Inverse Identification of the Bond-Slip Law for Sisal Fibers in High-Performance Cementitious Matrices

The use of Natural Fibers (NFs) in Fiber-Reinforced Cementitious Composites (FRCCs) is an innovative technical solution, which has been recently employed also in High-Performance FRCCs. However, NFs are generally characterized by complex microstructure and significant heterogeneity, which influence their interaction with cementitious matrices, whose identification requires further advances in the current state of knowledge. This paper presents the results of pull-out tests carried out on sisal fibers embedded in a cementitious mortar. These results are considered for identifying the bond-slip law that describes the interaction between the sisal fibers and the cementitious matrix. A theoretical model, capable of simulating the various stages of a pull-out test, is employed as part of an inverse identification procedure of the bond-slip law. The accuracy of the resulting simulations demonstrates the soundness of the proposed theoretical model for sisal fibers embedded in a cementitious matrix.


INTRODUCTION
In the last decade many researches have been developed with the aim of exploring the potential of composite materials, based on either polymeric or cementitious matrices, internally reinforced by fibers derived by plant leaves or branches (Netravali & Chabba, 2003). These fibers, generally referred to as either "vegetal" or "natural", highlighted promising properties in terms of both strength (Silva et al. 2010) and durability (Melo Filho et al. 2013, Ferrara et al. 2014Ferrara et al., 2015). Moreover, they have an apparent potential for enhanced sustainability with respect to similar materials reinforced with industrial fibers made of either steel (Toledo Filho, 1997) or plastic fibers (Sreekumar et al. 2009).
The aforementioned researches unveiled the multifold potential of Natural-Fiber-Reinforced Cementitious Composites in reducing the demand of raw materials, as they are mainly based on using re-newable resources, and the supply and production costs, as the original plants are widely available, especially in tropical and sub-tropical zones.
Among the various Natural Fibers (NFs) investigated so far, those made from sisal (agave sisalana) leaves ) have attracted a great interest in both material scientists and concrete technologists (Netravali & Chabba, 2003). More specifically, their excellent properties in terms of tensile strength is the main motivation for using them as a reinforcement in composite materials (Silva et al. 2008). However, it should be recognized that the weak chemical bonds that can be established with matrices based on Portland cement results in low mechanical bond between these fibers and matrices, whose maximum strength might be estimated in the range of 0.32 and 0.72 MPa, according to experimental results reported in the scientific literature (Silva et al. 2011). Moreover, the high water absorption capacity of sisal fibers results in a volume expansion when Inverse identification of the bond-slip law for Sisal fibers in High-Performance Cementitious Matrices Identificazione inversa della legge aderenza-scorrimento per fibre di Sisal in matrici cementizie ad alte prestazioni they are added to the fresh cementitious matrix and, conversely, it produces a contraction when the matrix dries and, hence, a partial detachment between fibers and matrix at the hardened state.
Different procedures have been proposed for reducing water absorption capacity in natural fibers and improving fiber-matrix bond interaction: they are based on applying chemical and physical treatments of both matrix and fibers (Ferraz et al. 2011). For instance, the partial replacement of cement with microsilica have led to increasing the pullout resistance by about 24% (Toledo Filho, 1997). This increase is related to the fineness of microsilica, which is capable to reduce porosity in the transition zone, hence enhancing the fiber-matrix bond. Furthermore, the use of alkaline solutions (Saha et al. 2010;Kundu et al. 2012) removes most of the surface non-cellulosic substances and increases roughness of their surface, hence enhancing the fibermatrix bond. Simple treatments, such as soaking the fibers in distilled water followed by a drying process, also result in improving the fiber-matrix bond (Li et al. 2008). Moreover, a reduction in the fiber hydrophilicity can be achieved by means of wetting and drying cycles promoting hornification (namely, stiffening of the polymeric structure present in lignocellulosic materials, as defined by Claramunt et al., 2010). This treatment promotes a reduction in volumetric changes of pulps and fibers of natural origin, as well as a significant alteration in their mechanical properties, while acting also as a bridge between fibers and cementitious matrices and, hence, strengthening the interfacial bond (Claramunt et al. 2010).
This paper summarizes the results of pull-out tests carried out on hornified sisal fibers embedded in a cementitious mortar. Then, these results are employed in identifying the bond-slip law that describes the interaction between sisal fibers and cementbased matrix: an inverse identification procedure, based on a theoretical model capable of simulating the various stages of a pull-out test, is applied for this task (Ferreira et al. 2016).

