crystals

Article Behavior of Single-Crystal in Different Crystal Orientations

Shizhan Huang 1,2, Jiaming Lin 1,2, Ningchang Wang 3,4, Bicheng Guo 1,2, Feng Jiang 1,2,*, Qiuling Wen 1,2 and Xizhao Lu 5

1 Institute of Manufacturing Engineering, Huaqiao University, Xiamen 361021, China; [email protected] (S.H.); [email protected] (J.L.); [email protected] (B.G.); [email protected] (Q.W.) 2 National & Local Joint Engineering Research Center for Intelligent Manufacturing Technology of Brittle Materials Products, Xiamen 361021, China 3 Zhengzhou Research Institute for Abrasives & Grinding Co., Ltd., Zhengzhou 450001, China; [email protected] 4 State Key Laboratory of Superabrasives, Zhengzhou 450001, China 5 College of Mechanical Engineering and Automation, Huaqiao University, Quanzhou 361021, China; [email protected] * Correspondence: [email protected]

Abstract: In order to study the anisotropy of fracture toughness and fracture mechanism of single- crystal sapphire, the three-point bending tests and the single-edge V-notch beam (SEVNB) were used to test the fracture toughness of A-plane, C-plane, and M-plane sapphire, which are widely used in the , aerospace, and other high-tech fields. Fracture morphology was investigated by a scanning electron microscope and three-dimensional video microscopy. The fracture toughness

 and fracture morphology of different crystal planes of sapphire showed obvious anisotropy and  were related to the loading surfaces. C-plane sapphire showed the maximal fracture toughness of · 1/2 Citation: Huang, S.; Lin, J.; Wang, N.; 4.24 MPa m , and fracture toughness decreases in the order of C-plane, M-plane, and A-plane. Guo, B.; Jiang, F.; Wen, Q.; Lu, X. The surface roughness is related to the dissipation of fracture energy. The surface roughness of the Fracture Behavior of Single-Crystal fracture surface is in the same order as C-plane > M-plane > A-plane. The fracture behavior and Sapphire in Different Crystal morphology of experiments were consistent with the theoretical analysis. C-plane sapphire cleavages Orientations. Crystals 2021, 11, 930. along the R-plane with an angle of 57.6 degrees and the rhombohedral twin were activated. M-plane https://doi.org/10.3390/cryst11080930 and A-plane sapphire cleavages along their cross-section.

Academic Editor: Tomasz Sadowski Keywords: single crystal sapphire; fracture toughness; three-point bending test; single-edge V-notch beam; cleavage Received: 19 June 2021 Accepted: 6 August 2021 Published: 11 August 2021 1. Introduction Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in Due to their ultra-high hardness, wear resistance, corrosion resistance, and excellent published maps and institutional affil- light transmittance, sapphire materials are widely used in the aerospace industry, national iations. defense [1], optical industry, substrate manufacturing, etc. [2]. However, it is difficult to process the precision sapphire parts with complex structures or high surface quality, due to the high brittleness of sapphire materials. As one of the intrinsic mechanical properties of sapphire materials, fracture toughness is the only indicator of characterization materials to resist crack extension and material brittleness. The fracture toughness of brittle material Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. (single crystal, glass, polycrystalline ceramic) can greatly affect the removal processing of This article is an open access article the material and subsurface damage. Optimizing the processing of brittle materials, it was distributed under the terms and essential to control fracture (crack propagation) to reduce the depth of harmful surface conditions of the Creative Commons damage [3]. Single crystal with different crystal plane orientations have different Attribution (CC BY) license (https:// uses in the industry. In this paper, the fracture toughness and mechanism of different crystal creativecommons.org/licenses/by/ plane orientations were studied, which can be used as the basis for industrial material 4.0/). selection and machining to avoid the great harm caused by brittle fracture at low stress.

Crystals 2021, 11, 930. https://doi.org/10.3390/cryst11080930 https://www.mdpi.com/journal/crystals Crystals 2021, 11, 930 2 of 16

There are many ways to test the fracture toughness of brittle materials. Prefabricating the initial cracks of the appropriate length, can be used to accurately evaluate the fracture toughness of the material [4–6]. Zhao et al. used a femtosecond laser to prefabricate super sharp V-notch in the single-edge V-notch beam (SEVNB) method to obtain the fracture toughness of structural ceramics accurately and reliably [7]. Quinn et al. used the surface crack in flexure (SCF) method and the single-edged pre-cracked beam (SEPB) method to test the fracture toughness of glass. The accuracy of the test results was largely determined by the quality of the prefabricated cracks [8]. Yanaba et al. discussed the relationship between fracture toughness and flexural fracture area of WC-10 mass% Co cemented carbide and nitride ceramics. The experimental results of the SEPB method were in good agreement with the results of theoretical calculation [9]. However, many researchers focus on the fracture mechanism of anisotropic materials, such as ceramics, glass, and cemented carbide. Due to anisotropy, the physical, chemi- cal, and optical properties of materials with different crystal orientations show obvious differences, which have a great impact on the processing performance of materials, and seriously affect the material removal and the surface quality of processing. The optimal machining direction can be obtained by defining the fracture behavior of these materials. In the ultra-precision machining of KDP crystal, Zhao et al. found that the change of cutting force was caused by the anisotropy of crystal, and the change of roughness was also related to the anisotropy [10]. Due to the characteristic hexagonal and obvious anisotropy mate- rial of single-crystal sapphire, the processing of sapphire is challenging. Studying the fracture and removal mechanisms of sapphire is very essential for the optimization of processing parameters. In order to study the material removal rate (MRR) and workability of sapphire with different crystal orientations, Wen et al. performed focused ion beam (FIB) milling on single-crystal sapphire with A-, C-, and M-orientations. The experimental results show that: The MRR of A-plane sapphire is slightly higher than that of C-plane and M-plane sapphires; and the Sa of A-plane sapphire, after FIB treatment, is the smallest among the three different crystal orientations [11]. In addition, Wen et al. irradiated sapphire with different crystal orientations by the femtosecond laser, and the damage threshold of C-plane < M-plane < A-plane < R-plane was obtained. The damage accumulation of sapphire with M-plane was the largest, and it was easier to form cracks under multi-pulse irradiation [12]. Wang et al. revealed the removal mechanism for each orientation of single-crystal sapphire by double-sided planetary grinding experiments. The R-plane was removed in the form of large pieces of spalled material and had the highest MRR and the largest surface roughness (Sa) of approximately 780 nm among the orientations studied. The C-plane was mainly removed in the form of unique large step-like pieces of spalled material, had the lowest MRR among the orientations observed, and exhibited an Sa of approximately 430 nm [13]. Luo et al. used the sol-gel (SG) polishing pad to machine the C-plane, A-plane, and M-plane sapphires. The polishing results showed that the C-orientation, with a surface roughness of about 2 nm, is smoother than the A- and M-orientations and the MRR of C-orientation is higher than that of them [14]. Wang et al. used a wire saw to cut A-plane sapphire in different cutting directions to explore its machinability. It was concluded that the cutting direction along the M-plane was the best, considering the minimum cutting force and the minimum material volume removal could be obtained [15]. To study the mechanism of crack propagation and fracture damage evolution of sapphire with different crystal orientations, Luan et al. performed dynamic and quasi- static indentation tests on the c-plane and a-plane of sapphires by Hopkinson pressure bar tester and continuous indentation tester, respectively. It was found that the bearing capacity of sapphire is related to the loading velocity, while the crack propagation is affected by the crystal orientation. The R-planes of sapphire are weaker than other crystal planes and are prone to crack propagation [16]. Jiang et al. tested the dynamic mechanical properties of C- plane sapphire by also using the Hopkinson pressure bar tester. The true stress-strain curve Crystals 2021, 11, 930 3 of 16

