber dosages in Table 1 are below the electrical percolation threshold. Accordingly, it is expected that there is no continuous steel fiber pathway between the electrodes. In this circuit, Rf represents electronic conduction through the steel fibers; the interface between the steel fibers and the cement matrix is represented by Rfi/CPEfi, and the cement matrix between the fibers associated with this pathway is represented by Rf-cp/CPEf-sm. In addition to these elements, the following are also present, (3) a circuit comprising Rel/CPEel representing the response from the electrode/sample interface; and, (4) a resistor Rs representing the projected intercept of the high-frequency end of the high frequency arc with the real axis. For illustrative purposes, Fig. 6 presents the measured and simulated responses for Mixes M1, M3 and M6 at 7-days curing with the simulation parameters presented in Table 3, together with those for Mixes M2, M4 and M5. The measured and simulated responses presented in Fig. 6 show good agreement over the frequency range, being slightly degraded at the high frequency end of the response. The most important finding from these simulations is that the fiber–matrix interface plays a significant role in the response. As the steel-fiber dosage is increased from 0.15% to 1.0%, the Rfi increases markedly, increasing by over two orders of magnitude. Further refinement is required to determine the contribution of fly-ash which causes the development of the U-shaped valley in the impedance response of Mix M1.

Fig. 7(a) displays the relative permittivity, ε'r(ω), for Mix M1 which has been de-embedded from the impedance spectra using Eq. (3) above. The relative permittivity at any frequency provides a quantitative measure of the sum of all polarization mechanisms operative at that frequency and by plotting this parameter in the frequency domain allows identification of the dominant polarization process(es). Fig. 7(a) indicates that dispersion in permittivity (i.e. the decrease in permittivity with increasing frequency) is detected across the entire frequency range which extends over seven decades; if there existed a single, dominant relaxation process the region of dispersion would, typically, be contained within one decade of frequency [49]. This figure clearly shows that the permittivity decreases by approximately six to seven orders of magnitude over this frequency range and would indicate that more than one polarization process is operative. Consider, for example, the response at 7-days hydration where the permittivity attains an anomalously high value of ~6 × 108 at 1 Hz and attributable to polarization processes at the sample–electrode interface; at 1.5 kHz this value has been reduced to ~ 1.6 × 104. It is also interesting to note that the rate of change of dispersion reduces at this frequency thereafter attaining values of ~440 at 100 kHz, 150 at 1 MHz and ~90 at 10 MHz. The frequencies indicated (by arrows) on the dispersion curves in Fig. 7(a) occur at the minimum point within the U-shaped valley region of the impedance response presented in Fig. 3(a). It is proposed that the dispersion in permittivity presented for Mix M1 in Fig. 7(a) is a result of three possible polarization mechanisms: a polarization process at the electrode/specimen interface dominant in the range 1 Hz–~1 kHz together with a superimposed electrochemical double-layer polarization process and a Maxwell–Wagner interfacial polarization process operative over the range ~ 1 kHz–10 MHz. Both double-layer and interfacial processes relax in this frequency range, although double-layer polarization is a low-frequency mechanism relaxing within the low kHz region [50] whereas interfacial polarization is a mid-frequency mechanism relaxing within the MHz region [49]. Regarding double-layer processes, porous materials saturated with conductive liquids have been shown to exhibit high dielectric permittivity [51] and in ECCs this would result from polarization of charges electrostatically held onto the cement gel surfaces. Interfacial processes, on the other hand, would result from charge separation at pore-fluid/crystal boundary interfaces. Under the application of an electric field, charged carriers can be blocked by internal crystal boundaries leading to a separation of charge which will contribute to the polarizability of the sample. Fig. 7(a) would indicate that double-layer processes dominate over the range ~ 1 kHz–~100 kHz, whereas interfacial effects are operative over the range ~ 100 kHz–10 MHz, with the tilde indicating that processes will overlap at the delineating frequencies viz. 1 kHz (electrode/double-layer) and 100 kHz (double-layer/interfacial). Fig. 7(a) also highlights the influence of curing time on relative permittivity, which is seen as a gradual downward displacement of the curves. As the ECC hydrates, the capillary pore network becomes more tortuous,

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Table 3 Equivalent circuit simulation parameters for all mixes at 7-days curing. Mix

M1

M2

M3

M4

M5

M6

Fibre dosage (%) Rs (Ω) Rcp (Ω) CPEsm CPEsm (p) Rf (Ω) Rfi (kΩ) CPEfi CPEfi (p) Rf-cp (Ω) CPEf-sm CPEf-sm (p) Rel (kΩ) CPEel CPEel (p)

