Bimodal grain structure effect on the static and dynamic mechanical properties of transparent polycrystalline magnesium aluminate (spinel)

Ceramics International 45 (2019) 20362–20367

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Bimodal grain structure effect on the static and dynamic mechanical properties of transparent polycrystalline magnesium aluminate (spinel)

T

Wen Jianga,b, Xingwang Chenga,b,*, Zhiping Xionga,b, Tayyeb Alia,b, Hongnian Caia,b, Jian Zhangc a

School of Materials Science and Engineering, Beijing Institute of Technology, Beijing, 100081, China National Key Laboratory of Science and Technology on Materials under Shock and Impact, Beijing, 100081, China c Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai, 200050, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Spinel Bimodal grain structure Static mechanical property Dynamic mechanical property

Transparent polycrystalline magnesium aluminate (spinel) with bimodal and unimodal grain structures were prepared. The influence of grain size distribution on static and dynamic mechanical properties were systematically investigated. The results showed that bimodal grain structure spinel has larger flexural strength (236.31 MPa) compared to unimodal grain structure spinel (221.38 MPa). Whereas, their values of hardness are very similar (15.1 vs 14.7 GPa) and fracture toughness remains unchanged (1.1 MPa∙m1/2 for both spinel). Although static compression strength of bimodal grain structure spinel (1236 MPa) is higher than that of unimodal one (1078 MPa) due to a smaller average grain size in the former, the negative effect of bimodal grain structure reduced the spinel strength compared to theoretically predicted value. Bimodal grain structure spinel shows slightly lower increment (49%) in compression strength from static to dynamic loading compared to that of unimodal one (57%) due to a decreased strain-rate sensitivity ascribed to bimodal grain structure. A brittle mode in inelastic deformation at Hugoniot elastic limit was demonstrated in both bimodal and unimodal grain structures. Bimodal grain structure has an influence on the Hall-Petch-like relation of yield strength under planar impact loading.

1. Introduction The grain size (D), which significantly affects mechanical properties of ceramics (such as flexural strength and hardness), is a key factor in developing ceramic materials with excellent performance. The normal approach to study the relationship between mechanical properties and grain size is to establish the dependence of mechanical properties such as yield strength and hardness on the square root of average grain size (Da) [1–5]. Determining the Da has been well established in previous literatures. However, the effect of grain size distribution should also be considered. Investigations have suggested that the fracture of Al2O3 with inhomogeneous distribution of grain size is usually initiated from relatively large grains [6], indicating that using the maximum value of grain size (Dm) is more appropriate when fitting the Hall-Petch-like relationship between mechanical properties and grain size [4]. Therefore, it is worth noting that when the ceramic has abnormal large grains, the value of Da deviates greatly from the effective grain size. Transparent polycrystalline magnesium aluminate (spinel) is widely used in many applications, where specific transparency and excellent

mechanical properties are both required. Based on different compositions and fabrication technologies, spinel can have bimodal or unimodal grain structure with an average grain size ranging from ~5 to over 300 μm [7–10]. The difference in size between fine and coarse grains in the bimodal grain structure sometimes varies by orders of magnitude. Similar to most of ceramics, grain size strongly affects the mechanical properties of spinel. Published articles reported that hardness of spinel with grain sizes in micron rang varied from 15 to 17 GPa and the flexural strength varied from 150 to 300 MPa [11–15]. Although the dependence of mechanical properties of spinel on the average grain size has been well studied, the influence of grain size distribution was hardly considered in previous works. Whether there is any difference in mechanical properties between spinel with bimodal and unimodal grain structures remains unclear. In present study, hardness, flexural strength and fracture toughness of bimodal and unimodal grain structures spinel were measured in order to investigate the effect of grain size distribution on static mechanical properties. To clarify the influence of grain size distribution on the strain-rate sensitivity and inelastic deformation, dynamic and quasi-static uniaxial compression, and planar impact tests

* Corresponding author. School of Materials Science and Engineering, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing, 100081, China. E-mail address: [email protected] (X. Cheng).

https://doi.org/10.1016/j.ceramint.2019.07.010 Received 7 May 2019; Received in revised form 27 June 2019; Accepted 1 July 2019 Available online 02 July 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

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were also performed.

