《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_measurement of residual stress distribution

Availableonlineatwww.sciencedirect.com SCIENCE Acta materialia ELSEVIER Acta Materialia 53(2005)1511-1520 www.actamat-journals.com Measurement of residual stress distributions in Al2O3/3Y-TZP multilayered composites by fluorescence and aman microprobe plezo-spectroscopy Goffredo de portu Lorenzo Micele a, b, Yutaka Sekiguchi, Giuseppe Pezzotti b National Research Council, CNR-ISTEC, Faenza, Italy b Department of Materials, Ceramic Physics Laboratory Research Institute for Nanoscience, RIN, Kyoto Institute of Technology Sakyo-ku, Matsugasaki, 606-8.5 NGK Spark Plug Co, Ltd, R&D Center, Kommaki-shi, Aichi 485-8510, Japan Received 16 September 2003: received in revised form 14 July 2004: accepted 1 December 2004 Available online 8 January 2005 Abstract Microscopic distributions of residual stresses were evaluated in multilayered composite specimens consisting of AlO3/3 mol% Y2O3-stabilized zrO2 (3Y-TZP) layers with different compositions and thicknesses. Residual stress measurements were performed both by raman and fluorescence piezo-spectroscopy, and they revealed the existence of tensile and compressive hydrostatic stresses in the zirconia and alumina phases, respectively. Residual stresses mainly arose from thermal expansion and elastic mismatch between the constituent ceramic phases. However, the overall residual stress field consisted of two separate components: ()a micro- scopic stress field originating on the microstructural scale from grain-to-grain thermal and elastic mismatches between Al2O3 and From a comparison between stress data collected according to different piezo-spectroscopic techniques (i.e, based on fluorescence and Raman band shift for Cr-doped Al2O3 and 3Y-TZP, respectively), a reliability assessment of the stress measurement could be also obtained. The macroscopic stress field piled up among different layers could be separated from the microscopic grain-to-grain stress field and quantitatively evaluated to a degree of precision by employing a calibration procedure using chromophoric Al2O3 phase as a"stress sensor". Some fine details of the internal stress distribution were also revealed, as for example the existence of a anabolic stress profile within 3Y-TZP layers with substantial stress intensification nearby the junctions between neighbouring lay- ers. The total stress field was found to remarkably depend on layer thickness for given constant dimensions of the multilay ructure c 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved Keywords: Multilayered composite structures; Residual stress distribution; Raman and fluorescence piezospectroscopy 1. Introduction tively thick layers made of different phases. Residual tresses arise from mismatches in coefficients of thermal Ceramic multilayered composites may undergo resid- expansion(CTE)and elastic constants between the con ual stresses of remarkable magnitude upon cooling from stituent phases and among neighbouring layers [1]. In sintering temperature, especially if they consist of rela he phase(or layers)with lower CTE, compressive resid ual stresses are produced, while tensile residual stresses Corresponding author. Tel:+81 75 7247568; fax: +81 75 724 usually appear in the phase(or layers)with higher CTE In addition, it is known that the magnitude of these resid ual stresses is proportional to the CTE mismatch between 1359-6454$30.00 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved doi: 10. 1016/.actamat. 2004.12.003

Measurement of residual stress distributions in Al2O3/3Y-TZP multilayered composites by fluorescence and Raman microprobe piezo-spectroscopy Goffredo de Portu a , Lorenzo Micele a,b, Yutaka Sekiguchi c , Giuseppe Pezzotti b,* a National Research Council, CNR-ISTEC, Faenza, Italy b Department of Materials, Ceramic Physics Laboratory & Research Institute for Nanoscience, RIN, Kyoto Institute of Technology, Sakyo-ku, Matsugasaki, 606-8585 Kyoto, Japan c NGK Spark Plug Co., Ltd., R&D Center, Komaki-shi, Aichi 485-8510, Japan Received 16 September 2003; received in revised form 14 July 2004; accepted 1 December 2004 Available online 8 January 2005 Abstract Microscopic distributions of residual stresses were evaluated in multilayered composite specimens consisting of Al2O3/3 mol% Y2O3-stabilized ZrO2 (3Y-TZP) layers with different compositions and thicknesses. Residual stress measurements were performed both by Raman and fluorescence piezo-spectroscopy, and they revealed the existence of tensile and compressive hydrostatic stresses in the zirconia and alumina phases, respectively. Residual stresses mainly arose from thermal expansion and elastic mismatch between the constituent ceramic phases. However, the overall residual stress field consisted of two separate components: (i) a micro￾scopic stress field originating on the microstructural scale from grain-to-grain thermal and elastic mismatches between Al2O3 and 3Y-TZP phases; and, (ii) a macroscopic stress field, which is established to obey equilibrium conditions between adjacent layers. From a comparison between stress data collected according to different piezo-spectroscopic techniques (i.e., based on fluorescence and Raman band shift for Cr3+-doped Al2O3 and 3Y-TZP, respectively), a reliability assessment of the stress measurement could be also obtained. The macroscopic stress field piled up among different layers could be separated from the microscopic grain-to-grain stress field and quantitatively evaluated to a degree of precision by employing a calibration procedure using chromophoric Al2O3 phase as a ‘‘stress sensor’’. Some fine details of the internal stress distribution were also revealed, as for example the existence of a parabolic stress profile within 3Y-TZP layers with substantial stress intensification nearby the junctions between neighbouring lay￾ers. The total stress field was found to remarkably depend on layer thickness for given constant dimensions of the multilayered structure.
2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Multilayered composite structures; Residual stress distribution; Raman and fluorescence piezo-spectroscopy 1. Introduction Ceramic multilayered composites may undergo resid￾ual stresses of remarkable magnitude upon cooling from sintering temperature, especially if they consist of rela￾tively thick layers made of different phases. Residual stresses arise from mismatches in coefficients of thermal expansion (CTE) and elastic constants between the con￾stituent phases and among neighbouring layers [1]. In the phase (or layers) with lower CTE, compressive resid￾ual stresses are produced, while tensile residual stresses usually appear in the phase (or layers) with higher CTE. In addition, it is known that the magnitude of these resid￾ual stresses is proportional to the CTE mismatch between 1359-6454/$30.00
2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.12.003 * Corresponding author. Tel.: +81 75 724 7568; fax: +81 75 724 7580. E-mail address: pezzotti@ipc.kit.ac.jp (G. Pezzotti). Acta Materialia 53 (2005) 1511–1520 www.actamat-journals.com

