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 4evaluate 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