Failure mode, ferroelastic behavior and toughening effect of bismuth titanate ferroelectric ceramics under uniaxial compression load

Accepted Manuscript Failure mode, ferroelastic behavior and toughening effect of bismuth titanate ferroelectric ceramics under uniaxial compression load

Yu Chen, Jiageng Xu, Shaoxiong Xie, Rui Nie, Jing Yuan, Qingyuan Wang, Jianguo Zhu PII: DOI: Reference:

S0264-1275(18)30334-4 doi:10.1016/j.matdes.2018.04.055 JMADE 3868

To appear in:

Materials & Design

Received date: Revised date: Accepted date:

20 January 2018 9 April 2018 19 April 2018

Please cite this article as: Yu Chen, Jiageng Xu, Shaoxiong Xie, Rui Nie, Jing Yuan, Qingyuan Wang, Jianguo Zhu , Failure mode, ferroelastic behavior and toughening effect of bismuth titanate ferroelectric ceramics under uniaxial compression load. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Jmade(2017), doi:10.1016/j.matdes.2018.04.055

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ACCEPTED MANUSCRIPT Failure mode, ferroelastic behavior and toughening effect of bismuth titanate ferroelectric ceramics under uniaxial compression load Yu Chena, b, Jiageng Xuc, Shaoxiong Xied, Rui Nieb, Jing Yuanb, Qingyuan Wanga, d, e*, Jianguo Zhub* a

School of Mechanical Engineering, Chengdu University, Chengdu 610106, China College of Materials Science and Engineering, Sichuan University, Chengdu 610065, China c School of Architecture and Civil Engineering, Chengdu University, Chengdu 610106, China d College of Architecture and Environment, Sichuan University, Chengdu 610065, China e Failure mechanics and Engineering Disaster Prevention and Mitigation Key Laboratory of Sichuan Province, Chengdu 610065, China

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b

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Abstract

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A typic BLSF ceramics: bismuth titanate (Bi4Ti3O12), whose failure mode, ferroelastic behavior and toughening effect under uniaxial compression load were comprehensively assessed. Firstly, a series of crystallographic

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parameters including lattice constants (a, b, c and v), orthorhombicity (g) and single-crystal distortion (S0lattice) were calculated from XRD patterns. The ferroelastic behavior referred to the 90o switching of domains with compression

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stress was identified by the nonlinear stress-strain curve, and the underlying micromechanism was more accurately described by the non-180o domain wall motion. SEM observation on the fracture surface of the broken sample reveals its failure mode in terms of microcrack initiation and propagation behaviors. Further, a simplified domain

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distribution model was constructed for unpoled ferroelectric ceramics based on a constitutive framework, which

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deduced their constitutive relation subjected to uniaxial compression load. The ferroelasticity induced toughening was verified by indentation test, and further analyzed by a micromechanics model of crack propagation. The

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expression of toughening effect (ΔГ/Г) was also deduced from the indentation fracture mechanics. Finally, the evolution in mechanical properties (including coercive stress (σc), switching strain (εzz), apparent elastic modulus

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(E) and compression strength (σcf)) of Bi4Ti3O12 ceramics with the doping content of W was also quantified by the compression test.

Keywords: Bi4Ti3O12 ceramics; ferroelastic domain switching; microcracks; compression load; toughening effect

1. Introduction Ferroelectric materials are one important category of functional materials with the piezoelectric effect which enables the conversion between mechanical energy and electrical energy, which have been commonly used as sensitive element for many electric devices including piezoelectric sensors, electromechanical transducer, *The corresponding author QY. Wang, Tel/Fax: +86 28 85405389; E-mail: [email protected]; *The corresponding author JG. Zhu, Tel/Fax: +86 28 85412022; E-mail: [email protected];

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ACCEPTED MANUSCRIPT non-volatile memories, etc [1]. It is the essential attribute of ferroelectrics that the domain state can be modified by electrical or mechanical loadings of sufficient magnitude, which gives rise to the reorientation of polarization/strain along external loadings. Specifically, domains can be switched 180o or 90o from the original direction by an electric field, which is called “ferroelectricity (or ferroelectric behavior)”, and domains can be switched only 90o by a mechanical stress, which is so-called “ferroelasticity (or ferroelastic behavior)” [2]. In most piezoelectric sensors and actuators, ferroelectric materials are prone to fatigue due to cyclic electrical or mechanical loadings. The

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fatigue manifests its effect as a reduction in domain switching or domain wall movement and subsequent premature

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failure of devices [3, 4]. Recent research reported a discussion of switching kinetics for ferroelectrics, demonstrating experimentally that nucleation can be the more important step, rather than domain wall

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forward-growth or sidways velocities [5].

Ferroelastic domain textures generated by an interchanging of the crystallographic degenerate and preferred axes

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result in a macroscopic strain component [6], while both lattice strain and ferroelastic strain contribute to the large signal macroscopic strain response during an applied bipolar electric field [7]. The spontaneous strain generated by domain switching can be simulated directly by dislocations, Xie. C et al. [8] extended the dislocation simulation

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method of domain switching toughening to piezoelectric coupling field. 90o ferroelectric/ferroelastic domain

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reorientation was observed in a cantilever comprised of a 500 nm thick lead zirconate titanate (Pb(Zr, Ti)O3, PZT)) film on a 3 μm thick elastic layer composite of SiO2 and Si3N4 [9]. For both electrical and mechanical switching,

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ferroelastic switching is found to occur most readily at the highly active needle points in ferroelastic domains [10]. The dynamic properties of domain reorientation under mechanical cyclic loading in bulk PZT ceramics are studied

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by Pojprapai S et al. [11]. A distinctive ferroelastic creep was observed at 293 K during the mechanical deformation of lanthanum strontium cobalt ferrite under uniaxial compression [12]. Comparison of neutron diffraction and Raman spectroscopic studies of the ferroelastic behavior of ceria-stabilized zirconia at elevated temperatures was conducted by Bolon A M et al. [13]. On the other hand, the reorientation of ferroelastic domains around the crack tip is also proposed as a toughening mechanism for ferroelectric ceramics [14-17]. Moreover, the domain switching of ferroelectric ceramics is also found to be related with the crystalline structure of materials. Li J Y et al. [18] used a combined theoretical and experimental approach to establish a relation between crystallographic symmetry and the ability of a ferroelectric polycrystalline ceramics to switch. Fu J et al. [19] investigated the domain switching and lattice strains in (Ka, Na)NbO3-based lead-free ceramics across orthorhombic-tetragonal phase boundary. 2

ACCEPTED MANUSCRIPT Bismuth titanate, Bi4Ti3O12 (BIT), was identified as a typical bismuth layer-structured ferroelectrics (BLSFs or Aurivillius phase) with high Curie temperature (Tc=675 ℃) and large spontaneous polarization (Ps(a-axis)=49 uC/cm2) [20]. Many works have been devoted to the research on the structural, optical, dielectric and electrical properties of BIT [21-23]. However, many important mechanical problems seem to be less discussed for BLSFs. In our previous works, W/Cr co-doped Bi4Ti3O12 ceramics have been developed to achieve both good electrical and mechanical properties, aiming at the high-temperature piezoelectric application [24-27]. In this work, some

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mechanical problems with respected to ferroelastic domain switching were elaborately investigated for this kind of

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of the microcrack propagation and the ferroelasticity toughening.