0 450 510 3.0 × 10−9 0.80 + + + + + + + 10 3.5 × 10−4 0.90

0.15 345 840 1.0 × 10−9 0.83 10−3 2.4 7.0 × 10−6 0.77 550 1.0 × 10−9 0.83 10 3.5 × 10−4 0.94

0.25 300 870 1.0 × 10−9 0.83 10−3 3.0 7.0 × 10−6 0.80 420 1.0 × 10−9 0.83 10 3.0 × 10−4 0.94

0.50 235 925 1.0 × 10−9 0.84 10−3 14 7.0 × 10−6 0.80 320 1.0 × 10−9 0.84 10 4.0 × 10−4 0.90

0.75 185 950 2.5 × 10−9 0.81 10−3 100 1.0 × 10−5 0.78 200 2.0 × 10−9 0.81 10 3.0 × 10−4 0.97

1.0 170 980 2.5 × 10−9 0.84 10−3 500 1.0 × 10−5 0.80 150 2.5 × 10−9 0.84 10 3.3 × 10−4 0.95

+ = not determined.

constricted and disconnected, with free-water consumed in the hydration reactions resulting in an irrotational binding of charges/water. These physico-chemical processes result in an overall reduction in bulk polarization, hence dielectric permittivity, across the entire frequency range. Fig. 7(b) displays the conductivity, which has been de-embedded from the impedance spectra using Eq. (2). The conductivity increases with frequency across the entire frequency range and decreases with increasing curing time. The overall decrease in conductivity with time will be due to continual refinement of pore-structure as a result of on-going hydration and pozzolanic reaction. Conductivity can be regarded as a measure of all loss processes operative within the material and quantifies the energy dissipated by the motion of charges in an applied electric field. For the ECC, this would include the movement of ions in the continuous, water-filled capillary pore network (i.e. ionic conduction process), together with losses associated with relaxation/dispersion of the polarization process (i.e. double-layer and interfacial). The

Fig. 7. (a) Relative permittivity and (b) conductivity of Mix 1 at 7, 14 and 28 days curing. The arrows indicate the permittivity/conductivity responses corresponding to the minimum point within the U-shaped valley region of the impedance response presented in Fig. 3(a).

cumulative effect of these losses would result in an increase in conductivity with increasing frequency hence the conductivity, σ(ω), at angular frequency, ω, can be written as, σ ðωÞ ¼ σ d ðωÞ þ σ ð0Þ

ð4Þ

where σ(0) is the low-frequency, ionic conductivity and σd(ω) is the dielectric conductivity resulting from dissipative polarization processes. With reference to Fig. 7(b), within the frequency range ∼ 100 Hz– 1 MHz, conduction will be dominated by ionic transfer through the continuous water-filled capillary pores. Superimposed on this loss mechanism will be contributions from double-layer relaxation processes over the range 100 Hz–100 kHz (albeit a very weak contribution) and a stronger contribution from interfacial processes at frequencies N1 MHz. Fig. 8(a)–(c) presents the relative permittivity and Fig. 9(a)–(c) the conductivity for all ECC mixes. With reference to the permittivity results presented in Fig. 8(a)–(c), it is immediately evident that when compared with Mix M1, the addition of steel fibers results in a significant enhancement in relative permittivity — hence polarizability of the composite - across the entire frequency range with the permittivity increasing with increasing fiber dosage. The increase in permittivity is particularly prominent in the range ~ 50 Hz–5 kHz causing a shoulder to occur in the frequency-domain response. The permittivity is progressively reduced with increasing curing time as a result of the hydration and pozzolanic processes (causing, for example, pore structure refinement and irrotational binding of charges), however, the enhanced permittivity due to steel fiber additions is still prominent across the bandwidth. It is also evident from Fig. 9(a)–(c) that over the frequency range ~ 50 Hz–5 kHz the conductivity increases rapidly although this feature decreases with decreasing fiber dosage. Increasing hydration time also has a marked effect on the conductivity of the ECC: at 7-days hydration (Fig. 9(a)), at frequencies b ~50 Hz, the addition of steel fibers does not result in any significant change in the conductivity of the composite relative to Mix M1 which has no steel fibers. As hydration time increases (Fig. 9(b) and (c)), relative to Mix M1, the conductivity of Mixes M2–M4 increased across the entire frequency range of the investigation. However, at frequencies b~50 Hz, Mixes M5 and M6, with higher steel fiber contents, display a reduced conductivity relative to Mix M1 attributed to the development of a non-conductive barrier at the steel fiber– matrix interface (i.e. the circuit element Rfi/CPEfi discussed above); whereas at frequencies N 50 Hz the enhancement in conductivity becomes increasingly more evident. For illustrative purposes, the salient frequencies identified from the impedance spectra for Mixes M1 and M6 at 7-days curing (see Fig. 4(a)) are presented in Fig. 10(a) and (b) on the respective relative permittivity and conductivity curves. In order to explain these features, the ECC can be considered as comprising highly conductive steel fibers randomly dispersed in a lossy

