titanium carbide sol-gel coated zirconium diboride composites prepared by spark plasma sintering

titanium carbide sol-gel coated zirconium diboride composites prepared by spark plasma sintering

Author’s Accepted Manuscript Carbon Nanotube/Titanium Carbide Sol-gel Coated Zirconium Diboride Composites Prepared by Spark Plasma Sintering Yang Mia...

1MB Sizes 0 Downloads 35 Views

Author’s Accepted Manuscript Carbon Nanotube/Titanium Carbide Sol-gel Coated Zirconium Diboride Composites Prepared by Spark Plasma Sintering Yang Miao, Xiaojing Wang, Yi-Bing Cheng www.elsevier.com/locate/ceri

PII: DOI: Reference:

S0272-8842(18)31878-9 https://doi.org/10.1016/j.ceramint.2018.07.151 CERI18873

To appear in: Ceramics International Received date: 24 May 2018 Revised date: 29 June 2018 Accepted date: 17 July 2018 Cite this article as: Yang Miao, Xiaojing Wang and Yi-Bing Cheng, Carbon Nanotube/Titanium Carbide Sol-gel Coated Zirconium Diboride Composites Prepared by Spark Plasma Sintering, Ceramics International, https://doi.org/10.1016/j.ceramint.2018.07.151 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. 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.

Carbon Nanotube/Titanium Carbide Sol-gel Coated Zirconium Diboride Composites Prepared by Spark Plasma Sintering Yang Miaoa*, Xiaojing Wangb, Yi-Bing Chengb, c* a

College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan, 030024, China b

c

Department of Materials Science and Engineering, Monash University, Melbourne, 3800, Australia

Department of Materials Science and Engineering, Wuhan University of Technology, Wuhan, 430070, China

Abstract With combination of a powder processing technique and a sol-gel process, carbon nanotube/titanium carbide coated zirconium diboride matrix composite was fabricated. Zirconium diboride (ZrB2) powders were coated with a functionalized carbon nanotubes (CNTs) mixed titanium carbide (TiC) sol-gel precursor. As the results suggests, the carbothermal reduction produced nanosized TiC grains at the surface of the ZrB2 particles with a homogenous distribution of CNTs. The densification of the CNT/TiC coated ZrB2 matrix composite was achieved via 1900 °C spark plasma sintering(SPS). The TiC grains and the CNTs were primarily concentrated in the grain boundaries of the ZrB2 and showed the pinning effects that restrained the growth of ZrB2 grain. The TiC grain diffusion in the sintering coarsened the grains from nanosizes to 1-2 μm, which improved the densification of the ZrB2. Due to the difference in coefficient of thermal expansion, CNTs bridged the gaps between the TiC and the ZrB2 matrix, which formed a weak-bonding interface. The major toughening mechanism found was crack deflection via the TiC grains on the ZrB2 matrix. Keywords: Carbon nanotube, Sol-gel, SPS, Titanium carbide, ZrB2

1. Introduction Zirconium diboride (ZrB2) is one of the most commonly used ultra-high temperature ceramics (UHTCs). By virtue of its melting point of 3040 °C and high mechanical strength, ZrB2 is an alternative for aerospace and military applications including the leading edges of hypersonic aerospace vehicles [1] [2]. The material seems to show the superior oxidation resistance and thermal and electrical conductivity than typical carbides. Yet densification is the largest challenge in the processing of ZrB2, as it requires a high melting temperature and covalent bonding. A dense ZrB2 could require a sintering temperature reaching 2000-2200 °C[3] [4]. Additives were used to improve the densification of ZrB2. Various metallic additives including Ir, W, Mo, and Nb served as additives to improve the densification of ZrB2[5] [6] [7]. The residual secondary phases reduce the high temperature performance of ZrB2. Other attempts involved the addition of nonmetallic refractory materials, such as carbides and nitrides[8]. These composites were generally prepared by mixing powder. The homogenous distribution of the second phase in ZrB2 matrix, particularly on the grain boundaries, is still challenging. Due to the agglomeration, the conventional powder mixing method used to fabricate composites is limited in achieving uniform distribution of fibers, whiskers, nanoparticles, and CNTs [9] [10]. The sol-gel process is characterized by the homogeneity on the molecular scale and good coating ability by virtue of its liquid characteristics. The Sol-gel technique can effectively yield a homogeneous and well-distributed dispersion of CNTs through a ceramic matrix[11] [12] [13]. This work used a CNTs mixed sol-gel coating for the ZrB2 powders. This method not only introduced the second phase in the ZrB2 matrix, but also improved the homogenous distribution