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ceramics under uniaxial compression load, with laying stress on both underlying mechanism and theoretical models

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2. Experimental procedure 2.1. Preparation of ceramics

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W/Cr co-doped Bi4Ti3O12 ceramics with a chemical composition of Bi4Ti3-xWxO12+x + 0.2 wt. % Cr2O3 (x=0, 0.025, 0.05, 0.075 and 0.1, abbreviated them as BITWx-0.2Cr) were fabricated by a traditional solid reaction process,

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according to the process technology described in our previous works [24, 25]. In addition, pure Bi4Ti3O12 (BIT)

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ceramics were also fabricated by the same process in this work. All these BIT-based ceramics were made into cylinders with a size of φ 10 mm × h 10 mm, as well as fine polished before the mechanical testing.

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2.2. Characterization of ceramics

2.2.1. Microstructural characterization

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The phase structure of ceramics was characterized by a powder X-ray diffractometer (XRD; DX2700, Dandong, China) employing Cu-Kα radiation (λ=1.5418 Å). The lattice strain and lattice spacing were determined by a single peak fitting approach using a specific code (Oringin 9.1 ware, OriginLab, USA) according to Gaussian functions. The microstructural morphology of ceramics was observed by a field-emission scanning electron microscopy (FE-SEM; JSM-7001F, JEOL, Japan).

2.2.2 Uniaxial compression test We focus on the uniaxial compression stress states since ferroelectric ceramics can be realized comparably easily 3

ACCEPTED MANUSCRIPT for a brittle material with low tensile strength, thus the uniaxial compression test was performed on an universal testing machine (8501, INSTRON, UK). A compression preload of 5 MPa was applied for the specimen fixation. The loading mode was in the displacement control at a stroke rate of 1 mm/min. The macroscopic strain of specimen was measured using an extensometer with a gauge length of 5 mm mounted to its middle, while the applied load of machine was automatically recorded by an internal force sensor. The failure stress referring to the compression failure of materials is defined as their compression strength (σcf), which is calculated according to the

P S

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cf 

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following equation:

(1)

2

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where P is the crushing load (N) and S is the cross-sectional area of the specimen (mm ).

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2.2.3 Vickers indentation test

Because only small samples could be obtained for ferroelectric ceramics using this fabrication method, the fracture

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toughness was estimated by microindentation techniques using a Vickers indenter (AKASHI AVK-A, Kanagawa, Japan). The fracture toughness with the form of the work of fracture (Г), which is related to the energy release rate,

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is preferred over the fracture toughness KIC (=ГE)1/2 because it is the more relevant parameter and independent of

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the elastic modulus (E), and Vickers hardness (Hv) could be calculated by two equations as follows,

d2

Γ  2ξ 2 P

Hv  0.464

c3 P

(2)

d2

(3)

where P is the indentation load, d is the half-length diagonal of the Vickers indentation, c is the half-length of the

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penny-shaped crack and ξ (0.016) is the non-dimensional coefficient. In this experiment, the indentation load of 19.6 N was applied and the holding time was 15 s. Cracks resulting from the Vickers indentation were measured by SEM immediately to avoid slow crack growth after printing, started by the stress field that acts upon loading. The crack extent was measured with an image analysis software (Leica Application Suite EZ; Leica Microsystems Ltd, Germany).

3. Results and discussions 3. 1. Crystallographic structures of BIT-based ceramics 4

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Fig. 1 XRD patterns of the Bi4Ti3O12 ceramic registered at room temperature (the inserted SEM image describes the microstructure of its polished and hot-etched cross section, the gray vertical lines at the bottom of the figure represent the peak positions and relative intensities derived from the JCPDS card.)

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A room-temperature XRD pattern, associated with a cross-section SEM image were derived from the BIT ceramic, which are shown in Fig. 1 (the data of BITWx-0.2Cr ceramics are similar to this and have been shown in [24]). In

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XRD pattern, all sets of reflections could be well indexed in the parent compound of Bi4Ti3O12 (JCPDS card

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No.72-1019) with an pseudo-orthorhombic structure and a space group of B2cb(41), and there is no obvious second phase existing in the matrix. As observed from the SEM image that, a dense microstructure constructed by many randomly orientated plate-like grains has been developed in the BIT ceramic, even, a typic layer structure can be

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seen from the fractured surface of several coarse grains indistinctly. Futhermore, the (1 1 7) plane shows the highest diffracted intensity, which agrees with the fact that the randomly orientated BLSFs usually reflect the

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strongest diffraction in their (1 1 2m+1) crystallographic planes [28-30], which are closely related to their layer structure along the c-axis. In addition, many reflections with crystallographic index of (h k l)/(k h l) such as (2 0 0)/(0 2 0) are observed to split into two peaks, which is due to the typical orthorhombic structure with a slight difference between the lattice constants of a and b. Here, orthorhombicity (g) is used for evaluating the orthorhombic degree of the structure, which could be calculated by the following formula,

g

2(a-b) ab

(4)

On the other hand, for ferroelectrics, domain switching can yield a maximum degree of orientation that corresponds 5

ACCEPTED MANUSCRIPT to the maximum number of possible directions of ferroelastic structural distortions relative to a prototype unit cell. The single-crystal distortion (S0lattice) is defined as the difference of the ferroelastic unique axis (herein referred to as [h k l*]) relative to the crystallographic degenerate axis. BIT crystallizes into an orthorhombic system below the Curie temperature, with two orthogonal single-crystal distortion directions relative to the prototype tetragonal phase, and [0 1 0] is defined as [h k l*] [6]. S0lattice of BIT could be thus calculated by the following formula (a>b),

a-b b

(5)

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0 Slattice 

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According to the Rietveld 0refinement for the diffraction pattern, the cell parameters of Bi4Ti3O12 ceramic calculated are basically in agreement with the values determined by Ivanov et al. [31]. All these crystallographic

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parameters of BIT-based ceramics are listed in Table 1. As can be seen, a remarkable decrease of g (6.82→4.99) reveals a less orthorhombic distortion in BIT after the incorporation of Cr2O3 (x=0), which may be due to the

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released rotation state of oxygen octahedra by the substitution of Cr3+ for Ti4+. Except for an ephemeral increase (4.99→5.53) of g in the introduction of less W6+ (x=0.025), this factor seems to decrease with increasing the

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doping content of W6+ (x>0.025) linearly, which may be due to the gradually released tilting state of oxygen octahedra by the substitution of W6+ for Ti4+. In addition, it is also found that after introducing Cr2O3 into BIT, both

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(2 2 0) and (1 1 15) reflection shift to a lower 2θ angle, which could be related to the increase of lattice parameters

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according to the Bragg equation and the formula about interplanar spacing. Especially, (1 1 15) reflection is observed to disappear at x=0.1, which may be caused by the structure anomaly (possibly the second phase like Bi6Ti3WO18 or Bi6Ti5WO22 [32]) of BITW0.1-0.2Cr with a high W content. Based on the analysis above, for the

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ion-doped BIT system, the structure with a higher orthorhombicity (g) tends to contain a larger single-crystal

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distortion (S0lattice), which could be correlated with the larger displacements of cationic polarization within a more distorted structure.

