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Crack propagation behavior in lead zirconate titanate-based ferroelectric ceramics
Journal Pre-proof Crack propagation behavior in lead zirconate titanate-based ferroelectric ceramics Jiageng Xu, Shaoxiong Xie, Qian Xu, Qingyuan Wang, Yu Chen PII:
S0272-8842(20)30316-3
DOI:
https://doi.org/10.1016/j.ceramint.2020.02.005
Reference:
CERI 24228
To appear in:
Ceramics International
Received Date: 29 December 2019 Revised Date:
29 January 2020
Accepted Date: 1 February 2020
Please cite this article as: J. Xu, S. Xie, Q. Xu, Q. Wang, Y. Chen, Crack propagation behavior in lead zirconate titanate-based ferroelectric ceramics, Ceramics International (2020), doi: https:// doi.org/10.1016/j.ceramint.2020.02.005. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Crack Propagation Behavior in Lead Zirconate Titanate-Based Ferroelectric Ceramics Jiageng Xu,a Shaoxiong Xie,b Qian Xu,b Qingyuan Wang,b,c,d,* Yu Chenc,* a
School of Architecture and Civil Engineering, Chengdu University, Chengdu 610106,
China b
MOE Key Laboratory of Deep Earth Science and Engineering, College of Architecture
and Environment, Sichuan University, Chengdu 610065, China c
School of Mechanical Engineering, Chengdu University, Chengdu 610106, China
d
Institute for Advanced Study, Chengdu University, Chengdu 610106, China
ABSTRACT In this study, Vickers indentation was utilized to characterize the crack propagation anisotropy of Nb/Ce co-doped Pb(Zr0.52Ti0.48)O3 (ab. PZT-NC) ceramics in different media environments and under varying temperatures. Three-point bending associated with Weibull statistics was used to further evaluate the fracture properties. The results demonstrate that PZT-NC ceramics have the best fracture toughness in silicone oil and the worst in air. The fracture toughness and flexural strength of poled PZT-NC ceramics have significant anisotropy due to ferroelastic toughening (Ksh) with crack propagation. Parallel to the poling direction, the fracture toughness and reliability of the flexural strength of poled PZT-NC ceramics are higher. As the temperature increases (from 25
to 205 ), the fracture toughness of PZT-NC ceramics
dramatically decreases, which is attributed to the decrease in ferroelastic switching (Ksh). Keywords: PZT ceramics; fracture toughness; crack propagation; media environment; Weibull statistics
*
Correspondence to: School of Mechanical Engineering, Chengdu University, Chengdu 610106, China. Email: [email protected] (Q. Wang) and [email protected] (Y. Chen).
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1. Introduction Piezoelectric materials are widely used in actuators, transducers, and sensors because of their electromechanical coupling characteristics, rapid response, and small size [1]. Ferroelectric ceramics are the principal category of piezoelectric materials. Although they have significant mechanical and electrical properties, little is known about their mechanical properties and fracture behavior, which is paramount for their application in large electric, mechanical, and thermal fields [2-4]. Considerable research has been devoted to studying the fracture mechanics of piezoelectrics and ferroelectrics. Parton analyzed the deformation of a piezoelectric medium under mechanical stress [5]. Kuna reviewed and discussed piezoelectric fracture mechanics [6]. Many experiments have also investigated the fracture behavior of ferroelectric ceramics [7-9]. Over the past 30 years, indentation technology has been widely used to measure the mechanical properties of small-scale materials such as electric ceramics [10]. Vickers indentation experiments have been used to assess the prominent anisotropy of fracture toughness and its dependence on the external electric fields of polarized piezoelectric ceramics [11,12]. Because piezoelectric materials are usually applied to different complex environments, their crack propagation behavior in different media environments and under varying environmental temperatures plays a paramount role in the design of new applications. The stress corrosion cracking of piezoelectric ceramics in water, methanol, and formamide was characterized by single-edge notched tensile specimens [13,14]. The temperature-dependent crack propagation resistance (R-curve) behavior of 0.615Ba(Zr0.2Ti0.8)O3-0.385(Ba0.7Ca0.3)TiO3 ceramics was investigated using a compact tensile (CT) specimen at 25-60
[15]. The crack propagation resistance
behavior of polycrystalline Pb(Zr1-xTix)O3 was investigated using an original experiment from 24 to 140
[16]. To evaluate the reliability of materials and
understand their flexure strength, the Weibull distribution function [17] has been widely utilized to characterize the flexure strength of ceramic materials [18,19]. In our previous work [20], we found that Nb/Ce co-doped Pb(Zr0.52Ti0.48)O3 (PZT-NC) ceramics near the morphotropic phase boundary (MPB) had satisfactory electrical properties and excellent mechanical properties and can be considered extremely competitive candidates for piezoelectric devices. In the present study, we further investigated the crystal structure, microstructure, and component distribution of PZT-NC ceramics. Two different directions (parallel to the poling direction and
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perpendicular to the poling direction) of the fracture toughness of PZT-NC ceramics in different media environments (air, pure water, and silicone oil), and under varying environmental temperatures (from 25
to 205 ) were investigated using Vickers
indentation. The two different directions of the flexural strength of PZT-NC ceramics were tested via three-point bending, and Weibull statistics were utilized to statistically analyze the flexural strength. 2. Materials and methods 2.1. Sample preparation The material investigated in this experiment was Nb/Ce co doped PZT ceramics with the following chemical formula: Pb(Zr0.52Ti0.48)0.95Nb0.05O3+0.2wt%CeO2 (ab. PZT NC). The detailed preparation process was described in our prior work [20]. In the present study, the powder was pressed down a bulk of dimensions of 36 mm×4 mm×4 mm, and the specimens were poled along the Z axis (Fig. 1(a)). 2.2. Crystal structure refinement A mortar was used to crush the sintered PZT-NC ceramics into powder with ethanol. The phase structure of the powder was examined in the range of 2θ (10º-90º) using an X-ray powder diffractometer (XRPD, PANalytical, Netherlands) and Cuk α radiation in steps of 0.02° at a counting time of 15 s per step. The diffraction pattern of the XRPD experiment was analyzed via the Rietveld profile method utilizing the MAUD program (version 2.7, written by Luca Lutterotti, available free online). The crystal structure was analyzed utilizing the Diamond program (version 3.2, available free online). 2.3. Vickers indentation As indicated in Fig. 1(a), a Vickers diamond indenter (AVK-A, Akashi, Japan) is used to indent the specimen in the center of the YZ plane with a holding time of 5 s under a load of 19.6 N. To avoid interactions between the adjacent indentation stress fields and ensure the experiment’s accuracy, the distance between the adjacent indentations is strictly guaranteed to be more than 2.5 times the indentation diagonal, and the distance between the indentation and specimen edge is more than 2.5 times the indentation diagonal. Scanning electron microscopy (TM3000, Hitachi, Japan) is used to examine the crack morphology of the Vickers indentation. The lengths of the indentation cracks in the parallel and perpendicular poling directions are measured corresponding to the crack directions C⫽ and C⟘, respectively. The testing specimens
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are then indented in pure water and silicone oil the same as in air. The temperature of the silicon oil simultaneously increases from 25
to 205 .
