Nanoindentation-induced plasticity in cubic zirconia up to 500 °C

Acta Materialia 184 (2020) 59–68

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Nanoindentation-induced plasticity in cubic zirconia up to 500 °C Hiroshi Masuda1,∗, Koji Morita, Takahito Ohmura National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan

a r t i c l e

i n f o

Article history: Received 27 May 2019 Revised 30 August 2019 Accepted 10 November 2019 Available online 19 November 2019 Keywords: Ceramics Micromechanical property Crystal plasticity Dislocation Electron microscopy

a b s t r a c t Orientation-dependent crystal plasticity in cubic zirconia ceramics (8 mol% yttria-stabilized zirconia) was investigated from 25 °C to 500 °C, which is below the macroscopic brittle–ductile transition temperature. Nanoindentation experiments and subsequent electron microscope analysis revealed that dislocation activities on {001} planes predominantly governed small-scale plasticity at the grain interior for each crystal orientation in this temperature range. The maximum shear stress at yielding, τ max , necessary for plastic yielding, was comparable to the theoretical shear strength, τ th , estimated from the measured elastic modulus at low temperatures, while their ratio, τ max /τ th , almost monotonically decreased at elevated temperatures. This suggests that plastic yielding was predominantly mediated by atomistic shear processes at low temperatures and increasingly affected by thermally assisted processes at elevated temperatures. The orientation-dependent behavior switched in the vicinity of ~25° from <001> impression axes. In the near-[001] axis, plastic yielding occurred more smoothly at lower stresses, which can be attributed for the surface nucleation and forest-cutting interaction of dislocations on multiple {001} slip planes along and across the impression axes. In near-[101] and [111] axes, on the other hand, yielding was more burst-like and typically accompanied by pop-in events at higher stresses, which could result from the homogeneous dislocation nucleation and free-gliding motion of dislocations on {001} planes with considerable Schmid factors for the impression axes. © 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

1. Introduction Fully stabilized cubic zirconia (ZrO2 ) has been used for kinds of high-temperature applications, including top layers for thermal barrier coatings (TBCs) [1] and electrolytes for solid oxide fuel cells (SOFCs) [2]. This diversity is due to its superior thermal resistance [3], thermal insulativeness [4], ionic conductivity [5], and moderate compatibility with other metallic components for a thermal expansion coefficient relatively close to that of metals [6]. Zirconia components are typically exposed to severe thermal cycles, with temperature gaps up to 10 0 0 °C or above. Mechanical control in these wide temperature ranges is of importance for the engineering applications of this material, while its brittle character (fracture toughness, KIC ~ 1.6 MPa m1/2 at room temperature [7]) has been highly problematic. This brittleness is more serious than partially stabilized tetragonal phase (KIC ~ 7.8 MPa m1/2 at room temperature [8]), which is toughened by stress-induced martensitic transformation [9].

∗

Corresponding author. E-mail addresses: [email protected] (H. Masuda), [email protected] (K. Morita), [email protected] (T. Ohmura). 1 Present address: Department of Materials Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. https://doi.org/10.1016/j.actamat.2019.11.028 1359-6454/© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

With the aim to overcome the aforementioned brittleness, many studies from the 1980s to the 20 0 0s were concentrated on understanding dislocation plasticity, which occurs even in the cubic phase [10–16]. These studies focused on the macroscopic character of dislocation plasticity, including stress–strain relations, slip systems, critical resolved shear stress (CRSS), and rate-controlling processes, from 400 °C to 1500 °C via uniaxial compression and Vickers indentation experiments in single crystals. They concluded that dislocations with Burgers vectors b = 12 110 predominantly governed the high-temperature plasticity with significant temperature and crystal orientation dependency. However, only limited data were reported for the lower-temperature plasticity in cubic zirconia because of the brittle–ductile transition near 400 °C to 500 °C for macroscopic compression [15,16] and near 800 °C for Vickers indentation [12]. Nevertheless, it is considerably important to understand the mechanical properties in this low-temperature range, wherein the brittle ceramics can be exposed to the most substantial damages in the TBC and/or SOFC applications under the severe thermal cycles. Today, it is possible to plastically deform even ceramics and to detect their mechanical characters below the macroscopic brittle– ductile transition temperature by miniaturizing the deformation volume to smaller than micrometer scales, as representatively achieved via nanoindentation techniques among various oxide

