Statistical Analysis of the Flexural Strength of Free-Standing Flame-Sprayed Alumina Coatings Prior and After Thermal Shock

The impact of thermal shock upon the scatter of flexural strength data of free-standing thin flame-sprayed Al2O3 coatings was examined. As published in the literature, thermally sprayed ceramic systems exhibit superior thermal shock resistance and against this background, the statistical evaluation of strength data prior and after the thermal shock was intensified. Thus, the Weibull parameters m and r0 were compared before and after thermal shock from 1000 C to room temperature. The flexural strength was determined utilising the ball-on-three-balls method. Although the general scale of the Weibull modulus m was rather low (\ 6), considerable differences were shown after thermal shocking as the Weibull modulus decreased by a factor of about 3.


Introduction
Nowadays, thermally sprayed ceramic coatings gained raised attention. Potential applications range from electrical components to high-temperature applications such as metal melt filtration. Their property profile is given through their unique lamellar microstructure, evincing numerous microcracks, amorphous zones, and pores, resulting from the thermal-spray process itself (Ref [1][2][3][4]. A key property to e.g. assess mechanical handling or thermal shock performance of ceramic components is the flexural strength. Within the characterisation of strength, the scatter of strength data represents a material property, whereas the scale of strength is related to the components' geometry and size, hence, to the effectively stressed volume. Against this background, the analysis of strength data in terms of Weibull theory addresses the quantification of that scatter by the scatter parameter m, called Weibull modulus. Moreover, a scale parameter, the characteristic strength r 0 , can be derived for the investigated effective specimen volume or effective surface area, respectively (Ref 5). The estimation of both is outlined in the European Standard EN 843-5 (2006).
Through literature review, a broad overview regarding the mechanical properties of free-standing thermally sprayed (more precisely flame-sprayed) alumina is provided (Ref [6][7][8]. Recently, fracture mechanical properties were investigated, such as fracture toughness or R-curve behaviour. When compared to sintered alumina, the fracture toughness K Ic was found lowered for flame-sprayed alumina (Ref 8). In agreement with that, a lowered strength was frequently reported for flame-sprayed Al 2 O 3 as well, which is mainly attributed to the weakened microstructure (Ref [6][7][8]. However, as shown by Aneziris et al. (Ref 7), the thermal shock performance of flame-sprayed alumina is superior compared to conventional oxidic ceramic products. By thermal shock experiments according to Hasselman (Ref 9, 10), critical temperature differences without strength degradation up to 800 K could be derived. In addition, a decrease in strength of about 40% only was reported for a temperature drop of about 1000 K. However, the determination of the Weibull parameters was not performed after thermal shocking. Back then, the Weibull modulus m prior to thermal shock amounted 4.7 (Ref 7). Key point of the presented research is the determination and comparison of the Weibull modulus m and r 0 before and after thermal shock. During industrial application though, e.g. as thermal barrier coatings, flame-sprayed coatings will be affected by multiple thermal shocks (Ref 11). Consequently, conception and validation of the flexural strength measurement after subjecting the coatings to a temperature difference appears highly relevant. Beyond describing the scatter and scale of the strength either prior or after thermal shock, both characteristics could be further utilised for the estimation of component lifetime under static or cyclic load, as described by Munz and Fett (Ref 5).

Experimental
All specimens were produced using commercial alumina rods (Rokide A) as feedstock and a MasterJet flame-spray gun (both from Saint-Gobain, Avignon, France). The molten alumina droplets were projected onto a graphite substrate (GM-154e, Graphite Materials, Oberasbach, Germany). Due to the differences in thermal expansion behaviour of graphite and alumina, the flame-sprayed alumina coatings detached after cooling down and could be removed from the graphite substrate without rupture. Table 1 lists the used settings for the thermal-spray process.