2.4. Three-point bending The bending strength of the PZT-NC ceramics under a three-point bending beam with a span of 30 mm and a loading speed of 0.5mm/min is measured using a universal testing machine (Instron 8501). Three-point bending fracture tests for the poled PZT-NC ceramics are conducted under two different loading modes. The loading force (P) parallel to the poling direction is shown in Fig. 1(b), and the loading force perpendicular to the poling direction is shown in Fig. 1(c). 3. Results and discussion Fig. 2 shows the sample’s XRPD after the Rietveld refinements, and the results are displayed in Table 1. The sample’s principal crystal phase is tetragonal (International Center for Diffraction Data #153692), and its peak value is based on the cubic perovskite unit. The sample’s second phase has a triangular phase (International Center for Diffraction Data #24562) because this phase cannot be completely eliminated from the sample prepared using mixed oxide [21, 22]. The two different phases in the sample weight are approximately 75% and 25%, respectively. The inconsistent parameters are the weighted scale coefficient sig=1.47 and the scale coefficient Rwp=5.82, which demonstrate that the redefined results are satisfactory. The PZT-NC structure shows that the tetragonal crystal has a P4mm space group and the triangular crystal has a R3mR space group. The fractional coordinate of each atom in the crystal structure can be obtained according to the Rietveld refinements, which are listed in Table 2 and Table 3. The unit cell diagrams of the tetragonal and triangular crystals are included in Fig. 2. Fig. 3(a) shows an SEM micrograph of the PZT-NC surface, which demonstrates that the sample has dense grains with grain sizes of approximately 0.2-2 mm and proves the sample is well-crystallized. Fig. 3(b) shows the EDS of the PZT-NC surface, which demonstrates the homogeneous distribution of each main component (Pb, Ti, Zr, and O) in the sample. The elemental analysis of the PZT-NC ceramic surface according to the EDS is presented in Table 4. However, the EDS cannot detect the doped elements Nb and Ce because of their low content. Fig. 4(a), (b), and (c) show SEM micrographs of the indentation cracks in air, pure water, and silicon oil, respectively. The lengths of the indentation cracks in the different media environments varied. The stress intensity factor KIC can be expressed as [23]:
5 /
= 0.016
/
,
(1)
where Y is Young's modulus, Hv is the material hardness, P is the applied indentation load, and c is the indentation crack length. According to the expression of the material hardness: =
/
,
(2)
where d is the semi-diagonal of the indentation pyramid, α, usually 136°, indicating the vertex angle of the Vickers diamond indenter. The indentation crack length can be utilized to determine the fracture toughness KIC according to the following equation: = 0.023
√ $ %/
,
(3)
where c is the measured crack length from the center of the indentation. The fracture toughness in different media environments is shown in Fig. 4(d). The fracture toughness parallel to the poling direction can be determined as approximately 1.06 MPa•m1/2, 1.21 MPa•m1/2, and 1.49 MPa•m1/2, in air, pure water, and silicon oil, respectively. The fracture toughness perpendicular to the poling direction can be determined as approximately 0.60MPa•m1/2, 0.65 MPa•m1/2, and 0.69 MPa•m1/2, in air, pure water, and silicon oil, respectively. The media environment has a significant effect on the fracture toughness. The fracture toughness in pure water was higher than in air, and the fracture toughness in silicon oil was higher than in pure water. Wiederhorn et al. described the influence of water on crack growth [24-27]. Fig. 4(b) demonstrates that when the PZT-NC ceramics were indented in water, there was considerable swelling around the indentation. Water penetrating into ceramics causes swelling around the crack surface, which is attributable to the volume expansion due to the elastic relaxation of the water-penetrated zone. When the crack propagates through the compression zone under the action of a mechanical force, the stress produced by the diffusion of water causes elastic rebounds, thereupon applying the shielding stress intensity factor Ksh at the crack tip to increase the material fracture toughness. By analogy with the influence of water penetrating into ceramics, under a silicon oil environment, the silicon oil molecule also penetrates the ceramics and impedes crack propagation, leading to greater fracture toughness. As shown in the SEM micrographs of the indentation cracks (Fig. 4(a-c)), the cracks parallel to the poling direction (C⫽) are clearly shorter than those perpendicular (C⟘) to the poling direction regardless of whether the sample is placed in air, pure water,
6
or silicone oil for indentation. In air, the value of the anisotropy coefficient can be determined as (
⫽
⫽
/
⟘
=1.77 according to the anisotropic fracture toughness parallel
) and perpendicular (
⟘
) to the poling direction. The poled ferroelectric ceramic
