University of Birmingham Quantitative analysis of the residual stress and dislocation density distributions around indentations in alumina and zirconia toughened alumina (ZTA) ceramics

Alumina, 10% and 20% nano ZTA with 1.5 mol% yttria stabiliser were subjected to Vickers indentation testing with loads from 1 to 20 kg. Cr 3+ fluorescence and Raman spectroscopy were applied to the indent centre and around the indentation in order to investigate the origin of the signal, the effect of indentation loads and zirconia phase transformation on the residual stress and plastic deformation in the plastic zone. The results suggested that with very strong laser scattering, the depth resolution of ZTA materials was very poor, which lead to a very significant amount of the signal being collected from the subsurface regions below the plastic zone. It was also found that zirconia phase transformation reduced the compressive residual stress in the alumina matrix within the plastic zone, except at the indentation centre, due to the tensile residual microstress generated by the zirconia phase transformation. In addition, the dislocation density on the indent surface of the ZTA samples was significantly reduced due to the restriction of crack propagation and energy absorption during the phase transformation process. At the indent centre, the zirconia phase transformation was suppressed by the high compressive stress, therefore, no significant difference between alumina and ZTA in terms of their residual stress and dislocation density were observed. Using TEM observation, it was found that the plastic zone microstructure of pure alumina is different from that of ZTA, which is consistent with the Cr 3+ fluorescence results. the microcrack density in the plastic zone of the ZTA was confirmed to be lower than that of the alumina sample.


Introduction
Zirconia toughened alumina (ZTA) has been extensively researched due to its outstanding properties of high toughness, hardness, wear resistance and chemical stability. [1][2][3] The zirconia additions toughen the alumina matrix via the tetragonal to monoclinic transformation that occurs in the stress field of growing cracks. The phase transformation results in a 4-5 vol% expansion, which provides a compressive stress that acts to reduce the propagation of the crack. Zirconia toughened alumina (ZTA) is already being used in a wide range of applications, from cutting tools, wear parts and biomechanical devices to ballistic protection. 4,5 Whilst the Vickers indentation toughness measurement technique is not a rigorous approach, it can be used to obtain a rough indication of the resistance to crack propagation in ceramics. Katagiri 6 has measured the amount of zirconia phase transformation around indents on pure zirconia using Raman spectroscopy and then quantitatively calculated the zirconia phase transformability. In addition, a Vickers indent leaves a plastically deformed zone beneath it. Generating, a better understanding of the residual stress and plastic deformation conditions induced by indentation in ZTA ceramics can help to investigate the effect of zirconia phase transformation on the plastic deformation of the alumina matrix and the stress field distribution after the indentation test.
For alumina-based ceramics, the residual stress can be investigated using Cr 3+ fluorescence spectroscopy. [7][8][9][10] Using an optical microprobe, a laser is focused on the sample surface. The chromium ions, Cr 3+ , a persistent impurity in alumina, interact with the laser and result in luminescence. When the crystal of the material is subject to a stress, the frequency of the luminescent peaks in the spectrum shifts correspondingly, allowing an indication of the mean stress distribution to be obtained. 7,11 In a polycrystal with randomly orientated grains the relationship between the mean peak shift and the hydrostatic component of the residual stress in the crystal is given by: (1) where Δν is the peak shift (cm -1 ) relative to the stress-free peak position, σ H is the hydrostatic stress component (GPa) and П H is the appropriate piezo-spectroscopic coefficient, which has a value of 7.6 cm -1 for the R1 peak. 8 Guo and Todd 12,13 have observed that the axial resolution of the microscope and the translucency of the material can significantly affect Cr 3+ fluorescence analysis. Studying the centre of an indent made in alumina using a 1 kg load revealed a single curve that contained four overlapping peaks, two broad peaks and two sharp peaks. By characterising the probe response function (PRF) and fitting the four peaks with an appropriate physical constraint, the two broad peaks were confirmed to originate from the plastic zone of the indentation, whilst the two sharp peaks were believed to have arisen from the elastically deformed region beneath it, Figure 1. The relatively high transparency of alumina meant that the laser could penetrate below the surface on which it was focused, leading to a large sampling volume covering both the material in the plastic zone and the subsurface region. This indicates that the axial resolution of the Cr 3+ fluorescence spectroscopy is not only controlled by the resolution of the equipment, but also by the transparency of the material. In order to investigate the residual stress distribution caused by the indentation of the ZTA ceramics, it is essential to determine the resolution of the microscope and the laser penetration depth so that it is possible to determine which fluorescence peaks represent the signal from the plastic zone.
In addition to the peak shift analysis, Ma et al. 8 also established that the fluorescence peaks from a plastically deformed material region, such as a plastic zone formed by an indentation, broaden significantly due to the resulting stress variations within the sampling volume. This was important as it demonstrated that the level of plastic deformation arising from dislocations having a high local stress field could be quantitatively determined from within a probed volume. According to an experimental and modelling study by Wu et al. 11 , the R1 peak broadening, , is proportional to the dislocation density, , in the probed position: (2) where k is a constant related to the lattice parameters of the alumina crystal and the piezospectroscopic coefficients and F(ρ) is a function correlated with the dislocation density.
In this work, three materials have been prepared and characterised, viz. monolithic alumina, 10% nano ZTA and 20% nano ZTA, where the zirconia additions were in the nano range and were partially stabilised using 1.5 mol% yttria. The grain size of the alumina phase was the same in each case. A high-resolution, confocal micro-Raman spectroscope was used to study the spatial distribution of indentation-induced phase transformations in the ZTA materials and Cr 3+ fluorescence analysis was used to determine the residual stresses around the indents. All the samples were subject to four indentation loads, viz. 1, 5, 10 and 20 kg, in order to validate the four peak fitting approach introduced by Guo and Todd and quantitatively analyse the residual stress under different indentation loads.

