MATERIALS IENGE& EGEERIG Materials Science and Engineering A 412(2005)146-152 www.elsevier.com/locate/msea Si3N4/BN fibrous monoliths: Mechanical properties and tribological responses K C. Goretta,*D. Singha. T.A. Cruse a. A. Erdemir a. J. L. Routbort a F. Gutierrez-Morab, A.R. de Arellano-Lopez b, T.S. Orlova", B I Smirnov c Energy Technology Division, Argonne National Laboratory Argonne, IL 60439-4838 USA b Departamento de Fisica de la Materia Condensada, Universidad de Sevilla, 41080 Sevilla, spain e loffe Physico-Technical Institute, Politekhnicheskaya ul. 26, St. Petersburg 194021, Russia Received in revised form 21 April 2005 Ceramic fibrous monoliths ( FMs)consist of fiber-like cells that surround a weaker matrix phase called the cell boundary. FMs based on Si, N4/BN exhibit many excellent mechanical properties, and much work has been done to characterize and understand the relations among their processing, microstructure,and properties. The following body of data and understanding for Si3 N4/BN FMs are discussed in this paper: processing, elastic onstants,in-plane fracture and modeling of fracture, thermal stresses, interfacial shear strength and tailoring of gross interface structure, creep, impact erosion resistance, and sliding wear resistance. Possibilities to improve their properties are also presented C 2005 Elsevier B V. All rights reserved Keywords: Fibrous monolith; Ceramic composite; Mechanical properties 1. Introduction Tucson, AZ). Substantial work continues on them to improve processing methods, lower fabrication costs, incorporate new Powder-derived fibrous monoliths(FMs) generally consist compositions, and produce new forms. The properties of exist- of strong cells, typically 100-500 um wide, that are surrounded ing ceramic FMs have been studied in detail for nearly a decade by a weaker cell boundary[1-8]. FMs are produced most often [3-8, 11-21]. This paper will summarize current knowledge and by extrusion of duplex filaments, followed by lay-up of the understanding of Si3 NA/BN FMs filaments into laminates. The extruded filaments consist of a cell phase surrounded by a sheath that forms a continuous cell boundary [2-8 2. Manufacture of Si3 Ng/BN fibrous monoliths FMs exhibit graceful failure in flexure. Energy dissipation arises from substantial sliding of the cells, and branching and All current ceramic FMs are based on a duplex microstructure deflection of cracks [8]. FMs constitute in some applications that consists of dense cells separated by a continuous cell bound lower cost alternatives to conventional continuous-fiber ceramic ary. The cells provide most of the strength of the FM. The cell omposites, and many ceramic FMs are available commercially boundary provides toughness by isolating the cells from each 9]. Cermet FMs are also produced; they have exhibited excep- other and promoting dissipation of fracture energy by mecha- nal performance drill bits nisms such as pullout of the cells [18] or deflection of a crack through the cell boundary [7, 18 Ceramic FMs based on Si3N4 cells and a Bn boundary Hexagonal BN [2-8, 11-20] is an effective cell boundary [2-8, 11-21] offer excellent mechanical performance, and they because it forms a dense, highly textured matrix that bonds only are a commercial product(Advanced Ceramics Research of weakly to the strong Si3N4 cells [13, 20]. Oxide sintering aids in the Si3N4 (generally Al2O3 and Y203)that leach into the BN cell boundary during hot pressing impart most of the bond Corresponding author. Tel: +1 630 2527761; fax: +1 630 252 3604 ing [20]- BN would be an ideal cell-boundary material, except Iress: gretta @anl. gov(K C. Coretta) for the fact that it can oxidize severely at elevated temperatures 0921-5093/S-see front matter o 2005 Elsevier B V. All rights reserved
Materials Science and Engineering A 412 (2005) 146–152 Si3N4/BN fibrous monoliths: Mechanical properties and tribological responses K.C. Goretta a,∗, D. Singh a, T.A. Cruse a, A. Erdemir a, J.L. Routbort a, F. Gutierrez-Mora b, A.R. de Arellano-Lopez b, T.S. Orlova c, B.I. Smirnov c a Energy Technology Division, Argonne National Laboratory, Argonne, IL 60439-4838, USA b Departamento de Fisica de la Materia Condensada, Universidad de Sevilla, 41080 Sevilla, Spain c Ioffe Physico-Technical Institute, Politekhnicheskaya ul. 26, St. Petersburg 194021, Russia Received in revised form 21 April 2005 Abstract Ceramic fibrous monoliths (FMs) consist of fiber-like cells that surround a weaker matrix phase called the cell boundary. FMs based on Si3N4/BN exhibit many excellent mechanical properties, and much work has been done to characterize and understand the relations among their processing, microstructure, and properties. The following body of data and understanding for Si3N4/BN FMs are discussed in this paper: processing, elastic constants, in-plane fracture and modeling of fracture, thermal stresses, interfacial shear strength and tailoring of gross interface structure, creep, impact erosion resistance, and sliding wear resistance. Possibilities to improve their properties are also presented. © 2005 Elsevier B.V. All rights reserved. Keywords: Fibrous monolith; Ceramic composite; Mechanical properties 1. Introduction Powder-derived fibrous monoliths (FMs) generally consist of strong cells, typically 100–500m wide, that are surrounded by a weaker cell boundary [1–8]. FMs are produced most often by extrusion of duplex filaments, followed by lay-up of the filaments into laminates. The extruded filaments consist of a cell phase surrounded by a sheath that forms a continuous cell boundary [2–8]. FMs exhibit graceful failure in flexure. Energy dissipation arises from substantial sliding of the cells, and branching and deflection of cracks [8]. FMs constitute in some applications lower cost alternatives to conventional continuous-fiber ceramic composites, and many ceramic FMs are available commercially [9]. Cermet FMs are also produced; they have exhibited exceptional performance as, for example, inserts for mining drill bits [10]. Ceramic FMs based on Si3N4 cells and a BN boundary [2–8,11–21] offer excellent mechanical performance, and they are a commercial product (Advanced Ceramics Research of ∗ Corresponding author. Tel.: +1 630 252 7761; fax: +1 630 252 3604. E-mail address: goretta@anl.gov (K.C. Goretta). Tucson, AZ). Substantial work continues on them to improve processing methods, lower fabrication costs, incorporate new compositions, and produce new forms. The properties of existing ceramic FMs have been studied in detail for nearly a decade [3–8,11–21]. This paper will summarize current knowledge and understanding of Si3N4/BN FMs. 2. Manufacture of Si3N4/BN fibrous monoliths All current ceramic FMs are based on a duplex microstructure that consists of dense cells separated by a continuous cell boundary. The cells provide most of the strength of the FM. The cell boundary provides toughness by isolating the cells from each other and promoting dissipation of fracture energy by mechanisms such as pullout of the cells [18] or deflection of a crack through the cell boundary [7,18]. Hexagonal BN [2–8,11–20] is an effective cell boundary because it forms a dense, highly textured matrix that bonds only weakly to the strong Si3N4 cells [13,20]. Oxide sintering aids in the Si3N4 (generally Al2O3 and Y2O3) that leach into the BN cell boundary during hot pressing impart most of the bonding [20]. BN would be an ideal cell-boundary material, except for the fact that it can oxidize severely at elevated temperatures 0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.08.042
K.C. Goretta et al /Materials Science and Engineering A 412(2005)146-152 Fig. 1. Schematic diagrams of(a)unidirectional FM and(b) four-ply laminate stacking. 22, 23]. A B2O3-based liquid is formed and rapid degradation and they develop a periodic distortion(pinching) along their of the FMensues For long-term use at elevated temperatures, in lengths(see the scanning electron microscopy(SEM) photomi many environments a highly effective environmental barrier will crographs in Fig. 2). The Si3N4/BN FMs that have been studied have to coat any FM that contains a BN-based cell boundary in detail have consisted of 80-85 vol. cells and 15-20 vol% Following the pioneering work by Halloran and co-workers cell boundary, and were generally >98%dense. An excellent [2-7, FMs are generally fabricated by a single processing review of their microstructural features can be found in Ref [7 sequence: blending of plastic masses of the cell and cell- boundary phases; coextruding a duplex filament consisting of a 3. Mechanical properties of Si3 N4/BN fibrous monoliths core and sheath, which form eventually the cell and cell bound- ary;optional bundling of duplex filaments and re-extruding to Mechanical properties that have been attained in Si3N4/BN form a filament with many smaller diameter cells surrounded FMs will be summarized. A series of papers by Halloran by a continuous cell boundary; assembly of the filaments into and co-workers examined, for various laminates, measurement a green body, removing the plastic constituents by heat treat- and modeling of thermal expansion, elastic properties, tensile ment; consolidating to a fibrous monolithic part by sintering or failure in various directions relative to lay-up, shear failure some type of hot pressing. Details on the processing sequence bending failure, and toughening mechanisms and the influ- and various plastic masses have been published [2-7, 12, 13]. ence of various materials properties on them. Ref [7] reviews Successful coextrusion requires matching of the rheological this body of work. Since that review, additional work has properties of the core and sheath plastic masses. Failure to match expanded greatly our knowledge of Si3 N4/BN FMs. In this them adequately can lead to pinching of cells or other structural section, we shall summarize recent studies of additional elas- irregularities, which lead to reduced properties tic properties and thermal expansion, in-plane fracture, and FMs can be unidirectional or cross-ply laminates(Fig. 1). Fil- residual and interfacial stresses. Because of likely exposure in ament placement can be by hand or, for example, by direct means service, we shall also summarize studies of high-temperature such as solid freeform fabrication[24, 26-28]. The resulting cells creep, resistance to solid-particle erosion, and dry and lubricated are typically 100-500 um wide. To date, high-quality Si3 N4/bn sliding wear FMs have been densified by hot pressing. The hot-pressing step The highly anisotropic thermal-expansion coefficient, a, of is the most costly single step in producing FMs Hot isostatic hexagonal BN(to 800C, axooc-l in the basal plane and pressing could possibly reduce costs significantly, and sintering aa 13-40 x 10-6oC-I perpendicular to the basal plane)con could reduce costs still further. The pressing steps induce sub- tributes to the weak bonding of cell boundary to the si3N4 stantial deformation of the cells In unidirectional laminates, the cells, and hence to the toughness of Si3 N4/BN FMs [7, 21].Ten- cells adopt a flattened-hexagonal cross-section; in cross-ply lam- sile strengths measured in flexure have exceeded 700 MPa, but inates, the cells are generally more rectangular in cross-section probably average closer to 450 MPa. Work-of-fracture value Fig. 2. SEM photomicrographs of cross-sections of (a)unidirectional and(b) cross-ply Si3Na/BN FMs; periodic distortions(arrows)along the lengths of cells evident in the cross-ply laminate
K.C. Goretta et al. / Materials Science and Engineering A 412 (2005) 146–152 147 Fig. 1. Schematic diagrams of (a) unidirectional FM and (b) four-ply laminate stacking. [22,23].AB2O3-based liquid is formed and rapid degradation of the FM ensues. For long-term use at elevated temperatures, in many environments a highly effective environmental barrier will have to coat any FM that contains a BN-based cell boundary. Following the pioneering work by Halloran and co-workers [2–7], FMs are generally fabricated by a single processing sequence: blending of plastic masses of the cell and cellboundary phases; coextruding a duplex filament consisting of a core and sheath, which form eventually the cell and cell boundary; optional bundling of duplex filaments and re-extruding to form a filament with many smaller diameter cells surrounded by a continuous cell boundary; assembly of the filaments into a green body; removing the plastic constituents by heat treatment; consolidating to a fibrous monolithic part by sintering or some type of hot pressing. Details on the processing