exhibits prominent anisotropy in the fracture toughness due to ferroelastic domain switching, which was observed in prior studies [28-31]. In ferroelectric ceramics, domain switching can be triggered by both electrical energy or mechanical energy, while mechanical energy can only cause 90º switching of ferroelectric domains (that is, ferroelastic switching), which plays an indispensable role in the toughening of materials [32]. For Vickers indentation, the plastic deformation under indentation causes tensile opening stress at the crack front, so that the crack propagates to a maximum length, and the resulting crack can be regarded as a semi-circular surface crack. For poled ferroelectric ceramics, due to the variable orientation of the ferroelectric domain, the residual stress in the plastic zone also differs. For poled ferroelectric ceramics, the residual stresses resulting from the plastic zone varies due to the difference in the ferroelectric domain orientation. As depicted in Fig. 5(a), for PZT-NC ceramics, the ferroelectric domain orientation is random and indeterminate. Nevertheless, after poling, the tetragonal distortion axis (C axis) will be in accordance with the poling direction, and the ferroelectric domains will be oriented to the poling direction. In the YZ plane, the crack propagating parallel to the poling direction (at location A), the high tensile stress (σyy) at the crack tip is sufficient to switch the ferroelectric domains in the vicinity of the crack tip to a new orientation perpendicular to the poling direction, which was identified as 90º switching. In theory, since ferroelectric domains are oriented perpendicular to the direction of main stress, they are supposed to be switched, and strong residual compressive stresses (σ('' ) can be triggered by strain mismatch with the scope of the switching zone. Conversely, a crack propagating perpendicular to the poling direction (at location B) as a consequence of high tensile stress (σzz) at the crack tip is applied to the C axis, and the ferroelectric domains in the vicinity of the crack tip should remain unaltered. As depicted in Fig. 5(b), provided that the ferroelectric domains are oriented parallel to the polarization direction, the high tensile stresses in the perpendicular direction of polarization lead to 90º switching of the ferroelectric domains around the crack tip, and this frontal region is regarded as the process zone. It increases with the crack growth and forms a domain switch band on both sides of the crack wake. The
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tensile stress at the crack tip causes strain mismatch in the switched and unswitched regions, which leads to residual strain in the crack wake. This zone transition strip triggers compressive stress perpendicular to the crack growth direction (that is, crack closure stress), which results in the shielding of the crack tip from remotely applied stress. Hence, the apparent fracture toughness increases (Kapp=Ksh+Ktip) [28]. Additionally, the crack closure stress is affected by the size and shape of the process zone, material stiffness, and strain mismatch between the process zone and surrounding zone [33]. The half-height (h) of the process region is crucial to the ferroelastic toughening model. It is progressive and continuous and physical saturation (that is, subcritical) will not occur [34]. It is assumed that the process zone height, h, scales with the crack propagating resistance, KIR, and then [18, 30] )
=
. +,-√/
*.
12
h= 3
456 78
,
,
(4) (5)
where Ksh is the shielding toughness resulting from ferroelastic switching; Y is Young’s modulus; εeffT is the effective switching strain, which is equivalent to the remnant strain (εr) in ferroelastic materials including reversible back-switching effects; ν is Poisson’s ratio; B=1/2π, is the scale factor of the plane stress state; and σc is the coercive stress, which is indispensable to drive the process zone. Substituting Eq. (5) into Eq. (4) results in: )
=
9
•
*.* ; +< , 12 78
(6)
As the crack propagates, the length of the process zone increases up to a point where KIR reaches its maximum or steady-state value (KIRmax) and Ksh saturates (Ksh=Kshmax). For PZT-NC ceramics, Ksh≈0.46 MPa•m1/2. In contrast, if the ferroelectric domains are oriented perpendicular to the polarization direction, the high tensile stresses cannot lead to 90º switching of the ferroelectric domains around the crack tip, so there is no domain switching. Such anisotropy can be reflected further by the three-point bending flexural strength experiment in two different directions. The flexural strength (σ) can be calculated using the following formula [35,36]: σ=
=>
?/
,
(7)
where F is the fracture load (that is, the maximum applied stress) and b, h, and L are the specimen’s width, the specimen’s thickness, and the distance between the two fixture
8
supports, respectively. Fig. 6(a) shows the probability statistics of the flexural strength in two different directions. The results apparently show the discreteness and volatility of the material flexural strength in two different directions. To determine the material flexural strength and its reliability in two different directions, Weibull statistics were utilized for the statistical analysis. The Weibull method is a distribution function established by Swedish scholar Weibull [17] and is based on the concept of the weakest link. When dealing with the strength of materials, the concept of the weakest ring can be simply expressed as follows: there are various types of inherent cracks at the interior or surface of the material, and when the stress concentration at any crack in the interior or surface is enough to cause the crack to be unstable and propagate, the material will break down. The fracture probability of the material at an applied stress level depends on the probability of the crack propagation in the local micro area where the inherent cracks are located. The flexural strengths of ceramic bodies depend considerably on the variability of the defect distribution. Weibull statistics are applied via Eq. (8): @
= 1 − exp E−
7 G
7F
H,
(8)
I 1 *.