G. de Portu et al Acta Materialia 53(2005)1511-1520 the materials of which each layer is composed [1]. How- size, 0.3 um) were used as raw ceramic materials. Pow ever, it should be noted that the residual stress field also ders, solvent(ethanol and methyl-ethylketone), surfac greatly depends on the geometry of the layered structure, tant (triolein, to enhance the powder dispersion affected by different shrinkage during sintering and CTE the mylar substrate)and 1/3 of the total binder volum o? in particular on layer thickness[2]. The overall stress field, characteristics and to facilitate removal of the tape fror mismatch between constituent phases/layers, mismatch (polyvinyl-butyral, PVB), were first ball-milled with in elastic constants between different phases/layers, and Al_O3 or ZrO, balls for 24 h. Then, the remaining part layers' geometry, may be rather complex and thus difficult of the binder and a plasticizer(dibuthyl phthalate, DBP to predict by theoretical calculations. In order to avoid were added and the mixtures ball-milled again for 24 h. cracking and delamination, a precise control of both Table I lists the formulations of the two slurries pre magnitude and distribution of residual stresses is manda- pared for tape casting, whose contents of ceramic pow- tory. In multilayered ceramic components, the develop- ders were 100% Al2O3(A) and 50 wt% Al2O3/50 wt% ment of a reliable experimental procedure for the 3Y-TZP(AZ). Slurries were filtered and degassed under evaluation of residual stresses is highly desirable. The vacuum for 5 min and tape-casting performed by means development of such a technique may also help to sub- of a doctor blade device onto a mylar substrate. Tapes stantially reduce the computational time required for (200 mm wide) were obtained at a casting speed of complete three-dimensional finite-element calculations 200 mm/min and with a blade gap of 0.8 and 1.1 mm Few techniques are available for assessing residual for A and AZ, respectively. After drying, the tapes stresses in ceramic materials, including X-ray diffraction, had an average thickness of 240 and 350 um for A neutron diffraction and piezo-spectroscopic analyses of and AZ, respectively. Dried tapes were peeled off from photo-stimulated fluorescence or Raman bands. In this the mylar and punched into 34 x 50 mm rectangular contribution, we present measurements of the residual moulds. Tapes were then stacked to form two kinds of stress and its dependence on geometry of multilayer laminates, in which the ratio between a and aZ thick Al,O3/3Y-TZP ceramics using the technique of piezo- ness was different: in one specimen(simply denominated pectroscopy applied both to the chromophoric fluores- A/AZ, henceforth) 13 layers were stacked by alternating cence of Al2O3 and to a selected Raman band of A and aZ layers according to a sequence A/AZ/. AZA; 3Y-TZP. The piezo-spectroscopic technique was first ap- another specimen(A/2AZ)consisted of 9 layers stacked plied by Grabner to the measurement of residual stresses according to the sequence A/2AZ/. /AZ/A. To ensure in Al2O3 [3]. The technique is also valid for Raman bonding among the stacked green-sheet, warm pressing assessments and it has been applied to some selected Ra- was carried out for 30 min at 80C, under a pressure man bands of ZrO: [4]. In the following section, expres- of 30 MPa. Specimens were then placed in a low sions are given relating the spectral shift of fluorescence temperature furnace at 600C for binder burnout. In and Raman bands to both magnitude and versus of the this processing step, heating and cooling rates were set mean normal stress; in addition, general piezo-spectro- at 3C/h. Finally, the laminates were sintered at 1550 scopic relationships are established according to exper oC for I h(heating and cooling rates set at 30C/h) mental calibration procedures [5]. Then, in Section 3, an After sintering the total thickness of the multilayered experimental analysis of residual stress as a function of specimens was 2.76 and 2.9 mm for the A/AZ and A layer geometry is proposed and discussed. The present 2AZ configuration, respectively. At the end of process- analysis extends and, for certain aspects, also improves ing procedure we obtained a laminated structure consist a previously presented analysis of laminate ceramics ing of 7 A and 6 AZ layers in the A/AZ material, and [6]because: (i) the effect of the elastic mismatch, in addi- 5 A and 4 AZ layers in the A/2AZ material. The final tion to CTE, on the microscopic residual stress field be- thickness for A, AZ and 2AZ laminae after sinter tween Al2O3 and 3Y-TZP phase is taken into ing was about 180, 250 and 500 um, respectively consideration;(ii the dependence on the layer geometry is studied in some detail; and (ii) experimental high-res- olution two-dimensional stress maps on areas as ex- Table I tended as the entire multilayered specimen thicknes Slip formulations of the two slurries prepared for tape casting" are. for the first time. collected Constituent AZ or 2AZ 2. Experimental and computational procedures Al,O 3Y-TZP Binder(PvB) 2. 1. Specimen preparation Plasticizer(DBP) Surfactant Al_O3 powder(Alcoa A16: average grain size, 0.3 um), Solvent and a 3Y-TZP powder (3Y-TZP Tosoh: average grain Values in grams

the materials of which each layer is composed [1]. How￾ever, it should be noted that the residual stress field also greatly depends on the geometry of the layered structure, in particular on layer thickness[2]. The overall stress field, affected by different shrinkage during sintering and CTE mismatch between constituent phases/layers, mismatch in elastic constants between different phases/layers, and layers
geometry, may be rather complex and thus difficult to predict by theoretical calculations. In order to avoid cracking and delamination, a precise control of both magnitude and distribution of residual stresses is manda￾tory. In multilayered ceramic components, the develop￾ment of a reliable experimental procedure for the evaluation of residual stresses is highly desirable. The development of such a technique may also help to sub￾stantially reduce the computational time required for complete three-dimensional finite-element calculations. Few techniques are available for assessing residual stresses in ceramic materials, including X-ray diffraction, neutron diffraction and piezo-spectroscopic analyses of photo-stimulated fluorescence or Raman bands. In this contribution, we present measurements of the residual stress and its dependence on geometry of multilayered Al2O3/3Y-TZP ceramics using the technique of piezo￾spectroscopy applied both to the chromophoric fluores￾cence of Al2O3 and to a selected Raman band of 3Y-TZP. The piezo-spectroscopic technique was first ap￾plied by Grabner to the measurement of residual stresses in Al2O3 [3]. The technique is also valid for Raman assessments and it has been applied to some selected Ra￾man bands of ZrO2 [4]. In the following section, expres￾sions are given relating the spectral shift of fluorescence and Raman bands to both magnitude and versus of the mean normal stress; in addition, general piezo-spectro￾scopic relationships are established according to experi￾mental calibration procedures [5]. Then, in Section 3, an experimental analysis of residual stress as a function of layer geometry is proposed and discussed. The present analysis extends and, for certain aspects, also improves a previously presented analysis of laminate ceramics [6] because: (i) the effect of the elastic mismatch, in addi￾tion to CTE, on the microscopic residual stress field be￾tween Al2O3 and 3Y-TZP phase is taken into consideration; (ii) the dependence on the layer geometry is studied in some detail; and (iii) experimental high-res￾olution two-dimensional stress maps on areas as ex￾tended as the entire multilayered specimen thickness are, for the first time, collected. 2. Experimental and computational procedures 2.1. Specimen preparation Al2O3 powder (Alcoa A16: average grain size, 0.3 lm), and a 3Y-TZP powder (3Y-TZP Tosoh: average grain size, 0.3 lm) were used as raw ceramic materials. Pow￾ders, solvent (ethanol and methyl-ethylketone), surfac￾tant (triolein, to enhance the powder dispersion characteristics and to facilitate removal of the tape from the mylar substrate) and 1/3 of the total binder volume (polyvinyl-butyral, PVB), were first ball-milled with Al2O3 or ZrO2 balls for 24 h. Then, the remaining part of the binder and a plasticizer (dibuthyl phthalate, DBP) were added and the mixtures ball-milled again for 24 h. Table 1 lists the formulations of the two slurries pre￾pared for tape casting, whose contents of ceramic pow￾ders were 100% Al2O3 (A) and 50 wt% Al2O3/50 wt% 3Y-TZP (AZ). Slurries were filtered and degassed under vacuum for 5 min and tape-casting performed by means of a doctor blade device onto a mylar substrate. Tapes (200 mm wide) were obtained at a casting speed of 200 mm/min and with a blade gap of 0.8 and 1.1 mm for A and AZ, respectively. After drying, the tapes had an average thickness of 240 and 350 lm for A and AZ, respectively. Dried tapes were peeled off from the mylar and punched into 34 · 50 mm rectangular moulds. Tapes were then stacked to form two kinds of laminates, in which the ratio between A and AZ thick￾ness was different: in one specimen (simply denominated A/AZ, henceforth) 13 layers were stacked by alternating A and AZ layers according to a sequence A/AZ/.../AZ/A; another specimen (A/2AZ) consisted of 9 layers stacked according to the sequence A/2AZ/.../2AZ/A. To ensure bonding among the stacked green-sheet, warm pressing was carried out for 30 min at 80 C, under a pressure of 30 MPa. Specimens were then placed in a low￾temperature furnace at 600 C for binder burnout. In this processing step, heating and cooling rates were set at 3 C/h. Finally, the laminates were sintered at 1550 C for 1 h (heating and cooling rates set at 30 C/h). After sintering the total thickness of the multilayered specimens was 2.76 and 2.9 mm for the A/AZ and A/ 2AZ configuration, respectively. At the end of process￾ing procedure we obtained a laminated structure consist￾ing of 7 A and 6 AZ layers in the A/AZ material, and 5 A and 4 AZ layers in the A/2AZ material. The final thickness for A, AZ and 2AZ laminae after sinter￾ing was about 180, 250 and 500 lm, respectively. Table 1 Slip formulations of the two slurries prepared for tape castinga Constituent Slip A AZ or 2AZ Al2O3 400 200 3Y-TZP – 200 Binder (PVB) 36 36 Plasticizer (DBP) 36 36 Surfactant 6.4 6.4 Solvent 188 188 a Values in grams. 1512 G. de Portu et al. / Acta Materialia 53 (2005) 1511–1520