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[17,18] and non-oxide [19–21] ceramics. Micromechanical characterization below macroscopic brittle–ductile transition temperatures may be profoundly important for the mechanical design applied under the large thermal cycles. The micromechanical responses of cubic zirconia have been previously characterized via nanoindentation experiments at room temperature. Some groups have evaluated the local stiffness, porosity fraction, and/or residual stress by measuring elastic moduli and microhardness in TBCs and SOFCs, which were synthesized by physical vapor deposition [22], plasma spraying [23], and sintering [24]. Several other research groups have characterized the crystal orientation effects and/or the deformation mechanisms involved in the small-scale plasticity in cubic zirconia [25–28]. Fujikane et al. [25] detected “pop-in” events, which possibly accompany the onset of plasticity with a strain burst during nanoindentation. Gaillard et al. [27] observed that slip lines developed around the impressions after pop-in events, and concluded that dislocation activities could mediate the plasticity in cubic zirconia even at room temperature. Despite these advances, limited attention has been paid to the relations among the pop-in events (i.e. plastic yielding), dislocation characteristics, and their temperature and orientation dependency in this material. However, nanoinentation experiments shoule be able to investigate the temperature and/or orientation effects on the micromechanical responses, as commonly reported among metallic materials [29–32]. This study aims to investigate the orientation-dependent crystal plasticity and dislocation characteristics in cubic zirconia ceramics, by focusing on the primitive mechanisms of plastic yielding (i.e. elastic–plastic transition) in the blanked temperature range between room temperature and 500 °C (i.e. around the macroscopic brittle–ductile transition temperature [15,16]), to improve our understanding on the lower-temperature crystal plasticity in this material. This scope was accomplished via automated nanoindentation experiments with a heating facility and subsequent electron microscope analysis.

Fig. 1. (a) Sample appearance as annealed at 1500 °C for 144 h, (b) X-ray diffraction profile using Cu Kα radiation, (c) inverse pole figure map, and (d) pole figure reconstructed from electron backscatter diffraction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 1 Numbers of effective datasets and averaged drift rates at different temperatures.

2. Methods 2.1. Materials 8 mol% Y2 O3 -stabilized ZrO2 (8YSZ) was used in this study. The commercial powder (TZ–8Y, Tosoh) was compacted to 10 × 40 × 3 mm3 via hand pressing at 0.6 MPa and cold isostatic pressing at 392 MPa for 10 min. This powder compact was sintered at 1250 °C for 40 h and annealed at 1500 °C for 144 h in air (Fig. 1(a)). This specimen was cut into 10 × 10 × 3 mm3 sample via a diamond wire saw, mechanically polished by finishing with 1-μm diamond paste, and annealed again at 1400 °C for 0.5 h to thermally etch the sample surface. The prepared sample exhibited single-phase cubic (Fig. 1(b)) and equiaxed grain structure with an average grain size of 4.2 ± 2.5 μm (Fig. 1(c)). The crystal orientation texture exhibited heterogeneous but disordered distribution at the observed scales of 400 × 400 μm2 (Fig. 1(d)). 2.2. Nanoindentation Nanoindentation experiments were performed on randomly oriented crystal grains from 25 °C to 500 °C in an air + argon mixture, by TI950 TriboIndenter equipped with xSol temperature control stage (Hysitron, USA). The sample was sandwiched and heated by resistance heater plates, each of which contained a thermocouple to measure and control the testing temperature, equipped with a water coolant and an argon gas flow system. The top plate had a tip hole with a diameter of 3 mm to insert a nanoindentation tip. The inserted tip was kept at a distance of 10 μm from the sample surface for 1 h until the thermal expansion became negligible after the temperature reached the target value. The measurements

Temperature, T [°C]

Number, n

Drift rate (nm s− 1 )

25 100 200 300 400 500

414 350 196 188 374 152

0.017 ± 0.024 0.047 ± 0.026 0.029 ± 0.046 0.006 ± 0.030 0.023 ± 0.036 −0.003 ± 0.044

were performed using Berkovich diamond indenters with tip radii, R, of 440 nm (for experiments at 25 °C) and 310 nm (for elevatedtemperature experiments). Indentations were executed under the load control mode with a loading rate of 50 μN s−1 to the maximum loads of 30 0 0 μN at 25 °C and 1500 μN at elevated temperatures, after automated tip drift collection. Only the data obtained from grain interiors were used for the subsequent analyses, with the number of effective datasets at each temperature shown in Table 1. Note that the tip drift was sufficiently restricted below 0.1 nm s−1 , as necessary for assuring the measurement accuracy [33], even at the elevated temperatures. Young’s modulus, E, and the maximum shear stress at yielding, τ max , were derived from the loading portion in each P–h relation, where P and h represent indentation load and depth measured during the nanoindentation experiments, respectively. First, reduced elastic modulus, E∗ , was fitted in elastic regimes in the P– h curves using the below Hertzian equation for the elastic contact condition between a sphere (tip) and a flat plane (material) [34]:

P=

4 ∗ 1 3 E R2 h2 , 3

(1)

where E∗ is represented by the following equation:

 ∗

E =

1 − νt2 1 − ν2 + Et E

−1 ,

(2)

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where Et is Young’s modulus of diamond (1140 GPa) and ν t and ν are Poisson’s ratios of diamond (0.07) and 8YSZ (0.31), respectively [35,36]. Second, E was derived from Eq. (2). Finally, τ max under the impressions were calculated by the following equation [16]:



τmax

6E ∗2 PC = [0.61 − 0.23(1 + ν )] π 3 R2

 13 ,

(3)

where PC represents the load at the yield point that was determined as the moment for each P–h relation to separate more than 1 nm from the fitting curve along Eq. (1). The above Hertzian equations can be applied for elastically isotropic solids in indentation depths approximately up to 50 nm, below which Berkovich tips can be approximated as spherical ones with certain tip radii [37]. The current material could satisfy the elastically isotropic condition under the nanoindentation experiments, as described in Section 3.2, and the measurement of τ max was performed with indentation depths approximately below 40 nm. These τ max values were compared with the theoretical shear strength, τ th , which was derived at each temperature from the below equation [38], to estimate the temperature effects on the plastic yielding behaviors:

τth =

G , 2π

(4)

where G is the shear modulus calculated from the measured E values and expressed as follows:

G=

E . 2 (1 + ν )

(5)

2.3. Microstructural characterization The sample surfaces after nanoindentation experiments were observed via scanning electron microscopy (SEM), JEM7001F (JEOL, Japan), after conductive coating of amorphous osmium with a thickness of approximately 1 nm via plasma chemical vapor deposition (Meiwafosis, Japan). Crystal orientations of the impressed grains were measured via electron backscatter diffraction (EBSD) at an acceleration voltage of 15 kV and a step size of 0.1 μm by CCD detector and OIM software (EDAX/TSL, USA) with referred crystal structure data of 8YSZ (space group, Fm3m; lattice parameter, a = 0.5132 nm [39]). Thin foils for transmission electron microscopy (TEM) observation were achieved via a Ga+ focused ion beam (FIB) technique from the cross sections of several individual impressions, which deformed closely along the [001] and [111] directions at 200 °C, 400 °C, and 500 °C, respectively. The sample surfaces were protected by carbon deposition, processed by FIB, picked up by a tungsten probe, and attached to molybdenum meshes. The attached samples picked up from [001] and [111] impressions were processed into thin foils parallel to (010) and (11¯ 0 ) planes, respectively. TEM observations were performed to characterize the dislocation structures underneath the impressions, at an acceleration voltage of 200 kV in JEM2100F (JEOL, Japan). The predominant slip systems were determined from the TEM bright-field images using g-vector excitations and g·b analysis, i.e. dislocations satisfying the below condition could be invisible:

g · b = 0.

(6)

3. Results 3.1. Load–displacement relations Fig. 2(a) shows a representative image quality + inverse pole figure map of an impressed area after automated nanoindentation

Fig. 2. (a) Representative inverse pole figure map observed by EBSD, (b) topological image of an impression observed by atomic force microscopy, and (c) (d) surface height profiles along the arrows indicated in (b), after nanoindentation experiments at 25 °C up to 30 0 0 μN. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

experiments at 25 °C. The experimental condition, mechanical response, and crystal orientation were associated together with each impression. Fig. 2(b) demonstrates an atomic force microscopy image around a representative impression, which does not exhibit any sign of cracks but rather pile-ups resulting from plastic flow, as confirmed in the surface profiles across and near the impression (Fig. 2(c) and (d)). This indicates that the nanoindentation experiments were not accompanied by crack failure but rather the plastic flow, even at room temperature. Fig. 3 shows typical load–displacement (P–h) relations during nanoindentation along the near-[001], [101], and [111] axes at different temperatures. The elastic regimes were well-fitted by the Hertzian contact curves, indicating that the elastic part could be approximated by the isotropic sphere–plane contact condition. Note that the indentation tip radius was almost kept constant below 400 °C, while the tip slowly wore and its radius gradually increased at 500 °C, as reflected in Hertzian fitting at this temperature (Fig. 3(d) and (h)). The wearing rate of the tip became too severe at 600 °C, above which indentation experiments could not be executed. All the P–h curves exhibited plastic yielding (i.e. separation from the Hertzian contact curves) in the loading regimes and left plastic strain after unloading. The yielding behavior presents significant temperature and crystal orientation dependency. With an increase in temperature, the yielding load, PC , typically decreased and the development of plastic strain after yielding was intensified (i.e. the materials became softer). The near-[001] axis exhibited smoother yielding behavior, while the near-[101] and [111] axes typically presented pop-in (i.e. strain burst) events at, or immedi-