where Pf is the probability of fracture (Pf =J K *.L) [37], i is the order of the specimen fracture strength from minimum to maximum, N is the total number of specimens, m is the shape parameter (Weibull modulus), and σ0 is the characteristic strength (σ63.21%). The results are then plotted in the usual function form of the Weibull expression: MNMN O
1 P
Q = RMNS − RMNS* ,
(9)
The linear regression of N numbers can be obtained by fitting a straight line to MNMN O
1 P
Q as a function of lnσ. The slope of the line is the Weibull modulus m, and
the intercept of the straight line easily determines the characteristic strength σ0 [38]. The Weibull distribution curve of the flexural strength in two different directions is shown in Fig. 6(b), and the Weibull statistical data in two different directions are shown in Table 5. The results demonstrate that the fitting lines in both the parallel and perpendicular directions have perfect correlation. The characteristic strength (σ0) and Weibull modulus (m) in parallel to the poling direction are greater than in the perpendicular direction. Thus, PZT-NC ceramics exhibit higher reliability in parallel to the poling direction. When the specimen is fractured along the Z axis (Fig. 1(b)), due
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to the tensile stress generated by the loading force (P), the fracture main crack occurs at the bottom of the specimen. As the loading force (P) increases, the fracture main crack propagates rapidly along the direction parallel to the polarization, which leads to ferroelastic toughening (Fig. 5(b)). Hence, the crack propagation is impeded, and the material flexural strength and its reliability are improved. In essence, a material’s flexural strength is affected by its fracture toughness. For PZT-NC ceramics, the contribution of ferroelastic toughening (Ksh) to flexural strength is approximately 3.66 MPa. Fig. 7(a-d) show SEM micrographs of the indentation cracks in silicon oil at different environmental temperatures. The SEM micrographs of the indentation cracks demonstrate that their lengths gradually increase as the temperature increases from 25 to 200 . Fig. 8 shows the fracture toughness of poled PZT-NC ceramics in silicon oil at different environmental temperatures. On the one hand, parallel to the poling direction, the fracture toughness dramatically decreases as the temperature increases, and finally the fracture toughness drops to almost the same level as the perpendicular direction when the temperature reaches 200 . On the other hand, perpendicular to the poling direction, the fracture toughness is almost stationary. The shielding toughness (Ksh) due to the ferroelastic switching (Fig. 5(b)) gradually tapers as the temperature increases. Meanwhile, the ferroelastic switching almost disappears until the temperature reaches 200 . The value of Ksh is approximately 0.80 MPa•m1/2 under a silicon oil environmental temperature of 25 . However, the value of Ksh is only approximately 0.26 MPa•m1/2 when the silicon oil environmental temperature increases to 205 . Prior studies reported that both the elastic modulus (Y) and remnant stress (εr) decreased as the temperature increased by the stress-strain curves during loading-unloading measurements at different temperatures [39-41]. Based on Eq. (6), the reduction in Ksh as the temperature increases can be reasonably explained. Perpendicular to the poling direction, because tensile stresses trigger little or no ferroelastic switching, the fracture toughness is mainly affected by environmental temperature corrosion. 4. Conclusions In summary, the fracture properties of Nb/Ce Co-doped Pb (Zr0.52Ti0.48) O3 (ab. PZT-NC) ceramics in different media (air, pure water, and silicone oil) were studied via Vickers indentation and three-point bending. PZT-NC ceramics have the best fracture toughness in silicone oil and the worst in air. The fracture toughness parallel to the poling direction is higher than that perpendicular to the poling direction. According to
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the Weibull analysis of the flexural strength, PZT-NC ceramics exhibit higher reliability parallel to the poling direction. The fracture toughness of PZT-NC ceramics gradually decreases as the temperature increases. Ferroelastic switching and increased water penetration are considered to play crucial roles in the toughening of materials. Acknowledgments This study was supported by the China Postdoctoral Science Foundation Project (2017M623025).
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Figures and tables Fig. 1. (a) Diagrammatic sketch of Vickers indentation. (b) Diagrammatic sketch of three-point bending parallel to the poling direction. (c) Diagrammatic sketch of three-point bending perpendicular to the poling direction. Fig. 2. XRPD results of PZT-NC ceramics after Rietveld refinements. Fig. 3. (a) SEM micrographs of PZT-NC ceramic surface. (b) EDS diagram of PZT-NC ceramic surface. Fig. 4. (a), (b), and (c) Diagram SEM micrographs of the indentation cracks of poled PZT-NC ceramics in air, pure water, and silicon oil, respectively. (e) Fracture toughness of poled PZT-NC ceramics in different media environments. Fig. 5. (a) Diagrammatic sketch of the indentation cracks. (b) Diagrammatic sketch of the mechanism of ferroelastic toughening in poled ferroelectric ceramics. Fig. 6. (a) Probability statistics diagram of the flexural strength in two different directions. (b) Weibull distribution curves diagram of the flexural strength in two different directions. Fig. 7. (a-d) SEM micrographs of the indentation cracks of poled PZT-NC ceramics in silicon oil at different environmental temperatures.
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Fig. 8. Fracture toughness of poled PZT-NC ceramics in silicon oil at different environmental temperatures. Table 1. Crystallographic data of PZT-NC ceramic crystals derived from Rietveld refinement Crystal
Formula
Space
system
a (Å)
α (º)
c (Å)
group
Weight (%)
Tetragonal
PbTi0.48Zr0.52O3
P4mm
4.040748
4.1315103
-
75.02
Trigonal
PbTi0.42Zr0.58O3
R3mR
4.075296
-
89.66839
24.98
Table 2. Atom positions of tetragonal crystals of PZT-NC ceramics Atom
x
y
z
Occupancy
Pb1
0.027885614
0.027885614
0.0011629091
0.25
Zr1
0.5
0.5
0.43704185
0.52
Ti1
0.5
0.5
0.43704185
0.48
O1
0.5
0.5
-0.07332134
1
O2
0.5
0
0.47294596
1
Table 3. Atom positions of trigonal crystals of PZT-NC ceramics Atom
x
y
z
Occupancy
Pb1
0.52628547
0.52628547
0.52628547
1
Zr1
-0.009008482
-0.009008482
-0.009008482
0.58
Ti1
-0.009008482
-0.009008482
-0.009008482
0.42
O1
-0.097509466
0.39049664
-0.097509466
1
Table 4. EDS elemental analysis of PZT-NC ceramic surface Element
Pb
Ti
Zr
O
Total
Weight percentage
53.83
6.43
29.61
10.13
100.00
Atomic percentage
19.22
9.93
24.01
46.84
100.00
Table 5. Weibull statistical data of the fracture toughness of poled PZT-NC ceramics in two different directions Direction
σ /MPa
m
σ0 /MPa
R2
Number
of
measurement samples Parallel direction
49.78
7.9
52.08
0.967
16
Perpendicular direction
44.24
4.8
48.42
0.970
16
Declaration of Interest Statement
Article Title:
Crack Propagation Behavior in Lead Zirconate Titanate Based
Ferroelectric Ceramics Authors:
Jiageng Xu, Shaoxiong Xie, Qian Xu, Qingyuan Wang, Yu Chen
All authors of this manuscript have directly participated in planning, execution, and/or analysis of this study. The contents of this manuscript have not been copyrighted or published previously. The contents of this manuscript are not now under consideration for publication elsewhere. There are no directly related manuscripts or abstracts, published or unpublished, by any authors of this manuscript. No financial support or incentive has been provided for this manuscript. I am sole author of this manuscript. I am one author signing on behalf of all co-authors of this manuscript, and attesting to the above.
