Royal Society Publishing

On a ferroelastic mechanism governing the toughness of metastable tetragonal-prime (t′) yttria-stabilized zirconia

C Mercer, J.R Williams, D.R Clarke, A.G Evans


This article investigates the toughness of yttria-stabilized zirconia (YSZ) with the tetragonal-prime (t′) structure. Such materials are used as durable thermal barriers in gas turbines. Their durability has been attributed to high toughness, relative to materials in the cubic phase field. Based on prior literature, a ferroelastic toughening mechanism is hypothesized and this assertion is examined by characterizing the material in the wake of an indentation-induced crack. Assessment by transmission electron microscopy, Raman spectroscopy and optical interferometry has affirmed the existence of a process zone, approximately 3 μm in width, containing a high density of nano-scale domains, with equal proportions of all three crystallographic variants. Outside the zone, individual grains contain a single variant (no domains) implying that the toughening mechanism is controlled by domain nucleation (rather than the motion of pre-existing twin boundaries). The viability of the ferroelastic toughening mechanism is assessed using a process zone model that relates the observed toughening to the stress/strain hysteresis accompanying domain formation. Based on the measured process zone size, the known tetragonality of t′-7 wt% YSZ and the enhancement in toughness relative to cubic YSZ, consistency between the model and the observed toughening is demonstrated for a reasonable choice of the coercive stress.


1. Introduction

The application of 7 wt% yttria-stabilized zirconia (YSZ) as a thermal barrier coating (TBC) on airfoils used in aero and power generation gas turbines has motivated interest in its thermomechanical properties. In the earliest implementations, the designs placed minimal reliance on the thermostructural integrity of the YSZ, so its mechanical properties were of secondary relevance. As the technology has advanced, knowledge of specific high temperature properties has become increasingly important. Among these, the fracture toughness is especially critical, owing to its central influence on the mechanisms that limit the durability. The mechanisms affected by the toughness include (i) large-scale delamination caused by strain misfit with the substrate, especially under thermal cycling conditions (Tolpygo & Clarke 1999; Evans et al. 2001; Mumm et al. 2001; Clarke & Levi 2003), (ii) material loss due to erosion and foreign object damage (FOD) (Chen et al. 2003), and (iii) delamination caused by penetration of molten calcium magnesium aluminosilicate (CMAS; Borom et al. 1996; Mercer et al. 2005). Given the importance of toughness, measurements are sparse for materials having the compositions, phases and microstructures found in actual thermal barrier systems. The purpose of the present assessment is to provide a perspective on mechanisms that dictate the toughness of YSZ and related compositions. The emphasis is on the materials generated at relatively low temperature (approx. 1000°C) from the vapour phase, particularly by electron beam physical vapour deposition (EB-PVD). Such materials contain phases that differ from those in materials with the same composition generated by sintering at higher temperature (Lange 1982). The 7 wt% YSZ used in most gas turbine applications is a metastable, single-phase tetragonal-prime, t′, having a columnar microstructure (figure 1), and 〈100〉 growth texture (Schulz et al. 2003). At this composition, the t′-phase has tetragonality (ratio of c-axis to a-axis lattice dimensions), c/a−1=1.1%.

Figure 1

Image of a columnar thermal barrier oxide produced by electron beam physical vapour decomposition (EB-PVD). The columnar structure and the gaps between the columns preclude toughness measurements without densification. Scale bar, 50 μm.

The focus of this investigation is on the mode I toughness, directly pertinent to failure by erosion, FOD and CMAS degradation (Chen et al. 2003; Mercer et al. 2005). Other failure mechanisms are controlled by the mode II toughness, such as edge and buckle delaminations (Choi et al. 1999). Since the mode II toughness is always larger than that in mode I (sometimes by over an order of magnitude; Suo & Hutchinson 1989), this investigation provides an understanding of the baseline fracture energy appropriate to TBC systems.

The article is organized as follows: (i) a synopsis of the known mechanisms of toughening in YSZ is presented, emphasizing the phases and the compositions applicable to each, (ii) a method for estimating the toughness of t′-materials made from the vapour phase is presented, (iii) procedures capable of characterizing process zones adjacent to cracks are used to measure features affecting the toughness, and (iv) process zone toughening models are used to interpret the measurements and to provide a direction for future investigation of materials with higher toughness.