of the CNTs in the composites. Sol-gel coating on particles was applied to the oxide and metal processing mixtures before sintering[14] [15]. The ZrC-ZrB2 composite has been produced using this method, which shows that nanosized ZrC particles could be produced in-situ with homogenous distribution throughout the ZrB2 powder. CNTs have served as the reinforcements in ceramic composites for many years, and the different ceramic matrixes show a remarkable increase in fracture toughness [16] [17] [18]. The following employed titanium-oxygen-carbon (Ti-O-C) sol-gel precursor mixed with CNTs to coat the ZrB2 powders. The fabricated TiC phase via the sol-gel process acted as the second phase in the composites[19] [20] [21]. The sol-gel process was used to produce TiC ceramic, and the fabricated TiC shows small grain size. The ZrC-ZrB2 and SiC-ZrB2 composites have been investigated, yet the study on the TiC-ZrB2 composites is still limited. The effect of carbon and TiC on the sintering behavior of ZrB2 has been studied, whereas the powder mixing was applied in the previous study. The sol-gel process was used to disperse CNT though it seems that no research has been reported on the use of the sol-gel coating to distribute CNTs in UHTC composites. This sol-gel coating technique is simple but unique. This paper describes the synthesis procedure and microstructure of the composites. The effect of the introduced second phase and the CNTs on the densification, microstructures and crack propagation of the composites was investigated.

2. Experimental Procedure 2.1 Chemicals and synthesis The procedure for the fabrication of the CNT/TiC coated ZrB2 composite is illustrated in Fig. 1. The Ti-O-C precursor was first fabricated by mixing poly(ethylene oxide)-bpoly(propylene oxide)-b-poly(ethylene oxide) copolymer Pluronic P123 (EO20PO70EO20, Mn ~ 5800; Sigma-Adrich), absolute ethanol (C2H5OH, 99.7%), titanium tetraisopropoxide (TTIP, Ti(OCH(CH3)2)4, 97%; Sigma-Adrich), hydrochloric acid (HCl, 10M), and furfuryl alcohol (FA, C5H6O2, 98%; Sigma-Adrich), which acted as a surfactant, a solvent, a titania source, a catalyst and a carbon source, respectively. The molar ratio of the P123/TTIP/HCl reached 1/50/20. The amount of FA added was established to yield a designed C/Ti molar ratio of 3.8. Based on the experiments, this could provide enough carbon for a fully carbothermal reduction with little residual carbon remaining. Continuous stirring was required in the whole process. After the sol-gel precursor had been prepared, 5 wt% CNTs were added directly for mixing. The multi-walled carbon nanotubes (Skyspring Nanomaterials, USA) that were manufactured by catalytic CVD had the diameter of 30-50 nm and the length of 5-20 μm. The CNTs were prewashed by mixed H2SO4 and HNO3 (H2SO4/HNO3 = 3/1 in volume). The mixed solution was then aged at ambient temperature for 3 days (around 25 °C) under stirring. The ZrB2 powders were weighted and pulled into the solution, and they were stirred continuously to produce a slurry. After the mixing, the slurry was pulled into a wide-open glass bowl and placed in the hot plate stirrer. The slurry was stirred and heated to 80 °C in the bowl to improve the evaporation of the solvent until the slurry dried. The molar ratios of the Ti/Zr varied from 0.1, 0.15, and 0.2.

