134 Int. J. Materials and Structural Integrity, Vol. 3, Nos. 2/3, 2009 Experimental and numerical nano-characterisation of two phases in concrete Aaron K. Reinhardt, Michael P. Sheyka, Andrew P. Garner, Marwan Al-Haik and Mahmoud M. Reda Taha* Department of Civil Engineering, University of New Mexico, Albuquerque, NM 87131-0001, USA E-mail: aaronr@unm.edu E-mail: shak@unm.edu E-mail: apgarner@unm.edu E-mail: alhaik@unm.edu E-mail: mrtaha@unm.edu *Corresponding author Abstract: Concrete is the most used material in construction worldwide. Concrete is a composite material including three phases: cement paste, aggregate and interfacial transition zone (ITZ). Previous research has demonstrated that the macro behaviour of concrete represents the integration of its constituent phases. Here, we present a methodology to experimentally and numerically characterise the mechanical performance of individual points within these constituent phases. Concrete samples made of high performance concrete are indented using state of the art nano-characterisation system. Using nano-positioning technique load-indentation curves are recorded at two individual points at the cement paste (CP) phase and at the ITZ phase. The load-indentation relationship showed a significant difference between the mechanical behaviours at both points. The finite element (FE) method is used to simulate behaviour at both phases. It is shown that the load-indentation curves can be simulated accurately using FE providing insight on intrinsic constitutive models. Keywords: nanoindentation; concrete composite; finite element analysis. Reference to this paper should be made as follows: Reinhardt, A.K., Sheyka, M.P., Garner, A.P., Al-Haik, M. and Reda Taha, M.M. (2009) Experimental and numerical nano-characterisation of two phases in concrete, Int. J. Materials and Structural Integrity, Vol. 3, Nos. 2/3, pp.134-146. Biographical notes: Aaron Reinhardt is an MSc student in the Department of Civil Engineering at the University of New Mexico, Albuquerque, NM 87131 USA. Michael Sheyka is a PhD student in the Department of Civil Engineering at the University of New Mexico, Albuquerque, NM 87131 USA. Andrew Garner is a BSc student in the Department of Civil Engineering at the University of New Mexico, Albuquerque, NM 87131 USA. Copyright 2009 Inderscience Enterprises Ltd.
Experimental and numerical nano-characterisation 135 Marwan Al-Haik is an Assistant Professor in the Department of Mechanical Engineering at the University of New Mexico, Albuquerque, NM 87131 USA. Mahmoud Reda Taha is an Associate Professor and Regents Lecturer in the Department of Civil Engineering at the University of New Mexico, Albuquerque, NM 87131 USA. 1 Introduction Microstructural optimisation of composite materials such as concrete aims at enhancing some pre-defined macro-scale properties. However, such optimisation requires that the mechanical properties of individual phases be known (Torquato, 2002). Nano-characterisation of concrete phases is therefore essential for possible optimisation of concrete composites. Nano-scale investigations of cement have enabled better understanding of the physical properties of cementitious materials and shed light on the complexity of the inter-atomic bond and its continuity in cement-based materials (Gmira et al., 2004). Moreover, it has been shown that nano-scale elastic modulus and hardness values are consistent with values obtained at the macroscale confirming the possible correlation across scales (Velez et al., 2001; Sonebi, 2008). This paper aims at providing a simple procedure to characterise the mechanical properties at individual points within the different phases of concrete at the nano-scale. Moreover, we demonstrate that the mechanical behaviour at representative points of each phase can be accurately simulated using the finite element method. Elastic perfectly-plastic stress strain curves were shown to accurately model steel and silica response under nanoindentation (Fischer-Cripps, 2004). We show here that elastic perfectly-plastic stress strain curves can also be used for modelling nanoindentation of concrete phases. A number of studies reported on characterising the nanostructure of concrete. Researchers reported two fundamental types of CSH, a low density phase (LD) and a high density phase (HD). While the properties of LD and HD phases are assumed intrinsic properties that are independent of concrete mixing proportions, the volume fraction of each phase seems to be dependent on the constituent materials (Jennings, 2004; Constantinides and Ulm, 2004; Zhu et al., 2007; Mondal et al., 2008). Being able to accurately model a high performance concrete at the nano-scale provides much needed insight about the material properties of the different microstructural phases of concrete making a step essential for microstructural optimisation. 2 Experimental methods The experiments presented in this article aim at mechanically characterising the two microstructural phases of concrete. The following sections describe the materials and the methods used in this experimental investigation.