Signature: Date: Printed Name: Institution:
December 29, 2019 Jiageng Xu School of Architecture and Civil Engineering, Chengdu University
S0272-8842(20)30316-3
DOI:
https://doi.org/10.1016/j.ceramint.2020.02.005
Reference:
CERI 24228
To appear in:
Ceramics International
Received Date: 29 December 2019 Revised Date:
29 January 2020
Accepted Date: 1 February 2020
Please cite this article as: J. Xu, S. Xie, Q. Xu, Q. Wang, Y. Chen, Crack propagation behavior in lead zirconate titanate-based ferroelectric ceramics, Ceramics International (2020), doi: https:// doi.org/10.1016/j.ceramint.2020.02.005. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Crack Propagation Behavior in Lead Zirconate Titanate-Based Ferroelectric Ceramics Jiageng Xu,a Shaoxiong Xie,b Qian Xu,b Qingyuan Wang,b,c,d,* Yu Chenc,* a
School of Architecture and Civil Engineering, Chengdu University, Chengdu 610106,
China b
MOE Key Laboratory of Deep Earth Science and Engineering, College of Architecture
and Environment, Sichuan University, Chengdu 610065, China c
School of Mechanical Engineering, Chengdu University, Chengdu 610106, China
d
Institute for Advanced Study, Chengdu University, Chengdu 610106, China
ABSTRACT In this study, Vickers indentation was utilized to characterize the crack propagation anisotropy of Nb/Ce co-doped Pb(Zr0.52Ti0.48)O3 (ab. PZT-NC) ceramics in different media environments and under varying temperatures. Three-point bending associated with Weibull statistics was used to further evaluate the fracture properties. The results demonstrate that PZT-NC ceramics have the best fracture toughness in silicone oil and the worst in air. The fracture toughness and flexural strength of poled PZT-NC ceramics have significant anisotropy due to ferroelastic toughening (Ksh) with crack propagation. Parallel to the poling direction, the fracture toughness and reliability of the flexural strength of poled PZT-NC ceramics are higher. As the temperature increases (from 25
to 205 ), the fracture toughness of PZT-NC ceramics
dramatically decreases, which is attributed to the decrease in ferroelastic switching (Ksh). Keywords: PZT ceramics; fracture toughness; crack propagation; media environment; Weibull statistics
*
Correspondence to: School of Mechanical Engineering, Chengdu University, Chengdu 610106, China. Email: [email protected] (Q. Wang) and [email protected] (Y. Chen).
2
1. Introduction Piezoelectric materials are widely used in actuators, transducers, and sensors because of their electromechanical coupling characteristics, rapid response, and small size [1]. Ferroelectric ceramics are the principal category of piezoelectric materials. Although they have significant mechanical and electrical properties, little is known about their mechanical properties and fracture behavior, which is paramount for their application in large electric, mechanical, and thermal fields [2-4]. Considerable research has been devoted to studying the fracture mechanics of piezoelectrics and ferroelectrics. Parton analyzed the deformation of a piezoelectric medium under mechanical stress [5]. Kuna reviewed and discussed piezoelectric fracture mechanics [6]. Many experiments have also investigated the fracture behavior of ferroelectric ceramics [7-9]. Over the past 30 years, indentation technology has been widely used to measure the mechanical properties of small-scale materials such as electric ceramics [10]. Vickers indentation experiments have been used to assess the prominent anisotropy of fracture toughness and its dependence on the external electric fields of polarized piezoelectric ceramics [11,12]. Because piezoelectric materials are usually applied to different complex environments, their crack propagation behavior in different media environments and under varying environmental temperatures plays a paramount role in the design of new applications. The stress corrosion cracking of piezoelectric ceramics in water, methanol, and formamide was characterized by single-edge notched tensile specimens [13,14]. The temperature-dependent crack propagation resistance (R-curve) behavior of 0.615Ba(Zr0.2Ti0.8)O3-0.385(Ba0.7Ca0.3)TiO3 ceramics was investigated using a compact tensile (CT) specimen at 25-60
[15]. The crack propagation resistance
behavior of polycrystalline Pb(Zr1-xTix)O3 was investigated using an original experiment from 24 to 140
[16]. To evaluate the reliability of materials and
understand their flexure strength, the Weibull distribution function [17] has been widely utilized to characterize the flexure strength of ceramic materials [18,19]. In our previous work [20], we found that Nb/Ce co-doped Pb(Zr0.52Ti0.48)O3 (PZT-NC) ceramics near the morphotropic phase boundary (MPB) had satisfactory electrical properties and excellent mechanical properties and can be considered extremely competitive candidates for piezoelectric devices. In the present study, we further investigated the crystal structure, microstructure, and component distribution of PZT-NC ceramics. Two different directions (parallel to the poling direction and
3
perpendicular to the poling direction) of the fracture toughness of PZT-NC ceramics in different media environments (air, pure water, and silicone oil), and under varying environmental temperatures (from 25
to 205 ) were investigated using Vickers
indentation. The two different directions of the flexural strength of PZT-NC ceramics were tested via three-point bending, and Weibull statistics were utilized to statistically analyze the flexural strength. 2. Materials and methods 2.1. Sample preparation The material investigated in this experiment was Nb/Ce co doped PZT ceramics with the following chemical formula: Pb(Zr0.52Ti0.48)0.95Nb0.05O3+0.2wt%CeO2 (ab. PZT NC). The detailed preparation process was described in our prior work [20]. In the present study, the powder was pressed down a bulk of dimensions of 36 mm×4 mm×4 mm, and the specimens were poled along the Z axis (Fig. 1(a)). 2.2. Crystal structure refinement A mortar was used to crush the sintered PZT-NC ceramics into powder with ethanol. The phase structure of the powder was examined in the range of 2θ (10º-90º) using an X-ray powder diffractometer (XRPD, PANalytical, Netherlands) and Cuk α radiation in steps of 0.02° at a counting time of 15 s per step. The diffraction pattern of the XRPD experiment was analyzed via the Rietveld profile method utilizing the MAUD program (version 2.7, written by Luca Lutterotti, available free online). The crystal structure was analyzed utilizing the Diamond program (version 3.2, available free online). 2.3. Vickers indentation As indicated in Fig. 1(a), a Vickers diamond indenter (AVK-A, Akashi, Japan) is used to indent the specimen in the center of the YZ plane with a holding time of 5 s under a load of 19.6 N. To avoid interactions between the adjacent indentation stress fields and ensure the experiment’s accuracy, the distance between the adjacent indentations is strictly guaranteed to be more than 2.5 times the indentation diagonal, and the distance between the indentation and specimen edge is more than 2.5 times the indentation diagonal. Scanning electron microscopy (TM3000, Hitachi, Japan) is used to examine the crack morphology of the Vickers indentation. The lengths of the indentation cracks in the parallel and perpendicular poling directions are measured corresponding to the crack directions C⫽ and C⟘, respectively. The testing specimens
4
are then indented in pure water and silicone oil the same as in air. The temperature of the silicon oil simultaneously increases from 25
to 205 .