of sapphire has been obtained at different velocities. It was found that the crystal orientation influences the crack path and crack pattern, which leads to different energy consumption during crack propagation [17]. Wang et al. used a Vickers indenter on a micrometer scale to study crack propagation that is induced by sequential indentation was investigated on the A-plane and C-plane of sapphire. Due to the different slip systems induced by an indentation on the different crystal planes of sapphire, increasing the indentation depth obviously increases the rate of crack propagation on the A-plane, but this effect is not so obvious on the C-plane. Moreover, some parallel linear traces along the A-plane, which fracture with increasing indentation depth, are observed from the residual indentation on the A-plane [18]. Wang et al. performed impact and static load tests on the A-plane, C-plane, M-plane, and R-plane of sapphire by the high-frequency cyclic impact test device, respectively. It was found that the crack propagation is affected by the crystal orientation, which leads to different characteristics of the surface morphology of the different crystal orientations sapphire after a fracture. Moreover, four different models of the crack system are proposed for A-plane, C-plane, M-plane, and R-plane, respectively [19]. Wan et al. found that the surface damage depth of the A-plane sapphire was greater than that of C- plane sapphire by precision grinding. The subsurface cracks of A-plane sapphire included transverse and radial cracks, while the subsurface cracks of C-plane sapphire were mainly transverse [20]. The occurrence of pop-in events at micro-scale always presents ductile-brittle transi- tion. Wang et al. developed a mechanical model for pop-in events of sapphire based on indentation test results obtained by a Rockwell indenter with a tip radius of 4.5 µm. The predicted pop-in loads showed good agreement with experimental values for sapphires with different crystal orientations. The pop-in load for the C-plane sapphire was the largest, followed in the order of M-plane, A-plane, and R-plane sapphires under the same load conditions [21]. To study the relationship between plastic deformation and fracture of sapphire, Lin et al. used the molecular dynamics method to simulate the nanoindentation process of sapphire. The results showed that the activation of the twin/slip system has an important influence on the sapphire indentation morphology [22]. Besides, Lin et al. studied the influ- ence of the scratching direction on surface morphology, stress distribution, and subsurface defects. The scratching surface morphology of sapphire is affected by the activation of slip systems. A smaller thickness of the subsurface damage layer was resulted by scratching along (1-010) and (1-100) directions [23]. The fracture mechanism and fracture toughness of single-crystal sapphire was studied by fracture mechanics experiments. Azhdari et al. prepared notched samples of sapphire with different crystal orientations. Through the compression fracture test, it was found that most of the samples fractured along the weak cleavage plane, and the two weakest families of cleavage planes were (-1012) and (10-11), especially, plane (-1102), plane (-1100) and plane (1-102) were the preferred fracture planes [24]. Konstantiniuk et al. used chemical vapor deposition to deposit single crystal and polycrystalline α-Al2O3 coatings on sapphire substrates with different crystal orientations, and prepared unnotched and notched microcantilevers. The (11-20) single crystalline coating which was aligned for fracture on the C-plane, exhibited the highest fracture stress and fracture toughness [25]. Graça et al. used the SEVNB method to explore the fracture resistance of single-crystal sapphire with different crystal orientations prepared by two processes. Estimation of the mosaic block boundary energy and application of the Griffith criterion for intergranular crack propagation allows the critical deflection angle below which intergranular fracture can take place to be determined [26]. Many researchers have tested the fracture toughness of sapphire with different crystal orientations, but there are still few reports on the relationship between the anisotropic fracture mechanism and fracture toughness of sapphire. In this paper, the fracture toughness of single-crystal sapphire with different crystal orientations was tested by three-point bending tests. Single crystal sapphire samples were Crystals 2021, 11, x FOR PEER REVIEW 4 of 15

Crystals 2021, 11, 930 4 of 16 In this paper, the fracture toughness of single-crystal sapphire with different crystal orientations was tested by three-point bending tests. Single crystal sapphire samples were prepared by the single-edge V-notch beam (SEVNB) method, including C-plane (0001), A- planeprepared (11-20), by theand single-edgeM-plane (10-10) V-notch sapphires. beam (SEVNB) In addition, method, this paper including further C-plane considered (0001), theA-plane influence (11-20), of the and loaded M-plane surface (10-10) during sapphires. the three-point In addition, bending this paper tests. Microscopic further considered mor- phologythe influence of the offracture the loaded surface surface was studied during theby a three-point scanning electron bending microscope tests. Microscopic (SEM), morphology of the fracture surface was studied by a scanning electron microscope (SEM), three-dimensional video microscopy. In addition, the roughness of the fracture surface three-dimensional video microscopy. In addition, the roughness of the fracture surface was was tested by a three-dimensional optical profiler. To study the anisotropy of single-crys- tested by a three-dimensional optical profiler. To study the anisotropy of single-crystal tal sapphire with different crystal orientations, the result of fracture toughness, displace- sapphire with different crystal orientations, the result of fracture toughness, displacement- ment-load curves, and fracture surface roughness were compared. The fracture mecha- load curves, and fracture surface roughness were compared. The fracture mechanism was nism was studied by the microscopic surface morphology of the fracture surface and the studied by the microscopic surface morphology of the fracture surface and the activation activation of the twin/slip system. of the twin/slip system.

2.2. Design Design of of Experiments Experiments 2.1.2.1. Sample Sample Preparation Preparation and and Orientation Orientation Single-crystalSingle-crystal sapphire sapphire is isa simple a simple coordination coordination type type oxide oxide crystal, crystal, belonging belonging to the to hexagonalthe hexagonal crystal , system, with lattice with latticeparameters parameters a = b = a0.4758= b = nm, 0.4758 c = nm,1.2991c = nm, 1.2991 α = β nm, = 90α°=, γβ == 120°. 90◦, γIt =is 120a typical◦. It is anisotropic a typical anisotropic material, and material, Figure and 1 shows Figure the1 shows crystal the structure crystal ofstructure the single-crystal of the single-crystal sapphire [1]. sapphire [1].

FigureFigure 1. 1. CrystalCrystal structure structure of of the the single-crystal single-crystal sapphire. sapphire. Cleavage fracture is a kind of transgranular fracture under normal stress. The fracture Cleavage fracture is a kind of transgranular fracture under normal stress. The frac- surface is separated along a certain crystal plane (cleavage plane). Low temperature, ture surface is separated along a certain crystal plane (cleavage plane). Low temperature, impact load, and stress concentration often promote cleavage fracture. Sapphire has been impact load, and stress concentration often promote cleavage fracture. Sapphire has been considered completely uncleavable for a long time. In theory, it has nine cleavage surfaces. considered completely uncleavable for a long time. In theory, it has nine cleavage surfaces. Six planes are parallel to the facets {11-20} and {10-10}, and to the C-axis; three planes Six planes are parallel to the facets {11-20} and {10-10}, and to the C-axis; three planes are are parallel to the facets {10-11}, the normal vectors to them make an angle of 57◦ with parallel to the facets {10-11}, the normal vectors to them make an angle of 57° with the C- the C-axis. The cleavage in sapphire occurs at the intersection of a pair of parallel nets axis. The cleavage in sapphire occurs at the intersection of a pair of parallel nets formed formed by anions. The larger the distance between the nets, the more vividly the cleavage by anions. The larger the distance between the nets, the more vividly the cleavage mani- manifests itself. In a perfect crystal, the plane of chipping must pass between these nets. fests itself. In a perfect crystal, the plane of chipping must pass between these nets. In the In the basal plane with interchanging O-Al-Al-O-Al-O layers, there are no conditions for basalcleavage, plane whereas with interchanging in the plane (10-11)O-Al-Al-O-Al-O with interchanging layers, there O-O-Al-O-Al-O-O-O-Al-O-Al-O are no conditions for cleav- age,layers whereas the bonds in the between plane (10-11) the layers with O-O interchanging located at aO-O-Al-O-Al-O-O-O-Al-O-Al-O distance of 1.06 Å are weakened. lay- So, ersthe the crystals bonds with between a small the number layers O-O of dislocations located at a and distance which of do 1.06 not Å contain are weakened. blocks may So, have the crystalsperfect with cleavage a small in the number plane of thedislocations morphological and which rhombohedron do not contain {10-11} blocks [27]. may have perfectDue cleavage to the in sapphire the plane plastic of the deformation morphological scale rhombohedron is relatively small, {10-11} material [27]. removal is multi-manifestationDue to the sapphire in actualplastic processing. deformation It scale is formed is relatively by the developmentsmall, material of removal the brittle- is multi-manifestationductile transition of in sapphire. actual processing. The plastic It deformation is formed by of sapphirethe development is mainly of twin the andbrittle- slip, ductileas shown transition in Table of1, sapphire. which was The summarized plastic deformation by Nowak of et sapphire al. at room is mainly temperature twin and [ 28]. slip, The ascritical shown resolved in Table shear 1, which stress was (CRSS) summarized of rhombohedral by Nowak twin et al. and at basal room twin temperature is the smallest, [28]. Theand critical far less resolved than other shear twin stress and (CRSS) slip systems. of rhombohedral The second twin is and cylinder basal twin slip andis the rhombic small- est,slip. and Due far to less the than CRSS other required twin and for base slip planesystems. slip The is the second largest, is cylinder it is more slip difficult and rhombic to occur slip.than Due other to twinthe CRSS and sliprequired systems. for base Two plane major slip twins is the are largest, the foundation it is more (C-plane) difficult twins to occur and rhombohedronal plane (R-plane) twins. Twinning in the planes {1011} is characterized by a lesser specific shear and is observed even at cryogenic temperatures.

