Alexander M. Efremov

Connecting the macro and microstrain responses in technical porous ceramics. Part II: microcracking

Following previous study on non-microcracked porous ceramics (SiC and alumina), we studied the micro and macrostrain response of honeycomb porous microcracked ceramics under applied uniaxial compressive stress. Cordierites of different porosities were compared. Both macroscopic and microscopic strains were measured, by extensometry and neutron diffraction, respectively. Lattice strains were determined using a single diffraction peak (steady-state neutron source) in both the axial and the transverse sample directions. Complementarily, we measured the macroscopic Young’s modulus of these materials as a function of temperature, at zero load, using high-temperature laser ultrasound spectroscopy. This allowed having a non-microcracked reference state for all the materials investigated. Confirming our previous study, we observed that macrostrain relaxation occurs at constant load, which is not observed in non-microcracked compounds, such as SiC. This relaxation effect increases as a function of porosity. Moreover, we generally observed a linear dependence of the diffraction modulus on porosity. However, for low and very high applied stress, the lattice strain behavior versus stress seems to be influenced by microcracking and shows considerable strain release, as already observed in other porous microcracked ceramics. We extended to microcracked porous ceramics (cordierite) the macro to microstrain and stress relations previously developed for non-microcracked ceramics, making use of the integrity factor (IF) model. Using the whole set of data available, the IF could also be calculated as a function of applied stress. It was confirmed that highly porous microcracked materials have great potential to become stiffer and more connected.

Thermal and Mechanical Response of Industrial Porous Ceramics

In this study, the mechanical behavior of porous thermally microcracked ceramics has been compared with that of solely porous materials, under compressive applied stress. The different aspects of the micro and macroscopic stress-strain curves have been inserted into a coherent analytical model and compared with finite element modeling calculations. The agreement between experiments and models is very good. It is shown that mechanical microcracking, as opposed to thermal, introduces an irreversible aspect in the deformation mechanisms of porous ceramics. In this concern, mechanical loads differentiate themselves from thermal cycling. This leads for instance to a change of the Young’s modulus as a function of applied load, which qualifies those materials as visco-elastic.

Modeling the impact of microcracking on the thermoelasticity of porous and microcracked ceramics

The foundations of the Integrity Factor Model are laid down and the model is discussed. The calculation of the internal stresses in microcracked materials (as a function of temperature) is done on the basis of both the macroscopic dilation and the lattice expansion measured by diffraction. The derivation is made starting from first principles for a single crystal, and then extending the approach to polycrystals, including complex microstructures, such as those containing porosity, microcracks, and multiple phases. Focus is cast on the fundamentals of the relationship between material properties and microstructure of anisotropic crystals, and on the resulting macroscopic behavior. The model is validated against experimental data, with the examples of the microcracked β-eucryptite and porous microcracked aluminum titanate composite.

Macro to Micro Stress and Strain Conversion in Porous Ceramics

In this work, we propose an analytical model, capable of distinguishing the contribution of porosity, pore morphology and solid domain properties to the macroscopic elasticity of a porous ceramic material. A practical method is shown for the evaluation of the dense material elastic properties in porous (and microcracked) polycrystalline materials, making use of in-situ neutron diffraction experiments. By this method, axial and transverse microstrains measurements can reveal the average values for Young’s modulus and Poisson’s ratio of the dense material, as well as the value of pore morphology at known porosity. The approach has been validated on porous SiC. Finite Element Modeling is shown to allow calculating the three-dimensional strain and stress state under applied uniaxial stress, highlighting that small but finite shear stresses arise. Stress-strain curves of porous and microcracked materials have been generated, which correlate qualitatively well with the measured properties and can be used for quantitative numerical simulation of the materials strength. Predictions of FEM coincide very well with analytical calculations, thus corroborating the validity of the analytical method proposed.