sequence and various plastic masses have been published [2–7,12,13]. Successful coextrusion requires matching of the rheological properties of the core and sheath plastic masses. Failure to match them adequately can lead to pinching of cells or other structural irregularities, which lead to reduced properties. FMs can be unidirectional or cross-ply laminates (Fig. 1). Filament placement can be by hand or, for example, by direct means such as solid freeform fabrication [24,26–28]. The resulting cells are typically 100–500m wide. To date, high-quality Si3N4/BN FMs have been densified by hot pressing. The hot-pressing step is the most costly single step in producing FMs. Hot isostatic pressing could possibly reduce costs significantly, and sintering could reduce costs still further. The pressing steps induce substantial deformation of the cells. In unidirectional laminates, the cells adopt a flattened-hexagonal cross-section; in cross-ply laminates, the cells are generally more rectangular in cross-section and they develop a periodic distortion (pinching) along their lengths (see the scanning electron microscopy (SEM) photomicrographs in Fig. 2). The Si3N4/BN FMs that have been studied in detail have consisted of 80–85 vol.% cells and 15–20 vol.% cell boundary, and were generally ≥98% dense. An excellent review of their microstructural features can be found in Ref. [7]. 3. Mechanical properties of Si3N4/BN fibrous monoliths Mechanical properties that have been attained in Si3N4/BN FMs will be summarized. A series of papers by Halloran and co-workers examined, for various laminates, measurement and modeling of thermal expansion, elastic properties, tensile failure in various directions relative to lay-up, shear failure, bending failure, and toughening mechanisms and the influence of various materials properties on them. Ref. [7] reviews this body of work. Since that review, additional work has expanded greatly our knowledge of Si3N4/BN FMs. In this section, we shall summarize recent studies of additional elastic properties and thermal expansion, in-plane fracture, and residual and interfacial stresses. Because of likely exposure in service, we shall also summarize studies of high-temperature creep, resistance to solid-particle erosion, and dry and lubricated sliding wear. The highly anisotropic thermal-expansion coefficient, α, of hexagonal BN (to 800 ◦C, α ≈ 0 ◦C−1 in the basal plane and α ≈ 13–40 × 10−6 ◦C−1 perpendicular to the basal plane) contributes to the weak bonding of cell boundary to the Si3N4 cells, and hence to the toughness of Si3N4/BN FMs [7,21]. Tensile strengths measured in flexure have exceeded 700 MPa, but probably average closer to 450 MPa. Work-of-fracture values Fig. 2. SEM photomicrographs of cross-sections of (a) unidirectional and (b) cross-ply Si3N4/BN FMs; periodic distortions (arrows) along the lengths of cells are evident in the cross-ply laminate
148 K.C. Gorenta et al /Materials Science and Engineering A 412 (2005)146-152 Table 2 Reported thermal-expansion coefficients of Si3 N4/BN and constituents [21] Material aat1200°C (×10-6K-1)(×10-6K-1) Siana Si3N4(through thickness) bn (in plane) BN(through thickness) 13 Si3 Na/Bn(O%, longitudinal) 94472 SiN4/BN(90°) Si3N4/BN(0/90, in plane) Si3Na/Bn(O/90, through thickness) 3.8 5.6 Fig 3 SEM photomicrograph of surface region of Si3 N4/BN FMs heated to els based on a"brick architecture matched the measured data 1200C in air, loss of BN is evident and some glass that formed on the surface reasonably well [7, 191 has been retained For reasons that remain unknown, vibrational testing consis- tently has yielded e values for BN of 36-37 GPa [ 19, 20, 24: for unidirectional Si3N4/BN FMs are generally 7.5 kJ/m2, but strain gauges and other direct measurements have yielded val- exhibit significant scatter and have exceeded 10 kJ/m2[3-7, 15]. ues of a21 GPa. We endorse the direct measurements [18, 241 In orientations for which the failure occurs through the bN cell Softening of the glass in the bn phase or, in the presence of oxy- boundary, the tensile strength has been reported to be 70 MPa gen, formation of a borate glass, has led to reduced properties and the shear strength 23 MPa [7]. Tests of fast fracture in at>800C flexure [7, 29 have revealed significant strength decreases at 1100C and above owing to oxidation of the bn cell bound- 3.2. Thermal expansion ary(Fig. 3) The mechanical properties of Si]N4/BN FMs in flexure are Thermal-expansion coefficients, a, have been measured from more than adequate for many structural applications, although room temperature(RT) to 1200C, and modeled analytically oxidation at elevated temperature remains a concern. Recent and numerically [19, 21]. The analytical solutions agreed well work on Si3N4/BN FMs focused on in-plane mechanical prop- with those from finite-element analysis, although some uncer- erties because in many applications thermal stresses, and hence tainty was introduced because of the texture of the Bn cell in-plane properties, are expected to dominate [1 boundary [21]. The thermal-expansion coefficients generally increased with temperature and were larger for the through 3.1. Elastic properties thickness direction than in-plane(Table 2) Both unidirectional and cross-ply laminates have been stud- 3.3 d extensively. Data for Youngs modulus, E, are summarized in Table 1. The monolithic Si3N4 and BN specimens were fab arious studies focused on primarily on cross-ply laminates ricated by Advanced Ceramics Research in a manner similar either 0/90 or +45. Notched three-and four-point speci- to that used to produce the FMs. Some specimen-to-specimen mens were initially tested, including loading/unloading events variation is obvious. For the FM measurements reported, mod- All laminates exhibited similar properties. In both orientations, crack growth occurred stably past the load maximum. The unloading/reloading loops revealed significant amounts of hys- Reported values of Youngs modulus of various specimens, and effects of tem- teresis, primarily because of interlocking and frictional sliding perature(n)to 600C, 0%refers to the extrusion direction between broken cells in the crack wake. The effects of this Material E(GPa) AE/AT(MPa/K) Reference crack-wake friction were also reflected in remarkably small changes in specimen compliance with increasing crack growth 7 In the initial tests the work-of-fracture values obtained from 3.66 the notched specimens were 2. 15 and 5.71 kJ/m- for the 0/90 19.6,22 and +45orientations, respectively. The corresponding values BN(through thickness) 5.6, 6.75 [24 of steady-state fracture resistance were 21.4 and 32.7 MPam 小NM BN(0°) which are much higher than the values typical of tough Si3N4 BN(0° 290,295 -4.70 9,24 (≈8MPam05) Si3N4/BN(90° Based on the preliminary results, crack-growth resistance was SiN4/BN(90°) 128,131 9,24 measured per ASTM Standard El152, "Standard Test Method Si3N4/BN(090° Si3N4/BN(090° 189,235.4,2285.39 9,24 for Determining J-R Curves. Both load-line displacement, 8 and the crack-mouth-opening displacement, CMOD, were mea-