Materials and processing
The sisal fibers used in the present study were obtained from sisal plants growing in farms located in the Bahia state, Brazil. They were extracted from the sisal plant leaves in the form of long fiber bundles: this process was executed by means of semiautomatic scrapers.
The cement-based matrix presented a mix design of 1:0.5:0.4 (binder: sand: water/binder ratio) by weight.
The binder was composed by 30% of Portland cement CP-32 F II, 30% of metakaolin and 40% of fly ash. This ratio of metakaolin and fly ash was aimed to guarantee the durability of the fiber once a matrix free of calcium hydroxide is obtained Melo Filho et al. 2013).
The fly ash also ensured higher workability to the matrix that, within the context of high-performance composites, is a desirable property, as it provided a better homogenization of the natural fibers .
The sand was processed to obtain a maximum diameter of 840μm and the superplasticizer was the Glenium 51 (type PA) with solids content of 31%. In addition, a viscosity modifier Rheomac UW 410, (manufactured by BASF), at a dosage of 0.8 kg/m 3 was also used in order to avoid segregation and bleeding during molding.
The matrix showed a flow table spread value of 450 mm according to the Brazilian standard NBR 13276 (2005) and a compressive strength at 28 days of 31 MPa, according to NBR 7215 (1996).
The mixtures were produced in a room with controlled temperature (21±1°C) using a mixer with capacity of 5 l. The mixing procedure consisted of the following stages: -all dry components were homogenized in the mixer; -the water and superplasticizer were added and mixed for 2 min at a speed of 125 RPM; -the process was stopped during 30 s to remove the material retained in the mixer; -the mixing procedure continued for 2 min at 220 RPM and, finally, for a further 5 min at 450 RPM. A special mold was developed for preparing the specimens. After filling the mold with the matrix, the top cap was fixed and the fiber stretched slightly for alignment. The mortar was placed in plastic bags before being placed in the mold as to facilitate the casting process. Embedment length of 25 was analyzed. After 24 hours, the specimens were demolded and placed in a fog room (HR% ≥ 95%) to moist curing for 7 days for the pullout test.

Hornification process
The sisal fibers were placed in a container with water (T = 22°C) during three hours to reach its maximum water absorption capacity. The drying process was carried out in a furnace at a temperature of 80°C. The furnace used was equipped with an elec- tronic temperature control and connected to a scale, with a tolerance of 0.01g to record the loss of water. The furnace was programmed to reach 80°C at a heating rate of 1°C/min and to maintain this temperature for 16 hours. After 16 hours of drying, the furnace was cooled down to the temperature of 22°C in order to avoid possible thermal shock to the fibers. This procedure was repeated ten times. More details can be obtained elsewhere .

Testing
The sisal fiber's microstructure was investigated using a Hitachi TM3000 Scanning Electron Microscope (SEM). The microscope was operated under an accelerating voltage of 15kV. A pre-coating with a thin layer of approximately 20 nm of gold was done to make the fiber conductive and suitable for analysis. In order to measure the fiber's crosssectional area, for each single fiber used in the pullout and tensile test, an adjacent piece of the fiber (immediately next to the one tested) was kept for future measurement and morphology characterization using the SEM. Fiber-matrix interface zone was also investigated. The obtained images were postprocessed using ImageJ, a Java-based image processing program.
The tensile tests were performed in an electromechanical testing machine Shimadzu AG-X with a load cell of 1kN. The tests were performed on 15 sisal fibers using a displacement rate of 0.1 mm/min. The fibers with a gage length of 50 mm were glued to a paper template for better alignment in the machine and for a better griping with the upper and lower jaws in accordance with ASTM C1557 (2013). To calculate the tensile strength of the fibers, their diameters were measured by image analysis from micrographs obtained in a scanning electron microscope.
The pullout tests were performed in an electromechanical testing machine Shimadzu AG-X with a load cell of 1kN. The tests were carried out using a displacement rate of 0.1 mm/min. The samples were fixed in the machine grips through a system with hinged-fixed boundary conditions. Fifteen tests were performed (embedded length of 25 mm).