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Fig. 8. Relative permittivity for all Mixes at (a) 7; (b) 14; and (c) 28 days.

Fig. 9. Conductivity for all Mixes at (a) 7; (b) 14; and (c) 28 days.

dielectric medium (i.e. the cementitious mortar). On application of an a.c. electrical field between the electrodes, electric current must pass across the interface between the cement-paste and the embedded steel fibres. There will be a change in conduction processes – ionic conduction through the cement paste and electronic conduction through the steel fibers. The ECC thus has a mixed ionic-electronic conduction process with the result that charges can accumulate at the interface and result in the development of an electrochemical over-potential. This will result in polarization at the interface which is quantified by enhancement of capacitance, hence permittivity, of the composite. This effect is shown schematically in Fig. 11 and would be similar to induced polarization phenomena that can develop in rocks containing metallic minerals [52]. As the steel-fiber dosage increases, the fiber–electrolyte contact area increases, resulting in an increase in polarizable surfaces and consequent increase in permittivity. This effect diminishes with increasing frequency although it is evident that it persists across the entire frequency range, and would be in addition to those polarization processes present in the ECC without steel fibers.

mid-frequency arc and high-frequency arc in the case of Mixes M2– M6 (i.e. at frequency fc,h as depicted on Fig. 4(a)). It is evident that the conductivity increases in a linear fashion over the range of steel fiber dosages considered in this investigation (0.15%–1.0%). Fig. 12 would also indicate that the highest fiber dosage is still below the fiber percolation threshold, with percolation occurring at a dosage which would create a continuous fiber pathway between the electrodes. To explain the increase in bulk conductivity of the composite with increasing steel fiber dosage, the Equivalent Inclusion Method (EIM) is used. The EIM was originally developed for studying heat conduction problems [53] and is based on the Effective Medium Theory. This mathematical model was chosen as it was derived primarily for short fiber inclusions. In this model, the predicted bulk conductivity, σc , of a composite reinforced with 3-D randomly oriented fibers is related to the matrix conductivity, σm , the fiber conductivity, σf , and the fiber volume fraction, ϕ, through the following relationship:

σc ¼ σm 3.5. Composite mixing laws Fig. 12 presents the measured conductivity of the ECC after 7, 14 and 28 days curing. The bulk conductivity, σbulk, of the specimens was obtained at the cusp-point within the valley region for mix M1 (at frequency fc as depicted on Fig. 4(a)) and at the cusp point between the


 
  ! φ σ m −σ f σ f −σ m ðS11 þ 2S33 Þ þ 3σ m ð5Þ 1−
2
 3 σ f −σ m ð1−φÞS11 S33 þ σ m σ f −σ m R þ 3σ 2m

where R ¼ 3ðS11 þ S33 Þ−φð2S11 þ S33 Þ

ð6Þ

B. Suryanto et al. / Materials and Design 105 (2016) 179–189

187

Fig. 10. Salient frequencies (refer also to Fig. 4(a)) for Mixes 1 and 6 on their respective dispersion curves: (a) conductivity; and (b) relative permittivity.

S11 ¼ S22

3 !0:5 L L2 −1 L 5 4 ¼  −1 − cosh 1:5 d d2 d 2 2 L2 −d Ld

2

S33 ¼ 1−2S22

2

ð7Þ

ð8Þ

The same relationships have recently been used by [54] to study the electrical resistivity of steel fiber reinforced concrete. When fibers become preferentially aligned in one direction, thereby forming a cosine fiber orientation distribution [53] and equivalent to a 2-D random orientation, the equation becomes σc ¼ σm

!
 
