alumina will favor the formation of the cracks on the tensile region of the cross-section of the ceramic material (opposite to the contact point of the upper ram).
Total applied mechanical stress is a function of the sample dimensions and test bench geometry as follows:
Figure 4. (a) 3-point bending test bench used for applying a mechanical prestress on alumina plates, (b) tensile stress is created at the bottom part of the alumina plate.
where M is the moment bending, l is the length of the support (outer) span, F is the load (force) at the fracture point, B is the base of the sample, h is the effective thickness of the sample.
Since the formation of a crack or a network of cracks reduces the effective section of the alumina plates, if a constant force is applied, the real stress will increase as the crack(s) propagate(s) along the thickness of the material. The final crack dimension will be then related to its initial size, the applied force and the time spent under such a force. A series of tests were performed to determine the mechanical prestress conditions (force and application time) prior to electrical breakdown. The characteristic of the time-to-breakdown (mechanical) vs. the applied force is shown in Figure 5.
The maximum force possible to apply is 180 N, which corresponds to the mechanical flexural strength of the studied alumina. An attempt was made to study the full range of applicable forces. However, samples needed to be transported from the mechanical test bench to the dielectric breakdown test bench, and for high values of the force (>100 N) even a short time of prestress could break the samples during their manipulation. For this study, samples were prestressed from 20 N to 80 N, applying the force for 1 minute. This allowed the samples to be handled without the risk of breaking them. Samples were marked with a felt-tip pen to identify the region where the force ram was in contact.
2.3. Dielectric Breakdown of Prestressed Alumina
The dielectric strength measurements were performed in a plane-tip configuration. The tip in contact with the sample is a cylinder of a diameter of 1 mm. An AC generator regulated by an autotransformer was controlled with a step motor to modulate the ramp of the amplitude of the applied voltage. Short term dielectric breakdown values were obtained with a ramp of 1.6 kV/s. Dielectric breakdown detection and voltage cutoff is triggered by the rapid increase in the current. Samples are immerged in a dielectric fluid (Galden HT270) to avoid surface flashovers. The felt-tip pen line helped to
Figure 5. Time-to-breakdown (mechanical) vs. applied mechanical force for 635 µm alumina plates under study.
position the tip in the region of the maximum stress in order to induce dielectric breakdown in this zone. The results of the dielectric breakdown values are plotted against the mechanical prestress for each sample.
A scheme of the followed procedure is shown in Figure 6.
3. Results and Discussion
Figure 7 shows the ceramic plates after the dielectric breakdown was performed. The size of the alumina plates allowed for 3 to 4 dielectric breakdown tests per sample.
When plotting the results in a Weibull chart we can easily identify that the dispersion of the results obtained for the prestressed samples are significantly higher than the ones obtained for the un-stressed sample (0 N) (Figure 8).
To better observe the impact of the mechanical prestress, only the α parameter (cumulative probability of 63.2%) of the dielectric breakdown extracted from a two-coef- ficient Weibull distribution was plotted (Figure 9).
Despite the significant dispersion of the values, we can observe a decrease in the dielectric strength of the alumina when it is mechanically prestress. The decrease on the α parameter is more important as the mechanical prestress value increases. One of the reasons for the large dispersion of the values of Ebr could originate from our inability to
(a) (b) (c)
Figure 6. (a) Reference sample with an initial crack length l0, (b) mechanical prestress that increases the crack length inside the ceramic, total length is l0 + lm, (c) dielectric breakdown of the prestressed ceramic.
Figure 7. Dielectrically broken down alumina sample. Top surface was submitted to compression (black line, felt-tip pen) and bottom suface under tensile stress. Red circles indicate the rupture channel exit points on the surface of the alumina.
Figure 8. Full results for the dielectric breakdown of prestressed alumina plates (0 to 80 N, 1 minute).
Figure 9. α values for the dielectric breakdown of prestressed alumina plates (0 to 80 N, for tappl = 1 minute), error bars correspond to the 90% confidence intervals.
perfectly align the high voltage tip with the maximum stress region. The felt-tip pen is 1 mm thick and the exact width of the stressed region is for the moment unknown. Another reason for the large dispersion of the Ebr values could arise from the nature of the crack propagation itself, especially if the cracks are not homogeneously distributed along the stressed plane.
The results of dielectric breakdown of alumina show higher dielectric strength for lower mechanical prestress.
Assuming a constant extension speed, the evolution of the dielectric strength was correlated with the evolution of cracks at prestressing, what supports the contribution of mechanical properties to dielectric breakdown phenomena in alumina. This could be explained by the fact that the dielectric failure mechanism of the alumina-based ceramic is strongly associated with the propagation of cracks, and a change in behavior of the latter will influence the dielectric strength.
We should consider that for application purposes, the alumina (or any other ceramic mentioned in section 1) is a part of a complex assembly with other materials, with a metal being in immediate ontact with the substrate assembly. While there are some studies that highlight the importance of the initial mechanical properties of the ceramic within the substrate assembly  , the data presented here indicates that the other processing parameters of the alumina could be relevant. This could indicate the need to take into account the mechanical history of the ceramic as having an impact on the dielectric strength value.
The dielectric breakdown of the studied alumina depends on the value of the mechanical prestress created by a 3-point bending test. Despite the large dispersion of the results, a global tendency satisfies the currently used model of electromechanical breakdown, where the defect size impacts the short-term dielectric strength of alumina. Higher values of mechanical prestress induce a decrease in the Ebr values. This could imply that not only the original dielectric properties of the ceramics should be taken into account for dimensioning purposes, but also their full mechanical history.
The authors acknowledge the assistance from E. Duhayon for providing access to the mechanical test bench. Z. Jouini thanks the French Ministry of Research and Higher Education for its financial support through a doctoral studies grant.
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