《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_Atomic force microscopy of transformation toughening

Availableonlineatwww.sciencedirect.com SCIENCE DIRECT● E噩≈S ELSEVIER Journal of the European Ceramic Society 25(2005)3089-3096 www.elsevier.com/locate/jeurceramsoc Atomic force microscopy of transformation toughening in ceria-stabilized zirconia Sylvain deville Hassan El attaoui. Jerome Chevalier* National Institute of Applied Science, Materials Department, Associate Research Unit 5510(GEMPPM-INSA) Bat B pascal. 20 avenue albert einstein. 6962/ Villeurbanne cedex. france Received 9 April 2004; received in revised form 9 July 2004; accepted 16 July 2004 Available online 27 September 2004 Abstract We demonstrate in this paper that atomic force microscopy can be successfully used to gain further insights into the understanding of transformation toughening in ceria-stabilized zirconia. Transformation was induced by stresses accumulated in the region surrounding propagating cracks in double torsion samples. The resolution provided by aFm at the surface of the samples made it possible to observe the formation of self-accommodated martensite pairs in the near crack areas. The potential for transformation is found to decrease with increasing alloying addition, and is totally suppressed for 16 mol%CeOz-TZP samples. A statistical analysis of the martensite pair orientation is performed, and the relationship with the applied stress and strain fields is discussed. The contribution to transformation toughening by transformation-induced plasticity occurring in the formation of martensitic variant pairs with small net shear is demonstrated. The influence of alloying addition content on the potential for transformation toughening and fracture toughness values is finally discussed C 2004 Elsevier Ltd. All rights reserved Keywords: Atomic force microscopy; Toughening: CeO2-ZrO2; AFM 1. Introduction studies over the last 30 years. The martensitic nature of the t-m transformation has been investigated by various methods The discovery by Garvie et al. of transformation tough- among which are X-ray diffraction, scanning electron mi potentiality for obtaining very high toughness materials by and more recently atomic force microscopy -10 cross ning of zirconia opened the way towards a very large field croscopy, optical microscopy with Normarsky contrast net of investigations for materials scientists and engineers. The tron powder diffraction,transmission electron careful control of the zirconia ceramics microstructure relies Several theories have been developed to describe and pre- on the metastable retention of the tetragonal phase at ambi- dict transformation toughening -16 They are based mainly ent temperature. 2 Upon the action ofexternal stresses, such as on mechanical or energetic considerations. Independently of in the surrounding zones of a propagating crack, tetragonal theory, it can be shown that the martensitic transformation grains may transform to their stable monoclinic structure emperature Ms can be reduced by alloy additions, so that ince the transformation is accompanied by a large shear spontaneous transformation upon cooling to room tempera (0. 16)and volume expansion(0.04), the stresses and strains ture does not occur. The net driving force of the transforma- induced by the transformation lead to the formation of a zone tion can then be lowered even down to room temperature. with large compressive stresses that can partially close the until such point as an external stress is applied to the sys- crack and slow down its propagation, increasing the material tem. This is the origin of transformation toughening. Sev- toughness. This phenomenon has been the object of numerous eral oxides are well known to retain zirconia in its tetragonal structure at ambient temperature, totally or partially, i.e. yttria Corresponding author. Tel: +33472426125; fax:+334 85 28. (Y203), ceria(CeO2)or magnesia(MgO). A great number 0955-2219/S-see front matter c 2004 Elsevier Ltd. All rights reserved doi: 10.1016/j. jeurceramsoc. 2004.07.029

Journal of the European Ceramic Society 25 (2005) 3089–3096 Atomic force microscopy of transformation toughening in ceria-stabilized zirconia Sylvain Deville, Hassan El Attaoui, Jer´ ome Chevalier ˆ ∗ National Institute of Applied Science, Materials Department, Associate Research Unit 5510 (GEMPPM-INSA), Bat B. Pascal, 20 avenue Albert Einstein, 69621 Villeurbanne Cedex, France Received 9 April 2004; received in revised form 9 July 2004; accepted 16 July 2004 Available online 27 September 2004 Abstract We demonstrate in this paper that atomic force microscopy can be successfully used to gain further insights into the understanding of transformation toughening in ceria-stabilized zirconia. Transformation was induced by stresses accumulated in the region surrounding propagating cracks in double torsion samples. The resolution provided by AFM at the surface of the samples made it possible to observe the formation of self-accommodated martensite pairs in the near crack areas. The potential for transformation is found to