148 K.C. Goretta et al. / Materials Science and Engineering A 412 (2005) 146–152 Fig. 3. SEM photomicrograph of surface region of Si3N4/BN FMs heated to 1200 ◦C in air, loss of BN is evident and some glass that formed on the surface has been retained. for unidirectional Si3N4/BN FMs are generally ≈7.5 kJ/m2, but exhibit significant scatter and have exceeded 10 kJ/m2 [3–7,15]. In orientations for which the failure occurs through the BN cell boundary, the tensile strength has been reported to be ≈70 MPa and the shear strength ≈23 MPa [7]. Tests of fast fracture in flexure [7,29] have revealed significant strength decreases at 1100 ◦C and above owing to oxidation of the BN cell boundary (Fig. 3). The mechanical properties of Si3N4/BN FMs in flexure are more than adequate for many structural applications, although oxidation at elevated temperature remains a concern. Recent work on Si3N4/BN FMs focused on in-plane mechanical properties because in many applications thermal stresses, and hence in-plane properties, are expected to dominate [18]. 3.1. Elastic properties Both unidirectional and cross-ply laminates have been studied extensively. Data for Young’s modulus, E, are summarized in Table 1. The monolithic Si3N4 and BN specimens were fabricated by Advanced Ceramics Research in a manner similar to that used to produce the FMs. Some specimen-to-specimen variation is obvious. For the FM measurements reported, modTable 1 Reported values of Young’s modulus of various specimens, and effects of temperature (T) to 600 ◦C; 0◦ refers to the extrusion direction Material E (GPa) E/T (MPa/K) Reference Si3N4 314 −10.31 [19] Si3N4 320 [7] BN 36 3.66 [19,30] BN 19.6, 22 – [7] BN 20.7 – [20] BN (through thickness) 5.6, 6.75 – [24] Si3N4/BN (0◦) 276 – [7] Si3N4/BN (0◦) 290, 295 −4.70 [19,24] Si3N4/BN (90◦) 127 – [7] Si3N4/BN (90◦) 128, 131 −5.96 [19,24] Si3N4/BN (0/90◦) 198 – [7] Si3N4/BN (0/90◦) 189, 235.4, 228 −5.39 [19,24] Table 2 Reported thermal-expansion coefficients of Si3N4/BN and constituents [21] Material α at RT (×10−6 K−1) α at 1200 ◦C (×10−6 K−1) Si3N4 (in plane) 2 1.9 Si3N4 (through thickness) 2.4 3.4 BN (in plane) 1.3 2.4 BN (through thickness) 13 15 Si3N4/BN (0◦, longitudinal) 2.3 3.7 Si3N4/BN (90◦) 2 6.2 Si3N4/BN (0/90◦, in plane) 2.4 3.7 Si3N4/BN (0/90◦, through thickness) 3.8 5.6 els based on a “brick” architecture matched the measured data reasonably well [7,19]. For reasons that remain unknown, vibrational testing consistently has yielded E values for BN of ≈36–37 GPa [19,20,24]; strain gauges and other direct measurements have yielded values of ≈21 GPa. We endorse the direct measurements [18,24]. Softening of the glass in the BN phase or, in the presence of oxygen, formation of a borate glass, has led to reduced properties at >800 ◦C. 3.2. Thermal expansion Thermal-expansion coefficients, α, have been measured from room temperature (RT) to 1200 ◦C, and modeled analytically and numerically [19,21]. The analytical solutions agreed well with those from finite-element analysis, although some uncertainty was introduced because of the texture of the BN cell boundary [21]. The thermal-expansion coefficients generally increased with temperature and were larger for the throughthickness direction than in-plane (Table 2). 3.3. In-plane fracture Various studies focused on primarily on cross-ply laminates, either 0/90◦ or ±45◦. Notched three- and four-point specimens were initially tested, including loading/unloading events. All laminates exhibited similar properties. In both orientations, crack growth occurred stably past the load maximum. The unloading/reloading loops revealed significant amounts of hysteresis, primarily because of interlocking and frictional sliding between broken cells in the crack wake. The effects of this crack-wake friction were also reflected in remarkably small changes in specimen compliance with increasing crack growth. In the initial tests, the work-of-fracture values obtained from the notched specimens were 2.15 and 5.71 kJ/m2 for the 0/90◦ and ±45◦ orientations, respectively. The corresponding values of steady-state fracture resistance were 21.4 and 32.7 MPa m0.5, which are much higher than the values typical of tough Si3N4 (≈8 MPa m0.5). Based on the preliminary results, crack-growth resistance was measured per ASTM Standard E1152, “Standard Test Method for Determining J–R Curves.” Both load-line displacement, δ, and the crack-mouth-opening displacement, CMOD, were mea-
K C Coretta et al. Materials Science and Engineering A 412(2005)146-152 Fig. 4. SEM photomicrographs of Si3 N4/BN FMs fractured in flexure:(a)0/90 cross-ply laminate and(b)+45 laminate; substantial sliding of cells is evident. sured with appropriate gauge for the purpose of ment [18]. Correlations among tests confirmed the validity of culating j and the latter for crack length through a the exponential form for Eq (1) compliance technique. Crack ion was monitored opti In the second approach, analysis of load/CMOD responses cally [18 yielded a similar equation Cracking occurred sequentially; the cracks deflected through offset slightly with respect to their neighbors. The non-coplanar b=0oexp-e) the bn cell boundary. At each crack, the cell locations became fracture sequence and the sliding that occurred between adjacent where ao is a characteristic strength related to the sliding stress cells were responsible for a large portion of the observed fracture and e is a characteristic length related to the pullout length. Eqs energy. The crack length increased with increasing CMOD, up (1)and (2)are related