G. de Portu et al. Acta Materialia 53(2005)1511-1520 Cross-sections of the laminates were ground and pol- where lli is the trace of the piezo-spectroscopic matrix ished with successively finer diamond pastes until opti- and oi is the first invariant of the stress tensor(aj/ lly flat surfaces were produced, suitable for being commonly referred to as the mean normal stress) spectroscopIc assessments Therefore, if Ii is known, the spectral shift Av can be As reference materials. a series of eight 3Y-TZP. considered to be a direct measure of the normal stres containing ceramics were investigated: a single-phase within the volume probed by the laser beam for each 3Y-TZP, and seven bi-phase Al2O3/ZrO2 materials, con- spectra acquisition. In laminate structures, far away taining 3, 10, 20, 50, 70, 90, 97 wt% Al2O3. For compar- from external edges [6], the residual stress field can be on,a dense monolithic alumina sample was also considered to be of a biaxial nature, accordingly, it prepared. The Al2 O3/ZrOz samples were sintered at should be computed as 3ay On the other hand, nearby 1550C for I h. Samples were ground and polished the edges the residual stress field is typically three- according to the same procedure adopted for the dimensional, thus requiring in Eq (1) the use of a mean cross-sections of multilayered specimens normal stress o 2.2. Applied and residual stress measurements 3. Results and discussion Microscopic stress distributions were measured by 3. 1. Piezo-spectroscopic calibrations and their reliability fluorescence and Raman piezo-spectroscopic methods by collecting either linear or two-dimensional arrays of spectra on the specimen side or cross-sections. The auto- Figs. 1(a)and(b)show typical fluorescence and Ra matically collected arrays of spectra in relatively large man spectra of Al2O3 and tetragonal ZrO2, respectively two-dimensional maps were typically 2 um-spaced and The stress dependences of the R, fluorescence band of the laser spot size was about 5 um (.e, using a 20x opti- chromophoric Al2O3 and of the 460 cm Raman band cal lens). Linear maps were collected either in the same of monolithic ZrO, as recorded in unconstrained mono- configuration of the two-dimensional maps or with lithic bodies are also shown in Fig. I(c)and( d), respec- I Am spacing and laser spot size of I um. Specimens tively. From a comparison between Figs. 1(c)and(d), were placed on a mapping device(lateral resolution of two features can be envisaged: (i) the trace piezo-spec 0.01 um), which was connected to a personal computer troscopic tensor, Ii, of the 460 cm ZrO2 band is to drive highly precise displacements(along both X about a half that of the R, fluorescence band of chromo and Y axes)on the specimen surface. The optical micro- phonic AlO3; (ii)a higher data scatter is envisaged for scope was used to both stimulate and collect the excited the trace piezo-spectroscopic tensor, i, of the fluorescence or Raman bands, which were analyzed 460 cm-I ZrO, band. Both circumstances may involve using an attached spectrometer (T-64000, Horiba/Jo- significant error in stress evaluation by the 460 cm bin-Ivon). An Ar-ion laser operating at a wavelength ZrO2 Raman band as compared to the Ri band of of 488 nm was used as the excitation source. In each Al2O3. The scatter of the data plot in Fig. 1(d), which map, the region of interest was first selected using the may arise from both inhomogeneity of the Y2O3 dopant optical microscope. Spectra were collected using a distribution and lack of intensity/sharpness of the ZrO2 CCD camera with an integration time of l and 4 s for Raman bands(as compared to the fluorescence bands of Al2O3 and ZrO2, respectively. Bands from a Hg/Ne Al,O3), reflects a confidence in the stress measurement lamp were used as an internal reference for spectral cal- of the order +100 MPa for the zirconia band, against ibrations. The collected data were automatically ana- the scatter +10 MPa allowed by the R fluorescence ed with curve fitting algorithms included in the band of alumina(Fig. I(c). Based on these preliminary LabSpec software package(LABSPEC 4.02, Horiba a/ assessments. we decided to develo perimental pr Jobin-lvon). Calibrations of spectral shift vs. externally cedure which, based only on the Ri fluorescence line of applied stress were made using a miniature four-point Al,O3, could enable us to extract the magnitude of the bending jig connected with a load-cell to measure in situ macroscopic stress field stored within layers avoiding the applied load. Details of the calibration procedures the large error involved in measuring the spectral shift were given in a previous report [5]. In a polycrystalline of Y-TZP Raman bands. Fig. 2(a) shows the shift(as ample(having no significant texture and a fine grained averaged on about 1000 measurements)measured for microstructure), the spectral shift, Av, of the Cr fluo- the R band of Al2O3 when different volume fractions rescence lines in AlO3(RI and R2 lines, henceforth) of Al2O phase were incorporated into a 3Y-TZP and of the Raman bands of 3Y-TzP under uniaxial tered body. In this preliminary spectroscopic assess stress can be expressed, to a linear approximation, as: ment, the specimens were neither assembled in layered △v=n structures nor subjected to external load, therefore the measured shifts merely represented the effect of

Cross-sections of the laminates were ground and pol￾ished with successively finer diamond pastes until opti￾cally flat surfaces were produced, suitable for spectroscopic assessments. As reference materials, a series of eight 3Y-TZP￾containing ceramics were investigated: a single-phase 3Y-TZP, and seven bi-phase Al2O3/ZrO2 materials, con￾taining 3, 10, 20, 50, 70, 90, 97 wt% Al2O3. For compar￾ison, a dense monolithic alumina sample was also prepared. The Al2O3/ZrO2 samples were sintered at 1550 C for 1 h. Samples were ground and polished according to the same procedure adopted for the cross-sections of multilayered specimens. 2.2. Applied and residual stress measurements Microscopic stress distributions were measured by fluorescence and Raman piezo-spectroscopic methods by collecting either linear or two-dimensional arrays of spectra on the specimen side or cross-sections. The auto￾matically collected arrays of spectra in relatively large two-dimensional maps were typically 2 lm-spaced and the laser spot size was about 5 lm (i.e., using a 20· opti￾cal lens). Linear maps were collected either in the same configuration of the two-dimensional maps or with 1 lm spacing and laser spot size of 1 lm. Specimens were placed on a mapping device (lateral resolution of 0.01 lm), which was connected to a personal computer to drive highly precise displacements (along both X and Y axes) on the specimen surface. The optical micro￾scope was used to both stimulate and collect the excited fluorescence or Raman bands, which were analyzed using an attached spectrometer (T-64000, Horiba/Jo￾bin-Ivon). An Ar-ion laser operating at a wavelength of 488 nm was used as the excitation source. In each map, the region of interest was first selected using the optical microscope. Spectra were collected using a CCD camera with an integration time of 1 and 4 s for Al2O3 and ZrO2, respectively. Bands from a Hg/Ne lamp were used as an internal reference for spectral cal￾ibrations. The collected data were automatically ana￾lyzed with curve fitting algorithms included in the LabSpec software package (LABSPEC 4.02’’, Horiba/ Jobin-Ivon). Calibrations of spectral shift vs. externally applied stress were made using a miniature four-point bending jig connected with a load-cell to measure in situ the applied load. Details of the calibration procedures were given in a previous report [5]. In a polycrystalline sample (having no significant texture and a fine grained microstructure), the spectral shift, Dm, of the Cr3+ fluo￾rescence lines in Al2O3 (R1 and R2 lines, henceforth) and of the Raman bands of 3Y-TZP under uniaxial stress can be expressed, to a linear approximation, as: Dm ¼ 1 3 Piirjj; ð1Þ where Pii is the trace of the piezo-spectroscopic matrix and rjj is the first invariant of the stress tensor (rjj/3 being commonly referred to as the mean normal stress). Therefore, if Pii is known, the spectral shift Dm can be considered to be a direct measure of the normal stress within the volume probed by the laser beam for each spectra acquisition. In laminate structures, far away from external edges [6], the residual stress field can be considered to be of a biaxial nature; accordingly, it should be computed as 2 3 rjj. On the other hand, nearby the edges the residual stress field is typically three￾dimensional, thus requiring in Eq. (1) the use of a mean normal stress rjj. 3. Results and discussion 3.1. Piezo-spectroscopic calibrations and their reliability assessment Figs. 1(a) and (b) show typical fluorescence and Ra￾man spectra of Al2O3 and tetragonal ZrO2, respectively. The stress dependences of the R1 fluorescence band of chromophoric Al2O3 and of the 460 cm
1 Raman band of monolithic ZrO2 as recorded in unconstrained mono￾lithic bodies are also shown in Fig. 1(c) and (d), respec￾tively. From a comparison between Figs. 1(c) and (d), two features can be envisaged: (i) the trace piezo-spec￾troscopic tensor, Pii, of the 460 cm
1 ZrO2 band is about a half that of the R1 fluorescence band of chromo￾phoric Al2O3; (ii) a higher data scatter is envisaged for the trace piezo-spectroscopic tensor, Pii, of the 460 cm
1 ZrO2 band. Both circumstances may involve significant error in stress evaluation by the 460 cm
1 ZrO2 Raman band as compared to the R1 band of Al2O3. The scatter of the data plot in Fig. 1(d), which may arise from both inhomogeneity of the Y2O3 dopant distribution and lack of intensity/sharpness of the ZrO2 Raman bands (as compared to the fluorescence bands of Al2O3), reflects a confidence in the stress measurement of the order ±100 MPa for the zirconia band, against the scatter ±10 MPa allowed by the R1 fluorescence band of alumina (Fig. 1(c)). Based on these preliminary assessments, we decided to develop an experimental pro￾cedure which, based only on the R1 fluorescence line of Al2O3, could enable us to extract the magnitude of the macroscopic stress field stored within layers avoiding the large error involved in measuring the spectral shift of Y-TZP Raman bands. Fig. 2(a) shows the shift (as averaged on about 1000 measurements) measured for the R1 band of Al2O3 when different volume fractions of Al2O3 phase were incorporated into a 3Y-TZP sin￾tered body. In this preliminary spectroscopic assess￾ment, the specimens were neither assembled in layered structures nor subjected to external load, therefore the measured shifts merely represented the effect of G. de Portu et al. / Acta Materialia 53 (2005) 1511–1520 1513