decrease with increasing alloying addition, and is totally suppressed for 16 mol% CeO2–TZP samples. A statistical analysis of the martensite pair orientation is performed, and the relationship with the applied stress and strain fields is discussed. The contribution to transformation toughening by transformation-induced plasticity occurring in the formation of martensitic variant pairs with small net shear is demonstrated. The influence of alloying addition content on the potential for transformation toughening and fracture toughness values is finally discussed. © 2004 Elsevier Ltd. All rights reserved. Keywords: Atomic force microscopy; Toughening; CeO2–ZrO2; AFM 1. Introduction The discovery by Garvie et al.1 of transformation tough￾ening of zirconia opened the way towards a very large field of investigations for materials scientists and engineers. The potentiality for obtaining very high toughness materials by careful control of the zirconia ceramics microstructure relies on the metastable retention of the tetragonal phase at ambi￾ent temperature.2 Upon the action of external stresses, such as in the surrounding zones of a propagating crack, tetragonal grains may transform to their stable monoclinic structure.3 Since the transformation is accompanied by a large shear (0.16) and volume expansion (0.04), the stresses and strains induced by the transformation lead to the formation of a zone with large compressive stresses that can partially close the crack and slow down its propagation, increasing the material toughness. This phenomenon has been the object of numerous ∗ Corresponding author. Tel.: +33 4 72 42 61 25; fax: +33 4 72 43 85 28. E-mail address: jerome.chevalier@insa-lyon.fr (J. Chevalier). studies over the last 30 years. The martensitic nature of the t-m transformation has been investigated by various methods among which are X-ray diffraction,4 scanning electron mi￾croscopy, optical microscopy with Normarsky contrast,5 neu￾tron powder diffraction,6 transmission electron microscopy,7 and more recently atomic force microscopy.8–10 Several theories have been developed to describe and pre￾dict transformation toughening.11–16 They are based mainly on mechanical or energetic considerations. Independently of theory, it can be shown that the martensitic transformation temperature Ms can be reduced by alloy additions, so that spontaneous transformation upon cooling to room tempera￾ture does not occur. The net driving force of the transforma￾tion can then be lowered even down to room temperature, until such point as an external stress is applied to the sys￾tem. This is the origin of transformation toughening. Sev￾eral oxides are well known to retain zirconia in its tetragonal structure at ambient temperature, totally or partially, i.e. yttria (Y2O3), ceria (CeO2) or magnesia (MgO). A great number of studies have been dedicated to these three types of mate- 0955-2219/$ – see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2004.07.029

3090 S Deville et al. /Journal of the European Ceramic Sociery 25(2005)3089-3096 rials. For a review on the subject, see the work of Green increasing stabilizer content, i.e. 10, 12 and 16 mol% Ceo2 Hannink et al. 17 Grain size(measured by the linear intercept method on ther Several reinforcing effects might account for an increase mally etched samples)and fracture toughness( measured by of material toughness. The critical stress intensity factor can double torsion experiments)are given in Table 1. This shows be described by the combination of the matrix intrinsic tough- that the grain size is the same for all the samples, the only ness and the addition of crack-shielding mechanisms, among difference lying in the alloying content. It is widely docu- which transformation toughening and crack bridging arise in mented from the literature2 that the larger the CeO, content the particular case of ceria-doped zirconia. The prediction of the lower the toughnes the toughness can be achieved by the prediction and quan- tification of these different crack-shielding mechanisms In 2.2. Double torsion tests particular, the development of a reliable theory of transforma- The double torsion test was used to induce stress-assisted and strain field distribution in the crack tip surrounding zone. phase transformation in the surrounding of the propagat crystallography(PTMC) 8 9 to ogical theory of martensitic The relevance of the phenomen ng crack and to assess quantitatively transformation tough describe the strain field ening effects. The details of the method may be found now recognized A contribution to transformation toughening elsewhere.20), 2I No guiding groove was machined in the spec by transformation-induced plasticity results from the forma- imen in order to avoid any residual stress intensity factor.A tion of martensitic variant pairs with large associated shear notch was machined with a diamond saw and an indentation strain, absorbing some energy in the formation of these vari- was performed at low load (10 kg)to initiate a small crack, ants, energy that would otherwise be available for crack prop- as seen in