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than other twin and slip systems. Two major twins are the foundation (C-plane) twins and rhombohedronal plane (R-plane) twins. Twinning in the planes {1011}is characterized by Crystals 2021, 11, 930 a lesser specific shear and is observed even at cryogenic temperatures. 5 of 16

Table 1. The twin and slip systems of sapphire at room temperature [28].

TableNum- 1. TheTwin twin & and Slip slip Sys- systemsPlastic of sapphire Deformation at room temperature Critical [28 Resolved]. Shear Stress ber tems Type (GPa)Critical Resolved Number Twin & Slip SystemsRhombohedral Plastic twin Deformation Type 1 <01-11> {01-12} 0.111Shear Stress (GPa) 1 <01-11> {01-12}(RT) Rhombohedral twin (RT) 0.111 2 2 <1-100> {0001} <1-100> {0001} Basal twin (BT) Basal twin (BT) 0.148 0.148 3 3 <2-1-10> {01-12} <2-1-10> Rhombohedral {01-12} Rhombohedral slip (RS) slip (RS) 3 3 4 4 <2-1-10> {0001} <2-1-10> {0001} Basal slip (BS) Basal slip (BS) 17 17 5 <1-210> {10-10} Prismatic slip (PRS) 1.2 5 <1-210> {10-10} Prismatic slip (PRS) 1.2

InIn this paper,paper, three three sapphire sapphire samples samples with with different different crystal crystal orientations orientations were were produced pro- ducedby Jiangsu by Jiangsu Ruibo Ruibo Optoelectronics Optoelectronics Technology Technology Co., Ltd. Co., TheLtd. raw The materialsraw materials were were cut into cut into35 mm 35 ×mm3 mm× 3 ×mm4 mm× 4 rectangularmm rectangular bars, andbars, then andpolished then polished by CMP by to CMP reach to the reach surface the surfaceroughness roughness Ra lower Ra than lower 0.3 than nm, 0.3 as shownnm, as inshown Figure in2 .Figure 2.

FigureFigure 2. 2. ThreeThree different different crystal orientations of sapphire samples.

2.2.2.2. Three-Point Three-Point Bending Bending Test Test and SEVNB ThereThere are several testing methods for fracture toughness. The single edge notched bendbend bar bar (SENB) (SENB) method method is is simple simple to toprepare prepare samples, samples, and and the the test test system system is easy is easy to op- to erate.operate. However, However, the width the width of the of incision the incision is limited is limited by the by thickness the thickness of the ofdiamond the diamond blade, andblade, a passivation and a passivation effect will effect occur will at occur the root at theof the root incision, of the incision, causing the causing measured the measured fracture toughnessfracture toughness to be higher to be than higher the thantrue thevalue true [29]. value The [29 single]. The edge single pre-cracked edge pre-cracked beam (SEPB) beam method,(SEPB) method, also known also as known the bridge as the compression bridge compression method, method,is the most is thereliable most and reliable accurate and testaccurate method test [30]. method The [test30]. results The test of resultsthe inden of thetation indentation method (IM) method are related (IM) are to related the smooth- to the nesssmoothness of sample of samplesurface, surface,crack form, crack and form, calculation and calculation formula, formula, and the and results the resultsunder differ- under entdifferent conditions conditions have large have deviation large deviation [31]. Th [e31 single-edge]. The single-edge V-notch V-notchbeam (SEVNB) beam (SEVNB) method wasmethod adopted was adoptedin this work, in this due work, to its due good to itsrepeatability good repeatability [32]. [32]. InIn this this study, study, the the three-point three-point bending bending test test and and SEVNB SEVNB method method were were based based on ISO on 23146ISO 23146 [33]. [The33]. three-point The three-point bending bending tests were tests performed were performed by the universal by the universal testing machine testing typedmachine Sans typed 5305, Sans and 5305, the sample and the fixture sample was fixture shown was in shown Figure in 3a. Figure The3 samplea. Thesample was placed was horizontallyplaced horizontally on the two on the bearing two bearing rollers. rollers. The height The heightof the oftwo the bearing two bearing rollers rollers was con- was consistent. The two bearing rollers were parallel and perpendicular to the length direction sistent. The two bearing rollers were parallel and perpendicular to the length direction of of the sample. Their spacing is 30mm. The radius of the pressure head and bearing rollers the sample. Their spacing is 30mm. The radius of the pressure head and bearing rollers is is 1.6 mm. The symmetrical center line intersected the centerline of the main shaft of the 1.6 mm. The symmetrical center line intersected the centerline of the main shaft of the universal testing machine vertically. universal testing machine vertically.

Crystals 2021, 11, 930 6 of 16 Crystals 2021, 11, x FOR PEER REVIEW 6 of 15

Crystals 2021,, 11,, xx FORFOR PEERPEER REVIEWREVIEW 6 of 15

FigureFigure 3.3. ((a)) Sample fixture fixture for the the three-point three-point bending bending test, test, where where FF isis the the loading loading force, force, RR isis the the

radius of pressure head and bearing rollers, and S0 is the span of three-point bending. (b) Dia- radius of pressure head and bearing rollers, and S0 is the span of three-point bending. (b) Diamond mond wireFigure saw. 3. ((a)) SampleSample fixturefixture forfor thethe three-pointthree-point bendingbending test,test, wherewhere F isis thethe loadingloading force,force, R isis thethe wire saw.radius of pressure head and bearing rollers, and S00 isis thethe spanspan ofof three-pointthree-point bending.bending. ((b)) Dia-Dia- mond wire saw. AA suddensudden pre-crackpre-crack inin thethe middlemiddle ofof thethe samplesample waswas preparedprepared byby twotwo steps.steps. InIn thethe firstfirst step,step, thetheA U-notch U-notchsudden pre-crack groovegroove was wasin the processedprocessed middle of byby the aa sample diamonddiamond was wirewire prepared sawsaw in inby the thetwo middlemiddle steps. In ofof the thethe loadingloadingfirst plane.plane. step, The The the wire U-notchwire diameter diameter groove of wasof diamond diamond processed wire wireby saw aa diamonddiamondsaw is 280 is µ280 wirem,wire μ the m,sawsaw diameter the inin thethediameter middlemiddle of diamond of thethedia- particlesmond particlesloadingloading is 80–90 plane.plane. isµ m,80–90 asTheThe shownμ wirewirem, as diameterdiameter in shown Figure ofofin3 b. diamond diamondFigure In the 3b.second wirewire In saw sawthe step, isissecond 280280 the μ V-notchm, step, the thediameter was V-notch processed of dia- was byprocessed a lasermond at by the particlesa laser bottom at is the of80–90 thebottom μ U-notchm, asof shownthe groove. U-no in tchFigure The groove. details 3b. In The the of processingseconddetails step,of processing parameters the V-notch param- werewas showneters were inprocessed Table shown2. Theby in a cuttingTablelaser at 2. the depth The bottom cutting was of 2 the mm.depth U-no Due wastch to groove. 2 the mm. wire The Due diameter, details to the of wireprocessing the actual diameter, param- cutting the eters were shown in Table 2. The cutting depth was 2 mm. Due to the wire diameter, the depthactual wascuttingeters about were depth 1shown mm. was Thein about Table cutting 12. mm.The depth cutting The ofcu depth thetting laser depthwas was 2 mm. of about the Due laser 0.5to the mm.was wire about diameter, 0.5 mm. the actual cutting depth was about 1 mm. The cutting depth of the laser was about 0.5 mm. Table 2. PreparingTable 2.thePreparing standard the sample. standard sample. Table 2. Preparing the standard sample.