The dried gel was heated for 5 h under nitrogen to 550 °C at 5 °C/min. The samples were then heated for an another 5 h to 1450 °C at 2 °C/min for carbothermal reduction. After the heat treatments, samples were ground to produce uniform powder particles. The CNT/TiC coated ZrB2 samples were sintered with SPS to 1900 °C at a maximum heating rate of 100 °C/min. A 5 min holding time and a uniaxial pressure of 40 MPa were applied under vacuum. The sintered samples were ground and polished for further characterizations. 2.2 Characterization The X-ray diffraction (XRD) analyses of phases present in the powders and composites were conducted using a X-ray diffractometer using CuKα radiation operate at 40 kV and 25 mA. The XRD patterns were recorded from 10° to 80° of the 2θ values, using a step size of 0.02° and a scan rate of 2°/min. The density and apparent porosity of the sintered samples was measured using the liquid displacement method. The hardness and fracture toughness of the sintered samples was calculated based on the measuring the indentation and generated crack length. The Vickers indentation test was carried out under a load of 20 kgf. An FEI Nova NanoSEM was used for microstructure characterization. The surface of the cross section was polished before SEM. Back scatted electron (BSE) images were taken for polished cross section in order to get better contrast between the matrix and second phase. Energy-dispersive X-ray spectroscopy (EDX) equipped on SEM was employed for elemental analysis to confirm the phase distribution in the microstructure.

3. Results and Discussion 3.1 Compositions and Microstructures of CNT/TiC Coated ZrB2 Composites

3.1.1 Microstructures of CNT/TiC Coated ZrB2 Powders

The XRD analyses of the samples under various firing stages suggested that the ZrB2 peaks were the major phase in the patterns (Fig. 2). After firing at 550 °C, only the peaks of ZrB2 were identified. Both anatase crystalline and amorphous carbon theoretically presented in the sol-gel precursor after the carbonization at 550 °C. Yet the low intensity of the anatase, resulted in the absence of the anatase phase in the XRD pattern as compared with the high intensity of the ZrB2. Some TiC peaks were identified following carbothermal reduction, yet the intensity was low in comparison with that of the ZrB2 peaks, which is attributed to the limited amount of the sol-gel coatings compared with the matrix. Some oxides (i.e. ZrO2) could have presented due to impurity content of the raw ZrB2 powders, yet the amount of oxides could be beyond the detection limits of the diffractometer applied. The microstructures of the ZrB2 powders following coating are shown in Fig. 3. The starting ZrB2 powders had an irregular shape with particles sizes around 5 μm (Fig. 3 (a)). After the carbonization at 550 °C, the ZrB2 particles showed a uniform coating of fine TiO2 grains and CNTs (Fig. 3 (b)). After the additional firing at 1450ºC, nano-sized TiC particles and CNTs were homogenously distributed at the surface of the ZrB2 particles (Fig. 3 (c)). Under high magnification, it was observed that the TiC particles had grown on the ZrB2 particles and had not only been adhered to the ZrB2 particles surface (Fig. 3 (d)).

3.1.2 Microstructures of CNT/TiC/ZrB2 Composites

The phases identified using SPS at 1900 °C were the same as using the carbothermal reduction. Both the ZrB2 and TiC phases were identified (Fig. 2). After the coated ZrB2 powders were sintered, a dense composite was formed. The composite had an interesting microstructure of fine TiC grains (i.e. the small dark particles due to low atomic number) that were primarily located at the grain boundaries though some were intragranular ZrB2 grains (i.e., the grey matrix due to high atomic number) (Fig. 4 (a)). The elements were confirmed under EDX spectra (Fig. 4 (d)), in which Ti was detected only on the small dark particles, and Zr was the major phase detected in the matrix. The grain size of the TiC was nearly 1-2 μm. Such composite was a substantial combination of TiC from nano size to micro size in comparison with the powders before SPS. There was not much grain growth of ZrB2 using SPS. The size of ZrB2 grain was similar to that of the starting powders, which suggested that the intergranular TiC grains could have had some pinning effect on restraining the grain growth of the ZrB2 in the sintering at high temperature. This effect was previously observed in ZrC modified ZrB2 composites[18]. Some gaps lied between the TiC particles and the ZrB2 matrix, up to a few nanometers in size (Fig. 4 (b) and (c)). These gaps could be largely attributed to the differences in the coefficient of thermal expansion (CTE) between the two phases (7.4 × 10-6 K-1 for TiC[29] and 5.9 × 10-6 K-1 for ZrB2), which also suggested a weak-bonding interface between the second phase and the matrix. Thus, these gaps could benefit the mechanical properties by crack absorption and deflection. Some CNTs were observed bridging the gap between the TiC particles and the ZrB2 matrix (Fig. 4 (c)).