Fig. 1. Crack rates versus KI curves were used agation, increasing thus the toughness of the material Using to determine the fracture toughness values of the materials the PTMC to describe transformation toughening is very ap. These curves will be discussed in another paper pealing indeed. However, even if the theory can predict pre cisely the local strain distribution, achieving the comparison 2.3. Atomic force microscopy and optical observations of theoretical calculations and experimental results has not yet been possible, as a result of the observational difficulties AFM experiments were carried out with a D3100 at the scale at which the transformation is occurring(a few nanoscope from Digital Instruments Inc, using oxide sharp- nanometers). Fortunately, the development of atomic force ened silicon nitride probes in contact mode, with an average microscopy provides a tool for investigating local relief of scanning speed of 10 ums. Since the t-m phase transfor few nanometers height. The potentiality to observe autoclave mation is accompanied by large strains(4% volume and 16% ageing induced martensitic relief in yttria stabilized zirconia shear), surface relief is modified by the formation of mon- with great has been demonstrated recently. 0 The aclinic phase. The lateral(2 nm)and vertical (0. I nm)res- aim of this study is to show that further insights can be gained olution of AFM makes it possible to follow very precisely from AFM experiments in the description and subsequent un- the transformation induced relief at the surface. The transfor derstanding of transformation toughening in zirconia mation zones were also photographed with an optical micro- scope using the Normarsky interference contrast technique (Zeiss Axiophot, Germany) 2. Materials and methods 2.1. Processing 3. Results Ceria-stabilized zirconia(CeO2-TZP)materials were pro- 3.1. Transformation bands cessed by a classical processing route, using Zirconia Sales Ltd. powders, with uniaxial pressing, cold isostatic pressing The surface of double torsion samples after partial crack and sintering at 1550C for two hours. Residual porosity was propagation observed by optical microscopy in Normarsky negligible. Different compositions have been processed, with contrast is shown in Fig. 1. Great differences in behavior are Table I Materials of the study Material Ceria content Fracture toughness ( mol% (MPam-I2 3 16Ce-TZP All the samples exhibit a similar grain size. The only variable is the stabilizer content. Fracture toughness values were provided by double torsion relaxation

3090 S. Deville et al. / Journal of the European Ceramic Society 25 (2005) 3089–3096 rials. For a review on the subject, see the work of Green2 or Hannink et al.17 Several reinforcing effects might account for an increase of material toughness. The critical stress intensity factor can be described by the combination of the matrix intrinsic tough￾ness and the addition of crack-shielding mechanisms, among which transformation toughening and crack bridging arise in the particular case of ceria-doped zirconia. The prediction of the toughness can be achieved by the prediction and quan￾tification of these different crack-shielding mechanisms. In particular, the development of a reliable theory of transforma￾tion toughening requires a deep understanding of the stress and strain field distribution in the crack tip surrounding zone. The relevance of the phenomenological theory of martensitic crystallography (PTMC)18,19 to describe the strain field is now recognized. A contribution to transformation toughening by transformation-induced plasticity results from the forma￾tion of martensitic variant pairs with large associated shear strain, absorbing some energy in the formation of these vari￾ants, energy that would otherwise be available for crack prop￾agation, increasing thus the toughness of the material. Using the PTMC to describe transformation toughening is very ap￾pealing indeed. However, even if the theory can predict pre￾cisely the local strain distribution, achieving the comparison of theoretical calculations and experimental results has not yet been possible, as a result of the observational difficulties at the scale at which the transformation is occurring (a few nanometers). Fortunately, the development of atomic force microscopy provides a tool for investigating local relief of a few nanometers height. The potentiality to observe autoclave ageing induced martensitic relief in yttria stabilized zirconia with great precision has been demonstrated recently.10 The aim of this study is to show that further insights can be gained from AFM experiments in the description and subsequent un￾derstanding of transformation toughening in zirconia. 2. Materials and methods 2.1. Processing Ceria-stabilized zirconia (CeO2–TZP) materials were pro￾cessed by a classical processing route, using Zirconia Sales Ltd. powders, with uniaxial pressing, cold isostatic pressing and sintering at 1550 ◦C for two hours. Residual porosity was negligible. Different compositions have been processed, with Table 1 Materials of the study Material Ceria content (mol%) Sintering temperature (◦C) Grain size (linear intercept) (