2.4. Three-point bending The bending strength of the PZT-NC ceramics under a three-point bending beam with a span of 30 mm and a loading speed of 0.5mm/min is measured using a universal testing machine (Instron 8501). Three-point bending fracture tests for the poled PZT-NC ceramics are conducted under two different loading modes. The loading force (P) parallel to the poling direction is shown in Fig. 1(b), and the loading force perpendicular to the poling direction is shown in Fig. 1(c). 3. Results and discussion Fig. 2 shows the sample’s XRPD after the Rietveld refinements, and the results are displayed in Table 1. The sample’s principal crystal phase is tetragonal (International Center for Diffraction Data #153692), and its peak value is based on the cubic perovskite unit. The sample’s second phase has a triangular phase (International Center for Diffraction Data #24562) because this phase cannot be completely eliminated from the sample prepared using mixed oxide [21, 22]. The two different phases in the sample weight are approximately 75% and 25%, respectively. The inconsistent parameters are the weighted scale coefficient sig=1.47 and the scale coefficient Rwp=5.82, which demonstrate that the redefined results are satisfactory. The PZT-NC structure shows that the tetragonal crystal has a P4mm space group and the triangular crystal has a R3mR space group. The fractional coordinate of each atom in the crystal structure can be obtained according to the Rietveld refinements, which are listed in Table 2 and Table 3. The unit cell diagrams of the tetragonal and triangular crystals are included in Fig. 2. Fig. 3(a) shows an SEM micrograph of the PZT-NC surface, which demonstrates that the sample has dense grains with grain sizes of approximately 0.2-2 mm and proves the sample is well-crystallized. Fig. 3(b) shows the EDS of the PZT-NC surface, which demonstrates the homogeneous distribution of each main component (Pb, Ti, Zr, and O) in the sample. The elemental analysis of the PZT-NC ceramic surface according to the EDS is presented in Table 4. However, the EDS cannot detect the doped elements Nb and Ce because of their low content. Fig. 4(a), (b), and (c) show SEM micrographs of the indentation cracks in air, pure water, and silicon oil, respectively. The lengths of the indentation cracks in the different media environments varied. The stress intensity factor KIC can be expressed as [23]:
5 /
= 0.016
/
,
(1)
where Y is Young's modulus, Hv is the material hardness, P is the applied indentation load, and c is the indentation crack length. According to the expression of the material hardness: =
/
,
(2)
where d is the semi-diagonal of the indentation pyramid, α, usually 136°, indicating the vertex angle of the Vickers diamond indenter. The indentation crack length can be utilized to determine the fracture toughness KIC according to the following equation: = 0.023
√ $ %/
,
(3)
where c is the measured crack length from the center of the indentation. The fracture toughness in different media environments is shown in Fig. 4(d). The fracture toughness parallel to the poling direction can be determined as approximately 1.06 MPa•m1/2, 1.21 MPa•m1/2, and 1.49 MPa•m1/2, in air, pure water, and silicon oil, respectively. The fracture toughness perpendicular to the poling direction can be determined as approximately 0.60MPa•m1/2, 0.65 MPa•m1/2, and 0.69 MPa•m1/2, in air, pure water, and silicon oil, respectively. The media environment has a significant effect on the fracture toughness. The fracture toughness in pure water was higher than in air, and the fracture toughness in silicon oil was higher than in pure water. Wiederhorn et al. described the influence of water on crack growth [24-27]. Fig. 4(b) demonstrates that when the PZT-NC ceramics were indented in water, there was considerable swelling around the indentation. Water penetrating into ceramics causes swelling around the crack surface, which is attributable to the volume expansion due to the elastic relaxation of the water-penetrated zone. When the crack propagates through the compression zone under the action of a mechanical force, the stress produced by the diffusion of water causes elastic rebounds, thereupon applying the shielding stress intensity factor Ksh at the crack tip to increase the material fracture toughness. By analogy with the influence of water penetrating into ceramics, under a silicon oil environment, the silicon oil molecule also penetrates the ceramics and impedes crack propagation, leading to greater fracture toughness. As shown in the SEM micrographs of the indentation cracks (Fig. 4(a-c)), the cracks parallel to the poling direction (C⫽) are clearly shorter than those perpendicular (C⟘) to the poling direction regardless of whether the sample is placed in air, pure water,
6
or silicone oil for indentation. In air, the value of the anisotropy coefficient can be determined as (
⫽
⫽
/
⟘
=1.77 according to the anisotropic fracture toughness parallel
) and perpendicular (
⟘
) to the poling direction. The poled ferroelectric ceramic