StepsSteps Steps MachineMachineMachine ParameterParameterParameter ResultResult Diamond wire cutting V = 1.8V m/sc =V 1.8cc = 1.8 m/s m/s StepStep 1: 1: Preparing PreparingStep 1: PreparingPreparing the U-notch thethe U-notchU-notchDiamond Diamond wire cutting wire cutting machine machine of c of machine of Shenyang kejing V = 0.3V mm/minf =V 0.3ff = 0.3mm/min mm/min U-notchgroove groove groove ShenyangShenyang kejing kejing STX-402 STX-402 f STX-402 ap = 2 mmap =ap 2 ==mm 22 mmmm λ= 355λ nm=λ 355= 355 nm nm τ = 15 nsτ = τ15 = 15ns ns Step 2: Preparing the Laser machine ofLaser SCABNLAB machine of SCABNLABVs = 1 mm/sVss = 1 mm/s Step 2: PreparingPreparing thethe V-notchV-notchLaser machine of SCABNLAB Vs = 1 mm/s Step 2: PreparingV-notch the V-notchBasiCube10 SN:545393BasiCube10 SN:545393 f = 50 kHzff == 5050 kHzkHz BasiCube10 SN:545393 f = 50 kHz d = 10 µm d == 1010 μm d = 10 μm n = 10 n == 1010 n = 10 Where Vc is thewhere linear Vcc velocityisis thethe linearlinear of diamond velocityvelocity wire, ofof diamonddiamondVf is the wire,wire, feed V rateff isis the ofthe diamond feedfeed raterate wire, ofof diamonddiamondap is the wire,wire, cutting ap depth,isis thethe cuttingcuttingW is the depth,depth, pulse W width isis thethe of pulsepulse laser, Vwheres is the V scanningc iswidth the linear speed, of laser, fvelocityis V thess isis laserthethe of scanningscanning diamond frequency, speed,speed, wire,d is the ff isisV spot fthethe is thelaserlaser diameter feed frequency,frequency, rate of laser, of d diamond is andis thethen spotspotis the wire, diameterdiameter repetition ap is ofof the times laser,laser, cutting of andand laser n depth, isis scanning. thethe repetitionrepetition W is the times timespulse width of laser,of laser Vs is scanning. the scanning speed, f is the laser frequency, d is the spot diameter of laser, and n is the repetition times of laser scanning. Single-crystal sapphire samples with different crystal orientations have one cross- section andSingle-crystal two side-faces. sapphire In addition samples with to the different cross-section, crystal orientations different side-faceshave one cross- in its section and two side-faces. In addition to the cross-section, different side-faces in its length lengthSingle-crystal will be loaded sapphire separately samples in this with study. different Therefore, crystal theorientations test groups have were one named cross- will be loaded separately in this study. Therefore, the test groups were named as “Num- assection “Number-Cross-section-Loaded and two side-faces. In addition surface”, to the cr withoss-section, a total ofdifferent six test si groups,de-faces as in shown its length in ber-Cross-section-Loaded surface”, with a total of six test groups, as shown in Table 3. For will be loaded separately in this study. Therefore, the test groups were named as “Num- Table3.example, For example, the test the “1-M-A” test “1-M-A” is the first is thetest firstgroup, test “M” group, is the “M” cross- issection the cross-section of the sapphire of ber-Cross-section-Loaded surface”, with a total of six test groups, as shown in Table 3. For the sapphiresample, sample, and “A” and is “A”the loaded is the surface loaded of surface the sapphire of the sample. sapphire Each sample. group Eachprepared group 7 preparedexample,samples 7the samples test and “1-M-A” repeated and repeated isthe the independent first the independent test gr testoup, seven “M” test times. sevenis the cross- times.section of the sapphire sample, and “A” is the loaded surface of the sapphire sample. Each group prepared 7 samples and repeatedTable the 3. Testingindependent groups. test seven times.

Test Groups Cross-Section Loaded Surface Test Groups Cross-Section Loaded Surface 1 M A 4 C A 2 M C 5 A C 3 C M 6 A M Where M is the crystal orientation of (10-10), C is the crystal orientation of (0001), and A is the crystal orientation of (11-20).

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Table 3. Testing groups.

Test Groups Cross-Section Loaded Surface Test Groups Cross-Section Loaded Surface 1 M A 4 C A 2 M C 5 A C 3 C M 6 A M where M is the crystal orientation of (10-10), C is the crystal orientation of (0001), and A is the crystal orientation of (11- Crystals 2021, 11, 930 7 of 16 20).

This test was in the air and at room temperature. The pressure head of the testing machineThis was test set was to ina load the air at anda constant at room rate temperature. of V = 0.05 Themm/min, pressure and headthe direction of the testing was verticalmachine down. was setThe to loading a load time, at a constant loading rateforce, of andV = displacement 0.05 mm/min, were and recorded. the direction was verticalAfter down. the samples The loading are fractured, time, loading according force, to and ISO displacement 23146 [33], the were ideal recorded. fracture mor- phologyAfter is shown the samples in Figure are fractured, 4, where accordingpart 1 is the to ISOfracture 23146 surface, [33], the part ideal 2 is fracture the processing morphol- surfaceogy is shownof the pre-fabricated in Figure4, where crack. part On 1 isthe the fracture fracture surface, surface, the part V-notch 2 is the depths processing at B/4, surface B/2, andof the 3B pre-fabricated/4 along the width crack. of On the the sample fracture were surface, selected the for V-notch measurement depths at andB/4, denotedB/2, and as 3B a/41, aalong2, a3. the width of the sample were selected for measurement and denoted as a1, a2, a3.

FigureFigure 4. 4. IdealIdeal fracture fracture surface. surface.

TheThe average average depth depth of of the the V-notch V-notch is is calculated calculated using using Formula Formula (1), (1), denoted denoted as as aa, ,and and mustmust satisfy satisfy the the Formula Formula (2) (2) to to lower lower the the calculation calculation error. error. The The average average relative relative V-notch V-notch depthdepth is is calculated calculated using using Formula Formula (3) (3) and and denoted denoted as as αα. .

𝑎=a =（(a𝑎1++𝑎a2++𝑎a3)/） 3/ 3 (1) (1) (𝑎 −𝑎 )/𝑎 ≤ 0.1 (2) (amax− amin)/a ≤ 0.1 (2) α𝛼=𝑎/𝑊= a/W (3)(3)

The fracture toughness K1C was calculated as follows: The fracture toughness K1C was calculated as follows: 𝐹 ×𝑆 ×10 3×(𝑎/𝑊)/  −6 " 3/2 # 𝐾 =Fmax × S0 ×/10 3 × (a/W) /∙𝑌 (4) KIC = 𝐵×𝑊 2×(1−𝑎/𝑊) ·Y (4) B × W3/2 2 × (1 − a/W)3/2 where Fmax is the maximum applied load at fracture, S0 is the span of three-point bending, Bwhere is the Fsamplemax is the width, maximum and W applied is the sample load at thickness; fracture, S Y0 is the spandimensionless of three-point shape bending, factor forB is average the sample V-notch width, depth and toW theis thethickness sample of thickness; the sampleY isW the ratio dimensionless [5]: shape factor for average V-notch1.99 − depth (𝑎/𝑊) to the ×(1 thickness − 𝑎/𝑊) of the × [2.15 sample −W 3.93ratio × [(𝑎/𝑊)5]: + 2.7 ×(𝑎/𝑊) ] 𝑌= (5) 1.99 − (a/W) × (1 − a/W) 1+2×(𝑎/𝑊)× [2.15 − 3.93 × (a/W) + 2.7 × a/W)2 Y = (5) 1 + 2 × (a/W) 3. Results and Discussion 3. Results and Discussion 3.1. Displace-Loading Curves 3.1. Displace-Loading Curves The displacement-load curves of each test group are shown in Figure5, and the repeata- bility of the tests was good. The fracture critical load of C-plane sapphire was significantly higher than that of other test groups. While the displacement of C-plane sapphire before fracture was also larger than that of the other test groups. The difference between the M-plane and A-plane sapphire was not obvious, the average value of fracture critical load was about 28 N and the average displacement with peak load was about 0.008 mm. Crystals 2021, 11, x FOR PEER REVIEW 8 of 15

The displacement-load curves of each test group are shown in Figure 5, and the re- peatability of the tests was good. The fracture critical load of C-plane sapphire was signif- icantly higher than that of other test groups. While the displacement of C-plane sapphire before fracture was also larger than that of the other test groups. The difference between

Crystals 2021, 11, 930 the M-plane and A-plane sapphire was not obvious, the average value of fracture8 of 16 critical load was about 28 N and the average displacement with peak load was about 0.008 mm.

Figure 5.5.Displacement-load Displacement-load curves curves of each of each test group. test group. (a) Test (a 1-M-A;) Test (1-M-A;b) Test 2-M-C; (b) Test (c) 2-M-C; Test 3-C-M; (c) Test 3-C- (M;d) Test(d) Test 4-C-A; 4-C-A; (e) Test (e) 5-A-C; Test 5-A-C; (f) Test ( 6-A-M.f) Test 6-A-M.

