J. L Jones et al. I Acta Materialia 55(2007)5538-5548 greatest magnitude of domain switching occurs, leading to in ferroelastic ceramics, the zone size is typically defined likely changes in constitutive behavior not considered in as the region within which any domain switching occurs the model. However, we cannot preclude the possibility and is therefore limited by the experimental resolution. In that slight deviations in the position of the crack front the LCD technique, the first onset of domain switching is through the thickness of the sample can also lead to the measured, or the first deviation from linear-elastic behav reductions in measured a111 strains near the crack tip. In ior, yielding a larger process zone size than earlier tech- ther words, the behavior at the apparent crack tip posi- niques based on the measurement of remanent plastic tion in Figs. 5 and 6 may be receive a contribution from strain [2]. The X-ray approach described in this work also positions slightly behind the crack tip in addition to those measures in situ the onset of domain switching as a devia- precisely at the crack tip. Such a case might lead to the tion from foo2=1.00 mrd. Accounting for the +0.02 mrd decreases in measured &111 strain near the crack tip variability, fo02=1.05 mrd can be considered as a lower (Fig. 6) but not decreases in preferred orientation of bound estimate for the size of the switching zone. Using domains(Fig. 5), since regions of high domain orientation this definition, the n=0 domain orientation maps in Figs intensity foo2)also occur in the crack wake(Fig. 7) 5 and 7 demonstrate process zone half-heights before and after crack propagation of >500 um (frontal) and 43. General discussion 100 um(wake), respectively. The frontal zone size, mea sured in situ under an applied stress intensity factor Several additional conclusions can be drawn from the below that required for crack propagation, is comparable domain switching distributions. Figs. 5 and 7 illustrate that to that measured in Ref. [2] under similar loadin there are different degrees of domain switching reversibility conditions at different distances from the passing crack tip For exam- The domain orientation maps in Figs. 5 and 7 also dem- ple, for a constant spatial position in each n=00 map onstrate that the switching zone size is dependent on the in- X=1.0 mm, Y=0.6 mm, identified with an arrow in plane direction. After crack propagation(Fig. 7), the half- Figs. 5 and 7), the foo2 domain switching intensity height is much larger at n=45(500 um) than n=00 lecreases from 1.06 to 1.00 mrd after the crack tip passes; (100 um). In other words, further from the crack there this position experiences partial reversibility. In contrast, a are greater preferences for domain orientations oriented position near the crack tip(e.g, X=0. 8 mm, Y=1.0 mm) 45 to the crack face than the preferences of domains ori- increases in intensity from 1. 12 to 1. 25 mrd after the crack ented perpendicular to the crack face(n=0%). This direc tip passes; this position experiences a larger degree of irre- tional dependence of the zone height is illustrated in versibility. The fact that the degree of preferred orientation Fig 9 Domains oriented at 45 to the crack face tend to increases as opposed to remaining constant near the crack have their c-axes(001 direction) oriented toward the crack tip could be due to a lower applied stress intensity factor in front and exhibit a larger process zone size than those ori- ig. 5 than that required to propagate the crack and the ented perpendicular to the crack face. The directionality of resulting high stresses preceding brittle fracture. In con- switching in the crack wake demonstrates a usefulness for trast, it is clear in comparing Figs 6 and 7 that the tensile post-mortem failure studies of fractured ferroelectrics E111 lattice strains are entirely relieved after the crack axes orientations are tilted towards the direction of crack passes. Compressive lattice strains exist in the region sur rounding the crack wake, though they are of small magni Before Propagation After Propagation m吗叫 The domain orientation maps in Figs. 5 and 7 also allow measure of the size of the zone in which domain switching occurs within the plane of the sample. The importance of the height of the switching zone in toughening of ceramics is inherited from the study of phase transformation tough ening in zirconia-containing ceramics, where models of oughening enhancement utilize the total volumetric strain 45 which is a function of several parameters including the, transformation strain and the process zone height [31, 32]. The half-height of the switching zone continues to remain ntegral to current models of ferroelastic toughening(a good review is given in Ref. [4]), though it is complicating in that domain switching is incremental and never physi- cally saturates (i.e. subcritical). Therefore, a distribution ig. 9. Schematic identifying regions of strongest domain preference and of domain switching exists throughout the process zone. unique process zone half-heights(h) for two different pseudo-cubic grain In prior experimental measurements of the process zone orientations before and after crack propagationgreatest magnitude of domain switching occurs, leading to likely changes in constitutive behavior not considered in the model. However, we cannot preclude the possibility that slight deviations in the position of the crack front through the thickness of the sample can also lead to the reductions in measured e111 strains near the crack tip. In other words, the behavior at the apparent crack tip posi￾tion in Figs. 5 and 6 may be receive a contribution from positions slightly behind the crack tip in addition to those precisely at the crack tip. Such a case might lead to the decreases in measured e111 strain near the crack tip (Fig. 6) but not decreases in preferred orientation of domains (Fig. 5), since regions of high domain orientation intensity (f002) also occur in the crack wake (Fig. 7). 