ANLYTICAL MODELING
An analytical model has been formulated for simulating the interaction between fiber and matrix in a pull-out process (Ferreira et al., 2016).
It assumes that: -the fiber behaves in a linear elastic way; -the matrix is supposed to be perfectly stiff; -the interaction between fiber and matrix is based on a bond-slip law -s, invariant throughout the fiber length. As for the last point, the model assumes the following bilinear bond-slip law ( Figure 1): where kel=max/sel is the slip modulus of the elastic branch ending at a slip value sel with a corresponding bond stress max. Moreover, r is the residual bond stress, and kin is the post-peak slip modulus, strictly positive in eq. (1), resulting in a linear variation of stresses from r to u, the latter being achieved for a slip su. (2) Moreover, the axial strain f developing in the fiber is strictly related to the interface slip s: Since the fiber is elastic f=Eff and, hence, equation (3) can be introduced in eq. (2), in order to obtain a well-known differential relationship between the second derivative of the interface slips and the corresponding bond stress  (Caggiano et al. 2012): Figure 2. Local equilibrium conditions on a free infinitesimal element of fiber / Condizioni di equilibrio locale su un segmento di fibra di lunghezza infinitesima.
A step-wise analytical solution can be obtained by considering the various states of stresses of the fiberto-matrix interface resulting from the bilinear bondslip law represented in Figure 1. Further details on both the mathematical derivation and the numerical implementation of this solution are available in Ferreira et al (2016).
Based on the above assumptions, the full range analytical expression of the applied pull-out force F0 can be, as a function of the displacement s0 at the end of the fiber embedment, on the loaded side.
Moreover, F0 also depends upon the actual bondslip law assumed for describing the interface behavior. Hence, the following conceptual relationship can be written: where q is a vector that collects the five parameters describing the interface law de-scribed in Figure 1: The aforementioned analytical model can be employed for determining the parameters describing the actual bond-slip interaction by means of an "inverse identification" procedure ). More specifically, the following optimization problem has to be solved: being (8) where s0,i is the displacement imposed on the free end of the fiber at the i-th increment of the experimental procedure, F0,iexp is the corresponding force and n is the number of displacement increments either in the experimental process or the current numerical analysis. Table 1 summarizes the results derived from the SEM analysis by presenting the measured value in terms of area, perimeter and fiber's shape. Based on the values of parameters reported in Table 1, the hornified sisal fiber presents high scattering in terms of morphological characterization. The area and perimeter values range from 0.001 to 0.003 mm 2 and 0.53 to 1.3 mm, respectively. This significant variation might be directly related to the significant variability in the shape of fibers' cross-sections. This clue is confirmed by Figure 3, which shows the three typical cross-section shapes exhibited by sisal fibers, each one presenting a different relationship between cross-section area and perimeter.

Morphological characterization of sisal fiber
As a matter of fact, within the leaf, there are three basic types of fibers, generally referred to as structural, arch and xylem fibers (Silva et al., 2011). Structural fibers have a horse shoe shape and a rough surface ( Figure 3a); arch shape fibers ( Figure  3b) grow in association with the conducting tissues of the plant (usually found in the middle of the leaf); xylem fibers grow opposite to the arch fibers, presenting a twisted shape (Figure 3c), similar to double-helical DNA model.

Mechanical properties
The results in terms of tensile strength and the corresponding elastic modulus for both untreated and hornified sisal fibers are summarized in Table 2. They show that hornification induce to a slight increase in tensile strength and strain at failure (about 5%), while it reduces the elastic modulus.
In fact, wetting and drying cycles change the microstructure in natural fibers, which, in turn, modifies the polymeric structure of the fiber-cells resulting in higher tensile strength and strain. Moreover, it is worth highlighting that hornification reduces the variability affecting the mechanical response of sisal fibers, both in terms of tensile strength (coefficient of variation slumps from 67 to 26%) and elastic modulus (CoV reduces from 3.5 to 2.7%).