G. de Portu et al Acta Materialia 53(2005)1511-1520 Wavenumber(cm) Wavenumber(cm 460cm1 =2600005cmGP =-140:±0.15 cm-I/GPa Stress(MPa) Fig. 1. Typical recorded for Al2O3(fluorescence)and 3Y-TZP(Raman) are shown in(a) and(b), respectively. Results of uniaxial stress in(c)and(d) for selected bands. The correspondent piezo spectroscopic coefficients Iu= l; 3 are shown together with the recorded data tent, especially at intermediate volume fractions. This means that not only the Cte mismatch between AlO3 and ZrO2 phase (which produces the spectral shift shown in Fig. 2(a)), but also the elastic mismatch be- tween these two phases(responsible for the dependence of li on Al2O3 volume fraction as shown in Fig. 2(b)) should be taken into account for a reliable residual stress evaluation in composite materials. Using the two Al,O3 volume fraction(%) master curves obtained from this set of calibrations (Fig. 2(a)and(b)), for an AlO3/ZrO2 composite con- taining a known volume fraction of Al_O3 dispersoid the"zero-stress"frequency and Ii value can be system atically obtained. It should be noted that average fre- quencies and piezo-spectroscopic matrix traces as a function of Al,O3 volume fraction(Fig. 2(a) and (b), respectively)can be regarded as values proper to uni- formly distributed composite materials, provided that the volume screened by the piezo-spectroscopic probe in each stress measurement is sufficiently large to include Al2O3 volume fraction(%) a statistically meaningful number of Al2O3 dispersoids Fig. 2. Dependence of the Ri band position of externally unstressed Using the"zero-stress "frequency and a li values from chromophore Al203 as a function of its volume fraction when Fig. 2(a)and(b), respectively, for obtaining stress mbedded in a 3Y-TZP matrix (a). Piezo-spectroscopic coefficient assessments through Eq. (1), the effect of the microstress Iu= 1i3 as recorded for the Ri band for specimens in(a) field on the experimentally determined spectral shift of the Al,O3 phase can be automatically subtracted from grain-to-grain residual stresses between Al2O, and 3Y- the net measured shift. In other words, the Al2O3 phase TZP phases. Fig. 2(b)represents the dependence on uni- can be used as a"stress sensor", because the shift of its axial stress of the trace of the piezo-spectroscopic ma- spectral lines directly reads the macroscopic stress field trix, Ili, for the R band of Al2O3, when Al,O3 fine piled up among different layers of the structure. In this powder was incorporated with different volume frac- context, it should be noted that, in a previous study of tions into sintered 3Y-TZP. As seen, the variation of residual stresses in AlO3/ZrO, laminates [6], the"stress Iii with volume fraction of AlO3 is of a significant ex- sensor"approach was similarly adopted to evaluate the

grain-to-grain residual stresses between Al2O3 and 3Y￾TZP phases. Fig. 2(b) represents the dependence on uni￾axial stress of the trace of the piezo-spectroscopic ma￾trix, Pii, for the R1 band of Al2O3, when Al2O3 fine powder was incorporated with different volume frac￾tions into sintered 3Y-TZP. As seen, the variation of Pii with volume fraction of Al2O3 is of a significant ex￾tent, especially at intermediate volume fractions. This means that not only the CTE mismatch between Al2O3 and ZrO2 phase (which produces the spectral shift shown in Fig. 2(a)), but also the elastic mismatch be￾tween these two phases (responsible for the dependence of Pii on Al2O3 volume fraction as shown in Fig. 2(b)) should be taken into account for a reliable residual stress evaluation in composite materials. Using the two master curves obtained from this set of calibrations (Fig. 2(a) and (b)), for an Al2O3/ZrO2 composite con￾taining a known volume fraction of Al2O3 dispersoid, the ‘‘zero-stress’’ frequency and Pii value can be system￾atically obtained. It should be noted that average fre￾quencies and piezo-spectroscopic matrix traces as a function of Al2O3 volume fraction (Fig. 2(a) and (b), respectively) can be regarded as values proper to uni￾formly distributed composite materials, provided that the volume screened by the piezo-spectroscopic probe in each stress measurement is sufficiently large to include a statistically meaningful number of Al2O3 dispersoids. Using the ‘‘zero-stress’’ frequency and a Pii values from Fig. 2(a) and (b), respectively, for obtaining stress assessments through Eq. (1), the effect of the microstress field on the experimentally determined spectral shift of the Al2O3 phase can be automatically subtracted from the net measured shift. In other words, the Al2O3 phase can be used as a ‘‘stress sensor’’, because the shift of its spectral lines directly reads the macroscopic stress field piled up among different layers of the structure. In this context, it should be noted that, in a previous study of residual stresses in Al2O3/ZrO2 laminates [6], the ‘‘stress sensor’’ approach was similarly adopted to evaluate the 200 400 600 Wavenumber (cm-1) Intensity (a.u.) 460 cm-1 -200 -100 0 100 200 -1 0 1 Stress (MPa) Peak shift (cm-1) 460 cm-1 Πu = -1.40:± 0.15 cm-1/GPa Peak shift (cm-1) -200 -100 0 100 200 -1 0 1 Stress (MPa) R1 Πu = -2.60:± 0.0025 cm-1/GPa 6000 6050 6100 6150 Intensity (a.u.) Wavenumber (cm-1) R1 R2 (a) (b) (c) (d) Fig. 1. Typical spectra recorded for Al2O3 (fluorescence) and 3Y-TZP (Raman) are shown in (a) and (b), respectively. Results of uniaxial stress calibrations are shown in (c) and (d) for selected bands. The correspondent piezo-spectroscopic coefficients Pu = Pii/3 are shown together with the recorded data scatter. 0 20 40 60 80 100 6085 6086 6087 6088 6089 6090 Al2O3 volume fraction (%) Zero-stress position (cm-1) Al2O3 volume fraction (%) PS coefficient (cm-1/GPa) 0 20 40 60 80 100 -3 -2 (a) (b) Fig. 2. Dependence of the R1 band position of externally unstressed chromophore Al2O3 as a function of its volume fraction when embedded in a 3Y-TZP matrix (a). Piezo-spectroscopic coefficient Pu = Pii/3 as recorded for the R1 band for specimens in (a). 1514 G. de Portu et al. / Acta Materialia 53 (2005) 1511–1520

G. de Portu et al. Acta Materialia 53(2005)1511-1520 residual macroscopic stress field stored in the structure thickness. This parabolic dependence, which is better after sintering. However, in that study, it was assumed envisaged in the uniaxial stress profile plotted in that grain-to-grain microstresses in the AlO3 phase re- Fig 3(b), was more emphasized in AZ as compared to sult solely from CTE mismatch with ZrOz and data A layers. An important feature of the stress field resides reduction was only pursued with respect to the"zero- in its high degree of symmetry, which is however limited stress"frequency of the fluorescence lines of Al_O3, to the inner layers On the other hand, the external A neglecting any variation of ll i. We newly show here that layers, free of constraint on one side, showed significant not only such a zero-stress frequency but also the ll va- stress relaxation toward the specimen free surfaces lue should be appropriately selected, which means to(a phenomenon referred to as"edge-stress effect "in pre- take into proper account the contribution to the grain- vious literature [6 ). Data in Fig. 3(a) and(b) merely to-grain microstress field arising from both CTE and represent the macroscopic residual stress field due to elastic property mismatch between Al2O3 and ZrO2 interaction among different layers within the structure and therefore are different from residual stresses re- corded (at the same locations) for Al2O, phase with 3.2. Stress analysis of multilayered composite specimens using the stress-free frequency and Ii value associated with unconstrained polycrystalline Al2O3 (i.e, a poly- A two-dimensional stress map is shown in Fig 3(a), crystalline material prepared from the same starting hich was collected over the entire thickness of the powder and according to the same sintering schedule cross-section of a specimen (3 x 4 x 30 mm in dimen- of A layers in the multilayered structure). The lli value sion) consisting of 13 alternate A and AZ layers(with measured for polycrystalline alumina, which is also A layers at both edges, cf. Fig. 3(a)). This stress map shown in Fig. 2(b), was in good agreement with litera was collected using the chromophoric Al2O3 phase ture values [9]. The corresponding two-dimensional a"stress sensor"(cf. previous section); therefore, the and linear stress maps for the Al2O3 phase are depicted map represents the macroscopic residual stress field in Fig 4(a)and(b), respectively. Note that, by choosing due to interaction among different layers within the the stress-free frequency and the lli value of polycrystal structure. From this map, the predominant effect of line alumina, only the stress field stored within the Al2O CtE between A and AZ layers can be clearly visualized phase is evaluated. Therefore, in AZ layers microscopi from examining the sign of the residual stresses, with A in-to-grain and macroscopic layer-to-layer stres layers under residual compression and AZ layers under fields are both included in the data displayed in Fig. 4 sidual tension as dictated by the lower CTE of A with On the other hand, the stress map collected in Fig. 4 respect to Az(CTE~9.0×10-°and~0.0×10-6K for the A layers(for which the microscopic stress field for A and AZ, respectively)[7]. The macroscopic resid- can be neglected, the measured stress just represents ual stress field was found quite homogeneously distrib- the macroscopic residual stress introduced by the ted along the longitudinal sections of the layers, but lamination process. To support the reliability assess- it experienced a clear parabolic profile along the layer ment discussed in Section 3. 1, it can be interesting to 2500 500 1000 500gm 185 MPa 010050050-100-150-200 Fig 3. Two-dimensional (a) and linear(b) residual stress maps as recorded with a laser beam-diameter of 5 um (spacing 2 um) in a 13layer composite specimen. These maps are computed by using the Ri band of chromophore Al2O3 as a stress sensor (i.., using the calib Fig. 2 for the respective volume fractions). Tensile stresses are represented by warm colours, while compressive stresses are negative numbers ed by cold colours