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Fig. 3. Representative load–displacement (P–h) curves during (a–d) near-[001], (e–h) near-[101], and (i–l) near-[111] impressions at temperatures of 25 °C, 20 0 °C, 40 0 °C, and 500 °C. Discontinuous jumps in P–h curves indicate the occurrence of pop-in events. The dotted curves show Hertzian elastic contact relations derived from Eq. (1). Only the early regimes of P–h curves are shown in (b–d), (f–h), and (j–l), with the P–h range indicated by dotted rectangles in (a), (e), and (i). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

ately after, yielding. The former behavior was confirmed in orientation ranges approximately 25° from the <001> axis (orientation 1), while the latter behavior typically appeared in the other orientation ranges (orientation 2). The P–h characters involving the existence of pop-in events could be recognized uniquely to each orientation throughout the temperature range up to 500 °C. 3.2. Elastic responses

similar materials. The values measured in this study were located nearly between these two reports rather than those measured by nanoindentations at room temperature with considerable scattering [25,41]. Note that the impulse excitation technique [36] reported a largely scattered dataset, around 400 °C, toward the upper side from the master curve, which might be relevant to the present result with an irregular increase in E around 400 °C. 3.3. Plastic responses

Fig. 4(a) shows a histogram of Young’s modulus, E, measured at 25 °C for orientations 1 (red data) and 2 (blue data). The E values measured in this study were almost independent of the crystal orientation, although the P–h curves exhibited considerable orientation dependency in their plastic responses (Fig. 3). This tendency suggests that the cubic zirconia was almost elastically isotropic under the nanoindentation experiments. Fig. 4(b) shows the E values averaged irrespectively of the measured orientations at different temperatures. E almost monotonically decreased between 25 °C and 300 °C, exceptionally increased at 400 °C, and decreased again at 500 °C. Fig. 4(b) also demonstrates the data reported via an impulse excitation technique [36] and a sonic measurement [40] for bulk specimens of

Fig. 5 shows histograms of the maximum shear stress at yielding, τ max , calculated from Eq. (3) at various temperatures. The histogram for 25 °C clearly shows a bimodal distribution of τ max ; the colored data columns derived from orientations 1 (red) and 2 (blue) exhibit significant separation with each other. This bimodal and orientation-dependent character is correlated with the different yielding behaviors in the P–h curves (Fig. 3). Orientation 1 was characterized by lower τ max and smoother yielding, while orientation 2 was typically accompanied by higher τ max and more burstlike yielding with pop-in events. This bimodal character weakened from 200 °C to 400 °C (Fig. 4(b) and (c)) and became clearer again at 500 °C (Fig. 4(d)).

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the macroscopic experiments wherein the CRSS in orientation 1 was consistently larger than that in orientation 2, even at the overlapping temperatures. This opposite orientation-dependent trend between the nanoindentation and the macroscopic compression is noteworthy, although the τ max values and the macroscopic CRSS should not be compared in a direct manner. 3.4. Microstructural characterization Fig. 7 shows the TEM micrographs underneath the impressions in the near-[001] axis (orientation 1) at different temperatures. Dislocation structures typically developed under the impressions and no strange diffraction spot associated with phase transformation nor twinning was observed, as demonstrated in a selected area diffraction (SAD) pattern (Fig. 7(g)). Dislocation lines of two different characters, i.e. aligned vertically (left columns) and horizontally (right columns), can be distinguished with different g 002 and g 200 excitations, respectively. These observations indicate that the dislocations satisfying Eq. (6) became invisible with each g excitation. In addition, these invisible dislocations apparently satisfy the below relation for each g vector:

g · ξ = 0,

Fig. 4. (a) Frequency histogram of Young’s modulus, E, measured from the unloading parts of P–h curves at 25 °C with peak loads of 30 0 0 μN. The red and blue columns indicate orientation ranges with similar color (i.e., orientations 1 and 2) in the standard triangle, respectively. (b) Young’s modulus at different temperatures, measured from the loading parts of P–h curves. Literature values reported by nanoindentations [25,41], an impulse excitation technique [36], and a sonic measurement [40] was also denoted. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