3.2. Calculation of K1C 3.2. CalculationThe results calculatedof K1C according to Formulas (4) and (5) are shown in Table4. The results calculated according to Formula (4) and (5) are shown in Table 4. 1/2 Table 4. Fracture toughness K1C of each test group. (Unit: MPa·m ).

Table 4. Fracture toughness K1C of each test group. (Unit: MPa·m1/2). Test Groups K1C-1 K1C-2 K1C-3 K1C-4 K1C-5 K1C-6 K1C-7 Average K1C

Test1-M-A Groups 2.39K1C 2.03-1 K1C 2.35-2 K1C 2.22-3 K1C-4 2.21 K1C-5 2.19 K1C-6 2.36K1C-7 2.25 Average K1C 2.42 2-M-C1-M-A 2.47 2.39 2.60 2.03 2.56 2.35 2.67 2.22 3.10 *2.21 2.70 2.19 2.512.36 2.59 2.25 3-C-M 4.04 4.26 4.45 4.44 * 4.27 4.13 4.12 4.21 4.24 2.42 4-C-A2-M-C 4.37 2.47 4.36 2.60 4.28 2.56 2.53 *2.67 4.30 3.10 3.95* 2.70 4.362.51 4.27 2.59 5-A-C 2.39 2.51 2.37 2.58 * 2.47 * 2.41 2.24 2.38 3-C-M 4.04 4.26 4.45 4.44 * 4.27 4.13 4.12 4.21 2.32 6-A-M 2.28 2.17 2.19 2.34 2.23 2.62 * 2.32 2.26 4.24 4-C-A 4.37 4.36 4.28 2.53 * 4.30 3.95 4.36 4.27 Where5-A-C the results marked * were2.39 not satisfied 2.51 with Formula 2.37 (2), and shall 2.58 be * removed. 2.47 The * experimental 2.41 fracture 2.24 toughness was 2.38 consistent with the previous studies. 2.32 6-A-M 2.28 2.17 2.19 2.34 2.23 2.62* 2.32 2.26 Where the results marked * wereThe not comparison satisfied with of Formula fracture toughness(2), and shall calculation be removed. results The of experimental sapphire with fracture different tough- ness was consistent with thecrystal previous orientations studies. is shown in Figure6. The fracture toughness of C-plane sapphire was about 4.24 MPa·m1/2, and that of the other sapphires were close, with an average of 2.37 MPaThe· mcomparison1/2. The fracture of fracture toughness toughness of C-plane calculation sapphire was results significantly of sapphire higher with than different others,crystal aboutorientations 77%. In is tests shown with in M-plane Figure sapphire, 6. The fracture the fracture toughness toughness of C-plane of pressuring sapphire was 1/2 C-planeabout 4.24 was MPa·m about 0.341/2, and MPa that·m ofhigher the other than sapphires that of pressuring were close, A-plane. with In an tests average with of 2.37 A-planeMPa·m1/2 sapphire,. The fracture the fracture toughness toughness of C-plane of pressuring sapph theire C-planewas significantly was close tohigher that of than oth- pressuringers, about M-plane.77%. In tests In general, with M-plane the experimental sapphir fracturee, the fracture toughness toughness of different of crystalpressuring C- planes decreases in the order of C-plane > M-plane > A-plane. plane was about 0.34 MPa·m1/2 higher than that of pressuring A-plane. In tests with A- plane sapphire, the fracture toughness of pressuring the C-plane was close to that of pres- suring M-plane. In general, the experimental fracture toughness of different crystal planes decreases in the order of C-plane > M-plane > A-plane. As a result, from the displacement-load curves and fracture toughness K1C, the frac- ture resistance of C-plane sapphire was much greater than that of sapphire with other orientations. Different crystal orientations showed anisotropy, and this was related to the loading plane.

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FigureFigure 6. 6. The averageaverage fracture fracture toughness toughness of each of group. each group. As a result, from the displacement-load curves and fracture toughness K1C, the frac- 3.3.ture Morphology resistance of of C-plane the Fractured sapphire Surface was much greater than that of sapphire with other orientations. Different crystal orientations showed anisotropy, and this was related to the loadingThe plane. results of the compressive fracture of three different sapphire samples are shown in Figure 7. The test results of the same type of sapphire have relatively consistent surface morphology.3.3. Morphology Assuming of the Fractured that Surface the sapphire samples tested have a perfect crystal structure, this paperThe results makes of thethe compressive following fractureanalysis. of three different sapphire samples are shown in Figure7. The test results of the same type of sapphire have relatively consistent surface Crystals 2021, 11, x FOR PEER REVIEW The cleavage direction of M-plane and A-plane sapphires are parallel to10 the of 15 cross- morphology. Assuming that the sapphire samples tested have a perfect crystal structure, section.this paper It makesis obvious the following that the analysis. cleavage direction of C-plane sapphire is deflected, it is not along the cross-section of the sample. In addition, the fracture toughness of C-plane sap- phire is the highest. According to the crystal structure of sapphire and the bond strength between different atoms, the results of experience are consistent with the expectation. In the C-plane sapphire tests, the angle between the cleavage direction and the cross-section (C-plane) is 33 degrees when the M-plane is used as the loading surface. When the A- plane is used as the loading surface, the angle between the cleavage direction and the cross-section (C-plane) is 42 degrees. Theoretically, along the c-direction, there are only interchanging O–Al layers and hence cleavage is not favored. On the other hand, along the r-direction, weaker O–O layers are present and so cleavage is favored [27]. In fact, measurements of the fracture surface energy previously performed by Wiederhorn et al. [34],Figure using 7. 7.Fractured Fractured the double-cantilever specimens. specimens. (a) Fracture(a) Fracture technique, of M-plane of M-plane sapphire,showed sapphire, where that “M”where a crack is the“M” cross-sectionpropagating is the cross-section of along of the C- planethethe sapphiresapphire requires sample, sample, over “A” “A” six and andtimes “C” “C” are more are the the loaded energy loaded surfaces surfaces than of along the of sapphirethe thesapphire R-plane. sample. sample. (b) In Fracture ( bthe) Fracture tests of of of C-planeA- sapphire,A-planeplane sapphire, sapphire, the pre-crack where “A”“A” is wasis the the cross-section oncross-section the C-plane, of the of sapphirethe sapphireand sample, it was sample, “C” predicted and “C” “M” and are “M”that the loaded are the the crack loaded would surfaces of the sapphire sample.c (c) Fracture of C-plane sapphire when loadingd M-plane. (d) Frac- propagatesurfaces of the along sapphire the sample. R-plane ( ) Fracture and cleavage of C-plane sapphirewould whenoccur. loading If the M-plane. cleavage( ) Fracture along the R-plane ofture C-plane of C-plane sapphire, sapphire, where “C”where is the “C” cross-section is the cross-section of the sapphire of the sample, sapphire “M” sample, and “A” “M” are theand “A” are occursloadedthe loaded when surfaces surfaces the of the M-plane of sapphire the sapphire sample.is used sample. (e )as Fracture the(e) Fracture loadin of C-plane gof surface,C-plane sapphire sapphire whenthe fracture loading when A-plane.loading surface A-plane. forms 32.4 degrees((ff)) FractureFracture with morphology morphology the m-direction. with with (i)-fracture (i)-fracture When zone, zone,the (ii)-V-notch A-plane (ii)-V-notch zone, is (iii)-U-notch zone,the loading (iii)-U-notch groove surface, zone. groove the zone. angle between the fracture surface and a-direction is 47 degrees. The experimental results are very close The cleavage direction of M-plane and A-plane sapphires are parallel to the cross- to the Theresults morphology of the crystallographic of the fractured surfaceanalysis wa, sso studied it can bybe a considered scanning electron that the micro- cleavage section.scope and It isthree-dimensional obvious that the cleavage video microscopy, direction of C-planeas shown sapphire in Figure is deflected, 7f. The fracture it is sur- planenot along of C-plane the cross-section sapphire of is the R-plane. sample. InThis addition, result the is fractureconsistent toughness with a of study C-plane by Graça et al., face cracks of single-crystal sapphire with different crystal orientations also showed obvi- andsapphire previous is the highest.research According [26]. Besides, to the crystal the structureresults of of sapphirethe M-plane and the and bond A-plane strength sapphire are ous anisotropy, with different degrees of crack propagation and surface fracture. similar,between and different cleavage atoms, was the results along of the experience cross-section. are consistent with the expectation. In the C-planeIn the sapphire M-plane tests, sapphire the angle tests, between when the the cleavage A-plane direction was used and theas the cross-section loading surface, (C- the cracks propagated vertically along a-direction, and then cleavage with long cracks. The cracks were large and very obvious, as shown in Figure 8a. At both sides of the section, the main cracks were about 30 degrees with a-direction. In addition, along the long cracks, there were many small transverse steps, as shown in Figure 8b. Swain et al. have explained this cleavage step deformation in brittle solids. Their occurrence could be satisfactorily explained in terms of a deflection in the base fracture of the near-symmetrical connecting sliver from one end to the other. Such a deflection would require only a small disturbance in stress conditions at the advancing crack front [35].