2. Synopsis of the toughness of yttria-stabilized zirconia

YSZ materials can exist in a variety of crystallographic phases depending on the yttria concentration and on the process used to make them. Available measurements of the ambient mode I toughness of a number of yttria-stabilized materials over the relevant compositional range are summarized in figure 2a,b (Lange 1982; Evans & Cannon 1986; Becher & Swain 1992). Also shown for comparison are the toughness levels (generally steady-state) for other ceramics and glasses (Wachtman 1996). Strikingly, the toughness of YSZ materials encompasses the entire range. Partially stabilized materials (denoted as tetragonal zirconia polycrystals; TZP), prepared by high temperature processes (such as sintering) have the highest toughness: a typical toughness is, Γss≈210 J m−2 for 4 wt% YSZ (Green et al. 1989). Conversely, the cubic materials are among the most brittle: Γss≈6 J m−2 for 20 wt% YSZ (Marrow et al. 1994). Moreover, for the compositions commonly used in TBCs, a wide toughness range exists, even at fixed composition: 45≤Γss≤150 J m−2 for 7 wt% YSZ. The highest values emerge from processing routes that create materials in the two-phase (cubic/tetragonal) equilibrium phase field. These materials exhibit transformation toughening, enabled by the tetragonal-to-monoclinic (tm) phase transformation during crack extension (Evans & Cannon 1986). Lower values apply to materials processed using vapour phase routes that result in the metastable t′-phase (Evans 1990). Nevertheless, the latter are preferred in gas turbine applications, because coatings in this phase field exhibit the greatest thermal cyclic durability (Levi 2004). The assertion is that the associated toughness, while not exceptional, is retained at elevated temperatures (for reasons elaborated below), whereas transformation toughening is only operational at low-to-moderate temperatures (Evans & Cannon 1986). The present study focuses on the toughness of YSZ with t′-phase, relative to that in the cubic field.

Figure 2

(a) Histogram of toughness levels found in a range of YSZ materials and comparisons with other ceramics. Note that the toughness scale is logarithmic. (b) The effects of composition on the toughness of a range of YSZ materials. The TZP materials are two-phase (cubic/tetragonal), made by sintering. The 7 wt% YSZ material is t′, made by vapour deposition. The 20 wt% YSZ is in the cubic phase field.

When the martensitic tm transformation is suppressed, the toughening exhibited by tetragonal materials (relative to their cubic counterparts) has been attributed to ferroelastic domain switching (Virkar & Matsumoto 1986; Srinivasan et al. 1989; Chan et al. 1991). Most unstrained ferroelastic materials contain equal proportions of domains with three orthogonal variants separated by 90° {110} twin boundaries. Upon unidirectional loading, say along 〈100〉, one set of variants can switch orientation. When this happens, there is an associated strain, ϵT=(1/3)(c/a−1) (figure 3) which occurs at a ‘constant’ coercive stress, σT. (In accordance with the volume constancy of the ferroelastic mechanism, it is assumed that this coercive stress is identical under tensile and compressive conditions.) Generally, the switching is irreversible, resulting in permanent strain. Whenever cracks extending in such materials cause one of the variants to switch (Jue & Virkar 1990), toughening can occur owing to the associated stress/strain hysteresis (figure 3). Stress/strain measurements on YSZ in the compositional range 6–16 mol% yttria have indicated that the coercive stress (and the hysteresis) are relatively temperature invariant (σT varies from 700 to 500 MPa between 500 and 1400°C; Baither et al. 2001). The implication is that the toughness associated with ferroelastic switching will also be insensitive to temperature.

Figure 3

A compressive stress/strain response at 500°C for a 3 mol% YSZ single crystal. Note the inelastic strain induced at the coercive stress. Reproduced from Baither et al. (2001).

These prior assessments have relied upon pre-existent domains capable of switching in the crack stress field. Yet, the available microscopy evidence precludes the existence of domains in either vapour-deposited or plasma-sprayed coatings of t′-7 wt% YSZ. Rather, in vapour-deposited systems, each column is a single crystal (incorporating sub-grains). Consequently, should a ferroelastic mechanism be identified, it will differ qualitatively from that discussed in the prior literature.