For ball-on-three-balls testing (B3B), discs of 0.5 mm in thickness and 8 mm in diameter were produced. This was realised by spraying onto the plane circular face of a graphite cylinder of the same diameter until the desired thickness was reached. Furthermore, thin stripes of two different sizes were prepared for four-point-bending tests (geometry I: 1.5 9 10 9 30 mm 3 and geometry II: 1.5 9 10 9 45 mm 3 ). Here, a side face of a graphite bar of either 10 9 30 mm 2 or 10 9 45 mm 2 was employed to set the basic specimen shape. The coating process was again terminated, as the intended coating thickness was attained. The spray distance between the torch and the graphite substrate amounted 100 mm in all spray trials. Both methods of preparation hold the advantage that none of the specimens required any further preparation prior to testing. It should be noted that thermal spraying was established as a coating technology, hence predominately aims for wide coatings of thicknesses less than 1 mm. The preparation of large free-standing components with dimensions [ 1 mm is strongly related to the process itself and requires a delicate control of the process conditions such as spray distance and angle. Otherwise, rupture appears as consequence of e.g. temperature gradients within the component during spraying. That would represent a pretesting or pre-application selection, which is considered impermissible. To maintain the coating character of the tested specimens and to keep the moment of inertia feasible, the thicknesses of the free-standing coatings were kept below 1 mm. In order to assess the suitability of the three geometries for statistical strength characterisation, the proportion of rejects r (specimens, not possible to remove from the substrate without rupture) was considered before measuring the flexural strength. This ratio was calculated by r = 1k/k a , where k is the number of usable specimens and k a the number of spray attempts, here fixed at 15. A reject proportion of r = 1 would thus mean that 0 specimens out of 15 spray attempts could be used, while 15 specimens out of 15 spray attempts were usable when r = 0 applies. For r \ 0.05, a geometry was considered suitable for the estimation of the Weibull parameters. Consequently, both stripe geometries needed to be excluded from strength testing, since none of them fulfilled this condition (r I = 0.13, r II = 0.40). In contrast, the reject proportion of the disc geometry was 0. This resulted in two test series for evaluating m and r 0 , 0TS and 1TS with 43 specimens each, as listed in Table 2.
For thermal shock, the specimens were annealed at 1000°C for 30 min before being subjected to sudden quenching in water of 20°C (stationary). Hence, the resulting temperature gradient DT amounted 980 K. The change of water temperature was neglectable due the sheer differences between total mass of all specimens per run (30 g to 50 g) and the mass of the water (10 kg). Since a stationary water bath was used, the bath depth was set to 10 cm in order to allow the specimens to sink through the water in the first moments of quenching. This was meant to minimise the impacts of local thermal insulation due to bubble formation at the specimen surface, as the bubbles detached during the sinking movement. It can be noted that neither an increase in water temperature nor bubbles could be observed. The total time between leaving the furnace and reaching the bottom of the water bath amounted less than 2.5 s. The internal structure of the material before and after thermal shock was characterised on disc specimens by the aid of 3D-image processing through x-ray microtomography. Such was realised in a CT-Alpha (Procon x-ray GmbH, Germany) equipped with a Dexela detector (1944 pixel 9 1526 pixel, type 1512, Perkin Elmer Inc.). Voxels of 9.8 lm edge length after reconstruction were given, due to the sample dimensions and position in between x-ray gun and detector.
The flexural strength was calculated from the maximum load at rupture F c , the specimen thickness t, and the dimensionless factor f*, depending on Poisson's ratio m as well as the ratio of specimen thickness or support radius R a to the specimen radius R: The underlying thickness of the specimens was determined in the centre, near the region of the maximum flexural momentum. A further detailed description of the test method and an empirical formula for f* can be found in the literature ( Ref 12). Some major advantages are the simple specimen geometry, the adaptivity for different specimen sizes, the tolerance against geometrical imperfections of the specimen, and a potential adaptation for elevated temperatures. In the present study, the Poisson's ratio m was approximated with 0.2, as done by Neumann et al. (Ref 8) for fracture mechanical considerations of freestanding flame-sprayed alumina. For the B3B test, the radius of the used ceramic balls (alumina) was 2.5 mm and the supporting radius R a was calculated from that according to Börger et al. (Ref 12). Loading in B3B was performed with a loading rate of 0.05 mm min -1 . In all bending tests, the specimen face, which represented the former contact face between substrate and coating, was subjected to tensile stresses. The strength data of both test series were statistically analysed in terms of Weibull theory according to EN 843-5 (2006), resulting in the (unbiased) Weibull modulus m (scatter parameter) and the characteristic strength r 0 (scale parameter). For the 0TS-series, the dependence of the strength on the specimen size was analysed following the Weibull theory, as described by Eq.  7)).