Sample preparation
As received, aqueous YSZ nanosuspension containing 1.5 mol% yttria (MEL Chemicals, Manchester, UK) was mixed with a fine submicron alumina aqueous suspension (Baikowski, Annecy, France), to form suspensions containing 0, 10 and 20 wt% YSZ in the final materials.
Details of the as-received suspensions are listed in Table 1. In order to achieve a high density green body, the as-mixed suspensions, which had solid contents of 40-50 wt%, were further concentrated to ~57 wt%. During the concentration, the suspensions were subjected to ultrasonic treatments every 30 minutes using an ultrasonicator (MSE Scientific Instruments, Manchester, UK) to break up any agglomerate that formed and hence to control the viscosity of the suspensions at ~80 mPa at 100 s -1 shear rate. Full details of the concentration method have been provided elsewhere 14,15 .
The suspensions were then spray freeze dried to yield granules that possessed high flowability, due to their spherical shape, and high crushability, due to their porous structure after the ice was sublimed. A foaming agent consisting of 2 vol% Freon (trichlorofluoromethane, Fisher Scientific UK Limited, UK) was added to the high solid content suspensions prior to the spray freeze drying to improve the granule crushability. In the spray freezing stage, the suspension was dripped onto an ultrasonic rod using a pipette so that droplets were formed that subsequently fell into liquid nitrogen and froze. The beakers containing the frozen granules were subsequently connected to a freeze dryer (Virtis®, Benchtop SLC, New York, USA), that was connected in turn to a double stage, oil-sealed, rotary vane vacuum pump (Leybold® D2.5B, Leybold vacuum GmbH, Oberkochen, Germany) with an exhaust filter allowing the droplets to be freeze dried under a vacuum of <100 mTorr at -50˚C; the process took about 2 days. Full details of the spray freeze drying method have been provided elsewhere 16 .
After drying, the granulated powder was sieved to achieve granules in the range 125 to 250 µm and die pressed at 250 MPa to achieve green densities of ~55% of theoretical. The pellets, which measured 10 mm diameter and 4 mm thickness, were then sintered at temperatures in the range 1400 to 1500˚C with a constant heating rate of 10˚C min -1 and hold time of 10 hours in order to achieve densities of >99%. The alumina grain sizes were ~1 µm in all samples, thus eliminating grain size variations from having an effect on the mechanical properties. The crystalline phases of the zirconia grains in the ZTA materials were analysed using X-ray diffraction (XRD), the result indicated that both the 10% and 15% ZTA showed 100% tetragonal zirconia phase. The details of the sintering conditions and the resultant densities and grain sizes are listed in Table 2.