through to a CMOd of 200 um, at which point each specimen was essentially cracked. Subsequently, substantial additional CMOd T =Cor vas accommodated without complete fracture, because of the interlocking and friction between the broken cells. Examinations Both approaches were based on a traction law that follows of the fracture surfaces revealed a more tortuous crack path and an exponential form, characterized by a bridging strength and greater amounts of cell pullout in the +450 specimens than in an effective pullout length. From the former approach, it was the o/90 specimens(Fig 4) inferred that the interfacial sliding stress t associated with pull Descriptions of crack-growth resistance were developed from out was 5-7MPa [18, 24]. By the latter approach, the sliding concepts of crack bridging. The problem was cast in a contin- stress was calculated to be 23-33 MPa[18]. By comparison,the lum mechanics framework. wherein crack-wake friction was values obtained from direct pushout measurements on a similar modeled by a continuous distribution of tractions acting across unidirectional SigNa/BN were t=25#7MPa(and the mea opposing faces of the crack. Results provided corroboration sured debond stress was 45+8MPa; Fig. 5)[20]. (The sliding that stress-intensity-dominated response was obtained (approx- stress for cell pushout was related to a clamping residual stress imately) in the 0/90 FMs, but not in the +450 FMs. In the on the Si3N4 cells. Residual strains were measured by neutron latter FMs, strength appeared to follow a simple net-section diffraction and a clamping stress of 120-150 MPa was calcu- prediction, which indicates highly notch-insensitive response lated. Coupled with a friction coefficient of x0. 2, the sliding stress was calculated to be 24-30 MPa [201) Two complementary approaches to determine the bridging law were developed: one based on a micromechanical model of cell pullout coupled with measurements of pullout lengths, the other based on the load-displacement response of the flexure specimens following fracture of all cells In the first approach, pullout of cells in the Si3N4/Bl likened to pullout in a conventional fiber-reinforced ceramic composite. The applicable bridging law was assumed, from experience, to follow an exponential relationship l 2 where ob is the bridging stress, t the sliding stress, h an effec- tive average pullout length, t the geometric mean of the cell cross-sectional dimensions, and u is the crack opening displace Fig. 5. Typical pushout test data for sliding of Si3N4 cells
K.C. Goretta et al. / Materials Science and Engineering A 412 (2005) 146–152 149 Fig. 4. SEM photomicrographs of Si3N4/BN FMs fractured in flexure: (a) 0/90◦ cross-ply laminate and (b) ±45◦ laminate; substantial sliding of cells is evident. sured with appropriate gauges; the former for the purpose of calculating J and the latter for inferring crack length through a compliance technique. Crack propagation was monitored optically [18]. Cracking occurred sequentially; the cracks deflected through the BN cell boundary. At each crack, the cell locations became offset slightly with respect to their neighbors. The non-coplanar fracture sequence and the sliding that occurred between adjacent cells were responsible for a large portion of the observed fracture energy. The crack length increased with increasing CMOD, up to a CMOD of ≈200m, at which point each specimen was essentially cracked. Subsequently, substantial additional CMOD was accommodated without complete fracture, because of the interlocking and friction between the broken cells. Examinations of the fracture surfaces revealed a more tortuous crack path and greater amounts of cell pullout in the ±45◦ specimens than in the 0/90◦ specimens (Fig. 4). Descriptions of crack-growth resistance were developed from concepts of crack bridging. The problem was cast in a continuum mechanics framework, wherein crack-wake friction was modeled by a continuous distribution of tractions acting across opposing faces of the crack. Results provided corroboration that stress-intensity-dominated response was obtained (approximately) in the 0/90◦ FMs, but not in the ±45◦ FMs. In the latter FMs, strength appeared to follow a simple net-section prediction, which indicates highly notch-insensitive response [18]. Two complementary approaches to determine the bridging law were developed: one based on a micromechanical model of cell pullout coupled with measurements of pullout lengths, the other based on the load–displacement response of the flexure specimens following fracture of all cells. In the first approach, pullout of cells in the Si3N4/BN was likened to pullout in a conventional fiber-reinforced ceramic composite. The applicable bridging law was assumed, from experience, to follow an exponential relationship σb = 2τ h∗ t exp − u h∗ (1) where σb is the bridging stress, τ the sliding stress, h* an effective average pullout length, t the geometric mean of the cell cross-sectional dimensions, and u is the crack opening displacement [18]. Correlations among tests confirmed the validity of the exponential form for Eq. (1). In the second approach, analysis of load/CMOD responses yielded a similar equation σb = σo exp −u (2) where σo is a characteristic strength related to the sliding stress and is a characteristic length related to the pullout length. Eqs. (1) and (2) are related through τ = σot 2 (3) Both approaches were based on a traction law that follows an exponential form, characterized by a bridging strength and an effective pullout length. From the former approach, it was inferred that the interfacial sliding stress τ associated with pullout was ≈5–7 MPa [18,24]. By the latter approach, the sliding stress was calculated to be 23–33 MPa [18]. By comparison, the values obtained from direct pushout measurements on a similar unidirectional Si3N4/BN were τ = 25 ± 7 MPa (and the measured debond stress was 45 ± 8 MPa; Fig. 5) [20]. (The sliding stress for cell pushout was related to a clamping residual stress on the Si3N4 cells. Residual strains were measured by neutron diffraction and a clamping stress of 120–150 MPa was calculated. Coupled with a friction coefficient of ≈0.2, the sliding stress was calculated to be 24–30 MPa [20].) Fig. 5. Typical pushout test data for sliding of Si3N4 cells.