The polished surface of the SPS sintered samples of the as-received ZrB2 powders and the sol-gel fabricated CNT/TiC coated ZrB2 composites is shown in in Fig. 5. Samples following the coating tended to have a denser microstructure with less pores in comparison with the asreceived ZrB2 following SPS at the same temperature. The ZrB2 grain size was smaller for the coated samples, which demonstrated the pinning effect of the TiC had on the grain boundaries of the ZrB2. Additional TiC phases (dark phases) had increased Ti/Zr ratios. The increase in concentration of TiC increased the porosity as well. More pores were observed in the samples with higher Ti/Zr ratios. The presence of a second phase (i.e. TiC) assisted the densification of the ZrB2. The coalescence of the TiC from nano size to micro size in the sintering caused the diffusion of the TiC grains at the surfaces of the ZrB2 particles. The diffusion also improved the densification (Fig. 6). Due to the high surface energy of the TiC nano particles, the intimate coating of the TiC nano particles on the surface of ZrB2 ensured that the solid-state diffusion occurred at the interface. This phenomenon was also found in the ZrC modified ZrB2 system. The increased porosity of the samples with higher TiC concentration could be a result of the large differences in the CTE between the two phases, which yielded additional pores in the cooling from high temperatures. This was also attributed to the increased amount of CNTs on the grain boundaries with higher TiC concentration, which restricted the movements of grains in the densification. 3.2 Mechanical Properties of CNT/TiC/ZrB2 Composites

3.2.1 Mechanical Properties

The density and the porosity of the sintered samples are shown in Fig. 7. The results agreed well with the SEM images, which proved that the porosity first decreased with the

increased TiC amount, and then increased with the higher TiC concentration. The density of the samples had the opposite trend to the porosity. Due to the high porosity, the sintered ZrB2 sample showed a lower density in comparison with the theoretical values. Because TiC had a lower density than the ZrB2, sample with the higher Ti/Zr ratio was lower in density. The variations of the hardness and fracture toughness of the samples are shown in Fig. 8. The fracture toughness increased with the Ti/Zr ratios, which suggested that the presence of the second phase enhanced the ZrB2 matrix. The enhancing effect improved with the increase of the amount of second phase. The high porosity was attributed to the high Ti/Zr ratio, which had some energy absorption effects. The hardness of the samples increased with the Ti/Zr ratio, as the TiC had a higher hardness than the ZrB2. The influence that the high porosity of sample with high TiC contents had made the hardness slightly and slowly increase for samples with high Ti/Zr ratios. The sample with a Ti/Zr ratio of 0.1 showed a dense microstructure with little porosity, high hardness, and high fracture toughness in comparison with the other compositions.

3.2.2 Toughening Mechanisms

The fracture behavior and the toughening mechanisms were studied under SEM. The samples showed mostly transgranular fractures mixed with some intergranular fractures as shown in Fig. 9. The TiC particles were observed on the grain boundaries of the ZrB2. The fracture surface of the sample showed some peel-off of the TiC particles, which further showed the weak-bonding interfaces between the TiC and the ZrB2 matrix. Because new surfaces were easy to form from the debonding, the weak-bonding interface benefitted the mechanical properties of the sample, which consumed energy from the cracks. The fracture mode had no change as compared with the pure ZrB2 sample. Most cracks propagated transgranularly with

some intergranular propagation. Some cracks were deflected by the TiC phases. The primary toughing mechanisms in the composites were possibly attributed to the crack deflection of the second phase and the energy consumption by the debonding between the second phase and the matrix. 4. Conclusions The CNT mixed sol-gel was used to coat the ZrB2 powders and form composites. As the results suggested, this novel method could fabricate dense composites with an interesting microstructure. The nano-sized TiC grains were formed at the surface of the ZrB2 particles with some CNTs distributed. Using SPS, the 1-2 μm TiC grains were primarily located at the grain boundaries of the ZrB2. The coalescence of the TiC before and after SPS was caused by the diffusion of the TiC grains in the course of SPS, which improved the densification of the ZrB2. The TiC grains located at the grain boundaries of the ZrB2 had the pinning effect on restraining the grain growth of the ZrB2. Due to the difference in coefficients of thermal expansion, CNTs bridged the gaps between the TiC and the ZrB2 matrix, which formed weak-bonding interface. The sample with a Ti/Zr ratio of 0.1 showed a dense microstructure with low porosity, high hardness and high fracture toughness. The toughening mechanisms consisted of the crack deflection via the TiC particles in the ZrB2 matrix and the energy consumption, through the debonding between the second phase and the matrix. Acknowledgments Yang Miao would like to acknowledge the scholarship from the CSC (China scholarship Council). The authors give thanks to the National Natural Science Foundation of China for support (NSFC, Grant no. 51775366).