m) Fracture toughness (MPa m−1/2) 10Ce–TZP 10 1550 3.7 18 12Ce–TZP 12 1550 3.5 8.1 16Ce–TZP 16 1550 3.4 4.3 All the samples exhibit a similar grain size. The only variable is the stabilizer content. Fracture toughness values were provided by double torsion relaxation experiments. increasing stabilizer content, i.e. 10, 12 and 16 mol% CeO2. Grain size (measured by the linear intercept method on ther￾mally etched samples) and fracture toughness (measured by double torsion experiments) are given in Table 1. This shows that the grain size is the same for all the samples, the only difference lying in the alloying content. It is widely docu￾mented from the literature2 that the larger the CeO2 content, the lower the toughness. 2.2. Double torsion tests The double torsion test was used to induce stress-assisted phase transformation in the surrounding of the propagat￾ing crack and to assess quantitatively transformation tough￾ening effects. The details of the method may be found elsewhere.20,21 No guiding groove was machined in the spec￾imen in order to avoid any residual stress intensity factor. A notch was machined with a diamond saw and an indentation was performed at low load (10 kg) to initiate a small crack, as seen in Fig. 1. Crack rates versus KI curves were used to determine the fracture toughness values of the materials. These curves will be discussed in another paper. 2.3. Atomic force microscopy and optical observations AFM experiments were carried out with a D3100 nanoscope from Digital Instruments Inc., using oxide sharp￾ened silicon nitride probes in contact mode, with an average scanning speed of 10
m s−1. Since the t–m phase transfor￾mation is accompanied by large strains (4% volume and 16% shear), surface relief is modified by the formation of mon￾oclinic phase. The lateral (2 nm) and vertical (0.1 nm) res￾olution of AFM makes it possible to follow very precisely the transformation induced relief at the surface. The transfor￾mation zones were also photographed with an optical micro￾scope using the Normarsky interference contrast technique (Zeiss Axiophot, Germany). 3. Results 3.1. Transformation bands The surface of double torsion samples after partial crack propagation observed by optical microscopy in Normarsky contrast is shown in Fig. 1. Great differences in behavior are

S Deville et al. / Journal of the European Ceramic Sociery 25(2005)3089-3096 10CeTZP cRack tip Crack propagation 500m 2 12CeTZ Fig. 2. AFM observation of a transformed band in 10Ce-TZP Some gr pop-out induced by polishing could be seen. The transformed band exhibiting typical martensitic relief is running through the entire micrograph Fig. 1. Optical observation of a partially propagated crack at the surface of Some finger-like elongated transformed for thermal martensite, 0 are also visible. The presence of ands could be seen around the crack of the 10Ce-TZP sample. The AFM large shear planes is observed, planes acting together to form bservation zones are indicated on the micrograph. Arrow indicates the crack self-accommodating martensitic variant pairs. The formation of smaller variant pairs to accommodate strain near the grain boundaries is observed. another zone extracted from the near observed when the alloying content is increased. For low sta- crack tip zone is shown in Fig 4. The same type of marten- bilizer content(10 mol%), the formation of elongated trans- sitic relief is observed, suggesting the near crack tip zones formed zones ahead of the crack tip is clearly observed. The and secondary transformed bands are formed by the same presence and shape of these zones have been the object of nu- mechanism. i.e. stress induced transformation nerous studies in the past,22-25and their presence is thought to be related to the autocatalytic behavior of the transforma- 3.2. Near crack transformation tion propagation of these materials Not only the material is transformed in the surrounding zones of the crack, but some AFM observations of the surroundings of a propagated finger-like transformed bands are also found on both sides of crack in 12Ce-TZP and 16Ce-TZP are shown in Figs. 5 and 6 the crack. These bands will later be referred to as secondary ands. All the following AFM observations were performed X 2.000 um/div in particular zones of these bands, as indicated in Fig. la. It Z 2000.000 Hm/div is already worth mentioning that the transformed bands may extend very far away from the crack tip, demonstrating thus the very high propensity for stress induced transformation of this particular composition. The formation mechanism of these bands will be discussed later When the stabilizer content is increased, the secondary bands disappeared, and the transformation around the crack becomes hardly visible with an optical microscope. No dif- ferences are optically observed between the 12Ce-TZP and 16Ce-TZP samples a detailed part of a secondary transformed band observed by AFM is shown in Fig. 2. Slight grain pop-out induced by the polishing process is visible at the surface, and the trans- formed band running through the micrograph is visible. A Fig 3. Detailed zone of Fig. 2(10Ce-TZP)showing a typical stack of self- typical feature of the relief is extracted in Fig. 3, where all accommodating martensitic variant pairs. Note the very large shear strain the martensitic characteristic features previously described induced by the transformation