Table 1 Crystallographic parameters of BIT-based ceramics

BIT

BITW0-0.2Cr

BITW0.025-0.2Cr

BITW0.05-0.2Cr

Crystal system

Orthorhombic

Space group

B2cb (41) 5.4457

5.4699

5.4578

5.4485

5.4464

5.4567

b(Å)

5.4087

5.4427

5.4277

5.4199

5.4215

5.4400

c(Å)

32.8378

32.9354

32.9155

32.8742

32.8320

32.9274

V(Å)

967

982

975

971

969

979

6.82

4.99

5.53

5.26

4.58

3.07

6.84

5.00

5.55

5.28

4.59

3.07

g(×10 ) S

BITW0.1-0.2Cr

a (Å)

-3

0

BITW0.075-02Cr

lattice (×10

-3

)

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ACCEPTED MANUSCRIPT *cell parameters of BITWx-0.2Cr ceramics were derived from our previous works [24].

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3.2. Stress-strain response of the unpoled BIT ceramic

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Fig. 2 Stress-strain response of the unpoled Bi4Ti3O12 ceramic subjected to uniaxial compression load, (a) total stress-strain curve and (b) decoupled strain-stress curves

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Fig. 2 shows the stress-strain response of the unpoled BIT ceramic subjected to uniaxial compression load. It can be seen from Fig. 2(a) that, the total stress-strain curve includes three segments with different slope, which indicates a

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typical nonlinear deformation process of the ceramic. Specifically, when a sufficiently small loading was exerted on

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the ceramic from the starting point O, lattice ions will be moved only slightly from their equilibrium positions and the ceramic begin to elastically deform (Eini=44 GPa) in this process (OA stage). After the load stress exceeds the minimum coercive stress (σc, min=45 MPa) of ferroelastic domains at the point A, their switching process will be

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initiated, leading the ceramic into a ferroelastic deformation process, where certain ions reach to new equilibrium positions such that the longer c-axis of domains orientates to a direction perpendicular to the compression load (90o

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switching). In this process (AB stage), both the switching strain (εzz) of those reorientated ferroelastic domains due to the interchanging of ferroelastic axis and the lattice strain (εlat) of several reconstituted lattice planes due to the d-spacing change of bismuth layer structure, as well as a slight elastic strain (εela) resulted from those unmoved domains whose longer c-axis are originally perpendicular to the compression stress, contribute to the macroscopic total strain of ceramic (Δεtol=εmax-εmin=εela+εzz+εlat=0.60%). Both domain switching and lattice reconstitution are inelastic and irreversible, their summations constitute the main part of remanent strain (εrem=0.65%) which was evaluated by the intercept of the loading curve of BC. Here, the remanent strain represents the macroscopic average of the spontaneous strains of unit cells when the domain structure is basically preserved (after backswitching) after 7

ACCEPTED MANUSCRIPT unloading, because the loading curve of BC derived from the failure stress to the switching-performaned stress, thus the remanent strain evaluated by this curve approximates to its actual value which should be determined by the unloading curve [12]. For ferroelectric ceramics, the driving force for domain switching is the minimisation of the elastic free energy within the frontal zone [33]. Because the volume change of unit cell during domain switching is zero thus only shear stresses will initiate the domain switching. As a result, if the matrix is not able to accommodate the twinning shear induced by the ferroelastic domain switching, many holes may form at the blocked domain walls

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and then develop into microcracks.

On the other hand, during ferroelastic domain switching, the apparent elastic modulus of materials tends to be

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gradually improved by the compressive stress due to the anisotropic elastic properties of noncubic unit cells such as

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Bi4Ti3O12 [34]. After most of possible (or achievable) domains were switched at point B (σc, max=73 MPa), the ceramic seems to react more elastically (Eld=70 GPa) to the applied stress until to the compression failure at point C (σcf=281 MPa; εtol=1.06%), since the displacement linearly increases with the load again. In this process (BC stage),

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with increasing the load, microcracks start closing and the apparent elastic modulus increases (E=44 GPa→70 GPa); if further increasing the load, damage takes over, which leads the ceramic to cracking finally. The underlying

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micromechanism can be futher stated as follows [35]: since the cracks perpendicular to the applied stress tend to

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close, with consequent stiffening of the body, while those parallel to the stress tend to open, with damage introduced to the material. Additionally, two decoupled strain-stress curves, which could reflect the elastic

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deformation resulted from the reversible ionic balance exercise (black line) and the inelastic deformation caused by the ferroelastic domain switching and lattice plane reconstitution (blue one), respectively, are depicted with the total

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deformation curve (red one) in Fig. 2(b).

In order to identify the failure mode of ceramic, SEM observation was conducted by focusing on the fracture surface of the broken sample. In Fig. 3, the ceramic behaves in the mode of transgranular fracture and a direct evidence of microcrack creation can be identified by those clearly visible microcracks. The very thin crack, such as the one indicated by the red arrow, may have nucleated upon cooling from the Curie temperature due to the release of grain microstresses. These thermal microcracks seem to remain closed in the process of loading since perpendicular to the applied stress. And the large opening microcracks, such as the two indicated by the blue arrow, may be initiated at some pore points of high tensile stress or evolved from those blocked ferroelastic domains in 8

ACCEPTED MANUSCRIPT switching during the mechanical loadings. As parallel to the applied stress, these mechanical microcracks tended to open, some of them further developed into macroscopic flaws, as exhibited in the inserted figure which shows the appearances of the broken sample. Here: thermal microcracks closure, with consequent stiffening of the body, and mechanical microcracks opening, with damage introduced to the material. Those two processes are considered to act in competition at lower loads , whhich may be responsible for the nonlinear step (as marked by the green circle)

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at point B in Fig. 2(a).