These tendencies are replotted as functions of temperature in Fig. 6, which shows the maximum shear stress at yielding, τ max (= τ 1 , τ 2 ), in orientations 1 (red) and 2 (blue) measured at different temperatures. This graph also demonstrates the value of the theoretical shear strength, τ th (black dots), derived by Eq. (4) at various temperatures. τ max was close to τ th at 25 °C, especially in orientation 2 (τ 2 /τ th = 0.98). The ratio, τ max /τ th , almost monotonically decreased with the temperature increase up to 400 °C, while its orientation dependency gradually became negligible (τ 1 /τ th = 0.41 and τ 2 /τ th = 0.47 at 400 °C). Finally, only τ 2 /τ th irregularly increased again at 500 °C (τ 2 /τ th = 0.54). CRSS values for {110} <11¯ 0> and {001} <110> slip systems, reported by the previous macroscopic compression in each orientation above 400 °C [15,16], are plotted with open symbols in Fig. 6. The shear stress levels for plastic yielding in these nanoindentation experiments were higher, almost by an order of magnitude, than the macroscopic data as indicated from the overlapping temperatures from 400 °C to 500 °C. Furthermore, the maximum shear stress at yielding, τ max , was typically smaller in orientation 1 than orientation 2 at most of the temperatures, as opposed to

(7)

where ξ is the line vector of the dislocations. The slip plane normal can be determined to be along b × ξ , which is perpendicular to each g vector according to Eqs. (6) and (7), unless the dislocations were of the perfect screw character. These criteria suggest that g 002 revealed dislocations belonging to (100) [011] and/or (100) [01¯ 1] slip systems (left column), while g 200 revealed those along (001) [110] and/or (001) [1¯ 10] slip systems (right column). Therefore, the nanoindentation-induced plasticity in orientation 1 was possibly mediated via dislocation activities belonging to multiple {001} <110> slip systems, which activated nearly along and across the impression axis. Fig. 8 shows TEM micrographs from underneath the impressions in the near-[111] axis (orientation 2) at different temperatures with different g vectors of 220 and 002, respectively. Dislocation structures developed under the impressions with no strange diffraction spots, as well as the case in orientation 1. The dislocation arrays aligned along the (001) plane traces 30° to 40° tilted from the impression axes are revealed by g 220 excitation (left columns), while these dislocations became invisible with g 002 (right column). These dislocations and g 002 excitation can also satisfy Eq. (7), indicating that the slip plane could be (001), unless the dislocations were of the perfect screw character. Another group of dislocations, which were the most clearly observed as bowing out in Fig. 8(a) and (b), might slip along other (100) and/or (010) planes. This suggests that the nanoindentation-induced plasticity in orientation 2 was mediated via dislocation activities along the {001} <110> slip systems with considerable Schmid factors against the impression axis. The geometries between dislocation structures and impression axes were unique to each orientation throughout the temperature range, while the traveling distance of dislocations typically increased with temperature. The dislocations reached approximately 30 0−40 0 nm at 200 °C, while those at 500 °C reached more than 1 μm.

4. Discussion 4.1. Temperature effect The maximum shear stress at yielding, τ max , was strongly affected by the testing temperature, as described in Section 3.3. The τ max values were close to the theoretical shear strength, τ th ,

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Fig. 5. Frequency histograms of the maximum shear stress at yielding, τ max , for nanoindentation experiments at (a) 25 °C, (b) 200 °C, (c) 40 0 °C, and (d) 50 0 °C. The red and blue columns indicate orientations 1 and 2 as indicated in the standard triangle in (a), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

at lower temperatures (e.g., τ 1 /τ th = 0.76 and τ 2 /τ th = 0.98 at 25 °C), while their ratio decreased at elevated temperatures (e.g., τ 1 /τ th = 0.41 and τ 2 /τ th = 0.47 at 400 °C). These ratios, τ max /τ th , represent the primitive processes of plastic yielding from defect-free zones at (sub)surfaces. The room-temperature yielding at nearly the theoretical shear strength, especially in orientation 2, was possibly via homogeneous nucleation of dislocations, which could be triggered by an atomistic shear process [38]. Zhang and Ohmura reported dislocation structures that developed from defect-free zones nearly at the theoretical shear strength [42]. On the other hand, the elevated-temperature plasticity was more affected by thermal atomic vibration, which could enable dislocation nucleation at lower stresses, as typically found among metals and alloys [43,44]. This temperature effect was also found in the increasing traveling distance of dislocations at elevated temperatures (Figs. 7 and 8). Note that abnormal elastic and plastic responses were found at 400 °C to 500 °C; E irregularly increased at 400 °C, while τ 2 /τ th showed a slight increase at 500 °C. This irregular behavior might be due to some intrinsic changes in the material. Giraud and Canel [35] also reported an anomalous scattering of the elastic constant around 400 °C, as presented in Fig. 4(b), and explained this by an order–disorder transition of the atomic positions of oxygen vacancies. This order–disorder transition was also reported around 600 °C via neutron diffraction [45]. In addition, ionic conductivity of oxygen vacancies was possible around 700 °C and above [5]. These diffusion-mediated processes might have been available in this study even at lower temperatures for rapid surface dif-