S. Deville et al. / Journal of the European Ceramic Society 25 (2005) 3089–3096 3091 Fig. 1. Optical observation of a partially propagated crack at the surface of the various double torsion samples. Some finger-like elongated transformed bands could be seen around the crack of the 10Ce–TZP sample. The AFM observation zones are indicated on the micrograph. Arrow indicates the crack tip. observed when the alloying content is increased. For low sta￾bilizer content (10 mol%), the formation of elongated trans￾formed zones ahead of the crack tip is clearly observed. The presence and shape of these zones have been the object of nu￾merous studies in the past,22–25 and their presence is thought to be related to the autocatalytic behavior of the transforma￾tion propagation of these materials. Not only the material is transformed in the surrounding zones of the crack, but some finger-like transformed bands are also found on both sides of the crack. These bands will later be referred to as secondary bands. All the following AFM observations were performed in particular zones of these bands, as indicated in Fig. 1a. It is already worth mentioning that the transformed bands may extend very far away from the crack tip, demonstrating thus the very high propensity for stress induced transformation of this particular composition. The formation mechanism of these bands will be discussed later. When the stabilizer content is increased, the secondary bands disappeared, and the transformation around the crack becomes hardly visible with an optical microscope. No dif￾ferences are optically observed between the 12Ce–TZP and 16Ce–TZP samples. A detailed part of a secondary transformed band observed by AFM is shown in Fig. 2. Slight grain pop-out induced by the polishing process is visible at the surface, and the trans￾formed band running through the micrograph is visible. A typical feature of the relief is extracted in Fig. 3, where all the martensitic characteristic features previously described Fig. 2. AFM observation of a transformed band in 10Ce–TZP. Some grain pop-out induced by polishing could be seen. The transformed band exhibiting typical martensitic relief is running through the entire micrograph. for thermal martensite,10 are also visible. The presence of large shear planes is observed, planes acting together to form self-accommodating martensitic variant pairs. The formation of smaller variant pairs to accommodate strain near the grain boundaries is observed. Another zone extracted from the near crack tip zone is shown in Fig. 4. The same type of marten￾sitic relief is observed, suggesting the near crack tip zones and secondary transformed bands are formed by the same mechanism, i.e. stress induced transformation. 3.2. Near crack transformation AFM observations of the surroundings of a propagated crack in 12Ce–TZP and 16Ce–TZP are shown in Figs. 5 and 6. Fig. 3. Detailed zone of Fig. 2 (10Ce–TZP) showing a typical stack of self￾accommodating martensitic variant pairs. Note the very large shear strain induced by the transformation

S Deville et al. /Journal of the European Ceramic Sociery 25(2005)3089-3096 transformed zone 2 Fig 4. Border zone of the surrounding of the propagated crack in 10Ce-TZP Transformed variants(a-c) perpendicular to the crack path are clearly visible, rains having their ct axis nearly perpendicular to the surface Some detailed zones are highlighted in Fig. 5, where the 2 um martensitic relief is further investigated. The formation of rows indicating the junction plane of such pairs. It is obvious Fig. 6. Surrounding of the propagated crack in 16Ce-TZP No transforma- that very few grains are transformed along the crack path. as opposed to what was observed for the I0Ce-TZP sample. 3.3. Transformation sequence Only some of the grains adjacent to the crack were able to transform under stress. This is a clear demonstration of the The very local observations of transformation induced re- variation of propensity for transformation with the alloying lief bring new information about the toughening mechanism addition modification. This point will be further discussed sequence. Fig. 8 shows a transformed grain with the prop- agated crack running through it. A fragmentation of trans- The transformation zone width( measured at the same dis- formed planes due to the crack is observed. It can therefore ance from the notch tip for all the samples)is much decreased be safely assumed that the transformation occurred before when stabilizer content is increased, and no transformation at crack propagation. While the crack is still stationary, stresses all is observed when the stabilizer content reaches 16 mol%. are building up in its surroundings. Once these stresses are Though very large stresses are expected in the surrounding of high enough, transformation of the grains in these zones the transformation energy barrier and trigger the transforma- increasing, the crack will be free to further tresses continue the crack, these stresses were not high enough to overcome tion. The variation of transformed zone width and toughness transformed zones These results have been confirmed by as a function of stabilizer content is plotted in Fig. 7. It is quite complementary acoustic emission experiments. 