Reference [1] J. Echeberria, N. Rodríguez, J. Vleugels, K. Vanmeensel, A. Reyes-Rojas, A. Garcia-Reyes, C. Domínguez-Rios, A. Aguilar-Elguézabal, M.H. Bocanegra-Bernal, Hard and tough carbon nanotube-reinforced zirconia-toughened alumina composites prepared by spark plasma sintering, Carbon, 50 (2012) 706-717. [2] X. Chen, S. Dong, Y. Kan, H. Zhou, J. Hu, D. Wang, 3D C f /SiC-ZrC-ZrB2 composites fabricated via sol-gel process combined with reactive melt infiltration, Journal of the European Ceramic Society, 36 (2016) 3607-3613. [3] X. Lv, S. Yu, M. Ge, Y. Tian, W. Zhang, Synthesis and microstructure of continuous composite ceramic fibres of ZrC/ZrB2 –SiC derived from polymeric precursors, Ceramics International, 42 (2016) 9299-9303. [4] C. Liu, L. Cao, J. Chen, L. Xue, X. Tang, Q. Huang, Microstructure and ablation behavior of SiC coated C/C–SiC–ZrC composites prepared by a hybrid infiltration process, Carbon, 65 (2013) 196-205. [5] C. Li, K. Li, H. Ouyang, J. Huang, H. Li, Y. Zhang, J. Fei, X. Kong, Effect of ZrO2 morphology on the ablation resistance of carbon/carbon composites containing ZrC prepared by the carbothermal reduction reaction, Corrosion Science, 102 (2016) 405-412. [6] Y. Yang, X. Liang, W. Chen, L. Cao, M. Li, B.W. Sheldon, J. Lou, Quantification and promotion of interfacial interactions between carbon nanotubes and polymer derived ceramics, Carbon, 95 (2015) 964-971. [7] J.-J. Han, D. Su, Z.-H. Zhao, X.-L. Li, H.-M. Ji, X. Yan, Z.-G. Jin, Fabrication and toughening behavior of carbon nanotube (CNT) scaffold reinforced SiBCN ceramic composites with high CNT loading, Ceramics International, 43 (2017) 9024-9031.

[8] H.-H. Kim, W. Han, H.-s. Lee, B.-G. Min, B.-J. Kim, Preparation and characterization of silicon nitride (SiN)-coated carbon fibers and their effects on thermal properties in composites, Materials Science and Engineering: B, 200 (2015) 132-138. [9] L. Li, Fatigue Life Prediction of Fiber-Reinforced Ceramic-Matrix Composites with Different Fiber Preforms at Room and Elevated Temperatures, Materials, 9 (2016). [10] J. Yang, J. Sprengard, L. Ju, A. Hao, M. Saei, R. Liang, G.J. Cheng, C. Xu, Threedimensional-linked carbon fiber-carbon nanotube hybrid structure for enhancing thermal conductivity of silicon carbonitride matrix composites, Carbon, 108 (2016) 38-46. [11] J.J. Sha, J. Li, S.H. Wang, Z.F. Zhang, Y.F. Zu, S. Flauder, W. Krenkel, Improved microstructure and fracture properties of short carbon fiber-toughened ZrB2-based UHTC composites via colloidal process, International Journal of Refractory Metals and Hard Materials, 60 (2016) 68-74. [12] S. Song, C. Bao, B. Wang, Effect of the addition of carbon fibres on the microstructure and mechanical properties of reaction bonded B4C/SiC composites, Journal of the European Ceramic Society, 36 (2016) 1905-1913. [13] T. Suo, X. Fan, G. Hu, Y. Li, Z. Tang, P. Xue, Compressive behavior of C/SiC composites over a wide range of strain rates and temperatures, Carbon, 62 (2013) 481-492. [14] L. Longbiao, Fatigue Life Prediction of Carbon Fiber-Reinforced Ceramic-Matrix Composites at Room and Elevated Temperatures. Part I: Experimental Analysis, Applied Composite Materials, 23 (2015) 101-117. [15] Y. Zhang, C. Chen, W. Chen, H. Cheng, L. Wang, A novel aqueous plasma electrolysis for carbon fiber, Chemical Engineering Journal, 304 (2016) 426-430.