Indentation
All specimens were sequentially polished using a series of diamond grits of 9, 3 and 1 µm To allow the plastic zone for each indent to be examined, two polished samples were bonded together using superglue and then the top, joined surface was polished again to 1 µm grit size. The indentations were then made along the join line and the two samples separated by dissolving the glue in acetone. A schematic drawing is shown in Figure 2 (a). The plastic zone was observed using optical microscopy, as shown in Figure 2 (b), and its size confirmed to be similar to the half-length of the diagonal of the indent.

Determination of the zirconia phases
The zirconia phases present in and around the indents were investigated using a highresolution confocal Raman spectrometer (Horiba Yvon Raman LabramHR, Horiba Jobin Yvon SAS, Villeneuve d΄Ascq, France) equipped with a liquid nitrogen cooled CCD detector and incident radiation from a He red laser at 633 nm. The laser power was 20 mW, the spectrum integration time was 40 s and an objective lens with ×100 magnification was used.
Raman spectra between 100 and 400 cm -1 were recorded. This range was selected as the main monoclinic bands are at 181 and 192 cm -1 , whilst the primary tetragonal bands are at 148 and 264 cm -1 . 6,17 A line scan of the zirconia phase transformation from the sample surface outside the indent towards its centre was carried out; a schematic drawing is shown in Figure 3.. The laser was first focused on the polished surface and then scanned towards the indent centre, the scanning lines were 60 µm long with a step of 3 µm and the laser was auto-focused at each step. The transformed monoclinic zirconia concentration (m) was quantitatively determined using the equation 17 : (3) where I is the intensity of the peaks and the subscript indicates the corresponding phase, whilst the superscript indicates the peak position in reciprocal centimetres.

Cr 3+ fluorescence spectroscopy
Cr 3+ fluorescence spectra were obtained using the same equipment as was used for the Raman spectra in section 2.3. The smallest surface spot size of 1.5 μm was achieved using a ×100 objective lens and a confocal aperture of 20 µm diameter (the spot size was measured by focusing the laser on a SiC surface and then measuring the size of the light spot directly).
For each measurement, a region of interest was selected using the optical microscope with white light.
The Cr 3+ fluorescence analysis was carried out in two stages. Firstly, a depth scan 12 was performed to investigate the confocal resolution and degree of laser transparency of each sample. To achieve this, the laser was initially focused on each 1 µm polished sample surface at a remote location from the indents, this position was set as zero; then the specimen stage was moved upward by 100 µm, so that the laser focal plane was below the surface. Scanning was then carried out in the direction normal to the sample surface in 2 µm steps from the starting position, -100 µm, to +50 µm above the surface with the Cr 3+ fluorescence spectra being collected at each step. Secondly, line scanning was again performed as described in section 2.3, but this time collecting the Cr 3+ fluorescence spectra. Note that for both the depth scanning and line mapping, the results were repeatable.
The collected data were subsequently analysed with a constrained 4-peak fitting method 13,18 using fitting software, Auto2Fit 5.5 (7-D software, China). Essentially, two doublets of the R1 and R2 peaks were fitted using a mixed Lorentzian and Gaussian function subject to the constraint that the R1 to R2 peak area ratio for any individual doublet was equal to 2.0 13 . Finally, the peak position and width were identified and used to investigate the residual stresses and dislocation densities after each indentation test. Since a certain amount of residual stresses could be generated during the sintering process and, particularly, surface polishing, all the peak shifts and broadenings of the indentation-tested samples were compared with data obtained after sintering and polishing but before indenting.