exhibits prominent anisotropy in the fracture toughness due to ferroelastic domain switching, which was observed in prior studies [28-31]. In ferroelectric ceramics, domain switching can be triggered by both electrical energy or mechanical energy, while mechanical energy can only cause 90º switching of ferroelectric domains (that is, ferroelastic switching), which plays an indispensable role in the toughening of materials [32]. For Vickers indentation, the plastic deformation under indentation causes tensile opening stress at the crack front, so that the crack propagates to a maximum length, and the resulting crack can be regarded as a semi-circular surface crack. For poled ferroelectric ceramics, due to the variable orientation of the ferroelectric domain, the residual stress in the plastic zone also differs. For poled ferroelectric ceramics, the residual stresses resulting from the plastic zone varies due to the difference in the ferroelectric domain orientation. As depicted in Fig. 5(a), for PZT-NC ceramics, the ferroelectric domain orientation is random and indeterminate. Nevertheless, after poling, the tetragonal distortion axis (C axis) will be in accordance with the poling direction, and the ferroelectric domains will be oriented to the poling direction. In the YZ plane, the crack propagating parallel to the poling direction (at location A), the high tensile stress (σyy) at the crack tip is sufficient to switch the ferroelectric domains in the vicinity of the crack tip to a new orientation perpendicular to the poling direction, which was identified as 90º switching. In theory, since ferroelectric domains are oriented perpendicular to the direction of main stress, they are supposed to be switched, and strong residual compressive stresses (σ('' ) can be triggered by strain mismatch with the scope of the switching zone. Conversely, a crack propagating perpendicular to the poling direction (at location B) as a consequence of high tensile stress (σzz) at the crack tip is applied to the C axis, and the ferroelectric domains in the vicinity of the crack tip should remain unaltered. As depicted in Fig. 5(b), provided that the ferroelectric domains are oriented parallel to the polarization direction, the high tensile stresses in the perpendicular direction of polarization lead to 90º switching of the ferroelectric domains around the crack tip, and this frontal region is regarded as the process zone. It increases with the crack growth and forms a domain switch band on both sides of the crack wake. The
7
tensile stress at the crack tip causes strain mismatch in the switched and unswitched regions, which leads to residual strain in the crack wake. This zone transition strip triggers compressive stress perpendicular to the crack growth direction (that is, crack closure stress), which results in the shielding of the crack tip from remotely applied stress. Hence, the apparent fracture toughness increases (Kapp=Ksh+Ktip) [28]. Additionally, the crack closure stress is affected by the size and shape of the process zone, material stiffness, and strain mismatch between the process zone and surrounding zone [33]. The half-height (h) of the process region is crucial to the ferroelastic toughening model. It is progressive and continuous and physical saturation (that is, subcritical) will not occur [34]. It is assumed that the process zone height, h, scales with the crack propagating resistance, KIR, and then [18, 30] )
=
. +,-√/
*.
12
h= 3
456 78
,
,
(4) (5)
where Ksh is the shielding toughness resulting from ferroelastic switching; Y is Young’s modulus; εeffT is the effective switching strain, which is equivalent to the remnant strain (εr) in ferroelastic materials including reversible back-switching effects; ν is Poisson’s ratio; B=1/2π, is the scale factor of the plane stress state; and σc is the coercive stress, which is indispensable to drive the process zone. Substituting Eq. (5) into Eq. (4) results in: )
=
9
•
*.* ; +< , 12 78
(6)
As the crack propagates, the length of the process zone increases up to a point where KIR reaches its maximum or steady-state value (KIRmax) and Ksh saturates (Ksh=Kshmax). For PZT-NC ceramics, Ksh≈0.46 MPa•m1/2. In contrast, if the ferroelectric domains are oriented perpendicular to the polarization direction, the high tensile stresses cannot lead to 90º switching of the ferroelectric domains around the crack tip, so there is no domain switching. Such anisotropy can be reflected further by the three-point bending flexural strength experiment in two different directions. The flexural strength (σ) can be calculated using the following formula [35,36]: σ=
=>
?/
,
(7)
where F is the fracture load (that is, the maximum applied stress) and b, h, and L are the specimen’s width, the specimen’s thickness, and the distance between the two fixture
8
supports, respectively. Fig. 6(a) shows the probability statistics of the flexural strength in two different directions. The results apparently show the discreteness and volatility of the material flexural strength in two different directions. To determine the material flexural strength and its reliability in two different directions, Weibull statistics were utilized for the statistical analysis. The Weibull method is a distribution function established by Swedish scholar Weibull [17] and is based on the concept of the weakest link. When dealing with the strength of materials, the concept of the weakest ring can be simply expressed as follows: there are various types of inherent cracks at the interior or surface of the material, and when the stress concentration at any crack in the interior or surface is enough to cause the crack to be unstable and propagate, the material will break down. The fracture probability of the material at an applied stress level depends on the probability of the crack propagation in the local micro area where the inherent cracks are located. The flexural strengths of ceramic bodies depend considerably on the variability of the defect distribution. Weibull statistics are applied via Eq. (8): @
= 1 − exp E−
7 G
7F
H,
(8)
I 1 *.