The mean effective surface area S eff of the B3B-discs was calculated using a FEM-model with specimen diameter and mean specimen thickness ( Ref 13). Thus, the surface-related characteristic strength of both other bending tests r b is given by: In here, r 0 is the characteristic strength of the corresponding test series. The effective surface area S b of a 3 9 5 9 45 mm 3 bar in four-point bending or a 0.8 9 10 9 40 mm 3 stripe in three-point bending was calculated according to Quinn (Ref 14).

Results and Discussion
A first indicator for their thermal shock performance can be found as all specimens survived the quenching from 1000°C without rupture and therefore could be tested for flexural strength. In Fig. 1, x-ray tomography scans of a disc prior (A) and post (B) thermal shock are displayed. Major cracks are indicated by arrows. From Fig. 1(a), one can see that in the as-sprayed state microcracks are visible, although difficult to visualise due to the given voxel size. Since SEM-micrographs of flame-sprayed alumina, presented in the literature, show a pronounced network of microcracks though, it is assumed that the majority of these cracks would appear smaller in extension than the resolution of the tomography scans would allow for visualisation (Ref 2). In turn, after thermal shock, next to these narrow cracks (black arrows) wider, more pronounced cracks are visible (white arrows), as shown in Fig. 1(b). Figure 1(c) showcases the lateral view of the thermal shocked specimen. In the emphasised region, it can be seen that the crack arrested within the volume. Hence, the propagation of the thermal shock-induced cracks (macrocracks) was restrained. As proposed by Aneziris et al. (Ref 7), such inhibition could be attributed to the present microcrack network. In agreement with that, pronounced R-curve behaviour could be evinced for flame-sprayed alumina, according to which the energy required for crack advance increases for a propagating crack. Reasons for the increase in crack resistance were outlined as energy consumptions due to the opening of the microcrack network and meandering of the macrocrack. In sum, such mechanisms result in a reduction in energy available for the growth of the macrocrack (Ref 8). Figure 2 shows exemplary load-displacement diagrams for B3B-testing before (black line) and after thermal shock (grey line). Similar for both is the nonlinear part near maximum loads. It is assumed that this deviation from linearity is related to subcritical crack growth of the present microcracks as a certain range of stress intensity is reached at their tips. Comparable behaviour can be seen from cyclic-loading tests of pre-notched specimens Taking the thickness of the discs into account, this geometric characteristic appeared scattered around the aimed 0.5 mm as well due to the rather chaotic flame-spray process. In Fig. 3, the measured flexural strength is plotted against the individual specimen thickness. As one can see, there is no clear trend or relation between both, neither for series 0TS, nor for series 1TS. Eventually, this hints for only minor influence of specimen thickness within the given range. It should be noted that for the lowest investigated specimen thicknesses (0.3-0.4 mm) individual strength values before and after thermal shock evinced about a similar scale. Again in individual cases, a comparable situation was found for thicknesses between 0.7 and 0.8 mm. Within the central range of investigated specimen thickness (0.4-0.7 mm), the differences between flexural Subfigure (c) shows the lateral view of the thermal shocked specimen. Arrows indicate major cracks (black: pre-existing microcracks, white: thermal shock-induced macrocracks) Fig. 2 Typical load versus displacement relation of the as-sprayed 0TS-series (black line) and the 1TS-series after one thermal shock (TS) from 1000°C to room temperature (grey line). The specimen thickness was similar for both selected specimens strength before and after thermal shock appeared more pronounced. To which extend such results could be attributed to a potential impact of thickness upon strength degradation through thermal shock or in turn to the natural scatter of the strength itself, remains an issue to be addressed in further specified investigations. For the present study though, Weibull analysis is performed covering all measurements per test series, also since the amount of data gets smaller for the aforementioned outer regions of specimen thicknesses. In that, the cumulative analysis allows for a general overview regarding sub-millimetre coatings and acts as starting point for future studies. The resulting Weibull parameters of both test series are listed in Table 3 . Other reports, addressing the variation of strength data of thermally sprayed compounds, e.g. Ostojic and Berndt (Ref 16), consider the results of tensile adhesion tests (TAT). There, a Weibull modulus of 3.3 can be found for the bond strength of thin alumina coatings, which is also of the same scale as the obtained Weibull modulus from this study. The Weibull plots of the strength data are given in detail in Fig. 4. As one can see, there are no outliers since all strength values can be found within the 90% confidence bands.