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Fig. 3 SEM image focusing on the fracture surface of the Bi4Ti3O12 ceramic broken by the compression load

Further, single peak fitting is an additional method by which to extract the lattice strain, however, its actual value

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should be given by an average of all lattice strains parallel to the compressive stress, weighted by their relative presence [36]. For Bi4Ti3O12 with the ferroelastic unique axis of [0 1 0], the interplanar spacing change of (0 2 0)

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plane could be considered as an estimate of bulk-averaged lattice strain of materials approximately parallel to the compression axis, thus the subtraction of the lattice strain from the total irreversible strain can yield the ferroelastic switching strain for the ferroelectric ceramics subjected to the compressive stress. For the BIT ceramic after compression at σc, max, the lattice strain can be evaluated as 0.44% (see Section 3.3), and the total irreversible strain (0.55%) was calculated by the macroscopic total strain (0.60%) subtracting the elastic strain ((σc, min)/Eave=0.05%),

max-σc,

thus the ferroelastic switching strain was determined as 0.11% finally. According to the

volume-weighted model proposed in [6], the calculated vaule of switching strain approximates 3/4 of its saturated value (εzz=0.212•S0lattice=0.15%) for the BIT ceramic. In fact, the realistically or attainable achievable domain switching textures are a fraction of this saturation texture because of the adverse microstructural interactions in real 9

ACCEPTED MANUSCRIPT ceramics (such as interactions between neighboring grains and domain-wall pinning due to point defects, etc.), as well as the number of possible ferroelastic structural distortion directions relative to the prototype phase.

3.3. Ferroelastic behavior and constitutive equation of unpoled ferroelectric ceramics For most of perovskite-type ferroelectrics, when they are cooled through the paraelectric-ferroelectric phase transition temperature, the combination of electric and elastic boundary conditions loading on the crystal usually

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leads to a complex domain structure with many 90o walls (to minimize the elastic energy) and 180o walls (to reduce the depolarizing electric fields). 90o walls are both ferroelectric and ferroelastic as they differ both in orientation of

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the spontaneous polarization vector (Ps) and the spontaneous strain tensor (xs). In a single crystal of Bi4Ti3O12, there

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has been reported that the ferroelectric domain switching with electric fields along the c axis involves a large change in the extinction angle with illumination along b [37], and these ferroelastic domain walls are established

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after the rearrangement of non-ferroelastic 180° domains accompanied by Ps(c) [38]. As a result, for the polycrystalline ceramics of Bi4Ti3O12, their ferroelastic domain switching are more accurately described by

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non-180o (mainly 90o) domain wall motion, whose micromechanism could be described by Fig. 4.

Fig. 4 Micromechanism of the ferroelastic behavior of unpoled ferroelectric ceramics

Here, in order to simplify the problem of ferroelastic domain switching in polycrystalline Bi4Ti3O12 ceramics, as well as in view of the comparability of tetragonal phase with orthorhombic phase in the interchange between long axis (c) and short axis (a/b), we assumed the orthorhombic Bi4Ti3O12 as the tetragonal phase in the later discussion and analysis with respect to its ferroelastic behaviors. The fresh-sintered ferroelectric ceramics could be considered as the thermally depoled piezoceramics with randomly orientated ferroelectric/ferroelastic domains (i.e. initially isotropic), which could be described by the state at point O. Starting at point A, a mechanical stress cannot trigger a 10

ACCEPTED MANUSCRIPT unique switching direction for the spontaneous strain of a unit cell like that, all the c-axis will prefer a position close to a plane perpendicular to the compression stress, the distribution of these c-axis domains within this plane will be random. It is worthy to noting that domain orientations with the c-axis in the range 0o<α<30o from the compression axis are easier to switch than those with the c-axis at an angle of 30o<α<60o [39], and the domains with a smaller coercive stress are earlier to switch than those with a larger coercive stress. As a result, in the cross section parallel to the compression stress, successional 90o switching of ferroelastic domains is practically in

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promoting the gradual shift of 90o domain walls between c-axis domains and a/b-axis ones situated at this plane.

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The corresponding bulk contributions to the driving force are caused by variations of the ferroelectric/ferroelastic anisotropy energy [40]. Ending at point B, the domain state induced by strong uniaxial compression stresses is

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transversely isotropic without macroscopic polarization, those domains switched left an irreversible deformation to

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the material, since the inelastic strain reaches to the maximum value.

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The switching process of ferroelastic domain yields a maximum degree of orientation that corresponds to the maximum number of possible directions of ferroelastic structural distortions relative to a prototype unit cell. In order to estimate the fraction of ferroelastic domains switched, using Kamlah-Jiang’s constitutive framework for

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reference [41], a simplified domain distribution model was built for unpoled ferroelectric ceramics in Fig. 5.

Fig. 5 Simplified domain distribution model of unpoled ferroelectric ceramics based on a constitutive framework

Here, the direction of uniaxial compression load is assumed to coincide with the z-axis, a region within a grain of the ferroelectric polycrystal where the c-axis of the unit cells (spontaneous strain axis) have the same orientation to 11

ACCEPTED MANUSCRIPT the loading direction is called a c-axis domain, all the domains within the cones of 45o angle with the z-axis being the cone axis are considered to be c-axis domain for simplicity. The unpoled ferroelectric ceramics are in the thermally depoled reference state, by the cutoff of the spherical surface by these cones, the fraction of c-axis domains is assumed to be 1/3, if we consider that the state of relative polarization of domains will have no influence on the remanent distortion of the lattice, and there is a simple linear relation between the accumulation of irreversible strain with the fraction of switched domains, the constitutive equation of an unpoled ferroelectric

 E

 Ss a(1t - 3 )

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S

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ceramic subjected to a uniaxial compression load could be expressed as follows,

(6)

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here, β represents the fraction of c-axis domains (1/3≥β≥0), which is decreasing with increasing load, Ssat is the maximum value of the macroscopic remanent strain of the ceramic which is assumed for a domain state of highest

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order with respect to a certain axis (i. e. β=0), S is the total strain, σ is the applied load and E is the Elastic modulus. Now, we considered a point close to the failure point C where most of possible (or achievable) domains

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have been switched by the stress, after substituting the corresponding parameters derived from the stress-strain curve into the Eq (6), the fraction of c-axis domains (β) which still stay in the cones of 45o angle is 4.66%, thus the

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corresponding switching fraction of c-axis domains is 86.01%(=1-3β), as for whole domains, the switching fraction

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is 28.67% (=1/3-β), which indicates that nearly all of c-axis domains switched to the direction perpendicular to the

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compression stress.