K.C. Gorenta et al /Materials Science and Engineering A 412 (2005)146-152 The discrepancy between the values of 5-7 and 25 MPa 3.4. Creep is believed to be associated mainly with variations in cross- section along the cell length, the result of intrusion of adja- High-temperature compressive creep of unidirectional cent transverse cells during consolidation by pressing( Fig. 2b). Si3 N4/BN has been studied in detail [32] and that of cross-ply The intrusions also led to formation of cusps at many of laminates preliminarily; monolithic BN and Si3N4 have the triple junctions between longitudinal and transverse cells. also been studied [33]. Tests were conducted in inert gas at These features allowed premature disengagement of the cells 1200-1500oC The BN cell-boundary material exhibited micro- during pullout, which led to an overestimation in the con- scopic plasticity, but did not truly creep. Its high-temperature tact area when the measured pullout lengths were used. The fracture strengths were substantially lower than the creep result was a low inferred sliding stress from the load/cMod stresses that the cells themselves could sustain The Fms approach, which is based on the response following complete exhibited good creep resistance in the direction of the cells. The cell fracture, the inferred sliding stress was 23-33 MPa, com- measured creep rates were slightly faster than those of the host parable to the one measured by pushout on a unidirectional Si3 N4 because the bn carried almost no load; a simple rule of material(25 MPa). This correlation indicates that the latter mixtures based on load-bearing area of Si3N4 was obtained approach for determining the bridging parameters was more Data from steady-state creep tests at 1400-1500oC were fit to reliable than the one based on pullout measurements alone. a standard equatio Nevertheless, the two approaches provided corroborating and de complementary information about the form of the bridging drAole-g/RT Bridging was further studied by measuring directly cell pull- where de/dt is the strain rate, Aa constant, o the stress, the out lengths. Two measurements were made for each cell, one stress exponent is unity, o the apparent activation energy, R on each of the two mating faces (a total of >400 measure- the gas constant, and T is absolute temperature. Q was obtained ments; Fig. 6). Pullout lengths were also determined from SEM directly by changing temperature at constant load on a single photomicrographs of cross-sections. The mean pullout length sample, and by comparing strain rates for multiple specimens was found to be 110 um, in broad agreement with the range at the same stress and various temperatures. The calculated inferred from the bridging model and the bending analysis activation energy for the two approaches were 570+150 and (70-90um) 625+40 kJ/mol, respectively. These two values are equal When used together, the two approaches to determine the within experimental error and are equal to that often reported bridging law also provide valuable insights into the factors that for monolithic Si3N4 [32, and references therein] ontrol the efficacy of the bridging, especially those related to the geometry of the cells. That is, the periodic variations in cell 3.5. Erosion and wear resistance cross-section and the cusps that occur at the triple points between the longitudinal and transverse cells limit the extent of debond The solid-particle erosion studies were conducted in vacuum ing and sliding through the bn to a distance comparable to the A stream of angular Sic particles 143 um in average diameter cell width. Elimination of those cusps by better filling space in impacted the targets at normal incidence and 100 m/s. The soft, the green state should increase pullout lengths and hence work- monolithic BN eroded very rapidly. The Si3N4/BN FMs eroded of-fracture values [18, 31] much more rapidly than did monolithic Si3 N4, and, in fact, faster of rule of mixture erosion of a Si3 N4+ BN composite. Rapid loss of the Bn cell boundary and subsequent large-scale removal of the unsupported Si3N4 cells were deemed to be responsible for the rapid erosion 4. Similar rapid erosion of an FM relative to a dens has been reported for ZrSio4-based FMs [35] Erosive damage did not, on the basis of stress, lower the average RT flexural strength of the FMs, but did lower that of he Si3 Na significantly (by 22%)[34] Friction and wear tests have recently been performed between sintered Si3N4(SN220, Kyocera, Kagoshima, Japan) pins and Si3N4(SN220, Kyocera)and Si3N4/BN FM flats, with and without oil lubrication(Mobil 10w30), in a pin-on-d tribometer(CSEM-THT, Neuchatel, Switzerland ). The surfaces of the Si3 N4 flats were initially rough to allow better comparison with wear of the FMs. The oil-lubricated tests were performed at temperatures to 120 C to 10N load in order to create a severe boundary-lubricated sliding regime and to assess the per Fig. 6. SEM photomicrograph of surface of fractured section of 0/90 cross-pl formance of test materials under such severe conditions Tests Si3N4/BN FM; the cell pullout lengths are short were performed up to 5000 m sliding distance to determine the
150 K.C. Goretta et al. / Materials Science and Engineering A 412 (2005) 146–152 The discrepancy between the values of 5–7 and ≈25 MPa is believed to be associated mainly with variations in crosssection along the cell length, the result of intrusion of adjacent transverse cells during consolidation by pressing (Fig. 2b). The intrusions also led to formation of cusps at many of the triple junctions between longitudinal and transverse cells. These features allowed premature disengagement of the cells during pullout, which led to an overestimation in the contact area when the measured pullout lengths were used. The result was a low inferred sliding stress. From the load/CMOD approach, which is based on the response following complete cell fracture, the inferred sliding stress was ≈23–33 MPa, comparable to the one measured by pushout on a unidirectional material (≈25 MPa). This correlation indicates that the latter approach for determining the bridging parameters was more reliable than the one based on pullout measurements alone. Nevertheless, the two approaches provided corroborating and complementary information about the form of the bridging