136 A.K. Reinhardt et al. 2.1 Materials A high performance concrete was used. The concrete mix included ordinary Portland cement (ASTM Type I). The aggregate used in this mix included a 9.5 mm nominal maximum size limestone and washed concrete sand. The mix had a water/cement ratio of 0.33. A standard superplasticiser was used with the mix. The mixture proportions of this concrete are presented in Table 1. The concrete had a 150 mm slump and a compressive strength of 61 MPa at 28 days. All properties were determined from replicates of three specimens. 2.2 Specimen preparation The concrete specimen was cured using standard water curing methods for 11 days. The specimen was then kept dry under laboratory conditions for 150 days, the time of indentation. The indentation specimen was then extracted by slicing a 10 mm 10 mm 3 mm section. The sliced section was then cast in acrylic epoxy. Upon drying of the epoxy the surface side of the sample was then ground using a mechanical polishing wheel. The specimen was rinsed continuously with running water during grinding. The grit sizes used for grinding were 120, 240, 600, 1000 and 2000, consecutively. After completion of the 2000 grit cycle the specimen was rinsed with distilled water and placed in a supersonic bath for ten minutes to displace lodged particles. The specimen was then polished using the same mechanical polishing wheel with 0.6 and 0.1 micron diamond pastes, consecutively. Again after this polishing process, the sample was rinsed with distilled water and placed in the supersonic bath. Finally, the specimen was dried using pressurised air and placed into a sealed specimen container to avoid contamination. Table 1 Mix proportions of concrete Weight (kg/m 3 ) Water 139 Cement 420 Fine aggregate Course aggregate 637 1173 Superplasticiser 4.05 (L/ m 3 ) 2.3 Nanoindentation experiments Nanoindentation was performed using a NanoTest TM 600 indenter system from Micro Materials, Inc., Wrexham, UK. In this system the load is applied electromagnetically to a vertically mounted specimen as schematically shown in Figure 1. An electrical current passes through the coil, causing polarisation and attraction of the coil towards the electromagnet. This action causes the pendulum to rotate about the frictionless pivot, thus indenting the sample. Change in the capacitance can be directly related to the depth of indention with a sub-nanometre resolution. All indentations presented here used a three-sided pyramidal shaped Berkovich diamond tip indenter with a face angle of 65.27. The indenter has a pyramid shape with a maximum depth of 1800 nm and a pyramid base width of 2000 nm. Each indentation cycle included loading
Experimental and numerical nano-characterisation 137 and unloading the specimen while recording the load and depth of indentation continuously. Figure 1 Schematic of the NanoTest TM equipment (see online version for colours) Figure 2 Micrograph of concrete specimen showing locations of indentation at point A within the cement paste and point B within the ITZ (see online version for colours)
138 A.K. Reinhardt et al. The two indented locations were within the ITZ phase and the cement paste phase. Figure 2 displays a micrograph of concrete showing cement paste and interfacial transition zone. Points A an B represent locations of nanoindentation. A total of 20 indentations were performed. Here, we present one indentation from each phase only. A nano-positioning technique was used to position the indenter within 10 nm from the aggregate surface. The use of nano-positioning technique is critical for indentation at the ITZ due to the need to accurately locate the indenter tip within the a few nanometres from the aggregate surface to ensure that the indentation lies in the ITZ. The ITZ is known to be the zone 50 um wide around the aggregate (Mehta and Monterio, 2006). 2.4 Experimental analysis The load-indentation data was analysed after Oliver and Pharr (1992). Properties of indented material are derived from the unloading portion of the load-depth curves gathered during nanoindentation experiments. The major parameters used in this analysis include the maximum load P max, depth at max load h max, contact depth h c, displacement of the surface at the perimeter of the indent h s and the initial unloading contact stiffness S. Figure 3 shows the parameters used for nanoindentation analysis. The total indentation depth is defined as the sum of h c and h s hmax = hc + hs (1) The contact area is then determined by relating the cross-sectional area to the