Fig. 6 XRD patterns of the Bi4Ti3O12 ceramic before and after compression at σc, max (73 MPa) On the other hand, the ferroelastic (or 90o) domain switching caused by the mechanical loading has been 12

ACCEPTED MANUSCRIPT determined previously by quantifying the intensity changes of specific peaks in a diffraction pattern, e.g. the “c”(0 0 l) and “a” (h 0 0) peaks in tetragonal perovskite ceramics [42, 43]. The orthorhombic Bi4Ti3O12 is also of perovskite units, Fig. 6 shows XRD patterns of the Bi4Ti3O12 ceramic before and after compression at σc,

max

(73

MPa). As can be seen from the enlarged drawing on the left side, after the ceramic was compressed, the intensity of the peak corresponding to (0 0 l) planes decreases, indicating the grains with c-axis oriented along with the pressing direction have been switched by the compress stress and added to the low degree of (0 0 l) favored orientation

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observed [44]. Further, to obtain a more quantitative analysis of the switching behavior and domain texture of BIT,

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the intensities measured in the diffraction experiment were used to calculate a density value which describes domain preferences in the unit multiple of a random distribution (MRD) and which is expressed through the

R ( I 0012/ I 0012 )

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MRD 

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following equation [45],

R R ( I 0012/ I 0012 )  2  ( I 200/ I 200 )

(7)

where I0012 and I200 are, respectively, the integrated intensities of the (0 0 12) and (2 0 0) peaks after poling or

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mechanical loading. IR0012 and IR200 are the intensities obtained from the sample with random domain texture (i.e. before compression). The evolution in the diffraction pattern of (0 0 12)/(2 0 0)/(0 2 0) peaks before and after

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compression is shown in the enlarged drawing on the right side. According to their relative intensity variation,

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MRD of the BIT ceramic can be identified as 0.4033, which is closed to that of unpoled PZT ceramics after cyclic compression at 140 MPa/1 Hz/100 times [46]. In addition, the interplanar spacing of (0 2 0) planes has a decrease

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after compression, indicating that the compression stress applied along the [0 1 0] direction of some unit cells has caused lattice strain for the structure. Here, the diffraction data obtained from the X-ray diffractometer were used to

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ascertain lattice strain, which is calculated from the difference between the lattice spacing before and after loading, expressed as [11]:

hkl 

0 dhkl  d hkl 0 d hkl

(8)

where εhkl is the lattice strain (denoted by εlattice in this work), and dhkl and d0hkl are the lattice spacings before and after loading. Therefore, the vale of lattice strain can be determined as 0.44% for the BIT ceramic after compression.

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3.4. Toughening effect resulted from ferroelastic behavior

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Fig. 7 SEM images of indentations and cracks produced in the Bi4Ti3O12 ceramic by a Vickers indenter. (a), (b) and (c) were derived from the upper surface of the sample before compression; (d), (e) and (f) were derived from the lower surface of the sample after compression (73 MPa). Three testpoints were used for the average measurements.

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Under the application of a Vickers indenter, the indentations and cracks produced in the BIT ceramic before and

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after compression are shown in Fig. 7. SEM observation reveals that a symmetric rhombic indentation has been introduced into the ceramic, and the resulting cracks tend to propagate along the diagonal direction of indentation.

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However, most of cracks seem to be shorter in the ceramic after compression, and some of them have even disappeared. According to Eq (2), the fracture toughness (Г) calculated from the length of cracks and indentations

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was determined as 32.21 J/m2 and 36.68 J/m2 for the BIT ceramic before and after compression, respectively, which presents an obvious toughening effect (ΔГ=4.47 J/m2). On the other hand, the Vickers hardness (Hv) was found to be 3.81 GPa and 3.49 GPa for the BIT ceramic before and after compression, respectively. It is well known that the hardness represents the ability of materials to resist the plastic deformation. The process zone of ferroelastic domain switching is more suitable for the movement of lattice dislocations due to the residual strain existing there, which tends to decrease the hardness of the ceramic. Moreover, after compression, the crack extention seems to be more anisotropic in view of their uneven length, the anisotropy of the indentation crack length and corresponding apparent fracture toughness could be related with the interaction of domain switching and residual strain, which has been observed in perovskite membrane materials [47]. 14

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Fig. 8 Micromechanics model for the propagation of indentation cracks within ferroelectric ceramics

Here, this toughening effect is derived from the ferroelastic domain switching, whose micromechanism can be

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illustrated by Fig. 8. As described by this micromechanics model for the propagation of indentation cracks within ferroelectric ceramics. When ferroelectric ceramics were compressed by a loading stress exceeding their coercive

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stress, ferroelastic domain (90o) switching has occurred (domains only orientated to the direction perpendicular to the compression load, which seems like those colorized bloc), the frontal region involved with domain switching is

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referred to as the process zone. In the contacting process of sharp indenter with the material surface, the maximum

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tensile stress occurs at the elastic/plastic interface, with fall-off within the plastic zone to a negative value at the indenter/specimen contact and within the surrounding elastic region to zero remote from the contact [48], which initiates the nucleation of crack at the vertex angle of indentation. When cracks begin to propagate along the

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diagonal line of indentation and grow into the process zone, those domains previously located in the process zone at the crack tip are now located in the crack wake. As the polar rotation of ferroelastic domains switched by 90o has

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caused a strain mismatch of up to 1% (0.12% for BIT in this case) there, compression stresses will be created perpendicular to the crack plane because of the preferred orientation of the longer axis of ferroelastic domains in this direction. When the crack extends, these compression stresses tend to act in the crack wake and cause shielding of the crack tip from the applied load as in the case of the second phase toughening the matrix [49]. In addition to compression stresses, tensile stresses are present parallel to the crack plane. However, the tensile stresses parallel to the crack plane are, in a first approximation, not of importance for the stress intensity factor at the crack tip. Moreover, TEM observation from C. Mercer, et al [50]. has presented compelling evidence for the irreversible deformation of ferroelastic domains in a process zone on either side of a crack formed by indentation. The 15

ACCEPTED MANUSCRIPT ferroelasticity induced toughening is supposed to have a quadratic relationship with the volume percent of T’ phase withinYSZ ceramics, which is also identified by the Vickers indentation test [51].

Fracture toughness, defined as the resistance to fast crack propagation at a critical stress level (KIC), is widely used for mechanical characterization of brittle ceramics. In view of the absorption of fracture energy during ferroelastic domain switching, the crack tip process zone is conducive to resisting the crack extension, resulting in an elevated

(9)

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Г  2  f  c  c  h

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fracture toughness for materials, thus the elevation of the steady-state toughness Г (J/m2) would scale as [51]:

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in which σc is the coercive stress related to switching of the orientation of ferroelastic domains, εc is the associated switching strain, σc.εc is the dissipated energy per unit volume associated with ferroelastic toughening, h is the

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width of the processing zone (it is assumed to remain constant in front of the crack tip during crack propagation), and f is the volume fraction of domains that switch within the zone. Here, Karun Mehta et. al. [52] used a similar

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approach for estimating the size of domain switching process zone with that of the crack tip plastic zone as follows,

h  0.08(

KIC 2 )

c

(10)

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And for the brittle materials such as ferroelectric ceramics under the application of a sharp indenter, another

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fracture toughness with the form of KIC could be calculated by the following formula based on the criterion of fracture mechanics [53],

K  0.016( E / H )1 / 2 ( P / C 3 / 2 )

(11)

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Here, P is the load, E is the Elastic modulus, Hv is the hardness, and C is the length of the crack measured from the

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centre of indent. According to the expression of fracture toughness Г from Eq. (2), we can deduce out the relationship between the two kinds of fracture toughness as follows,

KIC2=

Г E 0.928

(12)

Ultimately, substituting Eq. (10) and Eq. (12) into Eq. (9), we can get the expression of toughening effect (ΔГ/Г) with respect to the ferroelastic domain switching as follows,

Г 1  0.172  f  c  E  Г c 16

(13)

ACCEPTED MANUSCRIPT for the BIT ceramic, substituting its corresponding parameters (f=86.01%; σc, average=59 MPa; εc=0.11%; Eaverage=59 GPa) derived from its stress-strain curve (Fig. 2(a)) into Eq. (13), the toughening effect ΔГ/Г can be calculated to reach at 16.55%, which is slightly higher than its experimental data of 13.88 %.