4.3. General discussion Several additional conclusions can be drawn from the domain switching distributions. Figs. 5 and 7 illustrate that there are different degrees of domain switching reversibility at different distances from the passing crack tip. For exam￾ple, for a constant spatial position in each g = 0 map (X = 1.0 mm, Y = 0.6 mm, identified with an arrow in Figs. 5 and 7), the f002 domain switching intensity decreases from 1.06 to 1.00 mrd after the crack tip passes; this position experiences partial reversibility. In contrast, a position near the crack tip (e.g., X = 0.8 mm, Y = 1.0 mm) increases in intensity from 1.12 to 1.25 mrd after the crack tip passes; this position experiences a larger degree of irre￾versibility. The fact that the degree of preferred orientation increases as opposed to remaining constant near the crack tip could be due to a lower applied stress intensity factor in Fig. 5 than that required to propagate the crack and the resulting high stresses preceding brittle fracture. In con￾trast, it is clear in comparing Figs. 6 and 7 that the tensile e111 lattice strains are entirely relieved after the crack passes. Compressive lattice strains exist in the region sur￾rounding the crack wake, though they are of small magni￾tude and exhibit little identifiable trend in their distributions relative to the crack orientation. Compressive lattice strains are therefore omitted from Fig. 7 for clarity. The domain orientation maps in Figs. 5 and 7 also allow a measure of the size of the zone in which domain switching occurs within the plane of the sample. The importance of the height of the switching zone in toughening of ceramics is inherited from the study of phase transformation tough￾ening in zirconia-containing ceramics, where models of toughening enhancement utilize the total volumetric strain which is a function of several parameters including the transformation strain and the process zone height [31,32]. The half-height of the switching zone continues to remain integral to current models of ferroelastic toughening (a good review is given in Ref. [4]), though it is complicating in that domain switching is incremental and never physi￾cally saturates (i.e. subcritical). Therefore, a distribution of domain switching exists throughout the process zone. In prior experimental measurements of the process zone in ferroelastic ceramics, the zone size is typically defined as the region within which any domain switching occurs and is therefore limited by the experimental resolution. In the LCD technique, the first onset of domain switching is measured, or the first deviation from linear-elastic behav￾ior, yielding a larger process zone size than earlier tech￾niques based on the measurement of remanent plastic strain [2]. The X-ray approach described in this work also measures in situ the onset of domain switching as a devia￾tion from f002 = 1.00 mrd. Accounting for the ±0.02 mrd variability, f002 = 1.05 mrd can be considered as a lower bound estimate for the size of the switching zone. Using this definition, the g = 0 domain orientation maps in Figs. 5 and 7 demonstrate process zone half-heights before and after crack propagation of >500 lm (frontal) and 100 lm (wake), respectively. The frontal zone size, mea￾sured in situ under an applied stress intensity factor just below that required for crack propagation, is comparable to that measured in Ref. [2] under similar loading conditions. The domain orientation maps in Figs. 5 and 7 also dem￾onstrate that the switching zone size is dependent on the in￾plane direction. After crack propagation (Fig. 7), the half￾height is much larger at g=45 (>500 lm) than g = 0 (100 lm). In other words, further from the crack there are greater preferences for domain orientations oriented 45 to the crack face than the preferences of domains ori￾ented perpendicular to the crack face (g = 0). This direc￾tional dependence of the zone height is illustrated in Fig. 9. Domains oriented at 45 to the crack face tend to have their c-axes (0 0 1 direction) oriented toward the crack front and exhibit a larger process zone size than those ori￾ented perpendicular to the crack face. The directionality of switching in the crack wake demonstrates a usefulness for post-mortem failure studies of fractured ferroelectrics; c￾axes orientations are tilted towards the direction of crack 45° 0° Before Propagation After Propagation h h Fig. 9. Schematic identifying regions of strongest domain preference and unique process zone half-heights (h) for two different pseudo-cubic grain orientations before and after crack propagation. 5546 J.L. Jones et al. / Acta Materialia 55 (2007) 5538–5548