FIB lift-out from the indentation centre and TEM analysis
In order to observe the microstructure inside each indent, transmission electron microscopy (TEM, JEOL 2000FX) was carried out on thin foil samples lifted out from the centre of 1 kg indents made in the alumina and 10% ZTA.
To prepare the lift-out samples, a focused ion beam system (Nova Nanolab 600, FEI, Netherlands) was used and the lift-out procedure is illustrated in Fig. 4 where n is the number of intercepts and L is the overall length of the lines.

Results and Discussion
The densities, grain sizes, mechanical properties and zirconia phase conditions of the samples to be studied are listed in Table 3.

Depth scanning and laser penetration
The depth scanning results of the Cr 3+ fluorescence are shown in Figure 63, which plots the R1 peak intensity, normalized using the maximum intensity, covering stage displacements from 100 µm (i.e. focus is below the surface) to +50 µm. For all the three materials, alumina,

Cr 3+ fluorescence analysis on the indentation centre -origin of the sharp peaks and broad peaks
The Cr 3+ fluorescence spectra from the indent centres of the three materials are shown in Figure 74. All the spectra were 4-peak fitted to separate the two doublets; examples of the curve fitting are shown in Figure 85, which shows one doublet with broad R1 and R2 peaks and the other doublet with sharp R1 and R2 peaks in each example. The broad peaks, which displayed very significant negative peak shift and peak broadening, are believed to originate from within the plastic zone as the materials experienced extensive plastic deformation caused by the high compressive load during indentation. On the other hand, very limited peak shift and peak broadening were observed for the sharp peaks from each sample, which suggests that these peaks may have originated from outside the plastic zone.
Measurements of broad peak percentage, peak shift and peak width were made on the broad peaks from the alumina, as a baseline material, and are listed in Table 4. The broad peak percentage was measured by calculating the area ratio of the broad R1 peak compared to the sum of the broad and sharp R1 peaks. When a 1 kg indentation was used, about 79% of the signal was collected from the plastic zone; the data also showed a ~32 cm -1 shift of the broad peak and broadening of ~56 cm -1 . This result is very consistent with that of Guo and forming freshly yielded zones outside the previously formed plastic zone, without affecting the stress level beneath the indenter significantly. 19 The result also confirmed that the fitted broad peaks are physically meaningful and that the fitting work was applicable to the full range of indentation loads used in this study.
The same broad peak analysis was also performed on the ZTA samples. Compared to the case for alumina, the broad peak percentages were significantly reduced for the ZTA indentations for all the indentation loads. The values as a function of plastic zone size are shown in Figure 96, confirming that the strong, sharp peak doublets in the ZTA originated from the material outside the plastic zone due to the much greater laser scattering with the ZTA samples.

