Cement based materials are the dominant construction materials in the world [1
]. Since cement paste is the most basic and complex component of these materials, the understanding of its mechanical properties and fracture behaviour is of significant practical importance and scientific interest. Contrary to homogenous isotropic materials, the stress field inside this highly heterogeneous material is not uniform even under uniform loading, which leads to microcracking at a number of locations prior to crack localization [2
]. These microcracks eventually develop and coalesce to form a critical macrocrack leading to the failure of this material at a low strain level.
Since the critical scale for studying and understanding the fracture behaviour of cement paste is the microscale [2
], researchers have tried various methods to simulate the fracture performance and mechanical properties of cement at this scale. In these approaches, two aspects should be included. The first one is how to obtain a realistic microstructure. This can be achieved by numerical models or experiments. Compared with experiments, the computer generated microstructural models, such as cement hydration model, are easier and faster. However, cement particles are commonly simulated as spheres [3
], which will influence the simulated hydration of cement [6
]. Therefore, although the experimentally obtained microstructure has a disadvantage in terms of spatial resolution, the realistic particle shape and phase distribution after the onset of hydration can be captured. Over the past decades, huge advances have been made in microstructural characterisation techniques. A good resolution of the microstructure can be provided by using backscattered electron imaging (BSE) in the scanning electron microscope (SEM) [7
]. However, the main shortcoming of this technique is the lack of 3D information. To overcome this, X-ray microcomputed tomography (μCT), which provides a non-destructive way of obtaining three dimensional information on the interior of materials, has been applied in the study of cement based materials over the last two decades [8
]. By applying synchrotron radiation as the X-ray source, an improved resolution of between 0.5 and 1.0 μm for cement-based materials can be achieved [11
], which provides very detailed information about the 3D microstructural evolution of these materials.
The second aspect is how to include the local micromechanical properties of different phases in cement paste. Usually micromechanical properties of different phases are derived from standard nano-indentation measurements [14
]. Meanwhile, an alternative way is to use molecular dynamics simulations to calculate the micromechanical properties of cement phases, e.g., Calcium-Silicate-Hydrate (C–S–H) [18
]. Once the microstructure and the micromechanical properties are available, the micromechanical modelling approaches can be applied to simulate the fracture behaviour and mechanical properties of cement paste. Generally, the micromechanical modelling approaches can be classified in two categories: continuum approaches and discrete (lattice) approaches. Although continuum approaches are more widely used to predict the elastic properties of cement paste [20
], they have inherent difficulties when dealing with strain localization (fracture) processes. On the other hand, lattice models show a great advantage because not only the stress-strain response, but also cracks pattern and microcracks propagation, can be simulated [24
]. Continuum material behaviour can be, with certain limitations, reproduced by this class of models [27
]. In lattice models, the continuum is replaced by a lattice system of beam elements and the crack growth is realized by using a sequentially-linear solution procedure [29
]. This procedure implies performing a linear elastic analysis in every step; then, a single element with the highest stress/strength ratio is identified and removed from the mesh, thereby introducing a discontinuity; this procedure is then repeated until a global failure criterion is reached. Recently, the fracture process of micro cement paste cubes under uniaxial tension was simulated by Qian et al. [30
] and Lukovic et al. [31
] using the 3D lattice model. In spite of the similar applied simulation strategies, the obtained mechanical properties of cement paste are still not reliable because the relationship between the indentation hardness and the tensile strength (which is one of the main inputs for the model) of individual phases in hydrated cement paste is not known at present. Since inverse calculation of these local properties is possible only when an experiment on specimen size is available and uniaxial tensile testing on the micro-length scale is still impossible to achieve [2
], an important question arising here is how to validate the modelling results.
Recently, a new method named microcube indentation has been developed to test the global mechanical performance of micro cement cubes (100 × 100 × 100 µm3
) using nano-indenter, which provides an unprecedented opportunity for validation of mechanical simulation results at the microscale [32
]. The new method uses nano-indentation equipment to assess the fracture properties of small specimens, unlike regular nano-indentation testing that is used to assess elastic modulus and hardness. This method is further developed and presented in this paper. The method for experimental testing and numerical simulation of specimens on the same size under the same boundary conditions is addressed. The adopted mechanical properties of local phases are evaluated by comparing the simulated damage evolution and load displacement diagram with the experimental observation. In addition, the calibrated model is applied to predict the global mechanical properties of micro cement cube under uniaxial tension. The predicted results are compared with the results of the previous works.
This work presents an approach for the fitting and validation of micromechanical modelling of mechanical properties and fracture mechanism of cement paste. A procedure for micro specimen preparation and testing of global performance using nano-indenter was developed and employed. As a result, fracture pattern under different loading depth and load displacement diagrams were obtained. Two regimes were observed experimentally in the load displacement diagram. Since the displacement control of the nano-indenter equipment is not fast enough to capture the fast decrease in load when the specimen fails, a horizontal line existed in regime (II). Thus, the ascending branch in regime (I) was applied to calibrate the microstructure-informed lattice model. The softening regime was observed in the modelling result.
The 3D lattice model was built up based on a microstructure of cement paste obtained from X-ray computed tomography. The mechanical properties of local phases were calibrated by validating the simulated results with the experimental results. It is shown in this study that the adopted mechanical properties of local phases are critical for the investigation in terms of load displacement response and failure mechanism. Therefore, it is of great importance to fit these parameters by designing experiments on the specimens in the same size as well as under well-controlled boundary conditions.
Furthermore, the calibrated lattice model was applied to predict the fracture performance of the micro cement paste cubes with various w/c ratios under uniaxial tension. Since an experimental method was applied to calibrate the input mechanical properties of local phases, the proposed method in this paper gives more reliable prediction results. The predicted outcome can be used as an input in the multi-scale modelling of the failure mechanism in cement based materials in further study. The method adopted in this study also illustrates a basic investigation for future research to build upon, and an integrity system for the upscaling of the modelling and validation on every scale.