residual macroscopic stress field stored in the structure after sintering. However, in that study, it was assumed that grain-to-grain microstresses in the Al2O3 phase re￾sult solely from CTE mismatch with ZrO2 and data reduction was only pursued with respect to the ‘‘zero￾stress’’ frequency of the fluorescence lines of Al2O3, neglecting any variation of Pii. We newly show here that not only such a zero-stress frequency but also the Pii va￾lue should be appropriately selected, which means to take into proper account the contribution to the grain￾to-grain microstress field arising from both CTE and elastic property mismatch between Al2O3 and ZrO2 phases. 3.2. Stress analysis of multilayered composite specimens A two-dimensional stress map is shown in Fig. 3(a), which was collected over the entire thickness of the cross-section of a specimen (3 · 4 · 30 mm in dimen￾sion) consisting of 13 alternate A and AZ layers (with A layers at both edges, cf. Fig. 3(a)). This stress map was collected using the chromophoric Al2O3 phase as a ‘‘stress sensor’’ (cf. previous section); therefore, the map represents the macroscopic residual stress field due to interaction among different layers within the structure. From this map, the predominant effect of CTE between A and AZ layers can be clearly visualized from examining the sign of the residual stresses, with A layers under residual compression and AZ layers under residual tension as dictated by the lower CTE of A with respect to AZ (CTE 9.0 · 10
6 and 10.0 · 10
6 K
1 for A and AZ, respectively) [7]. The macroscopic resid￾ual stress field was found quite homogeneously distrib￾uted along the longitudinal sections of the layers, but it experienced a clear parabolic profile along the layer thickness. This parabolic dependence, which is better envisaged in the uniaxial stress profile plotted in Fig. 3(b), was more emphasized in AZ as compared to A layers. An important feature of the stress field resides in its high degree of symmetry, which is however limited to the inner layers. On the other hand, the external A layers, free of constraint on one side, showed significant stress relaxation toward the specimen free surfaces (a phenomenon referred to as ‘‘edge-stress effect’’ in pre￾vious literature [6]). Data in Fig. 3(a) and (b) merely represent the macroscopic residual stress field due to interaction among different layers within the structure and therefore are different from residual stresses re￾corded (at the same locations) for Al2O3 phase with using the stress-free frequency and Pii value associated with unconstrained polycrystalline Al2O3 (i.e., a poly￾crystalline material prepared from the same starting powder and according to the same sintering schedule of A layers in the multilayered structure). The Pii value measured for polycrystalline alumina, which is also shown in Fig. 2(b), was in good agreement with litera￾ture values [9]. The corresponding two-dimensional and linear stress maps for the Al2O3 phase are depicted in Fig. 4(a) and (b), respectively. Note that, by choosing the stress-free frequency and the Pii value of polycrystal￾line alumina, only the stress field stored within the Al2O3 phase is evaluated. Therefore, in AZ layers microscopic grain-to-grain and macroscopic layer-to-layer stress fields are both included in the data displayed in Fig. 4. On the other hand, the stress map collected in Fig. 4 for the A layers (for which the microscopic stress field can be neglected), the measured stress just represents the macroscopic residual stress introduced by the lamination process. To support the reliability assess￾ment discussed in Section 3.1, it can be interesting to Fig. 3. Two-dimensional (a) and linear (b) residual stress maps as recorded with a laser beam-diameter of 5 lm (spacing 2 lm) in a 13-layers composite specimen. These maps are computed by using the R1 band of chromophore Al2O3 as a stress sensor (i.e., using the calibration data given in Fig. 2 for the respective volume fractions). Tensile stresses are represented by warm colours, while compressive stresses are negative numbers represented by cold colours. G. de Portu et al. / Acta Materialia 53 (2005) 1511–1520 1515

G. de portu et al Acta Materialia 53(2005)1511-1520 目 1500 50-100-150-200250-300 Fig 4. Two-dimensional (a) and linear(b) residual stress maps as recorded with a laser beam-diameter of 5 um (spacing 2 um)in a 13-layers omposite specimen. These maps are computed by using the RI band of chromophore Al2O3 Stress-free band position and piezospectroscopic coefficient were those measured in monolithic Al,O3. The convention relating stress to colours is the same as that shown in Fig. 3. evaluate and compare the residual stress field stored with VA being the volume fraction of Al2O3 phase and within the 3Y-TzP phase in AZ layers either as mea- A and oz the grain-to-grain residual stresses in the sured using the spectral shift of the 460 cm Raman Al_O3 and ZrO, phase, respectively. According to band of ZrO,(Fig. I(d) or as obtained from data in Eqs.(2)and (3), macroscopic and microscopic residual Figs. 3 and 4 according to general equilibrium stress maps in the Al2O3 phase(Figs. 3 and 4, respec conditions tively) can be used to compute the microscopic residual For AZ layers on which no external stress is applied stresses stored in the Zro, phase. The results of this microscopic and macroscopic stress fields(henceforth computation are shown in Fig. 5(a) and(b)for two- referred to as m and M, respectively) must obey, at dimensional and linear stress maps, respectively. As pre- any location, the following equilibrium equation viously mentioned, the residual stress field in ZrO2 phase OM+om=0. (2) is tensile at any location, according to its higher cTe as compared to Al,O3. Fig. 5(b) shows the advantage, in where terms of measurement precision, of using the alumina hase as a stress sensor in evaluating the residual stress Om=VACA +(1-vA)o, (3) field of a laminate composite. As seen, the internal stress 500 MPa 2000 1000 500 um -300 MPa 475450425400 Fig. 5. Two-dimensional (a) and linear(b) residual stress maps as recorded with a laser beam-diameter of 5 um (spacing 2 um) These maps represent residual stresses stored within the 3Y-TZP phase and are computed from Ri band data ) open circles represent the internal stress state stored in the Zro2 phase using chromophore Al2O3 as a"stress the same stress field as obtained using the 460 cm- Raman band of 3Y- TZP(note the remarkable data scattering in this latter plot). The c relating stress to colours is the same as that shown in Figs. 3 and 4

evaluate and compare the residual stress field stored within the 3Y-TZP phase in AZ layers either as mea￾sured using the spectral shift of the 460 cm
1 Raman band of ZrO2 (Fig. 1(d)) or as obtained from data in Figs. 3 and 4 according to general equilibrium conditions. For AZ layers on which no external stress is applied microscopic and macroscopic stress fields (henceforth referred to as rm and rM, respectively) must obey, at any location, the following equilibrium equation: rM þ rm ¼ 0; ð2Þ where rm ¼ V ArA þ ð1
V AÞr; ð3Þ with VA being the volume fraction of Al2O3 phase and rA and rZ the grain-to-grain residual stresses in the Al2O3 and ZrO2 phase, respectively. According to Eqs. (2) and (3), macroscopic and microscopic residual stress maps in the Al2O3 phase (Figs. 3 and 4, respec￾tively) can be used to compute the microscopic residual stresses stored in the ZrO2 phase. The results of this computation are shown in Fig. 5(a) and (b) for two￾dimensional and linear stress maps, respectively. As pre￾viously mentioned, the residual stress field in ZrO2 phase is tensile at any location, according to its higher CTE as compared to Al2O3. Fig. 5(b) shows the advantage, in terms of measurement precision, of using the alumina phase as a stress sensor in evaluating the residual stress field of a laminate composite. As seen, the internal stress Fig. 5. Two-dimensional (a) and linear (b) residual stress maps as recorded with a laser beam-diameter of 5 lm (spacing 2 lm) in a 13-layers composite specimen. These maps represent residual stresses stored within the 3Y-TZP phase and are computed from R1 band data according to Eqs. (2) and (3). In (b), open circles represent the internal stress state stored in the ZrO2 phase using chromophore Al2O3 as a ‘‘stress sensor’’, while close circles represent the same stress field as obtained using the 460 cm
1 Raman band of 3Y-TZP (note the remarkable data scattering in this latter plot). The convention relating stress to colours is the same as that shown in Figs. 3 and 4. Fig. 4. Two-dimensional (a) and linear (b) residual stress maps as recorded with a laser beam-diameter of 5 lm (spacing 2 lm) in a 13-layers composite specimen. These maps are computed by using the R1 band of chromophore Al2O3. Stress-free band position and piezo-spectroscopic coefficient were those measured in monolithic Al2O3. The convention relating stress to colours is the same as that shown in Fig. 3. 1516 G. de Portu et al. / Acta Materialia 53 (2005) 1511–1520