Effect of zirconia phase transformation on the residual stress distribution around indents.
After confirming the origins of the sharp and broad peaks in alumina and ZTA, the residual stresses at the indent centres formed under different loads were studied based on the peak shift of the broad R1 fluorescence peaks, as shown in Figure 107. An increase in peak shift with increasing indentation load may be observed for all three materials, however, no significant difference can be observed in terms of their peak shift between alumina and ZTAs, which suggests that either the zirconia phase transformation did not happen at the indent centre or, if it did, it had a very limited effect on the residual stress change in the alumina grains. Determining which explanation was valid was achieved via Raman analysis of the zirconia phases inside and around the indents. A further factor that is important to note in interpreting these zirconia phase content results is that, like the Cr 3+ fluorescence results, they reflect the phase content in the total sampling volume, some of which lies outside the immediate region on which the laser is focused, particularly in the ZTAs. Because of the greater breadth of the Raman peaks compared with the Cr 3+ fluorescence peaks, however, the signal from the plastic zone cannot be extracted by multiple peak fitting. The phase contents measured should therefore be regarded as semiquantitative.
Nevertheless, the trend of a reduction in the degree of zirconia phase transformation towards the indentation centre is very clear; a similar result was obtained by Paul et al. 20 for nano zirconia. The cause is believed to originate in the increasingly high compressive stresses towards the indent centre, which will have suppressed the volume expansion that occurs during the phase transformation. However, the high monoclinic content near the edge of the indentation, where there are tensile stress components 20 , demonstrates unequivocally that the tetragonal to monoclinic transformation did take place in the region where permanent deformation was occurring as the indentation load increased. We tentatively suggest, therefore, that some of the monoclinic zirconia formed around the indenter during loading may also have transformed back to tetragonal zirconia as the indentation expanded and enveloped this initially transformed material in the highly compressive region beneath the indenter. Previous results on 3Y-TZP with conventional grain size 21 do not show this effect.
One reason for this may be that the significantly higher stiffness of ZTA compared with 3Y-TZP is expected to lead to correspondingly higher compressive stresses in the plastic zone, which would favour reverse transformation. It may also reflect differences between the transformability of nanosize zirconia grains with grain sizes close to nano range and conventional materials and clearly merits further investigation.
The same experiments were carried out on the 10% ZTA and the indents with different loads. The same trend of reduction in the degree of zirconia phase transformation towards the indentation centre was observed. The results are listed in Table 5, in which only the content of transformed monoclinic zirconia phase on the edge of the indent and in the indent centre are displayed. It should be noted that an error of about ± 5% was observed, due to the factors mentioned before which affected the accuracy of the quantitative measurements; within experimental error, no significant difference was observed with variation of either zirconia content or indentation load.
A line scan of the R1 peak shift with distance to the indent centre was made and the results are shown in Figure 129. For all samples, the compressive residual stress increased significantly from the unloaded surface to the indent centre owing to the constraint on the expanded indentation region from the unyielded material surrounding it. The peak shift inside the indent, in the range of 30 to 10 µm from the indent centre, displayed consistently lower values for the ZTA samples compared to the alumina, Figure 129. The mean difference was ~4 cm -1 , corresponding to a hydrostatic stress of ~500 MPa. Although there was virtually no zirconia monoclinic phase at the centre of the indent, the amount of transformation increased significantly on the inclined indent surface, particularly from 10 to 30 µm away from the centre, Figure 11 8 (a). Therefore, it is very likely that the observed lower residual stresses in the ZTAs compared to the alumina originated from the zirconia phase transformation.
Gregori et al. 22 found that there was a linear relationship between the degree of zirconia phase transformation and the residual tensile stress produced in the alumina matrix of ZTA.
The explanation is that during the zirconia phase transformation process, the volume expansion of transformed zirconia grains is resisted by the surrounding alumina matrix putting the zirconia into compression and the alumina into tension 23  The dislocation densities at the centre of the indents formed under different loads were compared using the peak width changes in the broad R1 fluorescence peaks, as shown in Figure 13 10 (a). In each case there was a clear increase in the peak broadening between the 10 and 20 kg indents, though it was less in the ZTA samples than the alumina. Assuming that dislocation formation was the dominant source of broadening, this indicates that the alumina dislocation densities at the indent centres of the ZTA materials were lower than in the pure alumina.
Following the same mapping points illustrated in Figure 129, the peak width change from the unloaded surface to the indent centres for the 10 kg indentations are shown in Figure 13 10 (b). The alumina sample showed a sharp increase in the values around the edge of the indent and the change of peak width, from about 10 to 55 cm -1 , remained fairly constant within the indent. For the ZTAs, however, the peak width increased reasonably smoothly along most of the mapping route, until reaching a similar value to that of the alumina at the indent centre. This more gradual peak broadening associated with the ZTAs could also have originated from the zirconia phase transformation inside the indentations. It can be observed that the peak width difference between the ZTAs and alumina was gradually reduced nearer to the indent centre, which is again consistent with the trend of a reduced zirconia transformation, i.e. the fraction of monoclinic phase, from the edge of the indentation to its centre, as discussed in Section 3.3. The volume change during transformation could directly contribute to the deformation at the edge of the plastic zone during loading but could be magnified considerable when the large shear deformation (~0.16) also occurring is taken into account. In isotropic conditions, the net shear is effectively removed by twinning 24 but in the presence of a deviatoric stress, such as exists at the edge of the indentation 19 , the twinning will occur in order to minimise the mechanical energy of the system, producing potentially large net shear strains that can also contribute to the deformation process, leaving less requirement for dislocation and twinning mediated plastic deformation in the alumina matrix.
Even if some reverse transformation does occur as indentation progresses, as suggested in section 3.3, a residual ferroelastic switching may remain, preserving the shape of the indentation and again reducing the plastic strain contributed by the alumina matrix.