⎧ ε˙ (t ) = 2C0/ L⋅εr (t ) τ ⎪ ε (t) = 2C0/ L⋅ ∫ εr dt ⎨ 0 ⎪ ⎩ σ (t) = E0 A/ As ⋅εt (t )

2. Experimental procedures 2.1. Materials The raw materials in powder were high-purity γ-Al2O3 (99.99%; 50 nm; Dalian Hiland Pothoelectric Material Co., Ltd) and MgO (99.99%; 150 nm; Konoshima Chemical Co., Ltd). The spinel compositions (MgO·nAl2O3) are stoichiometric (n=1) and alumina-rich (n=1.5) for the first group (A) and second group (B), respectively. Firstly, MgO and γ- Al2O3 powders were mixed with ethanol for 12 h using ball milling. Secondly, the mixtures were thoroughly dried at 60 °C in a drying oven and calcined at 800 °C for 6 h to remove residual ethanol. Thirdly, the dried mixtures were uniaxially compressed into pellets at a pressure of 20 MPa followed by cold isostatic pressing at 200 MPa in order to obtain green bodies. Following this, the green bodies were presintered at 1550 °C for 3 h using a chamber furnace (HTL 16/17, ThermConcept, Germany) in an atmospheric condition. Then, group A and B samples were hot isostatic pressed (HIP) under a pressure of 200 MPa at 1700 and 1550 °C for 3 h, respectively using a hot isostatic pressure sintering furnace (QIH6, ASEA Company, Switzerland) with argon atmosphere. Finally, both group samples were annealed at 1200 °C for 6 h in atmospheric condition using the chamber furnace.

2.2. Materials characterization A field emission-scanning electron microscope (FE-SEM) equipping with an electron backscattering diffraction (EBSD) detector (FEI Quanta 450F, FEI Company, America) was used to characterize the microstructure. Well-polished samples were examined at a working distance of 15 mm and an acceleration voltage of 30 kV. For EBSD canning, the step size was selected from 0.5 to 1 μm depending on the minimum grain size in scanned samples. The post-processing was performed using the TSLOIM software. Ultrasonic experiments at ambient conditions were carried out in order to determine Possion ratio (ν), and longitudinal (Cl) and shear wave velocities (Cτ). The sample density (ρ) was measured via Archimedean method.

2.3. Mechanical testing A Vickers hardness tester (LMV-50 V, Leco, America) was used to determine hardness values using a load of 1 kg for 15 s following ASTM Standard C-1327-15 [16]. The hardness value for each group was averaged from at least 15 indentations. An electromechanical testing machine (Instron 5582) was employed to measure flexural strength using a 3-point bending test following ASTM Standard C-1161-13 [17]. The same machine was also used to measure the fracture toughness by single edge notch bending method (KSENB) following ASTM Standard C1421 [18]. For 3-point bending and single edge notch bending tests, at least 10 measurements were performed for each group of samples. Uniaxial compression tests at quasi-static conditions were carried out using the electromechanical testing machine at a crosshead speed ranging from 0.03 to 0.3 mm min−1. Whereas, dynamic uniaxial compression was tested using well-established split-Hopkinson pressure bar (SHPB) technique. Since a dramatically increased load may cause the premature damage of brittle materials, a copper cushion (φ 8 × 1.2 mm2) was placed at the face of incident bar in order to change the incident wave from square shape to triangle shape [19]. Based on the recorded time-strain data, the stress (σ), strain (ε) and strain rate (ε˙ ) can be determined using following equations [20]:

(1)

where A and L are the sectional area and length of incident bar, respectively; E0 is the Young's modules and C0 is the elastic wave propagation speed of incident bar; εr and εt are the reflected and transmitted signals, respectively; likewise, As and t represent sectional area of sample and time, respectively. Samples for uniaxial compression tests were cut into cylinders of φ 5 × 5 mm2. To prevent the ceramic sample from penetrating into the load cell, a pair of tungsten carbide (WC) disks was used to transmit the forces from the ceramic sample. For minimization of the friction, the end faces of each sample were polished down to 0.25 μm and all the surfaces (disks and samples) were greased. The planar impact tests were performed using a single stage light gas gun with a 57-mm diameter 4-m length. The samples were impactloaded by a tungsten flyer with 1 mm thickness. Since the spinel with an average grain size of 0.14 μm has a Hugoniot elastic limit (HEL) of ~18 GPa [3], a compression stress of ~20 GPa was chosen to guarantee that the tested samples were loaded up to the stress exceeding their HEL. The impact velocity was recorded using electrically charged pins (velocity pin) located before the target. The velocity interferometer system for any reflector (VISAR), placed on the rear surface of target, was used to record the free surface velocity when the compression wave reaches the rear surface. The samples used in planar impact tests were cut into disk-shape of φ 30 × 6 mm2. 3. Results and discussion 3.1. Microstructure and static mechanical properties Spinel of group A has a bimodal grain structure as shown by the FESEM image (Fig. 1(a)) and EBSD inverse pole figure (IPF) map (Fig. 1(b)). The group A consisted of fine (< 5 μm) and coarse (> 20 μm) grains with an average grain size of 9.5 μm. In contrast, the grains of group B are equiaxed as represented in FE-SEM image (Fig. 1(c)) and IPF map (Fig. 1(d)), exhibiting a homogeneous microstructure with an average grain size of 18.2 μm. Fig. 2(a) and (b) show the grain size distribution of group A and B, respectively. Similar to the results displayed in Fig. 1, fine and coarse grains both have noticeable area fractions in group A, while the grains area fraction in group B is almost equal. The hardness, flexural strength and fracture toughness of group A and B are listed in Table 1. It shows flexural strength of group A is higher than that of group B. This result corresponds to the Hall-Petch type relation and similar results have been reported previously [3,5,15]. As for hardness, however, the values of group A and B are very similar. What should be noted is that the hardness of group A has a higher standard deviation (Std) value, which is caused by the bimodal grain structure. Indents in the fine-grained regions displayed a high hardness (average value is 17.3 GPa) while a low hardness (average value is 13.6 GPa) belongs to the indents located in coarse-grained regions. The fracture toughness of group A and B remains unchanged, while Tokariev et al. [15] reported that the fracture toughness of spinel was decreased from 1.8 to 1.0 MPa∙m1/2 when the average grain size increased from 5 to 60 μm. 3.2. Static and dynamic uniaxial compression The experimental dynamic compression strengths are plotted as a function of strain rate in Fig. 3(a). Quasi-static compression strengths conducted at strain rates ranging from 10−4 to 10−3 s−1, are also included in Fig. 3(a). It shows that at quasi-static condition, the average compression strength of group A (1263 MPa) is larger than that of

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Fig. 1. (a, c) FE-SEM micrographs and (b, d) inverse pole figure maps for (a, b) group A and (c, d) group B, showing (a, b) bimodal and (c, d) unimodal grain structures, respectively.

group B (1078 MPa). To identify the influence of grain size distribution on the uniaxial compression strength, the theoretical mode focusing on the “sliding crack”, which can relate the parameter “grain size” to “compression strength” [1], was used in this work. As it is well known that under nonhydrostatic compression loading, a “wing crack”, produced by the slip along the “main crack” of 2c length, would nucleate and develop once the shear stress along the main crack exceeds the frictional resistance of the material. The stress intensity factor at the wing crack tip decreases as the crack grows, which stabilizes propagation behavior of wing cracks [21]. Ashby and Hallam [22] found that the stress intensity factor was contributed by the crack interaction and provided the relationship between the mode I stress intensity factor KI at the tip of a wing crack and the wing crack length l:

KI 1

= [2ε0 (L + α )/ π ]1/2 ⋅{[1 − 8ε0 λ (L + α )3][1 − 2ε0 λ (L + α )3]}1/2

σ1 (πc ) 2 (2) where L=l/c, α=2

−1/2

, σ1 is the maximum compression stress,

Table 1 Hardness, flexural strength and fracture toughness of the tested samples. Sample group