26 clear from the graph that the toughness is directly related to Moreover, for lattice correspondence Cab (at, bt, ct axes the propensity for transformation of the tetragonal phase changes into cm, am, bm axis of the 5 um Primary junction plane Fig. 5. Surrounding of the propagated crack in 12Ce-TZP. Transformed variants are clearly visible. The transformed zone width is much smaller than for the 10Ce-TZP sample

3092 S. Deville et al. / Journal of the European Ceramic Society 25 (2005) 3089–3096 Fig. 4. Border zone of the surrounding of the propagated crack in 10Ce–TZP. Transformed variants (a–c) perpendicular to the crack path are clearly visible, for grains having their ct axis nearly perpendicular to the surface. Some detailed zones are highlighted in Fig. 5, where the martensitic relief is further investigated. The formation of self-accommodating variant pairs is also observed, with ar￾rows indicating the junction plane of such pairs. It is obvious that very few grains are transformed along the crack path, as opposed to what was observed for the 10Ce–TZP sample. Only some of the grains adjacent to the crack were able to transform under stress. This is a clear demonstration of the variation of propensity for transformation with the alloying addition modification. This point will be further discussed later. The transformation zone width (measured at the same dis￾tance from the notch tip for all the samples) is much decreased when stabilizer content is increased, and no transformation at all is observed when the stabilizer content reaches 16 mol%. Though very large stresses are expected in the surrounding of the crack, these stresses were not high enough to overcome the transformation energy barrier and trigger the transforma￾tion. The variation of transformed zone width and toughness as a function of stabilizer content is plotted in Fig. 7. It is quite clear from the graph that the toughness is directly related to the propensity for transformation. Fig. 5. Surrounding of the propagated crack in 12Ce–TZP. Transformed variants are clearly visible. The transformed zone width is much smaller than for the 10Ce–TZP sample. Fig. 6. Surrounding of the propagated crack in 16Ce–TZP. No transforma￾tion at all is observed. Residual scratches from polishing are observed. 3.3. Transformation sequence The very local observations of transformation induced re￾lief bring new information about the toughening mechanism sequence. Fig. 8 shows a transformed grain with the prop￾agated crack running through it. A fragmentation of trans￾formed planes due to the crack is observed. It can therefore be safely assumed that the transformation occurred before crack propagation. While the crack is still stationary, stresses are building up in its surroundings. Once these stresses are high enough, transformation of the grains in these zones is triggered, absorbing some of the stresses. If stresses continue increasing, the crack will be free to further propagate in the transformed zones. These results have been confirmed by complementary acoustic emission experiments.26 Moreover, for lattice correspondence CAB (at, bt, ct axes of the tetragonal phase changes into cm, am, bm axis of the

S Deville et al. / Journal of the European Ceramic Sociery 25(2005)3089-3096 band direction Crack propagation direction 14 Fig 9. Calculation of the orientation deviation of the transformed grain with the crack Fig. 7. Transformed zone width at surface and toughness as a function of loying content. The toughness is directly related to the width of the trans- ormation zone possible up to now, predictions relied only on the calcu- lations results. Almost all of the calculations developed so far are based on the Eshelby formalism,describing strains induced by the formation of the monoclinic products of the reaction in the tetragonal matrix. Further progress has then been made by using the PTMC, but the lack of compari- son with experimental evidence was still a great limitation of further improvement of the theories. The scale at which the relief can be described by AFM(e.g. see Fig. 2)is a great step toward a deeper understanding of the transforma tion mechanism and validation of the developed theories. In particular, the orientation relationship of the observed relief with the applied stress is worth further analysis. Based on the representation described in Fig 9, a statistical analysis of the orientation deviation of the variant pairs in the 10Ce-TZP Fragmented sample was performed. The orientation of 130 variant pairs transformed was measured, to get a