TEM analysis
As indicated earlier, in order to observe the microstructure inside the plastic zone, FIB liftout was performed on the 1 kg indents centre of a 10% ZTA and an alumina sample. The samples were then characterised using TEM. The results are shown in Figure 1411. It should be noted that the sizes of the 1 kg indents on the ZTA and alumia samples are around 20 µm, which is comparable to the final electron transparent part of the TEM lamellae. Therefore, the TEM observation from these lamellae should be representative to the microstructure of the plastic zones in ZTA and alumina. For both the samples, it was observed that there were very many dislocations inside the plastic zone, as expected. In the alumina sample, dislocation entanglements were observed across the whole lift-out sample area and the grain boundaries were not easily observed because of the high dislocation density, Figure 14 11 (a) and (c).
The situation was different for the 10% ZTA sample, however, where only the exact indent centre had a high dislocation density (as highlighted in Fig. 11 b and d) and across the rest of the lift-out sample the grain boundaries could be observed clearly, Figure 14 11 (b) and (d).
This observation is consistent with the peak broadening mapping shown in Figure 13 10 (b).
According to the change of peak width, which is about 55 to 60 cm -1 for both alumina and ZTA samples, the dislocation density in the plastic zone was as high as 10 16 -10 17 m -1 .
Therefore, it was difficult to quantify the difference in dislocation density between the alumina and the ZTA from the TEM observation. Using the high magnification TEM images (an example is shown in Figure 5), it was calculated that the microcrack densities of the alumina and 10% ZTA were 600±50 and 350±50 m -1 , respectively. The lower microcrack density in the ZTA confirmed the effect of the zirconia phase transformation on restricting crack propagation.

Conclusions
The residual stresses around 1 to 20 kg indentations in alumina and 10% and 20% nano ZTA have been measured using Cr 3+ fluorescence microscopy. According to depth scanning of the Cr 3+ fluorescence peak intensity, a significant laser scattering effect in the ZTA samples was observed. The broad peaks were confirmed to be generated inside the plastic zone, due to the consistency of the measured percentage of R1 broad peak and the expected percentage of signal from inside the plastic zone with different indentation loads The peak shift analysis on the three materials showed no significant difference in the residual stresses in the indent centres between alumina and ZTA samples. This is believed to be because, in the ZTA samples, the zirconia phase transformation at the indent centre was suppressed by the high compressive stress. The degree of zirconia transformation increased, however, towards the edge of indent and the ZTA samples showed ~500 MPa reduction in the net compressive residual stress in the alumina matrix compared to the pure alumina sample. This was probably caused by the generation of tensile residual microstresses in the alumina grains due to the zirconia phase transformation. The similarity in stress around the indentations suggested the mean residual stress in the indentation plastic zone was the same for all three materials.
In addition, it was found that the ZTA materials displayed lower dislocation densities on the indentation surfaces away from the centre, where the zirconia phase transformation occurred. This effect was considered to be caused by the contribution of the zirconia transformation to the total deformation. The TEM study has shown that the plasitic zone microstructure of pure alumina and ZTA are different, which also confirms the observation from Cr 3+ fluorescence study. The relatively lower microcrack density in the plastic zone for the ZTA materials was confirmed by examining the plastic zone microstructure using high resolution TEM.