G. de Portu et al. Acta Materialia 53(2005)1511-1520 state in the ZrO2 phase is assessed with a high degree of precision using chromophore Al2O3 as a"stress sensor on the other hand. the stress field obtained with using the 460 cm Raman band of ZrO2 is affected by remarkable scattering and, thus, by a high degree of uncertainty. Here, in addition to the causes of low reli- ability already cited for the ZrO, Raman data (cf. be considered, whose impact on the spectral shift of 3 the ZrO2 Raman bands is presently unknown 1500(m) 3.3. Effect of layer geometry on residual stresses 8-100 A comparison between residual stress fields stored in multilayered specimens with different geometry (A/AZ/A vs. A/2AZ/A)is shown in Fig. 6. The thickness ratio, az/ta for specimens A/AZ/A and A/2AZ/A correspond to 1. 4 and 2.8, respectively. From a qualitative point of view. the stress distribution is similar in both cases with the stress profile being parabolic and lacking of symme try nearby the free surfaces of the external A layers. However, the residual stress magnitude significantly in- creased with increasing the taz/ta ratio. The increase in magnitude of stresses stored in the 2AZ layer is particu larly pronounced nearby the junctions with the neigh 100 uring A layers, as compared to the central part of the layers. Fig. 6 also shows that the measured stress val ues strongly depend on the probe configuration adopted. 5 In Fig. 6(a) and(b), data collected on the same specimen are shown with a laser spot size of 5 and I um, respec- 2-100 tively. Changing the laser spot size(i.e, changing the lens of the microscope) involves a major change in the geom- try of the optical probe, both with respect to penetration lepth and lateral resolution. Residual stresses in lar nate materials as a function of the laser penetration depth can be theoretically predicted in areas nearby the Fig. 6. Linear maps collected with a laser beam-diameter of 5 cimen edges, according to the linear superposition (spacing 2 um)(a)and I um(spacing I um)(b)in 13-layers(A/AZ/A) method. A simplified procedure has been proposed in lit nd 9-layers(A/2AZ/A)composite specimens. Note the different trends erature [6,8], which assumes the macrostresses accompa for stress depending on probe configuration. nying lamination result from CtE and elastic (1+)∫EA△ mismatches among individual layers. According to this 1 IA EA procedure, a theoretical estimate of the three-dimen- sional(tensile)stress, ofth), developed (nearby the speci- +N(A +tAZ) men surface) within A and AZ layers can be obtained by solving the following system of equations Kr+N(A+tAZ)+22 2(1+vAz)JEAz△ tan-/x+N(AZ+tA)+tA (-VAz) x+N(tA +tAz)+tA x sin 4(1+vAz)EAz△e VE+N(A+1Az)+1A]+2 p=元(1-)(1+数 号Az-{x-tx+N(A+tA -tan-(x+(N+ 1)(tAZ+tA V蓝a2-kx-1+Na+

state in the ZrO2 phase is assessed with a high degree of precision using chromophore Al2O3 as a ‘‘stress sensor’’, on the other hand, the stress field obtained with using the 460 cm
1 Raman band of ZrO2 is affected by remarkable scattering and, thus, by a high degree of uncertainty. Here, in addition to the causes of low reli￾ability already cited for the ZrO2 Raman data (cf. Section 3.1), also the presence of shear stresses should be considered, whose impact on the spectral shift of the ZrO2 Raman bands is presently unknown. 3.3. Effect of layer geometry on residual stresses A comparison between residual stress fields stored in multilayered specimens with different geometry (A/AZ/A vs. A/2AZ/A) is shown in Fig. 6. The thickness ratio, tAZ/tA for specimens A/AZ/A and A/2AZ/A corresponds to 1.4 and 2.8, respectively. From a qualitative point of view, the stress distribution is similar in both cases, with the stress profile being parabolic and lacking of symme￾try nearby the free surfaces of the external A layers. However, the residual stress magnitude significantly in￾creased with increasing the tAZ/tA ratio. The increase in magnitude of stresses stored in the 2AZ layer is particu￾larly pronounced nearby the junctions with the neigh￾bouring A layers, as compared to the central part of the layers. Fig. 6 also shows that the measured stress val￾ues strongly depend on the probe configuration adopted. In Fig. 6(a) and (b), data collected on the same specimen are shown with a laser spot size of 5 and 1 lm, respec￾tively. Changing the laser spot size (i.e., changing the lens of the microscope) involves a major change in the geom￾etry of the optical probe, both with respect to penetration depth and lateral resolution. Residual stresses in lami￾nate materials as a function of the laser penetration depth can be theoretically predicted in areas nearby the specimen edges, according to the linear superposition method. A simplified procedure has been proposed in lit￾erature [6,8], which assumes the macrostresses accompa￾nying lamination result from CTE and elastic mismatches among individual layers. According to this procedure, a theoretical estimate of the three-dimen￾sional (tensile) stress, rðthÞ ii , developed (nearby the speci￾men surface) within A and AZ layers can be obtained by solving the following system of equations: ½rðthÞ ii ðeÞ AZ ¼
2 p ð1 þ mAZÞ ð1
mAZÞ EAZDe 1 þ tA tAZ EAZ EA ( )  sin
1 x þ NðtA þ tAZÞ þ tA ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½x þ NðtA þ tAZÞ þ tA 2 þ z2 q 0 B@ 1 CA 8 >:
tan
1 x þ ðN þ 1ÞðtAZ þ tAÞ z ) ; ð4Þ ½rðthÞ ii ðeÞ A ¼ 2 p ð1 þ mAÞ ð1
mAÞ EADe 1 þ tA tAZ EA EAZ ( )  sin
1 x þ NðtA þ tAZÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½x þ NðtA þ tAZÞ2 þ z2 q 0 B@ 1 CA 8 >:
tan
1 x þ NðtAZ þ tAÞ þ tA z 9 >= >; ; ð5Þ ½rðthÞ ii ðbÞ AZ ¼ 4 p ð1 þ mAZÞ ð1
mAZÞ EAZDe 1 þ tA tAZ EAZ EA ( )  Re ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 tAZ
x
1 2 tAZ þ NðtAZ þ tAÞ     1 2 tAZ
x
1 2 tAZ þ NðtAZ þ tAÞ         s ; ð6Þ Fig. 6. Linear maps collected with a laser beam-diameter of 5 lm (spacing 2 lm) (a) and 1 lm (spacing 1 lm) (b) in 13-layers (A/AZ/A) and 9-layers (A/2AZ/A) composite specimens. Note the different trends for stress depending on probe configuration. G. de Portu et al. / Acta Materialia 53 (2005) 1511–1520 1517