fusion because nanoindentations are highly sensitive to surface properties. 4.2. Orientation-dependent plastic responses and defect characteristics The τ max values remained almost homogeneous in each range of orientations 1 and 2, while the values switched in the vicinity of 25° from the <001> impression axis, at every temperature. In addition, the TEM micrographs demonstrated that the geometries of the dislocation structures were different between orientations 1 and 2 (Figs. 7 and 8). For orientation 1, dislocation structures typically developed along the multiple slip planes; [001] impression was accompanied by dislocations on (001) and (100) slip planes perpendicular and parallel to the impression axis, respectively. These slip planes cannot be observed in uniaxial experiments because of the nearly zero Schmid factors against the compression axis. Therefore, {001} slip planes were not confirmed but only {101} and/or {111} planes were reported for uniaxial experiments in orientation 1 [16]. If those slips were also active during the nanoindentation in this study, as predicted by the uniaxial experiment, the dislocation arrays tilted by nearly ±45° from the impression axes, e.g. dislocations belonging to (101) [1¯ 01] and/or (1¯ 01 ) [101] slip systems, should be recognized. In the TEM micrographs (Fig. 7), however, such dislocations could not be confirmed even with g 002 or g 200, neither of which satisfies the invisible condition represented by Eq. (6) for dislocations with the above Burgers vectors. For orientation 2, on

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Fig. 6. The maximum shear stress at yielding, τ max , from 25 °C to 500 °C. The red squares and blue triangles represent τ 1 and τ 2 , respectively. Black dots indicate the theoretical shear strength, τ th , derived from Eqs. (4) and (5). The open plots indicate the CRSS values for {001} <110> and {110} <110> slip systems measured via macroscopic compression experiments for single crystals in orientations 1 and 2, respectively [15,16]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

65

the other hand, dislocation arrays along the {001} planes tracked nearly 30° to 40° from the impression axes, as well as the uniaxial compression experiments [15], were confirmed. These slip systems were possibly activated for their considerable Schmid factors, calculated as 0.47 for the representative impression axis [111] and the predicted slip system (001) [110]. These differences, between orientations 1 and 2, were clearly correlated with the yielding behavior in the P–h curves (Fig. 3), i.e. smoother yielding in orientation 1 and burst-like yielding accompanied by pop-in events in orientation 2. Fig. 9 schematically illustrates a possible orientation-dependent trend on the yielding behavior. In orientation 1, each {001} plane could contain two different characters of dislocations with Burgers vectors of 12 110 and 12 11¯ 0, which could be nearly equivalent in the geometry of orientation 1. These multiple dislocations, crossing each other and on multiple slip planes, might cause forest-cutting interactions from the early stage of plasticity after the yielding. This forestcutting mechanism possibly caused a strain hardening subsequent to the yielding and resulted in the smooth elastic–plastic transition (Fig. 9(a)). In orientation 2, on the other hand, dislocations along well-defined {001} planes propagated radially and independently from each other. This suggests that dislocations slipped via a freeglide mechanism after the yielding with negligible interactions among different slip systems at substantial depths, which possibly

Fig. 7. Micrograph montages observed via TEM underneath the impressions in near-[001] directions (i.e., orientation 1) with peak loads of 1500 μN at (a) (b) 200 °C, (c) (d) 400 °C, and (e) (f) 500 °C. The TEM foils were prepared parallel to (010) planes and bright-field images were observed under two-beam conditions with transmitted and diffracted beams by tilting the foil from the [010] zone axis (ZA). The left columns (a, c, e) and right columns (b, d, f) demonstrate g 0 02 and g 20 0 excitations, respectively. (g) SAD patterns for [010] ZA around the impression at 500 °C.

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Fig. 8. Micrograph montages observed via TEM underneath the impressions in near-[111] directions (i.e., orientation 2) with peak loads of 150 0 μN at (a) (b) 20 0 °C, (c) (d) 400 °C, and (e) (f) 500 °C. The TEM foils were prepared parallel to (11¯ 0 ) planes and bright-field images were observed under two-beam conditions with transmitted and diffracted beams by tilting the foil from the [11¯ 0] ZA. The left columns (a, c, e) and right columns (b, d, f) demonstrate g 220 and g 002 excitations, respectively. (g) SAD patterns for [11¯ 0] ZA around the impression at 500 °C.