Figure 8. Morphology of the fractured surface in M-plane sapphire tests. (a) Fractured surface of M- A tests, “M” is the cross-section of the sapphire sample, “A” is the loaded surfaces. (b) Small trans- verse steps along cracks. (c) Fractured surface of M-C tests, “M” is the cross-section of the sapphire sample, “C” is the loaded surfaces. (d) Local cracks.

When the C-plane was used as the loading surface, cleavage was along the c-direc- tion. The fractured surface was smooth and flat with short pre-crack propagation, as shown in Figure 8c. The crack propagation in the middle of the section was along the c- direction. At both sides of the section, the main cracks were about 60 degrees with a-di- rection, as shown in Figure 8d. In C-plane sapphire tests, when the M-plane was used as the loading surface, ini- tially, there were thick and short triangular cracks along the m-direction, and when the cracks disappeared, the section became smooth and flat, as shown in Figure 9a,b. Earlier, it can be confirmed that the cleavage of C-plane sapphire is along the R-plane in Figure

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plane) is 33 degrees when the M-plane is used as the loading surface. When the A-plane is used as the loading surface, the angle between the cleavage direction and the cross-section (C-plane) is 42 degrees. Theoretically, along the c-direction, there are only interchanging O–Al layers and hence cleavage is not favored. On the other hand, along the r-direction, weaker O–O layers are present and so cleavage is favored [27]. In fact, measurements of the fracture surface energy previously performed by Wiederhorn et al. [34], using the double-cantilever technique, showed that a crack propagating along the C-plane requires over six times more energy than along the R-plane. In the tests of C-plane sapphire, the Figure 7. Fractured specimens. (a) Fracture of M-plane sapphire, where “M” is the cross-section of pre-crack was on the C-plane, and it was predicted that the crack would propagate along the sapphire sample, “A” and “C” are the loaded surfaces of the sapphire sample. (b) Fracture of A- the R-plane and cleavage would occur. If the cleavage along the R-plane occurs when plane sapphire, where “A” is the cross-section of the sapphire sample, “C” and “M” are the loaded the M-plane is used as the loading surface, the fracture surface forms 32.4 degrees with surfaces of the sapphire sample. (c) Fracture of C-plane sapphire when loading M-plane. (d) Frac- the m-direction. When the A-plane is the loading surface, the angle between the fracture ture of C-plane sapphire, where “C” is the cross-section of the sapphire sample, “M” and “A” are surface and a-direction is 47 degrees. The experimental results are very close to the results the loaded surfaces of the sapphire sample. (e) Fracture of C-plane sapphire when loading A-plane. of the crystallographic analysis, so it can be considered that the cleavage plane of C-plane (f) Fracture morphology with (i)-fracture zone, (ii)-V-notch zone, (iii)-U-notch groove zone. sapphire is R-plane. This result is consistent with a study by Graça et al., and previous research [26]. Besides, the results of the M-plane and A-plane sapphire are similar, and cleavageThe was morphology along the cross-section. of the fractured surface was studied by a scanning electron micro- scopeThe and morphology three-dimensional of the fractured video surface microscopy, was studied as shown by a scanning in Figure electron 7f. The micro- fracture sur- scopeface cracks and three-dimensional of single-crystal video sapphire microscopy, with different as shown crystal in Figure orientations7f. The fracture also surface showed obvi- cracksous anisotropy, of single-crystal with different sapphire withdegrees different of crack crystal propagation orientations and also surface showed fracture. obvious anisotropy,In the with M-plane different sapphire degrees tests, of crack when propagation the A-plane and was surface used fracture. as the loading surface, the cracksIn thepropagated M-plane sapphire vertically tests, along when a-direction, the A-plane and was usedthen ascleavage the loading with surface, long cracks. the The cracks propagated vertically along a-direction, and then cleavage with long cracks. The cracks were large and very obvious, as shown in Figure 8a. At both sides of the section, cracks were large and very obvious, as shown in Figure8a. At both sides of the section, thethe mainmain cracks cracks were were about about 30 degrees30 degrees with witha-direction. a-direction. In addition, In addition, along the along long the cracks, long cracks, therethere were were many many small small transverse transverse steps, steps, as shown as sh inown Figure in Figure8b. Swain 8b. etSwain al. have et al. explained have explained thisthis cleavagecleavage step step deformation deformation in brittlein brittle solids. soli Theirds. Their occurrence occurrence could becould satisfactorily be satisfactorily explained in in terms terms of of a deflectiona deflection in the in basethe base fracture fracture of the of near-symmetrical the near-symmetrical connecting connecting sliver from from one one end end to to the the other. other. Such Such a deflection a deflection would would require require only a smallonly a disturbance small disturbance inin stressstress conditions conditions at at the the advancing advancing crack crack front front [35]. [35].

Figure 8. 8.Morphology Morphology of of the the fractured fractured surface surfac ine M-planein M-plane sapphire sapphire tests. tests. (a) Fractured (a) Fractured surface surface of of M- M-AA tests, tests, “M” “M” is isthe the cross-section cross-section of of the the sa sapphirepphire sample,sample, “A” “A” is is the the loaded loaded surfaces. surfaces. (b )(b Small) Small trans- transverseverse steps steps along along cracks. cracks. (c) Fractured (c) Fractured surface surface of ofM-C M-C tests, tests, “M” “M” is is the the cross-section cross-section of of the the sapphire sapphiresample, sample,“C” is the “C” loaded is the loaded surfaces. surfaces. (d) Local (d) Local cracks. cracks. When the C-plane was used as the loading surface, cleavage was along the c-direction. The fracturedWhen the surface C-plane was smoothwas used and as flat the with load shorting pre-cracksurface, cleavage propagation, was as along shown the in c-direc- Figuretion. The8c. The fractured crack propagation surface was in the smooth middle ofand the flat section with was short along pre-crack the c-direction. propagation, At as bothshown sides in ofFigure the section, 8c. The the crack main crackspropagation were about in the 60 degrees middle with of thea-direction, section aswas shown along the c- indirection. Figure8d. At both sides of the section, the main cracks were about 60 degrees with a-di- rection,In C-plane as shown sapphire in Figure tests, when8d. the M-plane was used as the loading surface, initially, thereIn were C-plane thick and sapphire short triangular tests, when cracks the along M-pl theanem was-direction, used andas the when loading the cracks surface, ini- disappeared,tially, there thewere section thick became and short smooth triangular and flat, ascracks shown along in Figure the9 a,b.m-direction, Earlier, it canand be when the confirmedcracks disappeared, that the cleavage the section of C-plane became sapphire smooth is along and flat, the R-planeas shown in Figurein Figure7d. Due9a,b. Earlier, it can be confirmed that the cleavage of C-plane sapphire is along the R-plane in Figure

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7d. Due to the crystal structure being symmetrical along the m-direction in C-plane sap- phire, the trend of crack propagation along the r-direction is counteracted. So, the length 7d.ofto the Due initial crystal to the cracks structure crystal was structure being short, symmetrical and being the symmetrical sect alongion was the along smoothm-direction the and m-direction inflat. C-plane When in sapphire,C-planethe A-plane sap- the was phire,usedtrend as ofthe crackthe trend loading propagation of crack surface, propagation along the the wholer -directionalong fracture the isr-direction counteracted. surface is showed counteracted. So, the inclined length So, of longthe the length initialand thin ofcracks,cracks the initial wasas shown short,cracks andinwas Figure theshort, section 9c,d.and the wasCracks sect smoothion were was and formed smooth flat. Whenatand an flat. angle the When A-plane of the57 degreesA-plane was used waswith as m- useddirection.the loading as the It surface,loadingwas very thesurface, close whole tothe fracturethe whole angl surfaceefracture of 57.6 showed surfacedegrees inclinedshowed between longinclined the and M-plane thinlong cracks,and and thin r-direc- as cracks,tionshown from as in Figureshownthe crystal9 inc,d. Figure structure. Cracks 9c,d. were It Cracks also formed confirmed were at anformed angle that at ofthe an 57 cleavage degreesangle of withof57 the degreesm C-plane-direction. with sapphire m It- direction.iswas along very the closeIt wasR-plane; to very the angleclosehowever, to of the 57.6 due angl degrees toe theof 57.6 betweencrystal degrees structure the between M-plane was the and not M-planer symmetrical-direction and from r-direc- along the the tionacrystal-direction, from structure. the and crystal CR-cracks Italso structure. confirmed were It also formed. that confirmed the cleavage that the of thecleavage C-plane of sapphirethe C-plane is alongsapphire the isR-plane; along the however, R-plane; due however, to the crystal due tostructure the crystal was structure not symmetrical was not symmetrical along the a-direction, along the aand-direction, CR-cracks and were CR-cracks formed. were formed.

