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Microstructure-property connections for porous ceramics: The possibilities offered by micromechanics
(2016)
Microstructure of porous ceramics is highly “irregular”: it comprises pores and microcracks of diverse shapes and orientations.
This makes their quantitative modeling challenging, and one
often resorts to empirical relations containing Fitting Parameters and having somewhat uncertain range of applicability. We review the substantial progress made in modeling of “irregular” microstructures that does not seem to have been sufficiently utilized in the context of ceramics. We discuss the possibilities offered by micromechanics in developing microstructure–property relations for porous microcracked ceramics. After an overview of relevant micromechanics topics, we focus on several issues of specific interest for ceramics: nonlinear stress–strain behavior, effective elastic properties, and thermally induced microcracking. We discuss extraction of microscale Parameters (such as strength of the intergranular cohesion, density of cracks and pores, etc.) from macroscopic data and identify the extent of uncertainty in this process. We also argue that there is no quantitative correlation between fracturing process and the loss of elastic stiffness.
Zirconia-based cast refractories are widely used for glass furnace applications. Since they have to withstand harsh chemical as well as thermo-mechanical environments, internal stresses and microcracking are often present in such materials under operating conditions (sometimes in excess of 1700 °C). We studied the evolution of thermal (CTE) and mechanical (Young’s modulus) properties as a function of temperature in a fused-cast refractory containing 94 wt.% of monoclinic ZrO2 and 6 wt.% of a silicate glassy phase. With the aid of X-ray refraction techniques (yielding the internal specific surface in materials), we also monitored the evolution of microcracking as a function of thermal cycles (crossing the martensitic phase transformation around 1000 °C) under externally applied stress. We found that external compressive stress leads to a strong decrease of the internal surface per unit volume, but a tensile load has a similar (though not so strong) effect. In agreement with existing literature on -eucryptite microcracked ceramics, we could explain These phenomena by microcrack closure in the load direction in the compression case, and by microcrack propagation (rather than microcrack nucleation) under tensile conditions.
The combination of microstructural data with other experimental techniques and with modeling is paramount, if we want to extract the maximum amount of information on porous material properties. In particular, quantitative image analysis, statistical approaches, direct discretization of tomographic reconstructions represent concrete possibilities to extend the power of the tomographic 3D representation to insights into the material and component performance. I will show a few examples of possible use of X-ray tomographic data for quantitative assessment of porosity in ceramics.
Moreover, I will show how not-so-novel 2D characterization techniques, based X-ray refraction, can allow a great deal of insights in the damage evolution in microcracked (and porous) ceramics. I will show how X-ray refraction can detect objects (e.g. microcracks) below its own spatial resolution.
Finally, I will discuss the link between the microstructural findings and the mechanical properties of porous microcracked ceramics.
The effect of porosity and microcracking on the mechanical properties (strength, fracture toughness,Young’s modulus, and fracture energy) and thermal expansion of diesel particulate filter (DPF) gradecordierite materials has been investigated. A method to deconvolute the effect of porosity and microc-racking on Young’s modulus is proposed. In addition, the microcrack density and the pore morphologyfactor are calculated by applying a micromechanical differential scheme. The values of the investigatedmechanical properties are shown to decrease with an increase in porosity, but the thermal expansionvalues are insensitive to porosity. The variation in mechanical properties as a function of porosity leadsto distinct porosity dependence of thermal shock resistance for crack initiation and crack propagationfor DPF grade synthetic cordierite.
A constitutive model for the nonlinear or “pseudoplastic” mechanical behavior in a linear-elastic solid with thermally induced microcracks is developed and applied to experimental results. The model is termed strain dependent microcrack density approximation (SDMDA) and is an extension of the modified differential scheme that describes the slope of the stress-strain curves of microcracked solids. SDMDA allows a continuous variation in the microcrack density with tensile loading. Experimental uniaxial tensile response of β-eucryptite glass and ceramics with controlled levels of microcracking is reported. It is demonstrated that SDMDA can well describe the extent of non-linearity in the experimental uniaxial tensile response of β-eucryptite with varying levels of microcracking. The advantages of the SDMDA are discussed in regard to tensile loading.
