EFFECTIVE ELASTIC PROPERTIES OF ALUMINA-ZIRCONIA COMPOSITE CERAMICS

WILLI PABST, EVA GREGOROVÁ

Department of Glass and Ceramics, Institute of Chemical Technology Prague Technická 5, 166 28 Prague 6, Czech Republic

E-mail: pabstw@vscht.cz, gregoroe@vscht.cz

PART 1. RATIONAL CONTINUUM THEORY OF LINEAR ELASTICITY

Submitted November 26, 2002; accepted January 20, 2003

Abstract

In this first paper of a series on the effective elastic properties of alumina-zirconia composite ceramics the theoretical framework in which these properties arise, the linear theory of elasticity, is presented in an unconventional way. A rational continuum approach is chosen, but without the formal details necessary for a mathematically strict formulation. Using a referential (Lagrangian) formulation as long as useful, the constitutive equation for the stress tensor is derived for isotropic as well as for anisotropic materials. Particular emphasis is laid on the distinction between the (geometrical) linearization of the kinematic measures (strain tensors) and the (physical) linearization of the constitutive equation (material model). Recent results occurring in the literature are mentioned. Some standard textbook formulae are recalled for the purpose of easy reference in the subsequent papers of this series.

https://www.irsm.cas.cz/materialy/cs_content/2003/Pabst_CS_2003_0000.pdf

PART 2. MICROMECHANICAL MODELING

Submitted January 29, 2004; accepted February 23, 2004

Abstract

 In this second paper of a series on the effective elastic properties of alumina-zirconia composite ceramics, principles of micromechnical modeling are reviewed and the most important relations are recalled. Rigorous bounds (Voigt-Reuss bounds) are given for the (scalar) effective elastic moduli (tensile modulus E, shear modulus G and bulk modulus K) of polycrystalline ceramics as calculated from monocrystal data (i.e. components of the elasticity tensor). Voigt-Reuss bounds and HashinShtrikman bounds of the elastic moduli are given for two-phase composites. For porous materials, which can be considered as a degenerate case of two-phase composites where one phase is the void phase (with zero elastic moduli), micromechanical approximations (so-called dilute approximations, Dewey-Mackenzie formulae) are given. Apart from a heuristic extension of the dilute approximations in the form of so-called Coble-Kingery relations, semi-empirical extensions of the micromechanical approximations are given for the tensile modulus (Spriggs relation, modified exponential and Mooney-type relations, generalized / Archie-type power law relation, Phani-Niyogi / Krieger-type power law relation, Hasselman relation), including the new relation E/E0 = (1 - φ) · (1 - φ/φC), recently proposed by the authors, where E is the effective tensile modulus, φ the porosity, E0 the tensile modulus of the dense (i.e. pore-free) ceramic material and φC the critical porosity.

http://www.ceramics-silikaty.cz/2004/pdf/2004_01_014.pdf


 PART 3. CALCULATION OF ELASTIC MODULI OF POLYCRYSTALLINE ALUMINA AND ZIRCONIA FROM MONOCRYSTAL DATA

Submitted January 29, 2004; accepted February 23, 2004

Abstract

 In this third paper of a series on the effective elastic properties of alumina-zirconia composite ceramics the calculation of the effective elastic moduli of polycrystalline alumina (corundum, i.e. trigonal α-Al2O3) and tetragonal zirconia (t-ZrO2) from monocrystal data is recalled. The values estimated via the Voigt-Reuss-Hill average are compared with the most reliable published values. Standard formulae and theorems of elasticity theory and micromechanics are used as consistency tests for calculated and measured values. For dense polycrystalline α- Al2O3 the most reliable values calculated from monocrystal data are 402.7 GPa for the tensile modulus, 163.4 GPa for the shear modulus, 250.9 GPa for the bulk modulus and 0.23 for the Poisson ratio. In this case all the calculated values are in reasonable agreement with the measured values, taking into account the relatively large statistical errors of the latter. For dense polycrystalline zirconia values calculated from monocrystal data are 201.1 GPa for the tensile modulus, 78.7 GPa for the shear modulus, 150.6 GPa for the bulk modulus and 0.28 for the Poisson ratio. There is a discrepancy between calculated and measured values, especially for the bulk modulus, the measured values of which are approx. 180 ± 10 GPa and the Poisson ratio, the measured values of which are approx. 0.31. Possible reasons of this discrepancy are discussed.

http://www.ceramics-silikaty.cz/2004/pdf/2004_02_041.pdf


PART 4. TENSILE MODULUS OF POROUS ALUMINA AND ZIRCONIA

Submitted January 29, 2004; accepted February 23, 2004

Abstract

 In this fourth paper of a series on the effective elastic properties of alumina-zirconia composite ceramics the influence of porosity on the effective tensile modulus of alumina and zirconia ceramics is discussed. The examples investigated are alumina and zirconia ceramics prepared from submicron powders by starch consolidation casting using two different types of starch, potato starch (median size D50 =47.2 µm) and corn starch (median size D50 =13.7 µm). The dependence of effective tensile moduli E, on the porosity φ, measured for porosities in the ranges of approx. 19-55 vol.% and 10-42 vol.% for alumina and zirconia, respectively, using a resonant frequency technique, was evaluated by fitting with various model relations, including newly developed ones. A detailed comparison of the fitting results suggests the superiority of the new relation E/E0 = (1 - φ)·(1 - φ/φC), developed by the authors (with the tensile modulus of the dense ceramic material E0 and the critical porosity φC), over most other existing fit models. Only for special purposes and well-behaved data sets the recently proposed exponential relation E/E0 = exp [-Bφ/(1 - φ)] and the well-known Phani-Niyogi relation E/E0 = (1 - φ/φC) N might be preferable.

http://www.ceramics-silikaty.cz/2004/pdf/2004_04_165.pdf


PART 5. TENSILE MODULUS OF ALUMINA–ZIRCONIA COMPOSITE CERAMICS

 Submitted November 4, 2004; accepted January 20, 2005

Abstract

In this fifth and last paper of a series on the effective elastic properties of alumina-zirconia composite ceramics (AZ composites) the tensile moduli of dense and porous AZ composites are investigated from the theoretical point of view and compared with experimental data. For dense AZ composites the Hashin-Shtrikman bounds turn out to be sufficiently close to each other and excellent agreement is found between theoretically predicted and measured values, so that the arithmetic HashinShtrikman average can be used for predicting effective elastic moduli for arbitrary compositions. For dense zirconia-toughened alumina (ZTA) with 15 wt.% and dense alumina-containing tetragonal zirconia (ATZ) with 80 wt.% of zirconia the theoretically predicted effective tensile moduli are 375 GPa and 251 GPa, respectively. For porous AZ composites (prepared by starch consolidation casting) the consistency of the experimentally measured data is assessed with regard to the HashinShtrikman upper bound. Fitting results confirm the superiority of the new relation E/E0 = (1 - φ)·(1 - φ/φC), where E is the effective tensile modulus and φ the porosity, over most other fit models. Extrapolated E0 values are 351 GPa and 237 GPa and critical porosities φC are 0.796 and 0.882 for porous ZTA and ATZ, respectively

http://www.ceramics-silikaty.cz/2005/pdf/2005_02_077.pdf