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3. 5. Mechanical properties of unpoled BITWx-0.2Cr ceramics

Fig. 9 Stress-strain response of unpoled BITWx-0.2Cr ceramics subjected to uniaxial compression load

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Fig. 9 shows the stress-strain response of unpoled BITWx-0.2Cr ceramics subjected to uniaxial compression load.

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Clearly, the compressiion behavior of BITWx-0.2Cr ceramics are similar to that of BIT ceramic, also including the inelastic deformation caused by the ferroelastic domain switching. However, some specific difference can be observed from their stress-strain curves, as indicated by those saffron circles. Such as, BITW0-0.2Cr has the highest

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compression strength while BITW0.025-0.2Cr received the lowest one, BITW0.05-0.2Cr has a smaller ferroelastic deformation while BITW0.075-0.2Cr possesses a larger one. The inserted image gives out the change in the apparent

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elastic modulus (Eini and Eld) of each sample during the initial process and loading process. As can be seen, all the others except for BITW0.025-0.2Cr present an increased elastic modulus in the loading process, which is similar to the case of BIT. The unexpected increase in the elastic modulus may be attributed to the very samll ratio of microcracks (perpendicular to the applied stress) which tend to close during loading. Therefore, the premature failure of BITW0.025-0.2Cr is considered to be dominated by the plenty of microcracks (parallel to the applied stress) which tend to open during loading.

According to the classic Griffith theory [54], the strength of a material can be described as follows: 17

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f  i 

2 Ef 0 c

(14)

where σf-σi stands for the actual fracture strength (σf is the fracture strength without internal stress and σi is the part contributed on fracture strength by internal stress). c is the length of the critical crack, γf0 is the fracture surface energy without internal stress and E is the elastic modulus. Based on this theory, both the lower elastic modulus due

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to few “closed microcracks”, and more internal stress centralized by many “opening microcracks”, might contribute

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to the much lower strength of BITW0.025-0.2Cr as compared with others.

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Fig. 10 Mechanical properties of unpoled BITWx-0.2Cr ceramics as a function of the doping content of W (x), (a) σc vs g; (b) εzz vs S0lattice; (c) f vs εrem; (d) E vs σcf In order to quantify the evolution of mechanical properties for unpoled BITWx-0.2Cr ceramics, eight mechanical parameters related to the ferroelastic behavior were extracted from their stress-strain curves, which have been depicted as a function of the doping content of W (x) in Fig. 10. As can be seen from this complex pattern that, firstly, the variation of coercive stress (average) with x is just opposite to that of orthorhombicity (Fig. 10(a)), which shows that ferroelastic domains with a higher structural orthorhombicity tend to be switched by a smaller compression stress. And then, the varying trend of switching strain with x seems to agree with that of single-crystal distortion well (Fig. 10(b)), which has been decided by their tie-in equation of εzz=0.212•S0lattice based on a 18

ACCEPTED MANUSCRIPT volume-weighted average of the single-crystal distortions of each domain over the entire orientation space. Further, more switched domains certainly contribute to more irreversible deformation for ferroelectric ceramics, which has been presented by the similar trend of switching fraction to remanent strain in Fig. 10(c). Moreover, the remanent strain resulted from partial ferroelastic domain switching and several lattice-plane reconstitution contribute about 60% to the total strain of these BIT-based ferroelectric ceramic, which can be observed from their stress-strain curves. Finally, the brittle fracture usually occurs in ferroelectric ceramics during their elastic compression, the

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failure stress is mainly contingent on their elastic modulus, with the addition of partial influence exerted by the

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nonlinear ferroelastic behavior [55]. This mechanism could be reflected by the consistent varying trend between the two parameters when x is below 0.05, and the slight deviation when x is above 0.05 (both BITW0.075-0.2Cr and

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BITW0.1-02Cr have a larger switching strain), as shown in Fig. 10(d). In addition, as marked by the red rectangular

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frame, BITW0.05-0.2Cr with a medium W content possesses both good microcosmic switching properties (small coercive stress and large switching strain), and good macroscopic mechanical properties (high elastic modulus and

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compression strength).

Fig. 11 Testing fracture toughness (Г) and calculated toughening effect (ΔГ/Г) of unpoled BITWx-0.2Cr ceramics with different W content (x) Fig. 11 gives out both testing fracture toughness (Г) and calculated toughening effect (ΔГ/Г) for BITWx-0.2Cr ceramics with different W content (x). As can be seen, BITW0.05-0.2Cr gains the highest fracture toughness of 58.21 J/m2, as well as expected to be of a larger toughening effect (13.54%) than the others in the case of compression. A higher fracture toughness may be contributed by a larger grain size for the quasi-brittle fracture of ceramics, according to the prediction of ceramic fracture with normal distribution pertinent to grain size [56, 57]. Here, 19

ACCEPTED MANUSCRIPT BITW0.05-0.2Cr indeed has the largest grain size among BITWx-0.2Cr, which has been reported in one of our previous works [27]. Moreover, the reduced piezo-response is also expected relative to the bulk of the grain, due to the restricted domain-wall motion at grain boundaries. Therefore, such ferroelectric ceramics with coarse grains tend to present a higher piezoelectric ability after poling, which also agrees in the highest d33~28 pC/N of

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BITW0.05-0.2Cr ceramics as found by us in [25].

Conclusion

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For a typic number of bismuth layer-structured ferroelectric (BLSFs) ceramics: bismuth titanate (Bi4Ti3O12, BIT),

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its ferroelastic behavior subjected to uniaxial compression was detected by the nonlinear variation of the stress-strain curve. The switching strain could approximate 3/4 of its saturated value while the switching fraction of

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c-axis domains was 28.67%. SEM observation on the fracture surface reveals that it behaved in the mode of transgranular fracture and two types of microcracks (opening and closed) initiated in the matrix during mechanical

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loading. The ferroelastic domain switching was also been demonstrated by the diffraction evolution of (0 0 12)/(2 0 0)/(0 2 0) peaks after compression. The ferroelastic induced toughening effect (ΔГ/Г) reached to 16.55%. Among

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W/Cr co-doped Bi4Ti3O12 (BITWx-0.2Cr) ceramics, BITW0.025-0.2Cr gained the smallest coercive stress (σc=56 MPa) and lowest compression strength (σcf=134 MPa) while BITW0.05-0.2Cr possessed the highest fracture

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toughness (Г=58.21 J/m2) and a significant potential toughening effect (ΔГ/Г=13.54%). This research could not only help us to further understand the correlation between macroscopic properties and ferroelastic domain

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switching of BLSFs, but also effectively promote the possible application of BITWx-0.2Cr ceramics in

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high-temperature piezoelectric devices.