3. Toughness measurements

Measurement of the short crack, mode I toughness of vapour-deposited YSZ materials has proven challenging. The methods developed for large, dense ceramics cannot be used with a columnar TBC owing to the fragility of the inter-columnar regions. Indentation methods can be applied (Lawn 1975; Evans & Charles 1976; Anstis et al. 1981; Cook & Pharr 1990) provided that the material is first ‘densified’ at temperatures and pressures that retain the t′-phase. For the present work, a dense material has been prepared from the amorphous powders deposited on the cold walls of a commercial EB-PVD system and consolidated by hot-pressing. The steps taken to ensure that the hot pressed material did not decompose into an equilibrium mixture of cubic and tetragonal phase during densification are described elsewhere (Nychka et al. 2006). Briefly, the powders were hot consolidated at 1500°C, below the T0 line for the tetragonal-to-cubic transformation, thereby assuring that the t′-phase was retained. Analysis by both Raman spectroscopy and X-ray diffraction confirm that the resulting material retains its metastable tetragonal-prime structure. The grain size of the resulting dense material is in the range of 0.5–1 μm. Impressions emplaced into this material by a Vickers indenter generate well-delineated radial cracks (figure 4). To obtain explicit measurements, the indentation fracture toughness formula relating toughness to the crack length Embedded Image and indentation load is used (Lawn 1975; Anstis et al. 1981)Embedded Image(3.1)where P is the indentation load, H is the hardness of the (dense) material (measured in situ) and the non-dimensional coefficient, ξ=(0.016)2. The results indicate that, for t′-7 wt% YSZ, the toughness is Γss=45±5 J m−2, while that for the cubic 20 wt% YSZ is, Γss=6±2 J m−2 (Marrow et al. 1994; Watanabe et al. 2004).

Figure 4

Indentation cracks in a dense body of 7 wt% YSZ (courtesy of F. Pitek). Scale bar, 20 μm.

4. Characterization of the process zone

Establishing a toughening mechanism requires that hysteretic phenomena be identified within a process zone in the ‘wake’ of an induced crack (figure 5a). The governing hysteresis is predicated on a local stress/strain response of the type indicated on figure 5b, typical of the strains occurring at the coercive stress in association with ferroelastic domain switching (Baither et al. 2001). Two complementary approaches are used.

Figure 5

(a) A schematic of a ferroelastic process zone. (b) A proposed stress/strain curve representing the ferroelasticity in the present situation, where nucleation is important. The mechanism is activated when the shear stresses around the crack reach τT, resulting in a permanent shear strain, γT.

Method I. Recall that a process zone embodies permanent strains, symmetrically on both sides of the crack (Evans 1990), and that, at the intersection of the crack with a free surface, these strains cause the surface to distort from an initially flat plane. Accordingly, a method capable of detecting the uplift and ascertaining its spatial extent provides a means for mapping the entire process zone. Optical profilometry has the requisite attribute: namely, it can detect very small height differences over a wide spatial extent. Since surface uplift can be attributed to either a ferroelastic or a tm transformation mechanism, it is essential to check on the phases present within the zone by collecting Raman spectra from regions around the crack.

Method II. Complementary and confirmatory information is provided by transmission electron microscopy (TEM). The rationale being that ferroelastic domains can be distinguished from electron diffraction patterns and highlighted using dark-field contrast (Chan et al. 1991). Using the focused ion beam (FIB) system to obtain thin foils immediately adjacent to the crack plane and comparing with foils obtained from a remote location, the occurrence of crack-induced ferroelasticity can be ascertained.

(a) Optical interferometry

The surfaces of the indented t′-7 wt% YSZ samples were characterized using an optical imaging Mirau interferometer (Wyko NT1100 optical profiling system) to quantify the surface relief as a function of position around the cracks. A highly localized surface uplift was apparent on both sides of the cracks that extended continuously to the crack-tips (figure 6a). Height profiles (figure 6b) allowed the uplift zone to be quantified. Defining the process zone from the contour at which the surface relief was half of the maximum height, the width was found to be h≈3 μm. Within the limits of the lateral spatial resolution, the width of the uplift zone was found to be invariant along the length of the crack. Although the interferometer had insufficient lateral spatial resolution to reveal either the individual domains or fine details of the zone shape, the zone width was found to be commensurate with the zone size measured by TEM, described below. Together these measurements provide unambiguous evidence that a crack wake process zone is created in t′-7 wt% YSZ upon crack extension. It is noted that the image in figure 6a has been oriented to emphasize the uplift around crack A. This diminishes the contrast of crack C. Also, if the crack is not precisely normal to the surface, the relief is asymmetrical and can become masked by any mode III displacements perpendicular to the surface such as crack B.