G. de portu et al Acta Materialia 53(2005)1511-1520 4(1+vA) B(z)=0(z<0) (-)1+ where p is the probe length parameter(for an unfocused m, p tends to infinity and the right part of Eq. (10) x Re tA+N(tAz +IA tends to unity) and zo represents the location of the focal tA+N(Az +t, plane with respect to the selected origin of the cartesian (7) axes(i.e, 20=0 in the present calculation). According to Eqs.(4 (11), near-edge stress values were calculated as am]2(N)+[m)](N) a function of the abscissa x for different p values. The results of this calculation (for N=9) are presented in Fig. 7 in comparison with experimental data collected +m(N)+ on the A/2AZ specimen with a probe size of I um. In (8) the 2AZ layers, measured stresses are consistent with theoretical profiles calculated for p= 10 um. This is in where N is the number of laminate pairs, E and v are the good agreement with the experimental p= ll um value Youngs modulus and the Poissons ratio of the mate- reported in literature [6]. However, a markedly lower rial, t is the layer thickness and the subscripts A and stress value is recorded nearby the A/2AZ interfaces, AZ refer to the AlO3 and Al_O3/ZrO2 layer, respec- as compared to the calculated value. This trend of stress tively(EA and EAZ= 360 and 300 GPa, respectively). underestimation nearby the interface is also noted in the The superscripts(e)and(b)refer to edge and bulk stres- A layers On the other hand, the magnitude of the com ses, respectively. Cartesian axes x and z were taken per- pressive stress measured at the center of A layers was respectively. The origin of the xz cartesian axes Hap e, significantly higher than that calculated by using an pendicular and parallel to the A/Az interfac experimentally assessed value p=7.5 um, which was re- cted at the interception between the free surface of the ported for polycrystalline Al2O3 [6]. In this context, it sample and the A/AZ interface. As represents the strain can be interesting to comment about the causes of the mismatch between adjacent layers and equals the prod- above discrepancies between experimental and calcu- uct Ax(To- TRT), with Ax-1.0 x 10 K, and lated stress values. It should be noted that the adopted Tos 1200C [10] (TRT is room temperature). According convolution procedure (i.e, Eqs.(9HIl)) takes into ac- to eqs.(4(8), the near-edge residual stress distribution count only the laser penetration depth, while also the within the multilayered specimen can be plotted as a function of x, z, tAz and N, for a given Ia value G.e., 180 Hm). However, in order to obtain a direct comparison with the experimental stress values evalu 2AZ 2AZ ated by fluorescence spectroscopy, ofex), a convolution of the calculated values with the probe depth-response function should be performed [6, 11]. Any point in space within the volume of the probe gives rise to its own local optical scattered intensity spectrum of a given form(e.g Lorentzian). The contribution of this spectrum to the observed spectrum depends on the intensity of incident light and on the probe"sensitivity"at the given loca tion. Both these effects can be represented by an effective intensity (i. e, the probe response function, B(x,y,z, 200-400600-800-1000-1200-1400(m) xo,yo, ]o))of light scattered from the point (x, y, z)when he incident beam is focused on the point(xo, yo, zo). By neglecting variations within the probed volume along the x and y directions(on the focal plane of the measure- ment)and just considering the variation along the z axis, analytical stress predictions can be convoluted accord ing to the following equations oth(x, 2)B(2)dz, p-500 um Fig. 7. Results of theoretical calculations of near-edge residual st (cf. Eqs. (4)(I1))as a function of the laser probe geometry for th ≥ layers A/AZA specimen. A comparison is shown with experimental data collected with a laser beam-diameter of I um

½rðthÞ ii ðbÞ A ¼
4 p ð1 þ mAÞ ð1
mAÞ EADe 1 þ tA tAZ EA EAZ ( )  Re ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 tA
x
1 2 tA þ NðtAZ þ tAÞ     1 2 tA
x
1 2 tA þ NðtAZ þ tAÞ         s ; ð7Þ rðthÞ ii ¼ NX¼þ1 N¼
1 ½rðthÞ ii ðeÞ AZðNÞþ½rðthÞ ii ðeÞ A ðNÞ n þ rðthÞ ii h iðbÞ AZ ðNÞ þ rðthÞ ii h iðbÞ A ðNÞ  ; ð8Þ where N is the number of laminate pairs, E and m are the Young
s modulus and the Poisson
s ratio of the mate￾rial, t is the layer thickness and the subscripts A and AZ refer to the Al2O3 and Al2O3/ZrO2 layer, respec￾tively (EA and EAZ @ 360 and 300 GPa, respectively). The superscripts (e) and (b) refer to edge and bulk stres￾ses, respectively. Cartesian axes x and z were taken per￾pendicular and parallel to the A/AZ interface, respectively. The origin of the xz cartesian axes was se￾lected at the interception between the free surface of the sample and the A/AZ interface. De represents the strain mismatch between adjacent layers and equals the prod￾uct Da (T0
TRT), with Da 
1.0 · 10
6 K
1 , and T0  1200 C [10] (TRT is room temperature). According to Eqs. (4)–(8), the near-edge residual stress distribution within the multilayered specimen can be plotted as a function of x, z, tAZ and N, for a given tA value (i.e., = 180 lm). However, in order to obtain a direct comparison with the experimental stress values evalu￾ated by fluorescence spectroscopy, rðexÞ ii , a convolution of the calculated values with the probe depth-response function should be performed [6,11]. Any point in space within the volume of the probe gives rise to its own local optical scattered intensity spectrum of a given form (e.g., Lorentzian). The contribution of this spectrum to the observed spectrum depends on the intensity of incident light and on the probe ‘‘sensitivity’’ at the given loca￾tion. Both these effects can be represented by an effective intensity (i.e., the probe response function, B(x,y, z, x0,y0, z0)) of light scattered from the point (x,y, z) when the incident beam is focused on the point (x0,y0, z0). By neglecting variations within the probed volume along the x and y directions (on the focal plane of the measure￾ment) and just considering the variation along the z axis, analytical stress predictions can be convoluted accord￾ing to the following equations: rðexÞ ii ðx;zÞ ¼ Z þ1
1 rðthÞ ii ðx;z 0 ÞBðz 0 Þ dz 0 ; ð9Þ BðzÞ ¼ p=p ðz
z0Þ 2 þ p2 ðz P 0Þ; ð10Þ BðzÞ ¼ 0 ðz < 0Þ; ð11Þ where p is the probe length parameter (for an unfocused beam, p tends to infinity and the right part of Eq. (10) tends to unity) and z0 represents the location of the focal plane with respect to the selected origin of the cartesian axes (i.e., z0 = 0 in the present calculation). According to Eqs. (4)–(11), near-edge stress values were calculated as a function of the abscissa x for different p values. The results of this calculation (for N = 9) are presented in Fig. 7 in comparison with experimental data collected on the A/2AZ specimen with a probe size of 1 lm. In the 2AZ layers, measured stresses are consistent with theoretical profiles calculated for p = 10 lm. This is in good agreement with the experimental p = 11 lm value reported in literature [6]. However, a markedly lower stress value is recorded nearby the A/2AZ interfaces, as compared to the calculated value. This trend of stress underestimation nearby the interface is also noted in the A layers. On the other hand, the magnitude of the com￾pressive stress measured at the center of A layers was significantly higher than that calculated by using an experimentally assessed value p = 7.5 lm, which was re￾ported for polycrystalline Al2O3 [6]. In this context, it can be interesting to comment about the causes of the above discrepancies between experimental and calcu￾lated stress values. It should be noted that the adopted convolution procedure (i.e., Eqs. (9)–(11)) takes into ac￾count only the laser penetration depth, while also the Fig. 7. Results of theoretical calculations of near-edge residual stresses (cf. Eqs. (4)–(11)) as a function of the laser probe geometry for the 9- layers A/2AZ/A specimen. A comparison is shown with experimental data collected with a laser beam-diameter of 1 lm. 1518 G. de Portu et al. / Acta Materialia 53 (2005) 1511–1520