distance from the indenter tip. Typically the contact area for a Berkovich indenter A is given as A 2 = h (2) 24.5 c where h c equals h max h s from (1). Once the contact area is computed, the hardness of the specimen can then be computed. The hardness is defined as the ratio of P max to A. Pmax H = (3) 2 24.5h c Nanoindentation also allows evaluating the stiffness of the indented material represented by Young s modulus of elasticity. Here, the term reduced modulus is used in lieu of Young s modulus to express the affect of the indenter stiffness on measurements. The reduced modulus E r can be derived from equation (4) 2 2 1 1 v 1 v' = + (4) E E E' r where ѵ is Poisson s ratio and E is the Young s modulus of the indented phases and v' and E ' are the corresponding values for the indenter, typical values for diamond are 1141 GPa and 0.07 for Young s modulus and Poison s ratio, respectively. Considering the above geometrical relation, E r can be defined as E r = π S 2β 24.5 h 2 c (5)
Experimental and numerical nano-characterisation 139 where β represents the correction factor equal to 1.034 for the Berkovich indenter (Fischer-Cripps, 2004). Determining S requires curve fitting of the loading and unloading curves using a power function. For the unloading portion of the curve, the relation can be described as P h h r 2 = ω( ) (6) ω is a curve fitting constant. Expanding this equation gives a quadratic equation with three constants A, B, and C. 2 P A( h) B( h) C = + + (7) A, B, and C are determined by curve fitting. The slope of the unloading curve (S) can be computed as the gradient of the power function at maximum depth. dp S = hmax = 2A hmax + B (8) dh The elastic, total and plastic energies denoted U e, U t and U p can be defined as the areas under the unloading curves, loading curves and the difference between them. These energies can be calculated as U t h max = P ( h) dh (9) 0 L U e hmax = P ( h) dh (10) hr u Up = Ut Ue (11) where P L represents loading function and P U unloading function. Figure 3 Schematic representation of loading and unloading curves in nanoindentation showing parameters for material characterisation (see online version for colours) Notes: α is the vertical semi-angle of Berkovich pyramid of 65.27.
140 A.K. Reinhardt et al. 3 Numerical methods 3.1 Finite element model The nanoindentation experiments performed on the two phases were simulated using finite element method (FEM). A three dimensional (3D) finite element (FE) model was created in the ANSYS finite element program (ANSYS, 2007). The model exploited symmetry conditions of the indentation pyramid. Therefore, only one third of the specimen and one third of the nano-indenter tip were modelled. Since a Berkovich indenter tip was used in experiment, an axis-symmetric cone of semi angle of 70.3 with respect to the vertical was modelled. This is the equivalent cone angle that has the same area to depth relationship to a three-sided Berkovich pyramid with a vertical semi-angle (α) of 65.27 o (cf. Fisher-Cripps, 2004). The specimen is represented by an extruded triangle with dimensions including a base of 350 μm, a height of 100 μm and an extrusion depth of 100 μm. This reduces the effects of both the boundaries and the indentation effects upon the accuracy of the solution (Fischer-Cripps, 2004). An isometric image of the 3D finite element model is shown in Figure 4. Figure 4 FE model of nanoindentation showing one third of the Berkovich indenter and the FE mesh of indented material (see online version for colours) The FE model utilised three different types of elements in order to simulate the contact mechanics and the non-linear behaviour of the indented material. Soli 45 (ANSYS, 2007) was used to model both concrete phases. The element was defined with eight nodes in a cubic element and the element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities. Targe 170 is a target contact element used to simulate the surface of the indenter tip. The target surface was assumed to have infinite stiffness due to the fact that the Berkovich tip is made of diamond and the stiffness of diamond is much higher than the stiffness of all other modelled cement phases. Finally, another contact element, Conta 174, was used to simulate the surface of the modelled phases and perform the contact analysis (ANSYS, 2007). A total of 3462 nodes and 16,489 elements were used to model the nanoindentation process. The elements were refined at the contact region as shown in Figure 4 to increase the accuracy of the solution and aid in convergence.