[16] F. Reichert, A.M. Pérez-Mas, D. Barreda, C. Blanco, R. Santamaria, C. Kuttner, A. Fery, N. Langhof, W. Krenkel, Influence of the carbonization temperature on the mechanical properties of thermoplastic polymer derived C/C-SiC composites, Journal of the European Ceramic Society, 37 (2017) 523-529. [17] H.T. Liu, L.W. Yang, X. Sun, H.F. Cheng, C.Y. Wang, W.G. Mao, J.M. Molina-Aldareguia, Enhancing the fracture resistance of carbon fiber reinforced SiC matrix composites by interface modification through a simple fiber heat-treatment process, Carbon, 109 (2016) 435-443. [18] L. Longbiao, Hysteresis loops of carbon fiber-reinforced ceramic-matrix composites with different fiber preforms, Ceramics International, 42 (2016) 16535-16551. [19] Y. Zhang, L. Zhang, X. Yin, J. Zhang, Z. He, F. Ye, Oxidation behaviors and shear properties of z-pinned joint made of two-dimensional carbon fiber reinforced silicon carbide composite, Ceramics International, 42 (2016) 11974-11981. [20] Y. Zhang, P. Zhang, J. Ren, L. Zhang, J. Zhang, SiC nanowire-toughened MoSi2-WSi2-SiCSi multiphase coating for improved oxidation resistance of C/C composites, Ceramics International, 42 (2016) 12573-12580. [21] Y. Zhang, H. Hu, P. Zhang, Z. Hu, H. Li, L. Zhang, SiC/ZrB2–SiC–ZrC multilayer coating for carbon/carbon composites against ablation, Surface and Coatings Technology, 300 (2016) 19.

Fig. 1 Schematic diagram for the fabrication process of CNT/TiC coated ZrB2 composite.

Fig. 2 XRD patterns of CNT/TiC sol-gel coated ZrB2 composites samples after heat treatments at 550 °C and 1450 °C, and SPS at 1900 °C.

(b)

(a)

1um

1um

(d)

(c)

1um

100nm

Fig. 3 SEM micrographs of (a) starting powders of ZrB2; and sol-gel with CNTs coated ZrB2 composites with Ti/Zr ratio of 0.1 after (b) 550 ºC firing; (c) 1450ºC heat treatment and (d) enlarge area in Fig.3c.

(a)

(b) ZrB2 (Point 1)

Gap TiC (Point 2) (c) (d)

CNT s

Fig. 4 SEM micrographs of CNTs mixed sol-gel coated ZrB2 composites with Ti/Zr ratio of 0.1 sintered by SPS at 1900ºC in vacuum for 5 min; and EDX spectra of point 1 (grey matrix) and point 2 (dark phase) in Fig. 4 (b).

(a)

(b)

(c)

(d)

Fig. 5 SEM micrographs of samples after SPS at 1900ºC in vacuum for 5 min, including (a) as-received ZrB2; and sol-gel synthesized CNT/TiC coated ZrB2 composites with different Ti/Zr ratios of (b) 0.1; (c) 0.15; and (d) 0.2.

Fig. 6 Densification of ZrB2 facilitated by the coalescence of nano-sized TiC coated on the surface of ZrB2 powders.

Fig. 7 Density and porosity of SPS sintered sol-gel synthesized CNT/TiC coated ZrB2 composites with different Ti/Zr ratios.

Fig. 8 Hardness and fracture toughness of SPS sintered sol-gel synthesized CNT/TiC coated ZrB2 composites with different Ti/Zr ratios.

(a)

(b)

Fig. 9 SEM micrographs of sol-gel synthesized CNT/TiC coated ZrB2 composites with Ti/Zr ratio of 0.1, showing (a) fracture surface, and (b) crack deflection.