Figure 6

(a) Interferometric image illustrating the localized surface uplift on both sides of a crack, A, emanating from an indentation impression. (b) Height variation across crack A. The data points correspond to individual pixels and their spacing is at the minimum lateral spatial resolution of the interferometer, approximately 1 μm. From this measurement, the width of the process zone is approximately 3 μm.

(b) Raman spectroscopy

To exclude the possibility of crack-induced transformation to the monoclinic phase (as occurs in transformation toughening), Raman spectra were recorded using an optical probe that focuses down to approximately 1 μm diameter. At all locations, including crack tips and the corner of the indentations, the material remained t′. A typical Raman spectrum recorded at one of the indentation cracks using an approximately 2 μm probe is presented on figure 7. Had any monoclinic phase been present, a peak would have occurred at the frequency arrowed on the figure. Previous work, using less sensitive instrumentation, has shown that transformation zones as small as 5 μm can be readily detected by the presence of monoclinic peaks in the Raman spectra (Clarke & Adar 1982).

Figure 7

Raman spectrum obtained from a crack tip indicating that the structure remains tetragonal (t′). Any transformation to monoclinic would be evident from the appearance of a peak at the frequency indicated by the arrow.

(c) Transmission electron microscopy

Specimens for TEM analysis, prepared using an FEI Strata 235 FIB instrument, were taken from two locations relative to the indentation impression (figure 8). One encompassed the crack along a normal, close to its tip, assuring that the section resides well outside the plastic zone of the indentation. The second location was within material away from the indentation. Bright-field images close to the crack plane reveal a pattern of nanoscale domains (figure 9a). While it has not been possible to obtain images with better contrast, owing to the small scale of the individual domains, the appreciable strain contrast variations and the ion damage, the presence of twin variants is apparent in two orthogonal orientations (shown in more detail by the higher magnification inset in figure 9a). Tilting to capture a variety of diffraction conditions establishes that most of the grains adjacent to the crack contain such domains. In the remote section, similar tilting did not reveal contrast that could be attributed to domains (figure 9b). Furthermore, upon traversing both sides of the crack, the width of the zone containing domains has been ascertained to be, h≈3 μm (figure 10), entirely consistent with the foregoing uplift measurements made using interferometry. While there is not a well-delineated boundary demarking the edge of this zone, there is clearly a higher fraction of grains containing domains within approximately 3 μm of the crack (figure 10).

Figure 8

Scanning electron micrograph of micro-hardness indentation and associated cracking, showing the locations from where TEM specimens were taken by FIB. The image has been tilted to provide a perspective that includes the cracks and the sites where the FIB sections were extracted. Scale bar, 50 μm.

Figure 9

Bright-field TEM images. (a) Ferroelastic domains inside a grain within the process zone (inset shows domains in greater detail) and (b) an unaffected grain outside the process zone.

Figure 10

Bright-field TEM image showing the width of the process zone around an indentation crack. A greater volume fraction of grains containing domains is apparent within the process zone. Scale bar, 1 μm.

To determine the crystallographic nature of the domains in the process zone, selected area electron diffraction was performed. This involved tilting to a 〈111〉 zone axis and seeking the presence of {112} superlattice reflections. The number of such reflections in the diffraction pattern corresponds directly to the number of twin variants, as indicated by the schematics in figure 11 (Chan et al. 1991). A 〈111〉 diffraction pattern obtained from a grain with a large number of domains (figure 11a) reveals the presence of all three nonparallel {112} super-lattice reflections (highlighted by the white arrows on the figure). Comparison with the schematic indicates that all three variants are present. In marked contrast, the corresponding {112} reflection from a region outside the process zone (figure 11b), affirms that only a single (parent) variant exists in each grain.

Figure 11

Selected area diffraction patterns of the 〈111〉 zone and corresponding schematics. (a) Grain within the process zone showing presence of all three twin variants. (b) A grain outside the process zone. Schematics of the patterns are included for ease of explanation.