G. de Portu et al. Acta Materialia 53(2005)1511-1520 lateral resolution of the laser probe may play an impor- presented the technique of residual stress measurement tant role in the assessment of the stress value nearby the in multilayered structure observing residual stress values interfaces. A significant effect, arising from the finite very close to theoretical values. However, the present diameter of the laser spot, is suggested by the large dis- work suggests that the piezo-spectroscopic technique crepancy found between measured and calculated stress at its present stage of development fails to precisely as- values nearby the interfaces between different layer sess stresses nearby the interfaces of A/AZ laminates Underestimation of the tensile stress at the interface and additional refinements are needed for the technique from the 2AZ side and of the compressive stress from to be applied to the actual stress analysis of laminates the a side may both arise from spectral contributions gi- Possible refinements may include the application of la ven by Al2O3 grains belonging to the neighboring layer ser-probe confocal techniques and the use of polarized (i.e, A and 2AZ for 2AZ and A layers, respectively). In lenses to avoid subsurface digression of the laser beam other words, with increasing laser penetration depth, the toward the neighboring layer cross section of the optical beam enlarges following the shape of an hyperboloid [10] and may cross the inter face, thus partly reading the stress state in Al2O3 grains 4. Conclusion belonging to a different layer. Given the relativelyhigh transparency of the ceramic phases involved in the pres- Macroscopic and microscopic distributions of resid ent experiments, this phenomenon cannot be neglected ual stress within multilayered composites were collected in stress assessments, as shown by the present analysis. by means of the spectral shift of the chromophoric fluo- Fig. 8 shows both interface stresses from the AZ side rescence peak of AlO3. Such a fluorescence probe can (x= IA (AZ)and stresses at the center of the AZ layer be used for high-precision residual stress assessments (r=IA IAz/2), as calculated (according to Eqs. (4 provided that appropriate calibrations of both stress- (1)) as a function of the ratio tazIa (for Ia free frequency and piezo-spectroscopic coefficient are 180 um, and N>10). A relatively good agreement is collected as a function of AlO3 volume fraction. The found for the stress values at the center of the az layer, confidence of the stress measurement using Al,O3 as a independent of the tAz/ta ratio On the other hand, no "stress sensor"has been remarkably improved as com- such an agreement between calculated and measured pared to that obtained upon monitoring the shift of values was found for interfacial stress values. It should the 460 cm Raman band of the tetragonal ZrO2 phase be noted that this latter residual stress represents the Pronounced parabolic-shaped stress profiles were ob- maximum tensile magnitude within the laminate and served in Al2O3/ZrO2 composite layers, whose maxi- ts knowledge is important for fracture prediction and mum stress magnitude was in qualitative agreement for reliability considerations as well. From the compar- with theoretical predictions based on CTE and elastic son between calculated and experimental data, it ap- mismatch between different layers. Experimental data pears that, in AZ layers, a large underestimation is were discussed after incorporating both edge-effect and made in the experimental assessment of interfacial stres- the response function of the laser probe for a finit ses, independent of the tAz/tA ratio. Sergo et al. [6] have depth. A comparison, carried out between multilayered specimens with different thickness ratios, showed a remarkable change in the magnitude of maximum ten sile stress stored in the AZ layers nearby the A/AZ inter face, the thicker the Az layer the more intense the stress 500 The present study may represent an improvement in the assessment of residual stresses in multilayered struc- tures, with respect to a previous literature study of mul- tilayered structures based on fluorescence piezo pectroscopy [6), because the dependence of the piezo- spectroscopic coefficient (used for stress computation) n the volume fraction of the Al_O3 phase was taker into appropriate consideration References Fig. 8. Results of theoretical calculations of near-edge residual stresses at x=ta Iaz/2 (center of the AZ layer) and x=IA IAZ (A/AZ [1 Cai Pz. Green DJ, Messing GL. J Am Ceram Soc 1997: 80: 1929 interface from the Az side) as a function of the thickness ratio taz/Ia 2 Rao MP, Sanchez- Herencia A, Beltz GE, McMeeking RM is shown with experimental data(open and close circle Lange ff. science 1999: 286: 102. vely )collected with a laser beam- B Grabner L J Appl Phys 1978: 49: 580 diameter of I um. 4 Sergo V, Clarke DR, Pompe W.J Am Ceram Soc 1995: 78: 633

lateral resolution of the laser probe may play an impor￾tant role in the assessment of the stress value nearby the interfaces. A significant effect, arising from the finite diameter of the laser spot, is suggested by the large dis￾crepancy found between measured and calculated stress values nearby the interfaces between different layers. Underestimation of the tensile stress at the interface from the 2AZ side and of the compressive stress from the A side may both arise from spectral contributions gi￾ven by Al2O3 grains belonging to the neighboring layer (i.e., A and 2AZ for 2AZ and A layers, respectively). In other words, with increasing laser penetration depth, the cross section of the optical beam enlarges following the shape of an hyperboloid [10] and may cross the inter￾face, thus partly reading the stress state in Al2O3 grains belonging to a different layer. Given the relativelyhigh transparency of the ceramic phases involved in the pres￾ent experiments, this phenomenon cannot be neglected in stress assessments, as shown by the present analysis. Fig. 8 shows both interface stresses from the AZ side (x = tA + tAZ) and stresses at the center of the AZ layer (x = tA + tAZ/2), as calculated (according to Eqs. (4)– (11)) as a function of the ratio tAZ/tA (for tA = 180 lm, and N > 10). A relatively good agreement is found for the stress values at the center of the AZ layer, independent of the tAZ/tA ratio. On the other hand, no such an agreement between calculated and measured values was found for interfacial stress values. It should be noted that this latter residual stress represents the maximum tensile magnitude within the laminate and its knowledge is important for fracture prediction and for reliability considerations as well. From the compar￾ison between calculated and experimental data, it ap￾pears that, in AZ layers, a large underestimation is made in the experimental assessment of interfacial stres￾ses, independent of the tAZ/tA ratio. Sergo et al. [6] have presented the technique of residual stress measurement in multilayered structure observing residual stress values very close to theoretical values. However, the present work suggests that the piezo-spectroscopic technique at its present stage of development fails to precisely as￾sess stresses nearby the interfaces of A/AZ laminates and additional refinements are needed for the technique to be applied to the actual stress analysis of laminates. Possible refinements may include the application of la￾ser-probe confocal techniques and the use of polarized lenses to avoid subsurface digression of the laser beam toward the neighboring layer. 4. Conclusion Macroscopic and microscopic distributions of resid￾ual stress within multilayered composites were collected by means of the spectral shift of the chromophoric fluo￾rescence peak of Al2O3. Such a fluorescence probe can be used for high-precision residual stress assessments, provided that appropriate calibrations of both stress￾free frequency and piezo-spectroscopic coefficient are collected as a function of Al2O3 volume fraction. The confidence of the stress measurement using Al2O3 as a ‘‘stress sensor’’ has been remarkably improved as com￾pared to that obtained upon monitoring the shift of the 460 cm
1 Raman band of the tetragonal ZrO2 phase. Pronounced parabolic-shaped stress profiles were ob￾served in Al2O3/ZrO2 composite layers, whose maxi￾mum stress magnitude was in qualitative agreement with theoretical predictions based on CTE and elastic mismatch between different layers. Experimental data were discussed after incorporating both edge-effect and the response function of the laser probe for a finite depth. A comparison, carried out between multilayered specimens with different thickness ratios, showed a remarkable change in the magnitude of maximum ten￾sile stress stored in the AZ layers nearby the A/AZ inter￾face, the thicker the AZ layer the more intense the stress. The present study may represent an improvement in the assessment of residual stresses in multilayered struc￾tures, with respect to a previous literature study of mul￾tilayered structures based on fluorescence piezo￾spectroscopy [6], because the dependence of the piezo￾spectroscopic coefficient (used for stress computation) on the volume fraction of the Al2O3 phase was taken into appropriate consideration. References [1] Cai PZ, Green DJ, Messing GL. J Am Ceram Soc 1997;80:1929. [2] Rao MP, Sanchez-Herencia AJ, Beltz GE, McMeeking RM, Lange FF. Science 1999;286:102. [3] Grabner L. J Appl Phys 1978;49:580. [4] Sergo V, Clarke DR, Pompe W. J Am Ceram Soc 1995;78:633. Fig. 8. Results of theoretical calculations of near-edge residual stresses at x = tA + tAZ/2 (center of the AZ layer) and x = tA + tAZ (A/AZ interface from the AZ side) as a function of the thickness ratio tAZ/tA. A comparison is shown with experimental data (open and close circles for interface and layer center, respectively) collected with a laser beam￾diameter of 1 lm. G. de Portu et al. / Acta Materialia 53 (2005) 1511–1520 1519

1520 G. de Portu et al Acta Materialia 53(2005)1511-1520 5 Pezzotti G. J Raman Spectrosc 1999: 30:867 8 Ma Q, Clarke DR. J Am Ceram Soc 1994: 77: 289 pkin DM, De Portu G, Clarke DR. J Am Ceram Soc 9 Virkar A, Huang JL, Cutler RA. J Am Ceram Soc 1987: 70: 164 199780:1633 [10 Sergo V, Wang X-L, Clarke DR, Becher PF. J Am Ceram Soc 7 Toschi F, Melandri C, Pinasco P, Roncari E, Guicciardi S, de 1995:78:22l Portu G. j Am Ceram Soc 2003: 86: 1547 [l Lipkin DM, Clarke DR. J Appl Phys 1995: 77: 1855

[5] Pezzotti G. J Raman Spectrosc 1999;30:867. [6] Sergo V, Lipkin DM, De Portu G, Clarke DR. J Am Ceram Soc 1997;80:1633. [7] Toschi F, Melandri C, Pinasco P, Roncari E, Guicciardi S, de Portu G. J Am Ceram Soc 2003;86:1547. [8] Ma Q, Clarke DR. J Am Ceram Soc 1994;77:289. [9] Virkar A, Huang JL, Cutler RA. J Am Ceram Soc 1987;70:164. [10] Sergo V, Wang X-L, Clarke DR, Becher PF. J Am Ceram Soc 1995;78:2213. [11] Lipkin DM, Clarke DR. J Appl Phys 1995;77:1855. 1520 G. de Portu et al. / Acta Materialia 53 (2005) 1511–1520