Bond-slip law identification
The results of the inverse identification of the bondslip laws performed on hornified sisal single fiber pull-out tests, are summarized in Table 3. A total number of 15 tests were performed (embedded length equal to 25 mm), but 4 samples exhibited fiber fracture and for this reason their results are not considered in the present analysis for the bondslip law identification.
The quality of the approximation that can be achieved by means of the proposed model is demonstrated by comparing experimental results and analytical simulations (in terms of F0-s0 curves) for each test (Figure 4). The curves clearly demonstrate that the analytical solution proposed in this study is capable of accurately reproducing the bond behavior of hornified sisal fibers embedded in a cement matrix. However, the results reported in Table 3 highlight that the bond-slip laws identified for the various tests are fairly scattered. In other words, defining a unique bond-slip law capable to describe the bond behavior of natural fibers in cement matrix does not seem re-alistic. This can be justified by considering that sisal fibers are heterogeneous, in terms of both mechani-cal and geometric properties, and this heterogeneity leads to a significant variability in the resulting ad-hesion with mortar. In fact, the resulting bond be-havior in cement matrix is influenced by several pa-rameters, such as fiber shape, fiber cross section area variation along the longitudinal axis and surface tex-ture and roughness of the filaments.
Nevertheless, the identified bond-slip laws may be analyzed and compared in terms of some key me-chanical parameters, such as the specific fracture en-ergy GF, which represents the area under the local bond-slip law in Figure 1.
Before commenting into details the results in Ta-ble 3, it should be mentioned that the bond behavior of fibers in cement matrix can be mainly divided in three phases: adhesion, mechanical bond and fric-tional bond (Naaman, 1999). The first two mainly depends on the chemical compatibility between the fiber and the matrix and the surface texture of the fi-ber while the latter is, mainly, governed by the geo-metrical characteristic of the fiber.
Then, the values of GF reported in Table 3 can be interpreted in the light of the above considerations.
As regards fracture energy, it should be noticed that the high dispersion, in terms of coefficient of variation CoV (around 60% as highlighted in Table   3), presented by the GF can be mainly attributed to the morphological characteristics of sisal fibers. In fact, these fibers are characterized by a high variabil-ity in terms of transverse section properties (Pf and Af) as well as in terms of overall straightness and this heterogeneity influence the frictional bond mechanisms that play a fundamental role on the def-inition of the fracture energy. Conversely, the values of max presents a lower value in terms of CoV. This can be explained by considering that the elastic branch is mainly con-trolled by the adhesion and mechanical bond mecha-nism occurring between fiber and matrix, both being more related to the chemical adhesion between sisal fiber and cement based matrix, rather than their ge-ometric properties.

CONCLUSIONS / CONCLUSIONI
This paper was intended at investigating the bond behavior of hornified sisal fibers embedded in cement-based matrix. On the one hand, the reported experimental results demonstrate the potential of using sisal fibers as spear reinforcement in cementitious composites. On the other hand, the proposed theoretical model leads to scrutinizing the local bond-slip relationship characterizing the interaction between fiber and matrix.
The following main points can be remarked: -the pull-out tests highlighted good bond properties of hornified sisal fibers: since the majority of specimens failed in debonding, one can reasonably recognize that their transfer length is longer than 25 mm and, hence, the majority of the tested specimens can be considered for charactering the bond behavior of sisal fibers; -an analytical model, already formulated by the Authors for similar problems, was extended to the case of hornified fibers by introducing a more general bi-linear bond-slip law, whose characteristic features (e.g. discontinuities and non-zero ultimate stresses) resulted essential in simulating the observed behavior of the fibers under consideration; -in spite of the significant variability affecting the geometry of fibers, reasonably stable values of the key parameters of the identified bond-slip laws were determined for the various tested specimens. Particularly, the variability of two main parameters, such as bond strength and fracture energy was analyzed. The results of this study will pave the way towards a comprehensive understanding of the mechanical behavior of cementitious composites reinforced by natural fibers. Particularly, the research will move toward the structural scale by analyzing the response of structural members made of this the materials considered herein. Moreover, the proposed analytical model will be available for identifying the bond-slip laws resulting for other kinds of natural fibers (i.e. jute and curauá) and compare them with the one determined for hornified fibers.