Nanomechanical Explorations of Cementitious
Materials: Recent Results and Future
Perspectives
G. Constantinides, J.F. Smith, and F.-J. Ulm1
Abstract. Recent progress in experimental and theoretical nanomechanics makes
it possible to revisit the response of ubiquitous construction materials, like
concrete, reevaluate our existing knowledge and understanding, and device methodologies to optimize their macroscopic performance. Particularly, the advent of
instrumented indentation and the advancement of homogenization methods provide the mechanics community an unprecedented opportunity to probe the mechanical behavior of structural materials at the nanoscale (with length-resolution
in the nanometer and force-resolution in the nanoNewton) and quantitatively convey these information at the macroscopic scale. Furthermore, the capabilities offered in a spatial and temporal domain by these advanced instruments allow the
investigation of a number of additional phenomena: interface mechanics, strainrate effects, high temperature response, sources of anisotropy, chemo-mechanical
effects, etc. We here show the validation of a fluid cell module that allows acquisition of nanomechanical data in liquids.
1 Introduction
Recent advances in modeling [12, 17] allow one to upscale the mechanical response of complex heterogeneous material systems (concrete being an example)
G. Constantinides
Department of Mechanical Engineering and Materials Science and Engineering,
Cyprus University of Technology, Lemesos, CY
e-mail: [email protected], [email protected]
J.F. Smith
Micro Materials Ltd, Wrexham, UK
e-mail: [email protected]
G. Constantinides and F.-J. Ulm
Department of Civil and Environmental Engineering, Massachusetts
Institute of Technology, Cambridge, MA, US
e-mail: [email protected]
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G. Constantinides et al.
and obtain effective properties that can be used in structural mechanics applications. Upscaling techniques may vary from analytical, namely continuum micromechanics, to numerical, namely finite element solutions, utilizing in the process
physicochemical models that analytically [18] or digitally [1] synthesize microstructures. Such approaches, which have their origin at the level of the individual
chemical constituents of the composite material, provide a direct link between
physical chemistry and mechanics [9, 11]. Furthermore, they allow one to trace
the origin of chemo-mechanical degradation at the length scale where the chemical reactions occur [9]. A common requirement to all modeling approaches is the
need for intrinsic mechanical properties of the individual constituents composing
the composite material, and their temporal response as chemical softening or stiffening occurs. In the case of concrete, the main constituent phase that governs the
macroscopic response (Calcium Silicate Hydrates or in short C-S-H) manifests itself in the nm to µm length scale [14]. This constituent phase cannot be recapitulated effectively ex-situ; one has to, therefore, access the mechanical properties of
C-S-H in-situ at the length scale where it can be naturally found [11]. The advent
of instrumented indentation provided an unprecedented opportunity to probe the
mechanical response of these phases and incorporate the results in micromechanical models that can deliver the composite response. Herein we show recent results
on C-S-H mechanics and recent developments on nanoindentation that might allow further refinements on our understanding and future material optimization.
2 Nanomechanics of C-S-H
The advent of instrumented indentation enabled fundamental studies in the
nanomechanical response of metals, ceramics, polymers and composites (see i.e.,
[2]). Current technology allows for contact-based deformation of nanoscale load
and displacement resolution and has been leveraged for both general mechanical
characterization of small materials volumes and unprecedented access to the physics and deformations processes of materials. While nanoindentation was originally
developed for homogeneous metals and ceramics it was quickly appreciated that
nanoscale resolution can be of significant use to the decoding of C-S-H structure,
the binding phase of all cementitious materials. However, accurate nanomechanical analysis of natural composites requires advanced analysis that takes into
consideration the multi-phase, multi-scale nature of the material and its pressure
sensitive mechanical response [8, 10, 11, 13].
A typical nanoindentation test consists of establishing contact between an indenter (typically diamond) and a sample, while continuously measuring the load,
P and the penetration depth h. Analysis of the P-h response proceeds by applying
a continuum scale model [2] to derive the indentation modulus M and indentation
hardness H:
Nanomechanical Explorations of Cementitious Materials
M=
π
2
H=
S
Ac
Pmax
Ac
65
(1)
(2)
where S is the unloading slope at maximum depth hmax, Pmax is the maximum indentation force, and Ac is the projected contact area at hmax. Several empirical means to
estimate Ac exist, either through post-indentation inspection, geometric idealizations of the probe, or more commonly through analysis of the indentation response
for a materials of ostensibly known E and H to determine this area as a function of
Ac =Α(hc). These indirect means of geometry estimation work reasonably well but
can be subject to errors for nanoscale indentations, h <200nm. A more rigorous
approach was recently proposed [6, 22] in which one can determine directly Ac by
recourse to atomic force microscopy (AFM) images of the indenter probe. An example of AFM imaging of a Berkovich probe is shown in Fig. 1.