where Pf is the probability of fracture (Pf =J K *.L) [37], i is the order of the specimen fracture strength from minimum to maximum, N is the total number of specimens, m is the shape parameter (Weibull modulus), and σ0 is the characteristic strength (σ63.21%). The results are then plotted in the usual function form of the Weibull expression: MNMN O
1 P
Q = RMNS − RMNS* ,
(9)
The linear regression of N numbers can be obtained by fitting a straight line to MNMN O
1 P
Q as a function of lnσ. The slope of the line is the Weibull modulus m, and
the intercept of the straight line easily determines the characteristic strength σ0 [38]. The Weibull distribution curve of the flexural strength in two different directions is shown in Fig. 6(b), and the Weibull statistical data in two different directions are shown in Table 5. The results demonstrate that the fitting lines in both the parallel and perpendicular directions have perfect correlation. The characteristic strength (σ0) and Weibull modulus (m) in parallel to the poling direction are greater than in the perpendicular direction. Thus, PZT-NC ceramics exhibit higher reliability in parallel to the poling direction. When the specimen is fractured along the Z axis (Fig. 1(b)), due
9
to the tensile stress generated by the loading force (P), the fracture main crack occurs at the bottom of the specimen. As the loading force (P) increases, the fracture main crack propagates rapidly along the direction parallel to the polarization, which leads to ferroelastic toughening (Fig. 5(b)). Hence, the crack propagation is impeded, and the material flexural strength and its reliability are improved. In essence, a material’s flexural strength is affected by its fracture toughness. For PZT-NC ceramics, the contribution of ferroelastic toughening (Ksh) to flexural strength is approximately 3.66 MPa. Fig. 7(a-d) show SEM micrographs of the indentation cracks in silicon oil at different environmental temperatures. The SEM micrographs of the indentation cracks demonstrate that their lengths gradually increase as the temperature increases from 25 to 200 . Fig. 8 shows the fracture toughness of poled PZT-NC ceramics in silicon oil at different environmental temperatures. On the one hand, parallel to the poling direction, the fracture toughness dramatically decreases as the temperature increases, and finally the fracture toughness drops to almost the same level as the perpendicular direction when the temperature reaches 200 . On the other hand, perpendicular to the poling direction, the fracture toughness is almost stationary. The shielding toughness (Ksh) due to the ferroelastic switching (Fig. 5(b)) gradually tapers as the temperature increases. Meanwhile, the ferroelastic switching almost disappears until the temperature reaches 200 . The value of Ksh is approximately 0.80 MPa•m1/2 under a silicon oil environmental temperature of 25 . However, the value of Ksh is only approximately 0.26 MPa•m1/2 when the silicon oil environmental temperature increases to 205 . Prior studies reported that both the elastic modulus (Y) and remnant stress (εr) decreased as the temperature increased by the stress-strain curves during loading-unloading measurements at different temperatures [39-41]. Based on Eq. (6), the reduction in Ksh as the temperature increases can be reasonably explained. Perpendicular to the poling direction, because tensile stresses trigger little or no ferroelastic switching, the fracture toughness is mainly affected by environmental temperature corrosion. 4. Conclusions In summary, the fracture properties of Nb/Ce Co-doped Pb (Zr0.52Ti0.48) O3 (ab. PZT-NC) ceramics in different media (air, pure water, and silicone oil) were studied via Vickers indentation and three-point bending. PZT-NC ceramics have the best fracture toughness in silicone oil and the worst in air. The fracture toughness parallel to the poling direction is higher than that perpendicular to the poling direction. According to
10
the Weibull analysis of the flexural strength, PZT-NC ceramics exhibit higher reliability parallel to the poling direction. The fracture toughness of PZT-NC ceramics gradually decreases as the temperature increases. Ferroelastic switching and increased water penetration are considered to play crucial roles in the toughening of materials. Acknowledgments This study was supported by the China Postdoctoral Science Foundation Project (2017M623025).
11
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Figures and tables Fig. 1. (a) Diagrammatic sketch of Vickers indentation. (b) Diagrammatic sketch of three-point bending parallel to the poling direction. (c) Diagrammatic sketch of three-point bending perpendicular to the poling direction. Fig. 2. XRPD results of PZT-NC ceramics after Rietveld refinements. Fig. 3. (a) SEM micrographs of PZT-NC ceramic surface. (b) EDS diagram of PZT-NC ceramic surface. Fig. 4. (a), (b), and (c) Diagram SEM micrographs of the indentation cracks of poled PZT-NC ceramics in air, pure water, and silicon oil, respectively. (e) Fracture toughness of poled PZT-NC ceramics in different media environments. Fig. 5. (a) Diagrammatic sketch of the indentation cracks. (b) Diagrammatic sketch of the mechanism of ferroelastic toughening in poled ferroelectric ceramics. Fig. 6. (a) Probability statistics diagram of the flexural strength in two different directions. (b) Weibull distribution curves diagram of the flexural strength in two different directions. Fig. 7. (a-d) SEM micrographs of the indentation cracks of poled PZT-NC ceramics in silicon oil at different environmental temperatures.
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Fig. 8. Fracture toughness of poled PZT-NC ceramics in silicon oil at different environmental temperatures. Table 1. Crystallographic data of PZT-NC ceramic crystals derived from Rietveld refinement Crystal
Formula
Space
system
a (Å)
α (º)
c (Å)
group
Weight (%)
Tetragonal
PbTi0.48Zr0.52O3
P4mm
4.040748
4.1315103
-
75.02
Trigonal
PbTi0.42Zr0.58O3
R3mR
4.075296
-
89.66839
24.98
Table 2. Atom positions of tetragonal crystals of PZT-NC ceramics Atom
x
y
z
Occupancy
Pb1
0.027885614
0.027885614
0.0011629091
0.25
Zr1
0.5
0.5
0.43704185
0.52
Ti1
0.5
0.5
0.43704185
0.48
O1
0.5
0.5
-0.07332134
1
O2
0.5
0
0.47294596
1
Table 3. Atom positions of trigonal crystals of PZT-NC ceramics Atom
x
y
z
Occupancy
Pb1
0.52628547
0.52628547
0.52628547
1
Zr1
-0.009008482
-0.009008482
-0.009008482
0.58
Ti1
-0.009008482
-0.009008482
-0.009008482
0.42
O1
-0.097509466
0.39049664
-0.097509466
1
Table 4. EDS elemental analysis of PZT-NC ceramic surface Element
Pb
Ti
Zr
O
Total
Weight percentage
53.83
6.43
29.61
10.13
100.00
Atomic percentage
19.22
9.93
24.01
46.84
100.00
Table 5. Weibull statistical data of the fracture toughness of poled PZT-NC ceramics in two different directions Direction
σ /MPa
m
σ0 /MPa
R2
Number
of
measurement samples Parallel direction
49.78
7.9
52.08
0.967
16
Perpendicular direction
44.24
4.8
48.42
0.970
16
Declaration of Interest Statement
Article Title:
Crack Propagation Behavior in Lead Zirconate Titanate Based
Ferroelectric Ceramics Authors:
Jiageng Xu, Shaoxiong Xie, Qian Xu, Qingyuan Wang, Yu Chen
All authors of this manuscript have directly participated in planning, execution, and/or analysis of this study. The contents of this manuscript have not been copyrighted or published previously. The contents of this manuscript are not now under consideration for publication elsewhere. There are no directly related manuscripts or abstracts, published or unpublished, by any authors of this manuscript. No financial support or incentive has been provided for this manuscript. I am sole author of this manuscript. I am one author signing on behalf of all co-authors of this manuscript, and attesting to the above.
Signature: Date: Printed Name: Institution:
December 29, 2019 Jiageng Xu School of Architecture and Civil Engineering, Chengdu University