Fig. 9. Schematic illustrating the possible dislocation activities during nanoindentation along (a) [001] impression (i.e. orientation 1) and (b) [111] impression (i.e. orientation 2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

resulted in the burst-like behavior accompanied by pop-in events (Fig. 9(b)). Note again that τ max , derived from Eq. (3), does not involve any orientation variable as Schmid factors despite the significant difference between orientations 1 and 2. This suggests that the orientation effect confirmed in this study is not strongly correlated with the conventional Schmid’s law, as discussed in the below viewpoints: (i) the homogeneous τ max values in each orienta-

tion range, (ii) the activation of {001} slip throughout the orientation range, including orientation 1 with nearly zero Schmid factors, and (iii) the discontinuous change in τ max between orientations 1 and 2. (i) The yielding condition in this study can be well-represented by a sphere–plane contact condition, as indicated in Section 3.1. The stress state caused by spherical indenta-

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tion typically becomes more homogeneous and less affected by crystal orientation than uniaxial loading, as observed in metallic materials [46]. This was most significantly found in the highly isotropic Young’s modulus measured in this study (Fig. 4(a)), while the sonic measurement of Young’s modulus for single-crystal cubic zirconia typically shows a considerable orientation dependency with nearly a factor of 1.5 between <001> and <111> orientations [25]. A similar tendency could be found in the isotropic characters of τ max in each orientation range rather than the gradational change typically found for yield stress in uniaxial experiments. (ii) In such an isotropic state, active slip systems could be more dependent on the CRSS value itself rather than the Schmid factor [30], i.e. a slip system with lower CRSS could be more predominant with negligible effects of Schmid factors. The macroscopic compression experiments reported that the CRSS for {110} slip was higher than {001} slip by a factor of 1.5−2 [15,16]. In micromechanical experiments, moreover, the “smaller is stronger” trend of size effect is commonly known [47]. Therefore, a considerable difference of CRSS in a gigapascal order is expected between the {110} and the {001} slip systems for this low-temperature and small-scale conditions, which possibly resulted in the softer {001} slip to be more predominant throughout the orientation range in this study. (iii) The above discussion suggests that the orientationdependent change in the yielding responses, despite the same {001} slip activations, should be attributed for different dislocation nucleation mechanisms between orientations 1 and 2. A recent molecular dynamics simulation demonstrated that prismatic half loops of dislocations could nucleate from a free surface even onto slip planes perpendicular to the surface (i.e. with zero Schmid factor) during nanoindentation for covalent-bonding ceramics [48], which might be also promising for the yielding behavior of orientation 1 in this study. This surface dislocation nucleation might result in the maximum shear stress at yielding in orientation 1, typically lower than orientation 2 involving the homogeneous dislocation nucleation at the subsurface. According to the above discussions, the orientation-dependent yielding responses during nanoindentation could be cooperatively affected by several primitive processes, including the nucleation mechanisms, thermal assistance, and interaction mechanisms of dislocations belonging to {001} <110> slip systems. 5. Conclusions Orientation-dependent crystal plasticity in fully stabilized cubic zirconia was investigated from 25 °C to 500 °C, which is below the macroscopic brittle–ductile transition temperature. The plastic behavior characterized via nanoindentation and electron microscope techniques could be described by dislocation activities dependent on temperature and orientation, as follows: (1) Nanoindentation-induced plasticity was predominantly mediated by dislocation activities on {001} plane for each crystal orientation in this temperature range. (2) The maximum shear stress at yielding was comparable to the theoretical shear strength at 25 °C, while it decreased at elevated temperatures. Plastic yielding was predominantly mediated via atomistic shear processes at low temperatures and increasingly affected by thermal atomic vibrations at elevated temperatures. (3) The maximum shear stress at yielding, the presence/absence of pop-in events, and the dislocation structures showed a crystal orientation dependency in the dislocation activities.

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In orientation 1 (i.e. within 25° from <001>), plastic yielding occurred more smoothly at lower stresses, possibly attributed for the surface nucleation and forest-cutting interactions of dislocations on multiple {001} slip planes, parallel and perpendicular to the impression axis. In orientation 2 (i.e. the other range), the yielding was more burst-like and typically accompanied by pop-in events at higher stresses, which could result from the homogeneous nucleation and free gliding motion of dislocations on {001} planes with considerable Schmid factors for the impression axis.