A B

Hardness GPa

Flexural strength MPa

Fracture toughness MPa·m1/2

Average

Std

Average

Std

Average

Std

15.1 14.7

0.66 0.12

236.31 221.38

20.96 15.14

1.1 1.1

0.2 0.2

ε0 = c 2NA , and NA is the number of sliding cracks per unit area. Cracks propagation occurs when KI equals the mode I fracture toughness KIC. For this work, the crack length ‘2c’ is probably the most critical parameter, however, it is notoriously difficult to be measured [23]. Fortunately, microcracks in ceramics are generally attributed to the internal stresses induced during sintering process, elastic moduli anisotropy and mismatch. Theoretical analysis and microscopy of some ceramics such as B4C and Al2O3 have suggested that the length of such cracks is within grain size scale, so assuming 2c=D is reasonable for

Fig. 2. Grain size distribution of (a) group A and (b) group B, indicating inhomogeneous and homogeneous distributions of grain size, respectively. 20364

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Fig. 3. (a) Variation of uniaxial compression strengths with strain rate in group A and B,and (b) theoretical prediction compression strength as a function of grain size.

calculation [4]. Determination of the crack density ε0 is also subject to the difficulties noted above, since ε0 = c 2NA and NA is the number of sliding cracks per unit area. However, transparent ceramics with high light transmittance usually have high densification (> 99%), thus, often have few internal defects. Paliwal and Ramesh [24] suggested that transparent polycrystalline AlON has critical crack density not more than 12% before devastating failure occurs. Therefore, we believe ε0 = 0.03 (corresponds roughly to 10% sliding cracks per grain area) is a reasonable estimation (assuming circular grains). The value of KIC used in calculation is 1.1 MPa∙m1/2. The predicted compression strength is plotted as a function of grain size in Fig. 3(b). The experimentally determined average static compression strengths of group A and B are also added in Fig. 3(b). It shows that the predicted compression strength decreases with an increase of grain size. This is consistent with the experimental results of spinel reported by Kimberley and Ramesh [25], as well as corresponds to the theoretical calculation and experimental measurement results of some brittle rocks reported by Fredrich et al. [1]. Furthermore, the data point of experimental compression strength of group A locates below the model predicted curve, while the data point of group B almost locates on the predicted curve. It means the coarse grain in bimodal grain structure has a negative effect on the failure strength, and results in a lower compression strength compared to that of spinel with equivalent average grain size but unimodal grain structure. At strain rates above 102 s−1, there is a noticeable increase in compression strength for both group A and B as shown in Fig. 3(a). Such strain-rate strengthening behavior has been reported on fine- (average grain sizes are 0.4 and 1.4 μm) [25] and coarse-grained spinel (average grain sizes are 200–250 μm) [26]. In addition, group A did not show an obvious advantage in dynamic compression strength compared to that of group B. Group A and B have the average dynamic compression strength of 2459 and 2512 MPa (49% and 57% increase compared to static compression strengths), respectively. The slightly higher compression strength increment of group B under dynamic loading indicates that spinel with homogeneous microstructure is more strain-rate sensitive. Paliwal and Ramesh [27] have suggested that the higher crack propagation rates at peak stress would cause the stronger strainrate sensitivity of brittle materials, i.e., the larger increment of dynamic compression strength compared to static compression strength. Furthermore, the post-mortem FE-SEM image of fragments of group A (Fig. 4(a)) recovered after SHPB tests shows a large amount of intergranular fracture in fine-grained region (as indicated by red dotted circles), while the coarse grains displayed transgranular fracture along with the interlaced characteristic of these transgranular cracks (as indicated by white solid circles). The fragment morphology of group B demonstrated almost full transgranular fracture as showed in Fig. 4(b). Many cleavage steps across grains (as indicated by red arrows in Fig. 4(b)) indicate the propagation of cracks has less deflection and

interaction. These observations indicated that the fine-grained region in bimodal grain structure, creates more tortuous crack propagation paths. So being longer length of crack propagation, it required more time when the crack density reached the critical failure value. In other word, in group A, the crack propagation speed within a sample scale is reduced because of the bimodal grain structure, which also might be the reason for weaker strain-rate sensitivity. Therefore, group A did not show any advantage on dynamic compression strength, even with smaller average grain size, which should have a higher strength compared to group B. 3.3. Planar impact tests Typical velocity histories of group A and B after planar impact tests are presented in Fig. 5. It is observed that the waveforms are characterized by the existence of an elastic precursor with uHEL amplitude followed by an inelastic ramp. According to the velocity histories data, the HEL stress σHEL can be determined as [28]:

σHEL =

1 ρCl uHEL 2

(3)

where, the density ρ and longitudinal wave velocity Cl of group A were measured to be 3.573 g cm−3 and 9962 m s−1, respectively. For group B, the ρ and Cl were determined to be 3.575 g cm−3 and 9959 m s−1, respectively. The calculated values of σHEL are showed in Table 2. Through calculating the yield stress Y, the dynamic strength of material under 1- D strain loading condition can be compared with its static strength obtained under 1-D stress loading condition. Depending on the transition mode (brittle or ductile) of elastic to inelastic deformation at the HEL of material, value of Y can be estimated by different equation. The yield stress Yduct of material which yields in a ductile mode can be determine by the following expression:

Yduct =

1 − 2ν σHEL 1−ν

(4)

the expression to estimate the yield stress Ybrit of material yielding in a brittle mode is given by:

Ybrit =

(1 − 2ν )2 σHEL 1−ν

(5)

where ν is the Poisson's ratio [29]. The values of ν were measured to be 0.269 and 0.271 for group A and B, respectively. The calculated values of Yduct and Ybrit based on the σHEL are given in Table 2. It is obvious that the values of Yduct are larger than Ybrit. By comparing the Yduct and Ybrit with the static yield strength Ystatic (roughly equal to one third of the static Vickers hardness value, i.e., Ystatic ≈ HV /3) [30], it could be clarified whether Yduct or Ybrit is more appropriate to use in constitutive models. Therefore, the values of HV/3 are included together with the Yduct and Ybrit in Fig. 6. The abscissa was set as the inverse square root of

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Fig. 4. Fragments morphology of (a) group A and (b) B recovered after SHPB tests, showing transgranular and intergranular fracture.

Fig. 5. Representative velocity histories of group A and B during planar impact tests. Table 2 σHEL, Yduct and Ybrit of the tested samples. Sample group

σHEL GPa

Yduct GPa

Ybrit GPa

A

14.73 13.56 14.42

9.31 8.57 9.11

4.30 3.96 4.21

B

14.25 13.62 13.94

8.95 8.56 8.76

4.10 3.92 4.01

average grain size, Da−1/2, to facilitate the investigation of the HallPetch-like correlations. As it is observed from Fig. 6, Ybrit are closer to 1 the 3 HV than Yduct. It means the yielding mode of spinel from elastic to inelastic deformation at the HEL was brittle, and thus, the Ybrit values were used in following analysis to investigate relationship between grain size and dynamic yield strength. It is well known that for ceramics, plastic deformation and multiple wing cracks development occur inevitably during compressive failure process under planar impact loading [31,32]. The inelastic deformation is contributed mainly by shear stress, which could be calculated by a Hall-Petch-like relation τbrit = τ0 + k y0 D , where k y0 is the Hall-Petch constant for shear stress and τbrit = Ybrit /2 [3]. Based on these relations, the fitting line of Ybrit (plotted in Fig. 6) in present work can be expressed by the equation of Ybrit = 3.83 + 0.73D−1/2 , where the second term factors k y = 2k y0 . The yield strengths (Ybrit(Lit)) of spinel with homogeneous grain size distribution (average grain sizes are 0.98–25 μm) reported by Sokol et al. [3], as well as the fitting line of

Fig. 6. Ybrit and one third of static Vickers hardness together with the Ybrit obtained from spinel with a unimodal grain structure reported in Ref. [3] as a function of inverse square root of grain size.

