Influence of porosity on Young's modulus and Poisson's ratio in alumina ceramics
Introduction
Ceramic materials present interesting properties such as a good hardness, high wear and corrosion and temperature resistance which makes them candidates for thermomechanical applications. However, these advantages are counteracted by the brittleness of the ceramics. Consequently, the presence of small defects such as pores can lead to a dramatic decrease in strength value. Therefore, the use of ceramics as structural parts is conditioned by the development of non-destructive evaluation techniques such as ultrasonic methods which allow the porosity level and pore size determination through Young's modulus and Poisson's ratio measurements.
This paper reports on a study of the porosity influence in alumina parts on Young's modulus and Poisson's ratio by correlating the transverse and longitudinal ultrasonic wave velocities data with the measured density and porosity. The ultrasonic velocity method is non-destructive and very precise.1, 2 Moreover, the ultrasonic velocity through solids mainly depends on the intramolecular and intermolecular interaction potential. In the case of ceramics, this potential depends on the microstructural characteristics such as grain nature and size, porosity etc.
Several previous papers2, 3, 4 were already devoted to the study of Young's modulus dependence versus the porosity taking into account the spherical or cylindrical shape of pores. By comparison between experimental and calculated data, these authors have chosen for all porosity values (from a few to 40%) the cylindrical shape. Moreover, in these works, the Poisson ratio is always assumed to be constant versus the porosity.
In this work, the pore shape modification with the densification level is taken into account in the Young's modulus and Poisson's ratio calculations.
Section snippets
Theoretical approach
The relationships between longitudinal and transverse wave velocities with bulk modulus (K) and shear modulus (G) are:where ρ is the density of the material. For a porous medium, the density can be related to the porosity by the relation (3):where ρ0 is the theoretical density and p is the porosity level
, become:
For isotropic materials, the bulk and shear moduli are linked to Young's modulus (E) and Poisson's ratio by:
Elaboration of ceramics
Alumina pellets (diameter: 2.5 cm, thickness: 1 cm) were shaped by uniaxial pressing from Alcoa A16SG powder and then sintered at different temperatures (in the range 1300–1700°C) for 2 h in order to produce a wide range of porous samples (from 25% down to 2% of porosity). The porosity level was measured by Archimedes’ method. The porosity of various alumina ceramics are presented in Table 1, Po corresponds to the open porosity (fully interconnected pores of complex shapes), Pc, to the close
Wave velocities values
The measured transverse and longitudinal velocities plotted versus total porosity are shown in Fig. 1. It can be observed that the slope is approximately twice bigger in the case of longitudinal waves which would suggest that compression waves are more sensitive to the porosity than shear waves.
Young's modulus calculation
From the values of velocities for a pore-free sample deduced by extrapolation (no porosity) VL0=10904 m/s and VT0=6399 m/s, a Young's modulus value of 401 GPa is calculated; this value is very close
Conclusion
A very precise non-destructive technique on ultrasonic waves was used to determine the influence of the porosity on the compression and shear wave velocities through alumina samples. From those velocity values, Young's modulus and Poisson's ratio were determined for alumina parts containing different pore fractions. A linear decrease of Young's modulus versus the porosity level was observed. Boccaccini's model describing the Young's modulus dependence on the porosity can be applied on condition
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