Monitoring the Elastic Properties of Green Ceramics during Firing
IET can be used to measure elastic properties of materials at room temperature, as well as cryogenic and high temperatures.
Measuring the elastic properties of a green ceramic as it is being fired can be difficult and often requires sophisticated non-destructive testing (NDT) techniques. One effective method is called the the impulse excitation technique (IET).
IET is described in more detail in several standards (e.g., ASTM E1876 and C1259), but essentially involves measuring the natural frequencies of a test piece after it has been excited by a sharp mechanical impulse (light tap with a small hammer or impulse tool). The sample is supported and excited in such a way that a standing wave is produced in the sample. By supporting the sample at the nodes of the standing wave, external damping is minimized, and more accurate frequency and internal friction measurements can be obtained.
Elastic properties, typically Young’s modulus (E), shear modulus (G) and Poisson’s ratio (µ), are obtained from the natural frequencies and the size, mass, and shape of the sample. Because of the simplicity of the test, IET can be used to measure the elastic properties of materials not just at room temperature but also at cryogenic and high temperatures. Furthermore, it is relatively straightforward to fit testing equipment to an existing furnace or cryogenic chamber, and even vacuum systems (a laser vibrometer is required to measure the vibrations in this case).
A commercial instrument* was fitted to a furnace and used to perform IET during the firing of an extruded cylinder (11.73 x 113.97 mm) of a quartz porcelain mixture (50 wt% kaolin, 25 wt% quartz and 25 wt% feldspar) to ~1,100°C at a rate of 5°C/min-1. The sample was supported on two parallel ceramic fiber knife-edges placed at the nodes for flexural or bending vibrations. As shown in Figure 1, the impulse tool was a small alumina rod that was found to give reasonable excitation of the flexural frequencies over the entire temperature range (other materials such as mullite can be used to reduce the mass of the impulse tool).
From ASTM E1876, the Young’s modulus (E) for a cylinder is given by:
where m = mass, L = length, ff = flexural frequency, D = diameter, and T1 = correction for shear and rotary inertia. There was a linear shrinkage of 4.27% and 6.19% for the length and diameter of the cylinder, and an 8.01% mass loss after firing to 1,113°C. For the purposes of relating the elastic properties to phase and microstructural changes during firing, the changes in Young’s modulus can be approximated by the following equation:
where Ert = Young’s modulus at room temperature, Eht = Young’s modulus at high temperature, frt = flexural frequency at room temperature, and fht = flexural frequency at high temperature. Therefore, the Young’s modulus at high temperature is a function of the square of the flexural frequency. In this case then, it was sufficient to measure the flexural frequency during firing and relate that to the physical, phase and microstructural changes.
*BuzzMac’s Buzz-o-sonic NDT high-temperature testing kit.
The flexural frequency vs. temperature is shown in Figure 2. In general, the frequency is expected to decrease with temperature for a ceramic as the material becomes less stiff. Although this was the case initially, the frequency starts to increase at ~ 50°C. From thermal analysis, it is known that this material undergoes several dimension, phase, and mass changes1,2 (see Figure 3).
Three main regions of interest are indicated in Figure 3. First, as can clearly be seen in the TGA curve, water physically bound to the pore surfaces in the sample begins to be driven off at ~ 50°C. Second, the kaolinite in the green body transforms into metakaolinite over the temperature range of 400-700°C. Dehydroxilation takes place at ~ 420°C with a concomitant mass loss, as evidenced in the green TGA curve. Finally, as seen in the TDA curve, the sample begins to shrink significantly above 893°C. As is evident, the effects of the chemical reactions occurring in the quartz porcelain during firing that are shown by the thermal analysis data are also reflected in the resonant frequency curve (see Figure 4).
The initial rise in frequency matches the onset of water loss (1), the second rise in frequency matches the onset of the kaolinite-metakaolinite dihydroxylation (2), and the final and rapid rise in frequency matches the sample shrinkage (3). The sample shrinkage is due initially to a transformation of the metakaolinite into spinel or g-Al2O3 and then to the formation of mullite above 1,100°C1; this is also indicated by the DTA curve. In addition, sintering mechanisms will lead to more shrinkage and an increase in the stiffness, and hence flexural frequency.
Other subtler effects can be seen in the flexural frequency curve. For example, an inflection in the frequency curve can be seen to match the a-b quartz inversion shown in the TDA curve. Solid state sintering, which occurs above ~ 600°C,1 also gives rise to an increase in the flexural frequency (in addition to that due to mass loss, as seen in the TGA curve). Microcracking due to factors such as phase changes, shrinkages and expansion mismatches have also been shown to influence the resonant frequency curve.1,2
It is important to keep in mind that other parameters, such as internal friction (Q-1) and amplitude of vibration, can also be measured using IET. Both parameters are sometimes more sensitive to phase changes than resonant frequency.
Extending the impulse excitation technique to high-temperature testing (lightly tapping a sample during heating and monitoring the resulting vibrations) allows very useful elastic property information to be obtained, which can then be related to the physical, chemical, and microstructural changes. These results can be achieved with only a few hours of testing using relatively low-cost equipment.
Igor Stubna (Department of Physics, Constantine the Philosopher University, Slovakia) is gratefully acknowledged for providing the quartz porcelain sample and the thermal analysis data.
1. Igor Stubna, Frantisek Chmelık, Anton Trnık, Josef Pesicka, “Creation of Microcracks in Porcelain during Firing,” J. Eur. Ceram. Soc., Vol. 31, 2011, pp. 2205-2209.
2. Igor Stubna, Frantisek Chmelık, Anton Trnık, Peter Sin, “Acoustic Emission Study of Quartz Porcelain during Heating up to 1150°C,” Ceram. Int., Vol. 38, 2012, pp. 6919–6922.