statistically significant average orien- tation. The orientation ofeach pair was measured with respect crack to the crack propagation direction. The distribution of the ori entation deviation is plotted in Fig. 10. An average value of 27 was obtained, while the secondary band orientation was Fig 8. Surrounding of the propagated crack in 12Ce-TZP The grain was found to be 26, which means all the analyzed transformed transformed before crack propagation, and the transformed plane were frag- variants are lying in the direction of the transformed band mented when the crack ran through it. No residual stresses are expected when propagation. Some of the grains having their Ct axis close to the transformation strain is accommodated vertically, so that it was possible for the crack going through the transformed grain instead of avoiding it. monoclinic phase), all the transformation strain can be ac- commodated vertically if the grain has its Ct axis nearly per-a4y pendicular to free surface. 28 In this particular case, no residual stresses should be expected in the bulk once the grain is transformed. There will not be any stresses opposed to crack propagation. This can further explain the observation of the g crack running straight though the transformed grain, without being deviated from its initial path 3.4. Relationships with stress field 30 60 Among the inputs required by transformation toughening theories, -IS the nature and the magnitude of strain fields in Fig. 10. Orientation deviation distribution(see text for details). A preferen- tial orientation of the junction planes(26 to crack path) perpendicular to the surrounding zones of the crack tip are of prime impor- band direction(270 to crack path)is observed, suggesting a strong depen tance. Since the precise determination of these fields was not dence of the grains sensitivity to transformation to the crack path orientation

S. Deville et al. / Journal of the European Ceramic Society 25 (2005) 3089–3096 3093 Fig. 7. Transformed zone width at surface and toughness as a function of alloying content. The toughness is directly related to the width of the trans￾formation zone. Fig. 8. Surrounding of the propagated crack in 12Ce–TZP. The grain was transformed before crack propagation, and the transformed plane were frag￾mented when the crack ran through it. No residual stresses are expected when the transformation strain is accommodated vertically, so that it was possible for the crack going through the transformed grain instead of avoiding it. monoclinic phase), all the transformation strain can be ac￾commodated vertically if the grain has its ct axis nearly per￾pendicular to free surface.28 In this particular case, no residual stresses should be expected in the bulk once the grain is fully transformed. There will not be any stresses opposed to crack propagation. This can further explain the observation of the crack running straight though the transformed grain, without being deviated from its initial path. 3.4. Relationships with stress field Among the inputs required by transformation toughening theories,11–15 the nature and the magnitude of strain fields in the surrounding zones of the crack tip are of prime impor￾tance. Since the precise determination of these fields was not Fig. 9. Calculation of the orientation deviation of the transformed grain with the crack. possible up to now,17 predictions relied only on the calcu￾lations results. Almost all of the calculations developed so far are based on the Eshelby formalism,27 describing strains induced by the formation of the monoclinic products of the reaction in the tetragonal matrix. Further progress has then been made by using the PTMC, but the lack of compari￾son with experimental evidence was still a great limitation of further improvement of the theories. The scale at which the relief can be described by AFM (e.g. see Fig. 2) is a great step toward a deeper understanding of the transforma￾tion mechanism and validation of the developed theories. In particular, the orientation relationship of the observed relief with the applied stress is worth further analysis. Based on the representation described in Fig. 9, a statistical analysis of the orientation deviation of the variant pairs in the 10Ce–TZP sample was performed. The orientation of 130 variant pairs was measured, to get a statistically significant average orien￾tation. The orientation of each pair was measured with respect to the crack propagation direction. The distribution of the ori￾entation deviation is plotted in Fig. 10. An average value of 27◦ was obtained, while the secondary band orientation was found to be 26◦, which means all the analyzed transformed variants are lying in the direction of the transformed band propagation. Some of the grains having their ct axis close to Fig. 10. Orientation deviation distribution (see text for details). A preferen￾tial orientation of the junction planes (26◦ to crack path) perpendicular to band direction (27◦ to crack path) is observed, suggesting a strong depen￾dence of the grains sensitivity to transformation to the crack path orientation