Acknowledgement

This work was supported by the Applied Basic Research Program from Sichuan Province (2017JY0091), National Natural Science Foundation of China (Grant No. 11702037, 11572057 and 51332003), China Postdoctoral Science Foundation Funded Project (2017M623025), Special Funding for Post Doctoral Research Projects from Sichuan Province (2017, presided over by Yu Chen).

Data availability The datasets generated during the current study are available from the corresponding author on reasonable request. 20

ACCEPTED MANUSCRIPT References [1] Kobune M, Kuriyama T, Furotani R, et al. Ferroelectric materials and their applications. Japanese Journal of Applied Physics, 2015, 54(10S). [2] Kaltenbacher B, Krejčí P. A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte

PT

Mathematik und Mechanik, 2016, 96(7): 874-891. [3] Lupascu D, Rödel J. Fatigue in bulk lead zirconate titanate actuator materials. Advanced Engineering Materials,

RI

2005, 7(10): 882-898.

SC

[4] Chaiyo N, Cann D P, Vittayakorn N. Lead-free (Ba, Ca)(Ti, Zr)O3 ceramics within the polymorphic phase region exhibiting large, fatigue-free piezoelectric strains. Materials & Design, 2017, 133: 109-121.

NU

[5] Scott J F. A review of ferroelectric switching. Ferroelectrics, 2016, 503(1): 117-132. [6] Jones J L, Hoffman M, Bowman K J. Saturated domain switching textures and strains in ferroelastic ceramics.

MA

Journal of Applied Physics, 2005, 98(2): 024115.

[7] Ehmke M C, Khansur N H, Daniels J E, et al. Resolving structural contributions to the electric-field-induced

D

strain in lead-free (1-x)Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3, piezoceramics. Acta Materialia, 2014, 66(3):340-348.

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[8] Xie C, Fang Q H, Liu Y W, et al. Dislocation simulation of domain switching toughening in ferroelectric ceramics. International Journal of Solids and Structures, 2013, 50(9): 1325-1331. [9] Esteves G, Fancher C M, Wallace M, et al. In situ X-ray diffraction of lead zirconate titanate piezoMEMS

CE

cantilever during actuation[J]. Materials & Design, 2016, 111: 429-434. [10] Gao P, Britson J, Nelson C T, et al. Ferroelastic domain switching dynamics under electrical and mechanical

AC

excitations. Nature communications, 2014, 5: 3801. [11] Pojprapai S, Luo Z, Clausen B, et al. Dynamic processes of domain switching in lead zirconate titanate under cyclic mechanical loading by in situ neutron diffraction. Acta Materialia, 2010, 58(6): 1897-1908. [12] Araki W, Malzbender J. Ferroelastic deformation of La0.58Sr0.4Co0.2Fe0.8O3−δ under uniaxial compressive loading. Journal of the European Ceramic Society, 2013, 33(4): 805-812. [13] Bolon A M, Sisneros T A, Schubert A B, et al. Comparison of neutron diffraction and Raman spectroscopic studies of the ferroelastic behavior of ceria-stabilized zirconia at elevated temperatures. Journal of the European Ceramic Society, 2015, 35(2): 623-629. [14] Virkar A V, Jue J F, Smith P, et al. The role of ferroelasticity in toughening of brittle materials. Phase 21

ACCEPTED MANUSCRIPT Transitions, 2016, 35(1): 27-46. [15] Denkhaus S M, Vögler M, Novak N, et al. Short crack fracture toughness in (1−x)(Na1/2Bi1/2)TiO3–xBaTiO3 relaxor ferroelectrics. Journal of the American Ceramic Society, 2017, 100. [16] Vögler M, Daniels J E, Webber K G, et al. Absence of toughening behavior in 0.94(Na1/2Bi1/2) TiO3-0.06 BaTiO3 relaxor ceramic. Scripta Materialia, 2017, 136: 115-119. [17] Wang Y, Yang H, Liu R, et al. Ferroelastic domain switching toughening in spark plasma sintered t’-yttria

PT

stabilized zirconia/La2Zr2O7 composite ceramics. Ceramics International, 2017, 43(15): 13020-13024.

RI

[18] Li J Y, Rogan R C, Üstündag E, et al. Domain switching in polycrystalline ferroelectric ceramics. Nature materials, 2005, 4(10): 776-781.

SC

[19] Fu J, Zuo R, Xu Y, et al. Investigations of domain switching and lattice strains in (Na, K) NbO3-based

NU

lead-free ceramics across orthorhombic-tetragonal phase boundary. Journal of the European Ceramic Society, 2017, 37(3): 975-983.

MA

[20] Jardiel T, Caballero A C, Villegas M. Aurivillius Ceramics: Bi4Ti3O12-Based Piezoelectrics. Journal-Ceramic Society Japan, 2008, 116(1352): 511-518.

[21] Wong Y J, Hassan J, Chen S K, et al. Combined effects of thermal treatment and Er-substitution on phase

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Compounds, 2017, 723: 567-579.

D

formation, microstructure, and dielectric responses of Bi4Ti3O12 Aurivillius ceramics. Journal of Alloys and

[22] Bettaibi A, Jemai R, Wederni M A, et al. Effect of erbium concentration on the structural, optical and electrical

CE

properties of a Bi4Ti3O12 system. RSC Advances, 2017, 7(36): 22578-22586. [23] Rehman F, Wang L, Jin H B, et al. Effect of Fe/Ta doping on structural, dielectric, and electrical properties of

AC

Bi4Ti2.5Fe0.25Ta0.25O12 ceramics. Journal of the American Ceramic Society, 2017(2): 602-611. [24] Chen Y, Pen Z, Wang Q, et al. Crystalline structure, ferroelectric properties, and electrical conduction characteristics of W/Cr co-doped Bi4Ti3O12 ceramics. Journal of Alloys and Compounds, 2014, 612: 120-125. [25] Chen Y, Liang D, Wang Q, et al. Microstructures, dielectric, and piezoelectric properties of W/Cr co-doped Bi4Ti3O12 ceramics. Journal of Applied Physics, 2014, 116(7): 074108. [26] Chen Y, Miao C, Xie S, et al. Fracture Behaviors and Ferroelastic Deformation in W/Cr Co‐ Doped Bi4Ti3O12 Ceramics. Journal of the American Ceramic Society, 2016, 99(6): 2103-2109. [27] Chen Y, Miao C, Xie S, et al. Microstructural evolutions, elastic properties and mechanical behaviors of W/Cr Co-doped Bi4Ti3O12 ceramics. Materials & Design, 2016, 90: 628-634. 22

ACCEPTED MANUSCRIPT [28] Md I A, Gafur M A, Islam S M. Sintering characteristics of La/Nd doped Bi4Ti3O12 bismuth titanate ceramics. Science of Sintering, 2015, 47(2015):175-186. [29] Kumar S, Varma K B R. Dielectric relaxation in bismuth layer-structured BaBi4Ti4O15 ferroelectric ceramics. Current Applied Physics, 2011, 11(2): 203-210. [30] P. Fang, Z. Xi, W. Long, X. Li, and J. Li. Structure and electrical properties of SrBi2Nb2O9-based ferroelectric ceramics with lithium and cerium modification. Journal of Alloys and compounds, 2013, 575: 61–64.