While the problem of the identification of mechanisms of hydrogen assisted damage has and is being thoroughly studied, the quantitative analysis of such damage still lacks suitable tools. In fact, while, for instance, electron microscopy yields excellent characterization, the quantitative analysis of damage requires at the same time large field-of-views and high spatial resolution. Synchrotron X-ray refraction techniques do possess both features. In this work, we show how synchrotron X-ray refraction computed tomography (SXRCT) can quantify damage induced by hydrogen embrittlement in a lean duplex steel, yielding results that overperform even those achievable by synchrotron X-ray absorption computed tomography. As already reported in literature, but this time using a non-destructive technique, we show that the hydrogen charge does not penetrate to the center of tensile specimens. By the comparison between virgin and hydrogen-charged specimens, we deduce that cracks in the specimen bulk are due to the rolling process rather than hydrogen-assisted. We show that (micro)cracks propagate from the surface of tensile specimens to the interior with increasing applied strain, and we deduce that a significant crack propagation can only be observed short before rupture.
The goal of the Special Issue “Brittle Materials in Mechanical Extremes” was to spark a discussion of the analogies and the differences between different brittle materials, such as, for instance, ceramics and concrete. Indeed, the contributions to the Issue spanned from construction materials (asphalt and concrete) to structural ceramics, reaching as far as ice. The data shown in the issue were obtained by advanced microstructural techniques (microscopy, 3D imaging, etc.) and linked to mechanical properties (and their changes as a function of aging, composition, etc.). The description of the mechanical behavior of brittle materials under operational loads, for instance, concrete and ceramics under very high temperatures, offered an unconventional viewpoint on the behavior of brittle materials. This is not at all exhaustive, but a way to pave the road for intriguing and enriching comparisons.
In this Seminar cycle I will present first diffraction methods to determine residual stress and investigate micromechanical properties of complex materials, and then particularize the treatment with applications to porous microcracked ceramics for diesel particulate filter applications.
I will show that neutron diffraction is particularly suited for bulk studies, where 3D stresses are needed. The advantages to use Time-of-Flight or steady state sources will be discussed, together with the problematic of the determination of absolute RS values.
Finally, the behavior of DPF materials under applied load or at high temperatures will be discussed under the combination of macroscopic and microscopic tests.
In this Seminar cycle I will present first diffraction methods to determine residual stress and investigate micromechanical properties of complex materials, and then particularize the treatment with applications to porous microcracked ceramics for diesel particulate filter applications.
I will show that neutron diffraction is particularly suited for bulk studies, where 3D stresses are needed. The advantages to use Time-of-Flight or steady state sources will be discussed, together with the problematic of the determination of absolute RS values.
Finally, the behavior of DPF materials under applied load or at high temperatures will be discussed under the combination of macroscopic and microscopic tests.
While structural ceramics usually display a brittle mechanical behavior, their composites may show nonlinearities, mostly due to microcracking. Herein, the stiffness evolution of a sandwich-like laminate of an Al2O3 15%vol. ZrO2 matrix reinforced with Nextel 610 fibers is studied as a function of number of cycles N in tension. The stiffness of the composite degrades with increasing N, indicating microcracking. However, synchrotron X-ray refraction radiography shows that the internal specific surface of such cracks varies differently. A modeling strategy is developed for the calculation of the equivalent stiffness of mixtures (first the matrix and then the sandwich), based on the Voigt and Reuß schemes. The Bruno–Kachanov model is then used to estimate the initial microcrack density in the matrix (due to the thermal expansion mismatch) and the amount of microcracking increase upon cyclic loading. The stiffness in the composite degrades dramatically already after 20 000 cycles but then remains nearly constant. The combination of mechanical testing, quantitative imaging analysis, and modeling provides insights into the damage mechanisms acting: microcrack propagation is more active than microcrack initiation upon cyclic loading, but the second also occurs. This scenario is similar but not equal to previous results on porous and microcracked ceramics.