law. Bridging was further studied by measuring directly cell pullout lengths. Two measurements were made for each cell, one on each of the two mating faces (a total of >400 measurements; Fig. 6). Pullout lengths were also determined from SEM photomicrographs of cross-sections. The mean pullout length was found to be ≈110m, in broad agreement with the range inferred from the bridging model and the bending analysis (70–90m). When used together, the two approaches to determine the bridging law also provide valuable insights into the factors that control the efficacy of the bridging, especially those related to the geometry of the cells. That is, the periodic variations in cell cross-section and the cusps that occur at the triple points between the longitudinal and transverse cells limit the extent of debonding and sliding through the BN to a distance comparable to the cell width. Elimination of those cusps by better filling space in the green state should increase pullout lengths and hence workof-fracture values [18,31]. Fig. 6. SEM photomicrograph of surface of fractured section of 0/90◦ cross-ply Si3N4/BN FM; the cell pullout lengths are short. 3.4. Creep High-temperature compressive creep of unidirectional Si3N4/BN has been studied in detail [32] and that of cross-ply laminates preliminarily; monolithic BN and Si3N4 have also been studied [33]. Tests were conducted in inert gas at 1200–1500 ◦C. The BN cell-boundary material exhibited microscopic plasticity, but did not truly creep. Its high-temperature fracture strengths were substantially lower than the creep stresses that the cells themselves could sustain. The FMs exhibited good creep resistance in the direction of the cells. The measured creep rates were slightly faster than those of the host Si3N4 because the BN carried almost no load; a simple rule of mixtures based on load-bearing area of Si3N4 was obtained. Data from steady-state creep tests at 1400–1500 ◦C were fit to a standard equation: dε dt = Aσ1 e−Q/RT , (4) where dε/dt is the strain rate, A a constant, σ the stress, the stress exponent is unity, Q the apparent activation energy, R the gas constant, and T is absolute temperature. Q was obtained directly by changing temperature at constant load on a single sample, and by comparing strain rates for multiple specimens at the same stress and various temperatures. The calculated activation energy for the two approaches were 570 ± 150 and 625 ± 40 kJ/mol, respectively. These two values are equal within experimental error and are equal to that often reported for monolithic Si3N4 [32, and references therein]. 3.5. Erosion and wear resistance The solid-particle erosion studies were conducted in vacuum. A stream of angular SiC particles 143 m in average diameter impacted the targets at normal incidence and 100 m/s. The soft, monolithic BN eroded very rapidly. The Si3N4/BN FMs eroded much more rapidly than did monolithic Si3N4, and, in fact, faster than would be predicted by any sort of rule of mixtures for erosion of a Si3N4 + BN composite. Rapid loss of the BN cell boundary and subsequent large-scale removal of the unsupported Si3N4 cells were deemed to be responsible for the rapid erosion [34]. Similar rapid erosion of an FM relative to a dense monolith has been reported for ZrSiO4-based FMs [35]. Erosive damage did not, on the basis of stress, lower the average RT flexural strength of the FMs, but did lower that of the Si3N4 significantly (by 22%) [34]. Friction and wear tests have recently been performed between sintered Si3N4 (SN220, Kyocera, Kagoshima, Japan) pins and Si3N4 (SN220, Kyocera) and Si3N4/BN FM flats, with and without oil lubrication (Mobil 10W30), in a pin-on-disk tribometer (CSEM-THT, Neuchatel, Switzerland). The surfaces of the Si3N4 flats were initially rough to allow better comparison with wear of the FMs. The oil-lubricated tests were performed at temperatures to 120 ◦C to 10 N load in order to create a severe boundary-lubricated sliding regime and to assess the performance of test materials under such severe conditions. Tests were performed up to 5000 m sliding distance to determine the
K C. Goretta et al. Materials Science and Engineering A 412(2005)146-152 understanding attributable to their efforts We thank dr. jc McNulty for his excellent studies of fracture and for provid ing some of the photomicrographs that appear in this paper 13.3 um This work was supported by the Defense Advanced Research Projects Agency through an Interagency Agreement with the U.S. Department of Energy(DOE), and by doE itself, under Contract W-31-10 38, by North Atlantic Treaty Orga 1.0m zation Grant PSTCLG.977016, by the Russian Academy of Sciences; by the Ministerio de Educacion y Ciencias of Spain, 1.3 mm under CICYT Project MAT2000-1533-C03-03 Fig. 7. Profilometer scan of polished Si3N4/BN surface; removal of BN cell boundary is evident. References long-term frictional response. The linear sliding velocity was [1] w.S. Coblenz, U.S. Patent 4, 772, 524(1988) 0. I m/s and the relative humidity of the test environment was [2] D. Popovic, J.W. Halloran, G.E. Hilmas, G.A. Brady, S. Somas, A Bard, G. Zywicki, U.S. Patent 5, 645, 781(1997) 3]S. Baskaran, S. Nunn, D. Popovich, J.W. Halloran, J. Am. Ceram Soc. For Si3N4 balls sliding against dry Si3N4 and FM fats, fric- tion coefficients were 0.6-0.8. BN lubricant sprayed onto the [4]D Popovic, S Baskaran, G. Zywicki, C Arens, J.W. Halloran, Ceram FM flats produced modest reductions in friction coefficients Trans.42(1994)173-186 For lubricated sliding, friction coefficients for the Si3N4 flats [5]G. Hilmas, A. Brady, J.W. Halloran, Ceram.Trans.51(1995)609- were 0.05-0.15 and for the Fms were 0.01--0.08. The signif- icantly lower coefficients of friction for the FM were probably G. Hilmas, A Brady, U. Abdali, G. Zywicki, J.w. Halloran, Mater. Sci were due to removal of some of the BN cell-boundary mate- [7 D. Kovar, B.H. King, RW.Trice,W.Halloran,J.Am.CeramSoc al, leaving long grooves, typically 6-8 um deep, on the sliding 80(1997)2471-2487 surface (Fig. 7). These grooves likely acted as reservoirs to 8]Sw. Lee, D K. Kim, Ceram. Eng. Sci. Proc. 18(4)(1997)481-486 retain and distribute lubricant, and to trap wear debris. The [9] Advanced Ceramics Research, 3292 East Hemisphere Loop, Tucson, AZ average wear rates of Si3N4 balls were x10-mm'N-Im-I 85705-5013,USA 10]ZZ Fang, A. Griffo, B. White, G. Lockwood, D. Belnap, G. Hilmas, for dry sliding and A10-8 to 10-7mm- for lubri- J. Bitler, Int. J. Ref Met. Hard Mater. 