Considering a theoretical strength range of 0 MPa to 140 MPa, the probability density of flexural strength is plotted in Fig. 5 applying either of both distributions. Parameters of the Weibull distribution are the determined Weibull modulus and characteristic strength of the corresponding test series (without confidence band). Parameters of the Normal distribution are the mean and standard deviation, calculated from the 43 strength values per test series. As one can see, the deviation between Weibull and Normal distribution is rather low for 0TS, while the contrast in estimation for 1TS is more distinct, especially since for a strength of 0 MPa a probability density [ 0 is predicted. Hence, addressing a rough estimation and scatter of the flexural strength in the as-sprayed state, arithmetic mean and standard deviation appear adequate for thin flame-sprayed alumina coatings. Comparable results are assumed to apply for flame-sprayed materials with similar melting temperatures, as their microstructure would be similar. Addressing strength degradation and scatter after thermal shock, Weibull analysis could be preferred according those findings, as the arithmetic mean would underestimate the scale of strength degradation. Hence, the thermal shock performance could be overestimated.
The recalculation of the characteristic strength for fourpoint and three-point bending was performed using the determined characteristic strength r 0 for the as-sprayed state and its confidence band. Moreover, the determined Weibull modulus m and its upper and lower bounds were taken into account to calculate the effective surface area S b . For the calculation of the mean effective surface area of the   7), evinced a two-stage behaviour of the strength as function of DT. Below DT = 800 K, the strength was approximately constant, before it degraded at higher DT. Thus, a significant change of the characteristic strength r c can be expected for thermal shock gradients above 800 K. However, a similar prediction for the Weibull modulus m as a function of DT cannot be given, and therefore, the statistical measure m has to be determined discretely in dependence on the thermal shock conditions and thus on the microstructural evolution.

Conclusion
Scope of the presented research was the statistical treatment of flexural strength data of thin flame-sprayed alumina coatings (free-standing) prior and after thermal shock by standard Weibull method. The obtained results allowed for the following conclusions: • From the experimental aspects, the B3B-method allowed for the investigation of the flexural strength of thin flame-sprayed alumina coatings at room temperature without any pre-test selection. In perspective, the B3B-method also appears suitable for flexural testing at elevated temperatures. • As expected, the scatter of flexural strength is higher for flame-sprayed alumina coatings when compared to the Weibull modulus e.g. reported for hot-isostatic pressed alumina. • Thermal shock decreases the characteristic strength of flame-sprayed alumina according to the prediction and increases the scatter of flexural strength.  • For a rough estimation of median strength and strength scatter in the as-sprayed state, arithmetic mean and standard deviation based on a normal distribution appear adequate. This however can not be applied for the flexural strength after thermal shock.
Further potential studies could address the impact of repetitive thermal shocks.