Acknowledgment This work was supported by KAKENHI “Research Activity Startup” (18H05944, JSPS), ICYS Research Grant (NIMS), and TEM Station (NIMS). We thank Mr. Nakazato for technical support for the sample preparation by Ms. Nakagawa for the nanoindentation operation. We also thank Dr. Tohru Suzuki for sharing the osmium coating machine and Dr. Hideyuki Murakami for sharing the hightemperature nanoindentation facility. References [1] A.G. Evans, D.R. Mumm, J.W. Hutchinson, G.H. Meier, F.S. Pettit, Mechanisms controlling the durability of thermal barrier coatings, Prog. Mater. Sci. 46 (2001) 505–553. [2] N.Q. Minh, Ceramic fuel cells, J. Am. Ceram. Soc. 76 (1993) 563–588. [3] H.G. Scott, Phase relationships in the zirconia–yttria system, J. Mater. Sci. 10 (1975) 1527–1535. [4] K.W. Schlichting, N.P. Padture, P.G. Klemens, Thermal conductivity of dense and porous yttria-stabilized zirconia, J. Mater. Sci. 36 (2001) 3003–3010. [5] S.P.S. Badwal, Zirconia-based solid electrolytes: microstructure, stability and ionic conductivity, Solid State Ion. 52 (1992) 23–32. [6] H. Hayashi, T. Saitou, N. Maruyama, H. Inaba, K. Kawamur, M. Mori, Thermal expansion coefficient of yttria stabilized zirconia for various yttria contents, Solid State Ion. 176 (2005) 613–619. [7] M. Mazaheri, A.M. Zahedi, M.M. Hejazi, Processing of nanocrystalline 8 mol% yttria-stabilized zirconia by conventional, microwave-assisted and two-step sintering, Mater. Sci. Eng. A 492 (2008) 261–267. [8] M. Trunec, Effect of grain size on mechanical properties of 3Y-TZP ceramics, Ceram. Silik. 52 (2008) 165–171. [9] R.C. Garvie, R.H. Hannink, R.T. Pascoe, Ceramic steel? Nature 258 (1975) 703–704. ´ ´ [10] A. Domınguez-Rodrı guez , K.P.D. Lagerlöf, A.H. Heuer, Plastic deformation and solid-solution hardening of Y2 O3 -stabilized ZrO2 , J. Am. Ceram. Soc. 69 (1986) 281–284. ´ ´ [11] J. Martinez-Fernandez, M. Jimenez-Melendo, A. Domınguez-Rodrı guez , A.H. Heuer, High-temperature creep of yttria-stabilized zirconia single crystal, J. Am. Ceram. Soc. 73 (1990) 2452–2456. [12] G.N. Morscher, P. Pirouz, A.H. Heuer, Temperature dependence of hardness in yttria-stabilized zirconia single crystals, J. Am. Ceram. Soc. 74 (1991) 491–500. [13] R. Baufeld, M. Bartsch, U. Messerschmidt, D. Baither, Plastic deformation of cubic zirconia at temperatures between 1150 and 700 °C, Acta Metall. Mater. 43 (1995) 1925–1933. [14] R. Baufeld, D. Baither, M. Bartsch, U. Messerschmidt, Plastic deformation of cubic zirconia single crystals at 1400 °C, Phys. Stat. Sol. A 166 (1998) 127–153. [15] R. Baufeld, B.V. Petukhov, M. Bartsch, U. Messerschmidt, Transition of mechanisms controlling the dislocation motion in cubic ZrO2 below 700 °C, Acta Mater. 46 (1998) 3077–3085. [16] A. Tikhonovsky, M. Bartsch, U. Messerschmidt, Plastic deformation of yttria stabilized cubic zirconia single crystals I. Activation parameters of deformation, Phys. Stat. Sol. A 201 (2004) 26–45. [17] S.N. Dub, V.V. Brazhkin, N.V. Novikov, G.N. Tolmachova, P.M. Litvin, L.M. Lityagina, T.I. Dyuzheva, Comparative studies of mechanical properties of stishovite and sapphire single crystals by nanoindentation, J. Superhard Mater. 32 (2010) 406–414. [18] N. Dub, V.V. Brazhkin, V.A. Belous, G.N. Tolmacheva, P.V. Konevskii, Comparative nanoindentation of single crystals of hard and superhard oxides, J. Superhard Mater. 36 (2014) 217–230. [19] T. Csanádi, M. Bl’anda, N.Q. Chinh, P. Hvizdoš, J. Dusza, Orientation-dependent hardness and nanoindentation-induced deformation mechanisms of WC crystals, Acta Mater. 83 (2015) 397–407. [20] T. Csanádi, D. Németh, J. Dusza, Z. Lencˇ éš, P. Šajgalík, Nanoindentation induced deformation anisotropy in β -Si3 N4 ceramic crystals, J. Eur. Cera. Soc. 36 (2016) 3059–3066. [21] T. Csanádi, A. Kovalcˇ íková, J. Dusza, W.G. Fahrenholtz, G.E. Hilmas, Slip activation controlled nanohardness anisotropy of ZrB2 ceramic grains, Acta Mater. 10 (2017) 452–464.

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