Figure 9. Morphology of the fractured surface in C-plane sapphire tests. (a) Fractured surface of C- FigureMFigure tests, 9. “C” MorphologyMorphology is the cross-section of the fractured of the surfacesurface sapphire inin C-plane C-planesample, sapphire sapphire “M” is the tests. tests. loaded ( a()a Fractured) Fractured surfaces. surface surface (b) Local of of C-M C-cracks. M(tests,c) tests, Fractured “C” “C” is is the surface the cross-section cross-section of C-A tests, of of the the “C” sapphire sa pphireis the sample,cross- sample,section “M” “M” is isof thethe the loadedloaded sapphire surfaces.surfaces. sample, ( b) “A”Local Local is cracks. cracks.the loaded (surfaces.(cc)) Fractured Fractured (d) surfaceLocal surface cracks. of of C-A C-A tests, tests, “C” “C” is is the the cross- cross-sectionsection of the sapphire sample, “A” is the loaded surfaces.surfaces. ( (dd)) Local Local cracks. cracks. In the A-plane sapphire tests, the fracture direction was parallel to the section. No matterInIn theloading the A-plane C-plane sapphire or M-plane, tests, the thefracture section direction was smooth was parallel without to thecrack, section. as shown No in matterFigurematter loading10a,c. loading It C-plane C-planeis considered or or M-plane, that the the the cleavage section was direction smooth is alongwithout the crack, A-plane. as shown Cleavage in is FigurealongFigure the10a,c.10a,c. c-direction It It is is considered considered when thatloading that the the cleavage cleavagethe C-plane, direction direction as shownisis along along in the theFigure A-plane. A-plane. 10b. Cleavage CleavageOn the isother alonghand,is along thecleavage the c-directionc-direction is along when when the loading m loading-direction the the C-plane, C-plane,when loadingas as shown shown the in in M-plane,Figure Figure 10b.10 asb. Onshown On the the other in Figure hand,10d.hand, cleavage isis alongalong the them m-direction-direction when when loading loading the the M-plane, M-plane, as shownas shown in Figure in Figure 10d. 10d.

Figure 10. Morphology of the fractured surface in A-plane sapphire tests. (a) Fractured surface of Figure 10.10. MorphologyMorphology of of the the fractured fractured surface surface in inA-plane A-plane sapphire sapphire tests. tests. (a) Fractured(a) Fractured surface surface of of A-C tests,tests, “A” “A”“A” is isis the the the cross-section cross-section cross-section of of the of the sapphire the sa pphiresapphire sample, sample, sample, “C” “C” is the“C” is loaded the is theloaded surfaces. loaded surfaces. (bsurfaces.) Local (b) cracks. Local(b) Local cracks.(c) Fractured ((cc)) Fractured Fractured surface surface ofsurface A-M of tests, of A-M A-M “A” tests, tests, is the“A” “A” cross-section is theis the cross-section cross-section of the sapphire of the of thesapphire sample, sapphire sample, “M” sample, is the“M” loaded “M”is the is the loadedsurfaces. surfaces.surfaces. (d) Local ( d(d) cracks. )Local Local cracks. cracks.

TheThe fracture fracturefracture characteristics characteristics characteristics of of the the specimens specimens specimens are are summarized summarized in Table in Table5 5.. TheThe 5. M-planeTheM-plane M-plane sapphiresapphire and andand A-plane A-planeA-plane sapphire sapphire sapphire are are are cleaved cleaved al along ongalong the the cross-section, cross-section, which which showed showed lower lower fracturefracture toughness. toughness.toughness. The The The cleavage cleavage cleavage of of of C-plane C-plane C-plane sapphire sapphire sapphire is is along alongis along the the theR-plane, R-plane, and andit showed it showed the highest fracture toughness. the highesthighest fracture fracture toughness. toughness. InIn addition,addition, the the formation formation and and propagation propagation of ofcracks cracks must must also also be considered.be considered. Low- Low- mobility dislocations, dislocations, impurities, impurities, grain grain boundaries, boundaries, and and residual residual stresses stresses are potentialare potential fac- fac- tors forfor crackcrack nucleation nucleation and and propagation. propagation. The The high high density density and and low low mobility mobility growth growth dis- dis- locations in in the the material material lead lead to to a decreasea decrease in infracture fracture resistance. resistance. Due Due to not to notenough enough mov- mov- ing dislocations,dislocations, the the energy energy introduced introduced cannot cannot be bedissipated dissipated by theby theclassical classical plastic plastic defor- defor-

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Crystals 2021, 11, 930 12 of 16 mation mechanism, so it must be dissipated by fracture. In addition, impurities and crys- tal defects in the material lead to a decrease in fracture resistance. Besides, due to the grain boundary, crack propagation is restricted. For example, the grain boundary will lead to Table 5. Summary of the fracture characteristics of the specimens. crack deflection to decrease the stress intensity at the crack tip, and the driving force of Sample Loadedcrack propagation Surface is Cleavage reduced Direction[26]. The cracks formed Morphology and the of propagation the Fractured of Surface single-crystal sapphire is complex, which needs further study in this paper. M-Plane sapphire A-plane a-direction Long large cracks with small transverse steps M-Plane sapphire C-plane c-direction Flat and smooth with short crack growth C-Plane sapphireTable M-plane 5. Summary of the fracturer-direction characteristics of Flat the withspecimens. thick and short triangular cracks C-Plane sapphire A-plane r-direction Very rough surface with 57◦ cracks Sample Loaded Surface Cleavage Direction Morphology of the Fractured Surface A-Plane sapphire C-plane c-direction Flat and smooth without cracks M-PlaneA-Plane sapphire sapphire A-plane M-plane a-directionm-direction Long large Flatcracks and with smooth small without transverse cracks steps M-Plane sapphire C-plane c-direction Flat and smooth with short crack growth C-Plane sapphire M-plane r-direction Flat with thick and short triangular cracks In addition, the formation and propagation of cracks must also be considered. Low- C-Plane sapphire A-planemobility dislocations,r-direction impurities, grain boundaries, Very rough and surface residual with stresses 57° cracks are potential A-Plane sapphire C-planefactors for crack nucleationc-direction and propagation. TheFlat highand smooth density without and low cracks mobility growth A-Plane sapphire M-planedislocations in them-direction material lead to a decrease Flat in fracture and smooth resistance. without Due cracks to not enough moving dislocations, the energy introduced cannot be dissipated by the classical plastic deformation3.4. Roughness mechanism, of the Fractured so it Surface must be dissipated by fracture. In addition, impurities and crystalThe defects surface in roughness the material of leadthe fracture to a decrease section in was fracture measured resistance. by the Besides, three-dimensional due to the grainoptical boundary, profiler. crackThe measured propagation results is restricted. are shown For in example,Figure 11. the The grain single-crystal boundary willsapphire lead towith crack different deflection crystal to decreaseorientations the stressstill show intensityed obvious at the crackanisotropic. tip, and The the roughness driving force of dif- of crackferent propagation crystal planes isreduced decreased [26 in]. Thethe cracksorder of formed C-plane and > theM-plane propagation > A-plane, of single-crystal the same as sapphirethe order is of complex, fracture whichtoughness. needs Roughness further study affects in this the paper.dissipation of fracture energy and fracture toughness, the rougher the fracture surface is, the higher the fracture toughness 3.4. Roughness of the Fractured Surface is. TheThe surfacefracture roughness surfaces of of “1-M-A”, the fracture “2-M-C”, section “5-A-C”, was measured and “6-A-M” by the three-dimensional test groups were opticalvery smooth, profiler. because The measured of the intergranular results are shown fracture in Figure[36]. Even 11. Thethough single-crystal the fracture sapphire section withof “1-M-A” different test crystal has many orientations long cracks, still showedother zones obvious were anisotropic. also very smooth. The roughness Due to the of differentinclined crystalfracture planes of the decreased C-plane insapphire, the order the of C-planefracture> surface M-plane was > A-plane, very rough, the same andas it theshowed order a of strong fracture ability toughness. to resist Roughness fracture. With affects the the obvious dissipation oblique of fracturecracks, the energy “4-C-A” and fracturetest showed toughness, the largest the rougher surface theroughness. fracture surface is, the higher the fracture toughness is.