PT

[31] Ivanov S A, Sarkar T, Fortalnova E A, et al. Composition dependence of the multifunctional properties of

RI

Nd-doped Bi4Ti3O12 ceramics. Journal of Materials Science: Materials in Electronics, 2017, 28(11): 7692-7707.

Journal of the American Ceramic Society, 2008, 91(1):278–282.

SC

[32] Jardiel T, Villegas M, Caballero A, et al. Solid-State Compatibility in the System Bi2O3–TiO2 –Bi2WO6.

NU

[33] Pisarenko, G. G., V. M. Chushko, and S. P. Kovalev. Anisotropy of fracture toughness of piezoelectric ceramics. Journal of the American Ceramic Society, 1985, 68(5): 259-265.

MA

[34] Webber K G, Aulbach E, Key T, et al. Temperature-dependent ferroelastic switching of soft lead zirconate titanate. Acta Materialia, 2009, 57(15): 4614-4623.

[35] Pozdnyakova I, Bruno G, Efremov A M, et al. Stress-Dependent Elastic Properties of Porous Microcracked

D

Ceramics. Advanced Engineering Materials, 2010, 11(12): 1023-1029.

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[36] Daymond M R. The determination of a continuum mechanics equivalent elastic strain from the analysis of multiple diffraction peaks. Journal of Applied Physics, 2004, 96(8): 4263-4272.

CE

[37] Cummins S E, Cross L E. Electrical and optical properties of ferroelectric Bi4Ti3O12 single crystals. Journal of Applied Physics, 1968, 39(5): 2268-2274.

AC

[38] Kitanaka Y, Katayama S, Noguchi Y, et al. Electric-Field-Stabilized Ferroelastic Domain Walls in Monoclinic Bi4Ti3O12 Crystals. Japanese Journal of Applied Physics, 2007, 46(10): 7028-7030. [39] Jones J L, Hoffman M, Vogel S C. Ferroelastic domain switching in lead zirconate titanate measured by in situ neutron diffraction. Mechanics of materials, 2007, 39(4): 283-290. [40] Kessler H, Balke H. A continuum analysis of the driving force of ferroelectric/ferroelastic domain wall motions. Journal of the Mechanics & Physics of Solids, 2006, 54(1): 113-127. [41] Kamlah M, Jiang Q. A constitutive model for ferroelectric PZT ceramics under uniaxial loading. Smart Materials and Structures, 1999, 8(4): 441. [42] Jones J L, Hoffman M, Vogel S C. Domain switching under cyclic mechanical loading in lead zirconate 23

ACCEPTED MANUSCRIPT titanate. Journal of the American Ceramic Society, 2006, 89(11): 3567-3569. [43] Pojprapai S, Jones J L, Vodenitcharova T, et al. Investigation of the domain switching zone near a crack tip in pre-poled lead zirconate titanate ceramic via in situ X-ray diffraction. Scripta Materialia, 2011, 64(1): 1-4. [44] Azlan A A, Krengvirat W, Noor A F M, et al. Sintering and Characterization of Rare Earth Doped Bismuth Titanate Ceramics Prepared by Soft Combustion Synthesis[M]// Sintering of Ceramics - New Emerging Techniques. InTech, 2012.

RI

x-ray and neutron diffraction. Journal of Applied Physics, 2005, 97(3):1194.

PT

[45] Jones J L, Slamovich E B, Bowman K J. Domain texture distributions in tetragonal lead zirconate titanate by

[46] Pojprapai S, Jones J L, Studer A J, et al. Ferroelastic domain switching fatigue in lead zirconate titanate

SC

ceramics. Acta Materialia, 2008, 56(7): 1577-1587.

NU

[47] Huang B X, Malzbender J. The effect of an oxygen partial pressure gradient on the mechanical behavior of perovskite membrane materials. Journal of the European Ceramic Society, 2014, 34(7): 1777-1782.

MA

[48] Hill. R. The Mathematical Theory of Plasticity[M]. Clarendon Press, Oxford, 1950. [49] Meschke F, Kolleck A, Schneider G A. R-curve behaviour of BaTiO3 due to stress-induced ferroelastic domain switching. Journal of the European Ceramic Society, 1997, 17(9): 1143-1149.

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[50] Mercer C, Williams J R, Clarke D R, et al. On a ferroelastic mechanism governing the toughness of metastable

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tetragonal-prime (t′) yttria-stabilized zirconia[C]//Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, 2007, 463(2081): 1393-1408.

2014(69): 397-406.

CE

[51] X. Ren, W. Pan. Mechanical properties of high-temperature-degraded yttria-stabilized zirconia. Acta Materialia,

AC

[52] Mehta, Karun, and Anil V. Virkar. Fracture Mechanisms in Ferroelectric-Ferroelastic Lead Zirconate Titanate (Zr: Ti= 0.54: 0.46) Ceramics. Journal of the American Ceramic Society, 1990, 73(3): 567-574. [53] Anstis G R, Chantikul P, Lawn B R, et al. A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness. I.--Direct Crack Measurements. Journal of the American Ceramic Society, 1981, 64(9): 533-538. [54] Lawn B. Fracture of brittle solids[M]. Cambridge university press, 1993. [55] Cao H, Evans A G. Nonlinear deformation of ferroelectric ceramics. Journal of the American Ceramic Society, 1993, 76(4): 890-896. [56] Zhang C, Hu X, Sercombe T, et al. Prediction of ceramic fracture with normal distribution pertinent to grain 24

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near fully-dense boron carbide ceramics. Journal of the European Ceramic Society, 2016, 36(7): 1829-1834.

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Graphical abstract

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Highlights 1. Two types of microcracks (opening and closed) initiated in the matrix of Bi4Ti3O12 ceramic during mechanical loading. 2. The underlying micromechanism of ferroelastic domain switching was more accurately described by the non-180o domain wall motion. 3. The constitutive relation of unpoled ferroelectric ceramics subjected to uniaxial compression load was obtained by a simplified domain distribution model. 4. The expression of ferroelasticity induced toughening effect (ΔГ/Г) was deduced from the indentation fracture mechanics.

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