Experimental and numerical nano-characterisation 141 Boundary conditions and loads were applied to the FE model to simulate the symmetry of the one third representations. The bottom of the model was restricted from translating in the vertical direction. A displacement control was placed on the indenter tip in which the tip was restricted to displace in the vertical direction only. The indenter tip was displaced 600 nm in the vertical direction and then unloaded back to zero using 0.5 nm increments. An elastic perfectly-plastic stress-strain curve was used to represent the material properties of both microstructural phases of concrete. The stress-strain models of both phases are shown in Figure 5. The stress-strain of both phases was inferred through an iterative process to reduce the error between predicted and measured load-indentation curves during loading and unloading. A Poisson s ratio of 0.25 based on published cement properties was used (Haecker et al., 2005). Specific FE solution controls were implemented in the simulation to ensure convergence. The displacements were applied 0.5 nm per load step for a total of 2400 load steps. If the load step is too large the equivalent plastic strain will exceed the maximum strain and the solution will not converge. The minimum load step size was set as 0.001 so that if the FE solution did not converge in 0.5 nm increments the solution could bisect and use small increments within the load step. A pre-condition solver was used to calculate the non-linear solution. The maximum number of equilibrium iterations was set at 100. Automatic time stepping was used and the Newton-Raphson method was implemented. Figure 5 Inferred stress-strain relationships of continuum cement paste and ITZ used for nanoindentation simulation 2 1.5 Cement Paste ITZ Stress (nn/nm 2 ) 1 0.5 0 0 0.05 0.1 0.15 0.2 Strain (nm/nm) 4 Results and discussions Figure 6 shows load-indentation curves for loading and unloading for the two phases ITZ and cement paste. The significant difference of the response between the two phases is very obvious. The cement paste has much higher stiffness than that of the ITZ. Table 2 presents the mechanical properties of the cement paste and ITZ phases as computed by analysing the load-indentation curve of both phases. The ITZ showed a
142 A.K. Reinhardt et al. significantly higher depth of indentation for a lower load compared with that of the paste. The ITZ phase also has a much lower reduced modulus E r than that of cement paste. Moreover, the hardness for the ITZ was much lower than that of the paste region. The ITZ was not able to absorb as much energy as the cement phase. It is important to realise that statistical analysis of multiple indentations would be necessary for quantitative analysis of each phase given the well known variation within each phase. We present here analysis and simulation of a single representative point for proof of concept. Table 2 Characteristics of the two indented phases as inferred from nanoindentation analysis ITZ Cement paste E r (GPa) 13 55 H (GPa) 0.23 3.6 U p (nj) 0.69 5.2 The data simulated by the FE model for the cement paste and the ITZ phases are shown in Figures 7 and 8, respectively. For both cases the FE simulation environment was capable of accurately modelling the nanoindentation process. The elastic perfectly-plastic stress-strain curves (Figure 5) for both phases were capable of representing the constitutive relationship for these two phases at the nano-scale. It should be mentioned that these stress-strain curves are not necessarily equivalent to the stress strain curves of these materials at the macro-scale. However, they might provide some insight on the magnitudes of Young s modulus and the pseudo yield phenomenon of these phases at this length scale. Size effect plays an important role at the macroscale resulting in significant reduction of bulk material strength and stiffness due to microdefects (Bažant and Planas, 1997). Figure 6 Load indentation curves for two microstructural phases of concrete as measured in nanoindentation experiments (see online version for colours) 25 20 Cement Paste ITZ Load (mn) 15 10 5 0 0 100 200 300 400 500 600 700 Indentation Depth (nm)
Experimental and numerical nano-characterisation 143 Figure 7 Experimental and numerical load-nanoindentation curves for cement paste phase A (see online version for colours) 25 20 Experimental Numerical Load (mn) 15 10 5 0 0 100 200 300 400 500 600 700 Indenation Depth (nm) Figure 8 Experimental and numerical load-nanoindentation curves for ITZ phase B (see online version for colours) It shall also be pointed out that the maximum load required for producing a 600 nm indentation depths using a Berkovich indenter tip were 2.2 mn for phase B and 22 mn for phase A, respectively. The FE model calculates a lower required load during the indentation loading. The difference between experiment and simulation loads was less than 5%. The FE analysis enables inferring the constitutive relation of the material at that nano-scale providing valuable information for microstructural modelling. The validated FE model is then used to extract von Mises stresses and principal stress and strains. The von Mises stress distribution after unloading for the ITZ phase is shown in Figure 9.
