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: 633lateral 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