Dark-field images formed using the {112} reflections indicated roughly equal proportions of the three variants inside the process zone (figure 12). Again, the small width and the associated strain fields compromise the resolution and quality of the images. Numerical fast Fourier transforms of the individual images also showed distinctive streaking indicative of domain alignment in each variant. None was evident in the grains well away from the crack.

Figure 12

Dark-field imaging of the {112} reflections from a grain within the process zone, indicating approximately equal incidence of all three twin variants. Scale bar, 500 nm.

5. Discussion and implications

The preceding observations present compelling evidence for the irreversible formation of ferroelastic domains in a process zone on either side of a crack formed by indentation. According to models for the toughening due to the non-reversible ferroelasticity, the energy dissipated per unit volume of transformed material is associated with the resultant area under the stress/strain [τT(γT)] curve depicted on figure 5b. Under steady-state conditions, the increase in toughness (energy per area) has magnitude (Evans 1990)Embedded Image(5.1)where h is the width of the process zone (figure 5a) and f is the volume fraction of the material within the zone that experiences the strain γT. Equation (5.1) can be used to determine whether the measured toughness of t′-7 wt% YSZ derives from ferroelasticity. It is conducted in the following manner. In equation (5.1) the four quantities ΔΓss, f, γT and h can all be ascertained from the foregoing information. The only unknown is the coercive stress, τT. Consequently, if equation (5.1) is used to infer the operative τT, comparison with figure 3 (Baither et al. 2001) can be used to assess consistency.

Outside the process zone, each grain consists of a single variant. Inside the zone, domains are found with all three orthogonal variants. The associated coercive strain is thus directly related to the tetragonality by γT=(2/3)(c/a−1). The TEM observations indicate that the fraction of material transformed into domains within the process zone, f≈0.8. The increase in toughness caused by the mechanism is taken as the difference between that for t′-7 wt% YSZ (toughened) and cubic-20 wt% YSZ (not toughened). The difference is ΔΓss≈35 J m−2. Invoking equation (5.1), the coercive stress is inferred to be τT=580 MPa. This is, indeed, within the measured range (figure 3; Baither et al. 2001). It is pertinent to recall, however, that the τT measurements refer to stress-induced domain wall motion (Baither et al. 2001), while the present toughening involves both domain nucleation and propagation. A proposed stress/strain curve for nucleation-controlled ferroelastic toughening is depicted on figure 5b.

If, as indicated by this work, ferroelasticity is the primary toughening mechanism in metastable YSZ, then materials with greater tetragonality would exhibit even higher levels of toughness. The veracity of this implication has been substantiated by recent measurements conducted on a polycrystalline (YO1.5, TiO2)ZrO2 ternary fabricated under similar conditions, having c/a=1.023, which exhibited unprecedented toughness for a t′-composition, Γss=89 J m−2 (Schaedler 2006). The caveat is that the coercive stress is also likely to change. For instance, lowering the magnitude of τT increases the toughness because, in equation (5.1), the zone height scales is h∼1/(τT)2 (Evans 1990). Moreover, it remains to be established that the same ferroelastic toughening mechanism occurs in the single crystal columns found in the coatings deposited using electron beam methods.

6. Conclusion

The toughness of 7 wt% YSZ with the metastable tetragonal-prime (t′) structure has been investigated. A ferroelastic mechanism has been explored by characterizing the wake of an indentation-induced crack by using TEM and high-resolution optical interferometry. A crack process zone approximately 3 μm in width, containing a high density of nanoscale, twin-related, domains has been identified, consistent with a ferroelastic mechanism. Dark-field imaging by TEM has revealed equal proportions of all-three twin variants within the process zone. Such domains are not present in the virgin material remote from the process zone. Consequently, the toughening mechanism appears to be controlled by the nucleation of domains rather than the motion of pre-existing domain boundaries. Based on the measured process zone size and the strains attributable to the tetragonality, it has been shown that the measured toughness is consistent with a ferroelastic mechanism for a reasonable coercive stress. One implication is that oxides with still greater tetragonality have the possibility of even higher toughness than the t′-7 wt% YSZ compositions used in current thermal barrier systems.


The authors are grateful to Prof. Manfred Rühle for discussions on interpreting electron microscopy observations of ferroelastic domains in zirconia. We also acknowledge research support from the Office of Naval Research (MURI/N00014-00-1-0438).


    • Received December 15, 2006.
    • Accepted February 5, 2007.


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