FigureFigure 11. TheThe roughness roughness of of the the fracture fracture section. section. (a) ( aTest) Test 1-M-A; 1-M-A; (b) ( bTest) Test 2-M-C; 2-M-C; (c) (Testc) Test 3-C-M; 3-C-M; (d) (Testd) Test 4-C-A; 4-C-A; (e) (Teste) Test 5-A-C; 5-A-C; (f) (Testf) Test 6-A-M. 6-A-M.

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The fracture surfaces of “1-M-A”, “2-M-C”, “5-A-C”, and “6-A-M” test groups were very smooth, because of the intergranular fracture [36]. Even though the fracture section of “1-M-A” test has many long cracks, other zones were also very smooth. Due to the inclined Crystals 2021, 11, x FOR PEER REVIEW 13 of 15 fracture of the C-plane sapphire, the fracture surface was very rough, and it showed a strong ability to resist fracture. With the obvious oblique cracks, the “4-C-A” test showed the largest surface roughness. 4. The Critical Resolved Shear Stress for Fracture Opening 4. TheAbove Critical this Resolvedpaper, the ShearC-plane Stress sapphire for Fracture cleaves Openingalong the R-plane by analysis,Above and this M-, paper, A-plane the sapphires C-plane sapphire cleave al cleavesong their along cross-section. the R-plane Does by crystallography sapphire un- dergoanalysis, plastic and deformation M-, A-plane before sapphires dissociation cleave along fracture? their Mizu cross-section.moto et al. Does have sapphire conducted un- plunge-cutdergo plastic tests deformation to deeply analyze before dissociationthe brittle-ductile fracture? transition Mizumoto on the et al.basal have (0001) conducted plane. Theplunge-cut anisotropic tests deformation to deeply analyze behavior the of brittle-ductile sapphire is transitiondiscussed onin theterms basal of slip (0001) system, plane. cleavage,The anisotropic and twinning deformation [37]. behavior of sapphire is discussed in terms of slip system, cleavage,The tendency and twinning for plastic [37]. deformation can be expressed by the resolved shear stress on a specificThe tendency slip system. for plastic Schmid’s deformation law des cancribes be expressed the relationship by the resolved between shear the resolved stress on sheara specific stress slip and system. slip system Schmid’s [38] lawby: describes the relationship between the resolved shear stress and slip system [38] by: τ𝜏== σ a·𝜎 m∙𝑚 (6)(6) m𝑚= =cos 𝑐𝑜𝑠ϕcosλ 𝜑𝑐𝑜𝑠𝜆 (7)(7)

wherewhere ττ isis the the resolved resolved shear shear stress, stress, σa σisa theis the applied applied stress, stress, m ism theis theSchmid-factor, Schmid-factor, φ is theϕ is anglethe angle between between the applied the applied stress stress and slip and plane, slip plane, λ is theλ angleis the between angle between the applied the applied stress andstress slip and direction, slip direction, as shown as shownin Figure in Figure12. If the 12 resolved. If the resolved shear stress shear surpasses stress surpasses the CRSS, the theCRSS, slip thesystem slip systemwill be willactivated. be activated. The Schmid-factor The Schmid-factor m quantifiesm quantifies how easily how easily the slip the sys- slip temsystem is activated, is activated, and andso is sothe is twinning the twinning system. system. The CRSS The CRSS value value in possible in possible slip and slip twin and systemstwin systems of single-crystal of single-crystal sapphire sapphire is shown is shown in Table in Table1. 1.

FigureFigure 12. 12. SlipSlip deformation deformation of of a a single-crystal single-crystal specimen specimen under under uniaxial uniaxial tension. tension.

K InIn this this study, study, we we have have obtained obtained K1C1C ofof single-crystal single-crystal sapphire sapphire with with different different orienta- orienta- tions,tions, as as seen seen in in Table Table 44.. The applied stress can be calculated by:

K𝐾1C σa𝜎==√ (8)(8) √π𝜋𝑟r

wherewhere rr isis the the cutting cutting depth depth of of laser laser about about 0.5 0.5 mm. mm. TheThe resolved resolved shear shear stress stress was was calculated by FormulasFormula (6), (6)–(8). (7), and The (8). result The was result showed was showedin Table in6. Table 6. Only in C-plane sapphire tests, cleavage is along the R-plane with 57.6 degrees. The resolved shear stress (0.152 GPa) surpasses the CRSS (0.111 GPa), so the rhombohedral twin is activated probably before dissociation fracture. In other sample tests, the resolved shear stress did not surpass the CRSS of plastic deformation, and the plastic degeneration would not be activated before dissociation fracture.

Table 6. Calculation of the resolved shear stress [28].

CRSS (GPa) Activation Sample K1C (MPa·m1/2) r (mm) σa (MPa) Plastic Deformation φ (°) λ (°) m τ (GPa) Slip/Twin Slip/Twin Rhombohedral plane 3/0.111 57.6 32.4 0.45 0.087 N/N M-plane sapphire 2.42 0.5 193 Basal plane 17/0.148 0 90 0 0 N/N Prism plane 1.2/- 90 0 0 0 N/-

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Table 6. Calculation of the resolved shear stress [28].

1/2 CRSS (GPa) ◦ ◦ Activation Sample K1C (MPa·m ) r (mm) σa (MPa) Plastic Deformation ϕ ( ) λ ( ) m τ (GPa) Slip/Twin Slip/Twin Rhombohedral plane 3/0.111 57.6 32.4 0.45 0.087 N/N M-plane 2.42 0.5 193 sapphire Basal plane 17/0.148 0 90 0 0 N/N Prism plane 1.2/- 90 0 0 0 N/- Rhombohedral plane 3/0.111 32.4 57.6 0.45 0.152 N/Y C-plane 4.24 0.5 338 sapphire Basal plane 17/0.148 90 0 0 0 N/N Prism plane 1.2/- 0 90 0 0 N/- Rhombohedral plane 3/0.111 57.6 32.4 0.45 0.083 N/N A-plane 2.32 0.5 185 sapphire Basal plane 17/0.148 0 90 0 0 N/N Prism plane 1.2/- 90 0 0 0 N/- Where “N” means that plastic deformation is not activated, “Y” means that plastic deformation is activated.

Only in C-plane sapphire tests, cleavage is along the R-plane with 57.6 degrees. The resolved shear stress (0.152 GPa) surpasses the CRSS (0.111 GPa), so the rhombohedral twin is activated probably before dissociation fracture. In other sample tests, the resolved shear stress did not surpass the CRSS of plastic deformation, and the plastic degeneration would not be activated before dissociation fracture.

5. Conclusions (1) The fracture toughness of single-crystal sapphire with different crystal planes showed anisotropy. The fracture toughness of C-plane sapphire was highest than other orientations. Fracture toughness of different crystal planes decreases in the order of C-plane > M-plane > A-plane. (2) The fracture morphology of single-crystal sapphire with different crystal faces shows obvious anisotropy, different cracks growth, and morphology. In M-plane sapphire, there are many long cracks on the fracture when loading A-plane. In C-plane sapphire, the whole fracture presents inclined cracks with 57 degrees when loading A-plane. The fracture surfaces of other samples are smooth. The roughness of different crystal planes decreased in the order of C-plane > M-plane > A-plane, the same as the order of fracture toughness. The surface roughness will affect the dissipation of fracture energy. With a larger the fracture toughness value, the ability of sapphire to resist fracture is stronger. (3) C-plane sapphire cleavages along the R-plane with an angle of 57.6 degrees. M-plane and A-plane sapphire cleavages along their cross-section. The cleavage fracture of C-plane sapphire seems to be related to the rhombohedral twin. The rhombohedral twin promotes crack propagation and forms the fracture morphology of inclined cracks.

Author Contributions: Conceptualization, F.J. and S.H.; methodology, J.L.; validation, X.L., F.J. and Q.W.; formal analysis, S.H.; investigation, B.G.; resources, N.W.; data curation, S.H.; writing—original draft preparation, S.H.; writing—review and editing, F.J.; visualization, B.G.; supervision, Q.W.; project administration, F.J. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (No. 51805176) and the Natural Science Foundation of Fujian (Grant No. 2019J01059). Data Availability Statement: Data can be obtained by contacting the corresponding author. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study.

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