The effect of the packing density on the indentation hardness of cohesive-frictional porous materials

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2006.Includes bibliographical references (p. 170-178).Natural composites in general and sedimentary rocks in particular are highly heterogeneous materials which defy a straightforward implementation of the materials science paradigm of microstructure-properties-performance correlation. The application of nanoindentation to natural composites has provided the geomechanics community with a new versatile tool to test in situ phase properties and structures of geomaterials that cannot be recapitulated ex situ in bulk form. But it requires a rigorous indentation analysis to translate indentation data into meaningful mechanical properties. The development and implementation of such an indentation analysis for the strength properties of cohesive-frictional porous materials is the focus of this thesis. We report the development and implementation of a multi-scale indentation analysis based on limit analysis, which makes it possible to infer from an experimental hardness value and the solid's packing density the strength properties of the cohesive-frictional porous material.(cont.) Making use of most recent advances in non-linear strength homogenization theory, we implement a homogenized cohesive Cam-Clay type elliptical strength criterion which takes into account the strength properties of the constituents (cohesion and friction), the porosity and the microstructure, into a yield design approach to indentation analysis. Making use of the strong duality of the lower and upper bound theorem, we identify the resulting upper bound problem as a Second-Order Conical optimization problem, for which advanced solvers such as MOSEK became recently available. The originality of our approach lies in the combination of finite element discretization and advanced optimization techniques, which is readily implemented in standard tools of computational mechanics, such as MATLAB. The upper bound yield design solutions are benchmarked against solutions from comprehensive elastoplastic contact mechanics finite element solutions and compared with lower bound solutions, which all show an excellent agreement.(cont.) Furthermore, from a detailed parameter study based on intensive computational simulations, we show that it is possible to condense the indentation hardness-material properties relation of cohesive-frictional porous materials into a single hardness-packing density scaling relation. On this basis, it is possible to use the hardness-packing density scaling relation for reverse analysis of the strength parameters of cohesive-frictional solids from indentation. The procedure is illustrated for shale materials. From hardness values of six shale materials of different packing density and mineralogy, we deduce that the clay fabric in highly compacted shales is most likely a purely cohesive (friction-less) nano-granular material, having a uniaxial strength of roughly 440 MPa.by Sophie Cariou.S.M