Fig. 1 AFM image of a Berkovich nanoindenters probe (a) and the resulting cross-sectional
area as a function of the distance from the apex (b)
Equations 1 and 2 rely on the assumption of a semi-infinite half-space and
therefore caution should be taken when testing highly heterogeneous materials. In
particular, the number of tests should be significantly increased and the choice of
indentation depth should be carefully chosen [7, 8]. The two indentation properties
measured during a test (M, H) can then be linked to the elastic M=M(E, v) and
plastic H=(c, φ) properties of the indented materials, through advanced continuum
scale models [2, 13]. The extracted mechanical properties of the two types of C-SH measured on hundreds of specimens where found to be intrinsic to all cementbased materials (see Table 1 [11]).
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G. Constantinides et al.
Table 1 Nanomechanical properties of a low density (C-S-HLD) and a high density (C-SHHD) Calcium-Silicate-Hydrate found in all cementitious materials
C-S-HLD
C-S-HHD
Elastic Modulus, E [GPa]
Angle of Friction, φ [º]
21
31
12
12
Cohesion, c [MPa]
130
220
The fundamental mechanical properties of C-S-H together with estimates of the
volumetric proportions (fi) of all constituent phases (i) were incorporated in a
multi-scale homogenization scheme that can predict the composite macroscopic
elastic (Ehom,vhom=F(Ei,vi,fi)) and strength (chom, hom=F(ci, i,fi)) behavior [11, 12, 17],
where the only input requirements are the elastic (Ei,vi) and plastic (ci, i) properties
of the individual constituents and their volumetric proportions (fi). The morphological arrangement of the phases in space is taken into consideration in the choice
of the continuum micromechanical models. It has been found that for cementitious
materials a combination of Mori-Tanaka and Self-Consistent schemes appears to
deliver robust results [11]. Figure 2 demonstrates the predictive capabilities of the
proposed models.
Fig. 2 Micromechanical predictions and experimental data of the elastic (a) and uniaxial
strength (b) properties of cementitious materials
3 Advancements on Instrumented Nanoindentation
Instrumented nanoindenters are currently going through a phase of optimization
and as a consequence their performance is constantly reevaluated and improved.
New developments include the capabilities of high temperature testing (up to
800ºC) [5], high strain-rate testing [3, 5], indentation in liquids [4] or controlled
humidity environments, etc. On the theoretical side our understanding is improved
and new continuum models allow now analysis of indentation data on layered
systems, adhesive contact, anisotropic systems, cohesive-frictional materials,
visco-elastic-plastic materials, etc [13, 15, 16, 19, 20, 21]. Due to space constrains
Nanomechanical Explorations of Cementitious Materials
67
we here focus on the fluid-cell module extension that allows mechanical measurements of materials in liquid.
Figure 3 presents a straightforward modification of instrumented indentation
platform that allows acquisition of nanoscale force-displacement data in liquid
media without artifacts of buoyancy or surface tension. The indenter mount for
liquid cell applications is comprised of a stiff, corrosion resistant, stainless steel.
As shown in Fig.3a the extended indenter is immersed within the liquid cell. In
practice, this fluid cell inclusive of mounted samples is maneuvered into position
via automated stage displacement, and the indenter automatically contacts the
probe. Liquids can be added before or after this operation, and also exchanged intermittently.
We here demonstrate the validity of nanoindentation in fluid via elastoplastic
analysis of relatively stiff (E > 1000 kPa), water-insensitive materials (Borosilicate Glass and Polypropylene). We then consider the viscoelastic response and
representative mechanical properties of compliant, synthetic polymeric hydrogels
and biological tissues (E < 500 kPa). Examples from indentations on watersaturated synthetic (hydrogels) and natural materials (porcine liver and skin) are
presented. The elastic properties of the tested materials are in good agreement
with macroscopic data found in the literature, validating the accuracy of the proposed fluid-cell module and demonstrating its ability for nanoscale characterization of hard and soft systems in the kPa to GPa range. These capabilities can be of
great importance in the poromechanical and chemomechanical studies of construction materials, including cementitious composites, geomaterials and many more.
Fig. 3 (a) Schematic diagram of the fluid cell module extension. (b) Measured and literature
values of the tested hydrated specimens: borosilicate glass, polypropylene, porcine liver,
porcine skin, and PAAm-gels in various mol concentrations
4 Concluding Remarks
The field of nanoscale indentation mechanics is advancing in a rapid pace. As the
tools of experimentation and the resulting theoretical frameworks of data analysis
are developing, new opportunities for materials understanding and characteriza-
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G. Constantinides et al.
tion arise. This provides an unprecedented opportunity to probe long-used ubiquitous construction materials that have not been rigorously characterized and
modeled in the past and create a science-based platform for material optimization.
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