J. L Jones et al. Acta Materialia 55(2007)5538-5548 Fig. 2. Spatial distributions(X, Y of the projected deviatoric stress, s-, in Mode l, plane-stress geometry at a stress intensity factor of KI=0.71 MPam Projected deviatoric stresses are shown perpendicular to the crack face(=0), parallel to the crack propagation direction (n=90), and two intermediate sitions(=30% and =60). The crack face is illustrated in each figure as a heavy line at Y=1.0 (K350, Piezo Technologies, Indianapolis, IN, USA)was significantly increases when the irradiated area encom- used in this experiment. This material composition has passes the crack. Diffraction data were collected with a been used in earlier work and is believed to contain only 50 x 50 um- beam rastered in two dimensions around the the tetragonal phase [19, 20]. Compact tension(CT) speci- crack in steps of 100 um, mapping a total area approxi mens were obtained in the dimensions 50 x 48 x 1.5 mm mately 2 x2 mm-. At each position, the beam shutter was vith a machined notch 23 mm in length parallel to the opened for 10 S, exposing scattered X-rays onto a two- 50 mm dimension. Similar to the crack geometry described dimensional digital image plate detector(MAR 345. in Ref [21], a chevron notch was cut at a 45 angle to the 150 um pixel size, Mar USA, Inc. positioned 1634 mm major surface of the sample at the end of the 23 mm long behind the center of the sample. The diffraction geometry notch using a sharp razor blade with 6 um diamond paste is illustrated in Fig 3 as an abrasive. a precrack was initiated on the major sur- The detector was centered on the transmitted X-ray face opposite the opening of the chevron notch(on the side beam such that complete Debye-Scherrer rings were col- of higher stress)using a 500 g Vickers indentation. The pre- lected(see Fig. 3 for a typical pattern). For each diffraction crack was propagated by employing the controlled crack measurement at each spatial position, the collection of growth apparatus described below. After the precrack grains sampled were contained within a 50 50x was propagated through the chevron notch and was visibly 1500 um'matchstick'diffracting volume. This high present under an optical microscope on both major sur- energy transmission geometry and the resulting low Bragg faces, the specimen was thermally annealed for 2 h at angles allow diffracting vectors oriented to within 3 of the 600C. A custom built apparatus was used to apply a con- specimen plane to be sampled. Therefore, for all practical trolled stress intensity factor. The compact tension speci- purposes, the sampled diffraction vectors are considered mens were loaded in Mode I, perpendicular to the crack to lie within the specimen plane g a piezoelectric actuator. The load was recorded Using Fit2D(Ver. 12.077)[24, the diffracted image in-line with the actuator and sample using a l kN load cell. were"caked"(rebinned within polar coordinates) within The crack tip position and crack length were identified and 15 wide azimuth sectors to obtain integrated diffracted measured prior to loading with an optical microscope. The intensity as a function of 20 [25]. The tetragonal PZT peaks crack length, load, and sample geometry were all used to 101, 110, 111, 002, 200, 1 12, and 21 l and the cubic calculate the applied stress intensity factor (K1) via stan- ceria peaks 111, 200, 220, and 3 1 l were then fit using a dard formulations [22, 23 While the sample was under constant load, high-energy synchrotron X-rays (80.8 keV, wavelength iN0.1535 A) from beamline 1-ID-c at the advanced photon source (APS) were used to measure in-plane domain switching and lattice strains surrounding the crack tip. Ceria CeO2) powder was suspended in Vaseline and spread on 0 the exit-beam side of the sample over the switching zone strain and preferred orientation [18]. The crack tip was incident Xrays i9 This serves as a internal standard in that it provides an azi- muthally uniform powder pattern that is ideally free of relocated with respect to the diffraction geometry by using 20 x 20 um- beam and measuring the transmitted inten sity as a function of sample position (x, y). Because of Fig 3 Schematic of the diffraction geometry and a typical two-dimen- the crack opening displacement, the transmitted intensity sional detector image showing the Debye-Scherrer rings(K350, Piezo Technologies, Indianapolis, IN, USA) was used in this experiment. This material composition has been used in earlier work and is believed to contain only the tetragonal phase [19,20]. Compact tension (CT) speci￾mens were obtained in the dimensions 50 · 48 · 1.5 mm3 with a machined