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 coloursresidual 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