Ybrit(Lit) with an expression of Ybrit (Lit ) = 3.67 + 1.25D−1/2 , are also plotted in Fig. 6. It shows that the fitting line of Ybrit(Lit) diverges from that of Ybrit. Hall-Petch constant of Ybrit (0.365) in this work decreased by approximately 2-fold compared to that of Ybrit(Lit) (0.625). This means the bimodal grain structure of group A changed the Hall-Petchlike relationship of yielded strength in this work. It has been verified that the reduction of shear bands or twinning can decrease the HallPetch constant [3]. Furthermore, the possibility of twinning is more in coarse grains as compared to fine grains [33]. Therefore, group A may produce less twinning because of its large area of fine grains compared to the spinel of equal average grain size but homogeneous microstructure (like that reported in Ref. [3]). That's why the Hall-Petch constant obtained in present work is smaller than that obtained from spinel with homogeneous microstructure. In addition, it is suggested that the temperature at which deformation twins appear, decreases with the increase of strain rate for vanadium [34,35], i.e., material favors twinning under dynamic loading. This may explain why the 1 fitting line of 3 HV has a lower slope (0.56) than that of Ybrit. Although neither twinning nor shear bands can be supported by post-mortem microscopic examination because of the difficult collection of the extremely fine, dust-like fragments after each impact test, the shear bands and twinning have been observed in Al2O3 fragments recovered from planar impact tests [31,32].

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4. Conclusions For spinel having bimodal and unimodal grain structures, static and dynamic mechanical properties including Vickers hardness, flexural strength, fracture toughness, uniaxial compression strength and Hugoniot elastic limit were determined and analyzed. (1) The spinel with a bimodal grain structure has a smaller average grain size of 9.5 μm than 18.2 μm of unimodal grain structure spinel. Flexural strength in the former (236.31 MPa) is larger than that in the latter (221.38 MPa) due to a smaller average grain size. Whereas, the values of static Vickers hardness for bimodal and unimodal grain structures spinel are very similar (15.1 vs 14.7 GPa). Furthermore, their fracture toughness remains unchanged (1.1 MPa∙m1/2 for both spinel). (2) Bimodal grain structure significantly affected the failure behavior of spinel in terms of static and dynamic uniaxial compressions. Although the smaller average grain size of bimodal grain structure spinel leads to a higher static compression strength (1236 MPa) compared to unimodal spinel (1078 MPa), the negative effect of bimodal grain structure led to a lower strength compared to the theoretical value. Fine-grained region in bimodal grain structure reduced the crack propagation speed, resulting a weaker strain-rate sensitivity. Thus, bimodal grain structure spinel shows slightly lower increment (49%) in compression strength from static to dynamic loading compared to that of unimodal one (57%). (3) Yield strength of spinel (3.96–4.30 GPa and 3.92–4.10 GPa Ybrit for bimodal and unimodal grain structures) was calculated using Hugoniot elastic limit (13.56–14.72 GPa and 13.62–14.25 GPa for bimodal and unimodal grain structures). A brittle mode for inelastic deformation in spinel samples is determined by the comparison of yield strength with one third of the Vickers hardness. The dependence of Ybrit on D−1/2 in this work is different from that obtained from unimodal grain structure due to small grains in bimodal grain structure. Acknowledgments The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51271036). References [1] J.T. Fredrich, B. Evans, T.-F. Wong, Effect of grain size on brittle and semibrittle strength: implications for micromechanical modelling of failure in compression, J. Geophys. Res. 95 (1990) 10907–10920. [2] T. Koyama, A. Nishiyama, K. Niihara, Effect of grain morphology and grain size on the mechanical properties of Al2O3 ceramics, J. Mater. Sci. 29 (1994) 3949–3954. [3] M. Sokol, S. Kalabukhov, R. Shneck, E. Zaretsky, N. Frage, Effect of grain size on the static and dynamic mechanical properties of magnesium aluminate spinel (MgAl2O4), J. Eur. Ceram. Soc. 37 (2017) 3417–3424. [4] R.W. Rice, Ceramic tensile strength-grain size relations: grain sizes, slopes, and branch intersections, J. Mater. Sci. 32 (1997) 1673–1692. [5] A. Rothman, S. Kalabukhov, N. Sverdlov, M.P. Dariel, N. Frage, The effect of grain size on the mechanical and optical properties of spark plasma sintering-processed magnesium aluminate spinel MgAl2O4, Int. J. Appl. Ceram. Technol. 11 (2014) 146–153. [6] R.E. Tressler, R.A. Langensiepen, R.C. Bradt, Surface-finish effects on strength-vsgrain-size relations in polycrystalline Al2O3, J. Am. Ceram. Soc. 57 (1974) 226–227.

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