144 A.K. Reinhardt et al. It is important to note that performing an indentation in the cement paste or the ITZ phases can result in indenting one of many materials such as CSH, CH or unhydrated cement particles. It was not possible to identify this material at the time of indentation using the available nanoindentation technology. Two approaches can be used to address this problem. One, by performing many indentations (such as those reported by Constantinides and Ulm, 2004), categories of the indented phases can then be established using statistical clustering techniques. This can help in determining the volume fraction of each material and the mean mechanical property of this material (e.g. high and low density CSH). Another method is by comparing the observed mechanical properties to the mechanical properties of these materials as tested independently in the literature. The second approach is used here. The indentation at point A in the cement paste showed a reduced elastic modulus of 55 GPa indicating that such indentation occurred in CSH. On the other hand, indentation at point B in the ITZ zone showed a reduced elastic modulus of 13 GPa which lies within the values reported for the modulus of elasticity of CH (5 15 GPa) (Beaudoin, 1983). It is therefore suggested that the two materials indented and modelled at points A in the cement paste and point B in the ITZ are CSH and CH, respectively. Finally, we present a methodology for mechanical characterisation of the different microstructural phases of concrete. Such attempts are crucial for enabling multi-scale modelling for microstructural optimisation of concrete (Torquanto, 2002). The proposed method can further be used to realise the influence of nano-particles such as nano-silica, nano-rubber, nano-carbon fibres and carbon nanotubes on the mechanical properties of the different phases of concrete. Statistical analysis of a grid of nanoindentations of each phase shall enable realising the significance of nano-particles on the mechanical performance of that phase. Moreover, this method could lead to a better understanding of how different phases of concrete at the nano-scale affect the mechanical properties at the macro-scale. Figure 9 von Mises stress distribution in phase B ITZ after unloading (see online version for colours)
Experimental and numerical nano-characterisation 145 5 Conclusions We presented experimental and numerical methods to mechanically-characterise individual representative points in the cement paste and ITZ. The cement paste (most likely CSH) has superior mechanical properties at the nano-scale compared with the ITZ (most likely CH) showing higher reduced elastic modulus, higher hardness and higher plastic energy absorption. The FE method was capable of simulating the nanoindentation behaviour at both points with very good accuracy. Acknowledgements This research was funded by Defense Threat Reduction Agency (DTRA) grant number HDTRA1-07-1-0036 to UNM. The authors greatly acknowledge this support. The authors would like to extend their gratitude to Micromaterials Inc., UK for their valuable help. References ANSYS (2007) Ansys Reference Manual, Version 10.0, available at http://www.ansys.com. Bažant, Z.P. and Planas, J. (1997) Fracture and Size Effect in Concrete and Other Quasibrittle Materials, CRC Press, Boca Raton, FL, USA. Beaudoin, J.J. (1983) Comparison of mechanical properties of compacted calcium hydroxide and Portland cement paste systems, Cement and Concrete Research, Vol. 13, No. 3, pp.319 324. Constantinides, G. and Ulm, F-J. (2004) The effect of two types of C-S-H on the elasticity of cement-based materials: results from nanoindentation and micromechanical modeling, Cement and Concrete Research, Vol. 34, No. 1, pp.67 80. Fisher-Cripps, A.C. (2004) Nanoindentation, Second Edition, Springer, NY, USA. Gmira, A., Zabat. M., Pellenq, R.J-M. and Van Damme, H. (2004) Microscope physical basis of poromechnical behavior of cement-based materials, Materials and Structures, Vol. 37, No. 265, pp.3 14. Haecker, C-J., Garboczi, E.J., Bullard, J.W., Bohn, R.B., Sun, Z., Shah S.P. and Voigt T. (2005) Modeling the linear elastic properties of Portland cement paste, Cement and Concrete Research, Vol. 35, No. 10, pp.1948 1960 Jennings, H.M. (2004) Colloid model of C-S-H and implications to the problem of creep and shrinkage, Materials and Structures, Vol. 37, pp.59 70. Mehta, K. and Monterio, P.J.M. (2006) Concrete: Microstructure, Properties and Materials, Third Edition, McGraw-Hill Professional, NY, USA. Mondal, P., Shah, S.P. and Marks, L. (2008) Nanoscale characterization of cementitious materials, ACI Materials Journal, Vol. 105, pp.174 179. Oliver, W.C. and Pharr, G.M. (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation, Journal of Materials Research, Vol. 7, No. 6, pp.1564 1583. Sonebi, M. (2008) Utilization of micro-indentation technique to determine the micromechanical properties of ITZ in cementitious materials, ACI SP-254, Nanotechnology of Concrete, Sobolev & Shah Eds., pp.57 67. Torquauto, S. (2002) Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Springer-Verlag, NY, USA.
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