notch 23 mm in length parallel to the 50 mm dimension. Similar to the crack geometry described in Ref. [21], a chevron notch was cut at a 45 angle to the major surface of the sample at the end of the 23 mm long notch using a sharp razor blade with 6 lm diamond paste as an abrasive. A precrack was initiated on the major sur￾face opposite the opening of the chevron notch (on the side of higher stress) using a 500 g Vickers indentation. The pre￾crack was propagated by employing the controlled crack growth apparatus described below. After the precrack was propagated through the chevron notch and was visibly present under an optical microscope on both major sur￾faces, the specimen was thermally annealed for 2 h at 600 C. A custom built apparatus was used to apply a con￾trolled stress intensity factor. The compact tension speci￾mens were loaded in Mode I, perpendicular to the crack face, using a piezoelectric actuator. The load was recorded in-line with the actuator and sample using a 1 kN load cell. The crack tip position and crack length were identified and measured prior to loading with an optical microscope. The crack length, load, and sample geometry were all used to calculate the applied stress intensity factor (KI) via stan￾dard formulations [22,23]. While the sample was under constant load, high-energy synchrotron X-rays (80.8 keV, wavelength k  0.1535 A˚ ) from beamline 1-ID-C at the Advanced Photon Source (APS) were used to measure in-plane domain switching and lattice strains surrounding the crack tip. Ceria (CeO2) powder was suspended in Vaseline and spread on the exit-beam side of the sample over the switching zone. This serves as a internal standard in that it provides an azi￾muthally uniform powder pattern that is ideally free of strain and preferred orientation [18]. The crack tip was relocated with respect to the diffraction geometry by using a 20 · 20 lm2 beam and measuring the transmitted inten￾sity as a function of sample position (X, Y). Because of the crack opening displacement, the transmitted intensity significantly increases when the irradiated area encom￾passes the crack. Diffraction data were collected with a 50 · 50 lm2 beam rastered in two dimensions around the crack in steps of 100 lm, mapping a total area approxi￾mately 2 · 2 mm2 . At each position, the beam shutter was opened for 10 s, exposing scattered X-rays onto a two￾dimensional digital image plate detector (MAR 345, 150 lm pixel size, Mar USA, Inc.) positioned 1634 mm behind the center of the sample. The diffraction geometry is illustrated in Fig. 3. The detector was centered on the transmitted X-ray beam such that complete Debye–Scherrer rings were col￾lected (see Fig. 3 for a typical pattern). For each diffraction measurement at each spatial position, the collection of grains sampled were contained within a 50 · 50 · 1500 lm3 ‘‘matchstick’’ diffracting volume. This high￾energy transmission geometry and the resulting low Bragg angles allow diffracting vectors oriented to within 3 of the specimen plane to be sampled. Therefore, for all practical purposes, the sampled diffraction vectors are considered to lie within the specimen plane. Using Fit2D (Ver. 12.077) [24], the diffracted images were ‘‘caked’’ (rebinned within polar coordinates) within 15 wide azimuth sectors to obtain integrated diffracted intensity as a function of 2h [25]. The tetragonal PZT peaks 1 0 1, 1 1 0, 1 1 1, 0 0 2, 2 0 0, 1 1 2, and 2 1 1 and the cubic ceria peaks 1 1 1, 2 0 0, 2 2 0, and 3 1 1 were then fit using a 0 MPa 2 MPa 4 MPa 4 MPa 6 MPa 2 MPa 8 MPa 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 X [mm] Y [mm] 0 MPa 2 MPa 2 MPa 4 MPa 4 MPa 6 MPa 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 X [mm] Y [mm] 2 MPa 0 MPa 0 MPa 2 MPa 2 MPa 4 MPa 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 X [mm] Y [mm] 2 MPa 4 MPa 6 MPa 6 MPa 4 MPa 0 MPa 8 MPa 10 MPa 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 X [mm] Y [mm] 0o 30o 60o 90o Fig. 2. Spatial distributions (X, Y) of the projected deviatoric stress, s n *, in Mode I, plane-stress geometry at a stress intensity factor of KI = 0.71 MPa m1/2. Projected deviatoric stresses are shown perpendicular to the crack face (g = 0), parallel to the crack propagation direction (g = 90), and two intermediate positions (g = 30 and g = 60). The crack face is illustrated in each figure as a heavy line at Y = 1.0. in situ compact tension specimen η η = 0° incident X-rays Y X Fig. 3. Schematic of the diffraction geometry and a typical two-dimen￾sional detector image showing the Debye–Scherrer rings. 5540 J.L. Jones et al. / Acta Materialia 55 (2007) 5538–5548