Christian G. Hoover

Mesoscale texture of cement hydrates

Significance Calcium–silicate–hydrate (C–S–H) nanoscale gels are the main binding agent in cement and concrete, crucial for the strength and the long-term evolution of the material. Even more than the molecular structure, the C–S–H mesoscale amorphous texture over hundreds of nanometers plays a crucial role for material properties. We use a statistical physics framework for aggregating nanoparticles and numerical simulations to obtain a first, to our knowledge, quantitative model for such a complex material. The extensive comparison with experiments ranging from small-angle neutron scattering, SEM, adsorption/desorption of N2, and water to nanoindentation provides new fundamental insights into the microscopic origin of the properties measured. Strength and other mechanical properties of cement and concrete rely upon the formation of calcium–silicate–hydrates (C–S–H) during cement hydration. Controlling structure and properties of the C–S–H phase is a challenge, due to the complexity of this hydration product and of the mechanisms that drive its precipitation from the ionic solution upon dissolution of cement grains in water. Departing from traditional models mostly focused on length scales above the micrometer, recent research addressed the molecular structure of C–S–H. However, small-angle neutron scattering, electron-microscopy imaging, and nanoindentation experiments suggest that its mesoscale organization, extending over hundreds of nanometers, may be more important. Here we unveil the C–S–H mesoscale texture, a crucial step to connect the fundamental scales to the macroscale of engineering properties. We use simulations that combine information of the nanoscale building units of C–S–H and their effective interactions, obtained from atomistic simulations and experiments, into a statistical physics framework for aggregating nanoparticles. We compute small-angle scattering intensities, pore size distributions, specific surface area, local densities, indentation modulus, and hardness of the material, providing quantitative understanding of different experimental investigations. Our results provide insight into how the heterogeneities developed during the early stages of hydration persist in the structure of C–S–H and impact the mechanical performance of the hardened cement paste. Unraveling such links in cement hydrates can be groundbreaking and controlling them can be the key to smarter mix designs of cementitious materials.

Fracture toughness of calcium-silicate-hydrate from molecular dynamics simulations

Abstract Concrete is the most widely manufactured material in the world. Its binding phase, calcium–silicate–hydrate (C–S–H), is responsible for its mechanical properties and has an atomic structure fairly similar to that of usual calcium silicate glasses, which makes it appealing to study this material with tools and theories traditionally used for non-crystalline solids. Here, following this idea, we use molecular dynamics simulations to evaluate the fracture toughness of C–S–H, inaccessible experimentally. 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 one from using methods based on linear elastic fracture mechanics. Knowledge of the fracture properties of C–S–H at the atomic scale opens the way for an upscaling approach to the design of tougher cement paste, which would allow for the design of slender environment-friendly infrastructures, requiring less material.

Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests

The universal size-shape effect law is a law that describes the dependence of nominal strength of specimen or structure on both its size and the crack (or notch) length, over the entire range of interest, and exhibits the correct small-size and large-size asymptotic properties as required by the cohesive crack model (or crack band model). The main difficulty has been the transition of crack length from 0, in which case the size effect is Type 1, to deep cracks (or notches), in which case the size effect is Type 2 and is fundamentally different from Type 1, with different asymptotes. In this transition, the problem is not linearizable because the notch is not much larger than the fracture process zone. The previously proposed universal law could not be verified experimentally for the Type 1-Type 2 transition because sufficient test data were lacking. The current study is based on recently obtained comprehensive fracture test data for three-point bend beams cast from one batch of the same concrete and cured and tested under identical conditions. The test data reveal that the Type 1-Type 2 transition in the previous universal law has insufficient accuracy and cannot be captured by Taylor series expansion of the energy release rate function of linear elastic fracture mechanics. Instead, the size effect for a zero notch and for the transitional range is now characterized in terms of the strain gradient at the specimen surface, which is the main variable determining the degree of stress redistribution by the boundary layer of cracking. The new universal law is shown to fit the comprehensive data quite well, with a coefficient of variation of only 2.3%.

Problems with Hu-Duan Boundary Effect Model and Its Comparison to Size-Shape Effect Law for Quasi-Brittle Fracture

Recent disagreements on the mathematical modeling of fracture and size effect in concrete and other quasi-brittle materials are obstacles to improvements in design practice, and especially in design codes for concrete structures. In an attempt to overcome this impediment to progress, this paper compares the Hu-Duan boundary effect model BEM expounded since 2000 to the size-shape effect law SEL proposed at Northwestern University in 1984 and extended to the geometry or shape effects in 1990. It is found that within a rather limited part of the range of sizes and shapes, the fracture energy values identified by BEM and SEL from the test data on maximum loads are nearly the same. But in other parts of the range the BEM is either inferior or inapplicable. The material tensile strength values identified by BEM have a much larger error than those obtained from the SEL after calibration by the cohesive crack model. From the theoretical viewpoint, several hypotheses of BEM are shown to be unrealistic. DOI: 10.1061/ASCEEM.1943-7889.89 CE Database subject headings: Cracking; Concrete; Structural failures; Data analysis; Size effect. Author keywords: Fracture scaling; Fracture energy; Concrete; Asymptotics of fracture; Cohesive cracks; Failure of structures; Evalu- ation of experimental data.

Comparison of the Hu-Duan Boundary Effect Model with the Size-Shape Effect Law for Quasi-Brittle Fracture Based on New Comprehensive Fracture Tests

The boundary effect model (BEM) for concrete fracture and the effects of specimens size and crack length has previously been criticized on theoretical grounds, but the experimental evidence found in the literature, when taken alone, has been too limited to judge the validity of BEM conclusively. New, separately published, comprehensive fracture experiments, which were made on specimens cast from one and the same batch concrete and featured a broad ranges of both the size and the crack length (including a zero crack length), change the situation. The optimum fit of the data by Hu and Duan’s model shows major deviations from these new test results. On the other hand, the Type 1 and 2 size effect laws (SELs) and their amalgamation in the universal size effect law are found to give a far better fit of the test results. Thus, regardless of the previously expounded theoretical objections, the comparison with experimental evidence alone suffices to conclude that Hu and Duan’s model is not realistic.