Cement is the most widely used manufacturing material in the world and improving its toughness would allow for the design of slender infrastructure, requiring less material. To this end, we investigate by means of molecular dynamics simulations the fracture of calcium-silicate-hydrate (C-S-H), the binding phase of cement, responsible for its mechanical properties. For the first time, we report values of the fracture toughness, critical energy release rate, and surface energy of C-S-H grains. This allows us to discuss the brittleness of the material at the atomic scale. We show that, at this scale, C-S-H breaks in a ductile way, which prevents from using methods based on linear elastic fracture mechanics. Knowledge of the fracture properties of C-S-H at the nanoscale opens the way for an upscaling approach to the design of tougher cement.

In this work we study role of kerogen in the fracture properties of organic-rich shales, and in particular in the ductility of shales. The presence of kerogen and clays in shale is known to increase the ductility. We propose here a multiscale approach to develop of a fine understanding of shale ductility from the molecular scale. We develop and validate a methodology at the molecular scale that can capture the toughness and ductility of a material. We apply this methodology successfully to a silica polymorph and to a kerogen analog, and we confirm the significant ductility of kerogen. Interestingly the silica-kerogen interface exhibits a similar ductility, which is central for the properties of the heterogeneous shale. Finally, we consider a tentative upscaling considering the pull out phenomenon as a likely mechanism of fracture of the shale.

The elastic and failure properties of a typical clay, illite, are investigated by means of molecular simulation. 2 We employ a reactive (ReaxFF) as well as a non-reactive (ClayFF) force field to assess the elastic properties 3 of the clay. As far as the failure properties are concerned, ReaxFF was used throughout the study, however 4 some calculations were also performed with ClayFF. A crack parallel to the clay layers is found to have low 5 fracture resistance (equivalent fracture toughness K Ic = 0.09 MPa.m 1/2) when submitted to a tensile loading 6 perpendicular to the crack (mode I). The nanoscale mechanism of both yield and fracture failures is 7 decohesion in the interlayer space, and the critical energy release rate characterizes both failures. In contrast, 8 under shear loading (mode II), the nanoscale failure mechanism is a stick-slip between clay layers. No fracture 9 propagation is observed as the clay layers slide on top of each other. The low fracture resistance in mode I and 10 the stick-slip failure in mode II are both the consequence of the lack of chemical bonds between clay layers 11 where the cohesion is provided by electrostatic interactions only. We also consider the mode I loading of a 12 crack perpendicular to the clay layers and find that, in this case, the material exhibit strain softening as the 13 result of the clay layers breaking one after the other. In this orientation illite displays a much higher fracture 14 resistance (0.61 MPa.m 1/2) due to the breaking of chemical bonds involved when fracturing in this direction. 15 This work, which provides a description of the failure properties of clays at the microscopic scale, is a first 16 step needed to describe the failure of clays at a larger scale where the polycrystalline distribution of clay 17 grains is a key parameter that must be taken into account.

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The inherent computational cost of molecular simulations limits their use to the study of nanometric systems with potentially strong size effects. In the case of fracture mechanics, size effects due to yielding at the crack tip can affect strongly the mechanical response of small systems. In this paper we consider two examples: a silica crystal for which yielding is limited to a few atoms at the crack tip, and a nanoporous polymer for which the process zone is about one order of magnitude larger. We perform molecular simulations of fracture of those materials and investigate in particular the system and crack size effects. The simulated systems are periodic with an initial crack. Quasi-static loading is achieved by increasing the system size in the direction orthogonal to the crack while maintaining a constant temperature. As expected, the behaviors of the two materials are significantly different. We show that the behavior of the silica crystal is reasonably well described by the classical framework of linear elastic fracture mechanics (LEFM). Therefore, one can easily upscale engineering fracture properties from molecular simulation results. In contrast, LEFM fails capturing the behavior of the polymer and we propose an alternative analysis based on cohesive crack zone models. We show that with a linear decreasing cohesive law, this alternative approach captures well the behavior of the polymer. Using this cohesive law, one can anticipate the mechanical behavior at larger scale and assess engineering fracture properties. Thus, despite the large yielding of the polymer at the scale of the molecular simulation, the cohesive zone analysis offers a proper upscaling methodology.