  φ σ f −σ m σ f −σ m ðS11 þ S33 Þ þ 2σ m ð9Þ 1þ
2
 2 σ f −σ m ð1−φÞS11 S33 þ σ m σ f −σ m R0 þ 2σ 2m

where R0 ¼ ð2−φÞðS11 þ S33 Þ:

ð10Þ

In Eq. (7), L is the fiber length and d is the fiber diameter. In the calculations, the matrix conductivity (i.e. the cement mortar and PVA fibers) was determined from the impedance response of the control mix M1; from Fig. 3(a) these values are determined at the cusp-point frequency fc as: σm = 0.0975 S/m, 0.0525 S/m and 0.0265 S/m at 7, 14 and 28 days, respectively. The conductivity of the steel fibers, σf, was taken as 107 S/m and the geometrical properties of the fibers were L = 6 mm and d = 0.16 mm.

Fig. 12. Bulk conductivity of Mixes 1–6 at 7, 14 and 28 (d)ays curing.

Fig. 13(a)–(c) presents the predicted bulk conductivity using Eqs. (5) and (9) above together with the measured values for samples cured for 7, 14 and 28 days, respectively. It is apparent from Fig. 13 that, within the range of fiber volumes studied, the EIM 3-D random model (Eq. (5)) under-predicts the bulk conductivity, whereas the EIM 3-D cos (Eq. (9)) better fits the measured values, suggesting that the actual fiber orientation was not completely random and that a certain degree of fiber alignment occurred along one axis. This is not entirely unexpected and could be attributed to the wall effect [55] occurring during the casting process as fibers close to the side-walls of the mold will tend to align themselves parallel to the walls (i.e. parallel to the direction of the applied current), leading to a higher percentage of fibers aligned longitudinally. The underestimation of the predicted bulk conductivity for randomly oriented fibers could also be attributed to the fact that, although the fiber dosage is still below the percolation threshold, some fibers might be in direct contact with each other thereby increasing their effective length. It should be noted, however, in reality non-uniform fiber orientation and partial inter-fiber contacts occur concurrently and therefore it could be argued that the effective length should be closer to the actual fiber length. 4. Conclusions The following conclusions can be drawn from the work presented: 1. The inclusion of steel fibers in the ECC (up to 1% by volume) resulted in a transformation of the Nyquist plot from a single-arc response to a dual-arc response. The prominence of the new arc was found to be dependent upon steel fiber dosage and curing time, the latter resulting from on-going hydration of the cementitious component.

Fig. 11. Schematic showing induced polarization at steel fiber–pore solution interface.

2. An electrical model comprising resistive and constant phase circuit elements was developed which could simulate the response for the ECC containing conductive steel fibers. It was observed that the fiber–matrix interface plays a significant influence on the impedance

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Acknowledgements The authors wish to acknowledge the support of Kuraray Japan and Kuraray Europe GmbH for providing the PVA fibers, Bekaert for providing the steel fibers and BASF UK for providing the admixtures. Financial support from the School of Energy, Geoscience, Infrastructure and Environment, Heriot Watt University, is gratefully acknowledged. Thanks also expressed to Mr. D. Stone and Mr. K. Chronopoulos for assistance in the experimental work.

References

Fig. 13. Measured conductivity (σbulk) and simulated conductivity (σc) using Eq. (5) (3D random) and (9) (3D cos) at (a) 7; (b) 14; and (c) 28 (d)ays curing.

response. As the fiber dosage is increased from 0.15% to 1.0%, the resistance representing the fiber–matrix interface increases significantly by two orders of magnitude. 3. When presented in the frequency domain, the addition of steel fibers manifests itself as a dielectric enhancement over the entire frequency range under study, most notably in the frequency range ~ 50 Hz‐ 5 kHz causing a shoulder to occur in the frequency-domain response. The enhancement was attributed to an induced polarization effect whereby charges accumulate at the fiber/matrix interface thereby increasing the polarizability of the composite. Furthermore, it is shown that the permittivity is progressively reduced with increasing curing time as a result of hydration. 4. It was also found that the addition of steel fibers increases the conductivity of the composite at mid to high frequencies, with conductivity increasing with steel fiber dosage. A distinct increase in conductivity occurs within the frequency range ~10 Hz–500 Hz indicating dispersion in fiber–matrix interfacial polarization and the emergence of a new conduction pathway through the steel fibers and cement matrix in series. 5. The bulk electrical conductivity of the composite was found to conform to the Equivalent Inclusion Method. It was shown that the composite bulk conductivity increases as the fiber dosage increases although it was found that the highest fiber dosage (1% by volume) was still below the percolation threshold for the composite.

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