19(2001)453-458 cated sliding. The average specific wear rates of balls were of [11] J.L. Finch, J.M. Staehler, L P. Zawada, W.A. Ellingson, J.G. Sun, CM the same order as those measured with sliding on conventional emer, Ceram. Eng. Sci. Proc. 20(3)(1999)341-351 12].W. Trice, J.W. Halloran, J. Am. Ceram. Soc. 82(1999)2563- [13]RW.Trice, J.w. Halloran, J. Am. Ceram. Soc. 82(1999)2502-2508 4. Summary and assessment [14]SY. Lienard, D. Kovar, R.J. Moon, K.J. Bowm Mater.Sci.53(2000)3365-3371. Manufacture of Si3N4/Bn FMs and their resulting [15]RW Trice, J.W. Halloran, J. Am. Ceram. Soc. 83(2000)311-316 [16]M. Tlustochowitz, D. Singh, W.A. Ellingson, K.C. Goretta, M. Rigali, microstructures have been summarized. Measurements and M. Sutaria, Ceram. Trans. 103(2000)245-254. modeling of various mechanical properties were discussed; elas- [17 D. Singh, T.A. Cruse, D.J. Hermanson, K.C. Goretta, E.W. Zok, JC tic constants, thermal expansion, flexural failure, shear failure, McNulty, Ceram. Eng. Sci. Proc. 21(3)(2000)597-604 n-plane stresses and failure, toughening mechanisms, creep, and [18 J.C. MeNulty, M.R. Begley, F.W. Zok, J. Am. Ceram. Soc. 84(2001) tribological properties. Si3N4/BN FM laminates are relatively [19)B. 1. Smirnov, Y.A. Burenkov, B.K. Kardashev, D. Singh, K.C.Goretta, strong and stiff, very tough in flexure, and resistant to creep and A R de Arellano-Lopez, Phys. Solid State 43(2001)2094-2098. sliding wear. They exhibit, however, poor resistance to impact [20] D. Singh, K.C. Goretta, J W. Richardson Jr, A. de Arellano-lopez, by hard solid particles and are susceptible to oxidation at high Scripta Mater. 46(2002)747-751 temperatures. For use of Si3N4/BN FMs at high temperatures, [21] M.Y. He, D. Singh, J.C. McNulty, F.W. Zok, Comp. Sci. Technol. 62 either service times must be short or a highly effective environ- (2002)967-976 [22].N. Cox, F.W. Zok, Curr Opin. Solid State Sci. Mater. Sci. 1(1996) mental barrier must be applied The modest pullout of cells during fracture (pullout [23]NS Jacobson, E.J. Opila, K.N. Lee, Curr. Opin. Solid State Mater.Sci length 100 um) limits the toughness of Si3 N4/BN FMs. Bet- 5(2001)301-309 ter manufacturing, in which distortion of the cells along their [24] K.C. Goretta, et al. ANL-01/04: Development of Advanced Fibrous lengths is limited, should promote longer pullout lengths and Monoliths-Final Report for Project of 1998-2000, Argonne National [26]AG. Cooper, S. Kang, J w. Kietzman, F.B. Prinz, J. L. Lombardi, L.E. Weiss, Mater. Des. 20(1999)83-89 Acknowledgments 227].D. Cawley, Curr. Opin. Solid State Mater. Sci. 4(1999)483- [28]Jw. Halloran, Brit Ceram. Proc. 59(199
K.C. Goretta et al. / Materials Science and Engineering A 412 (2005) 146–152 151 Fig. 7. Profilometer scan of polished Si3N4/BN surface; removal of BN cell boundary is evident. long-term frictional response. The linear sliding velocity was 0.1 m/s and the relative humidity of the test environment was ≈40%. For Si3N4 balls sliding against dry Si3N4 and FM flats, friction coefficients were 0.6–0.8. BN lubricant sprayed onto the FM flats produced modest reductions in friction coefficients. For lubricated sliding, friction coefficients for the Si3N4 flats were ≈0.05–0.15 and for the FMs were 0.01–0.08. The significantly lower coefficients of friction for the FM were probably were due to removal of some of the BN cell-boundary material, leaving long grooves, typically 6–8m deep, on the sliding surface (Fig. 7). These grooves likely acted as reservoirs to retain and distribute lubricant, and to trap wear debris. The average wear rates of Si3N4 balls were ≈10−5 mm3 N−1 m−1 for dry sliding and ≈10−8 to 10−7 mm3 N−1 m−1 for lubricated sliding. The average specific wear rates of balls were of the same order as those measured with sliding on conventional Si3N4. 4. Summary and assessment Manufacture of Si3N4/BN FMs and their resulting microstructures have been summarized. Measurements and modeling of various mechanical properties were discussed: elastic constants, thermal expansion, flexural failure, shear failure, in-plane stresses and failure, toughening mechanisms, creep, and tribological properties. Si3N4/BN FM laminates are relatively strong and stiff, very tough in flexure, and resistant to creep and sliding wear. They exhibit, however, poor resistance to impact by hard solid particles and are susceptible to oxidation at high temperatures. For use of Si3N4/BN FMs at high temperatures, either service times must be short or a highly effective environmental barrier must be applied. The modest pullout of cells during fracture (pullout length ∼ 100m) limits the toughness of Si3N4/BN FMs. Better manufacturing, in which distortion of the cells along their lengths is limited, should promote longer pullout lengths and improved properties. Acknowledgments We thank our colleagues Prof. F.W. Zok and Dr. W.A. Ellingson for many helpful discussions and for the knowledge and understanding attributable to their efforts. We thank Dr. J.C. McNulty for his excellent studies of fracture and for providing some of the photomicrographs that appear in this paper. This work was supported by the Defense Advanced Research Projects Agency through an Interagency Agreement with the U.S. Department of Energy (DOE), and by DOE itself, under Contract W-31-109-Eng-38; by North Atlantic Treaty Organization Grant PST.CLG.977016; by the Russian Academy of Sciences; by the Ministerio de Educacion y Ciencias of Spain, ´ under CICYT Project MAT2000-1533-C03-03. References [1] W.S. Coblenz, U.S. Patent 4,772,524 (1988). [2] D. Popovic’, J.W. Halloran, G.E. Hilmas, G.A. Brady, S. Somas, A. Bard, G. Zywicki, U.S. Patent 5,645,781 (1997). [3] S. Baskaran, S. Nunn, D. Popovich, J.W. Halloran, J. Am. Ceram. Soc. 76 (1993) 2209–2216. [4] D. Popovic’, S. Baskaran, G. Zywicki, C. Arens, J.W. Halloran, Ceram. Trans. 42 (1994) 173–186. [5] G. Hilmas, A. Brady, J.W. Halloran, Ceram. Trans. 51 (1995) 609– 614. [6] G. Hilmas, A. Brady, U. Abdali, G. Zywicki, J.W. Halloran, Mater. Sci. Eng. 195A (1995) 263–268. [7] D. Kovar, B.H. King, R.W. Trice, J.W. Halloran, J. Am. Ceram. Soc. 80 (1997) 2471–2487. [8] S.W. Lee, D.K. Kim, Ceram. Eng. Sci. Proc. 18 (4) (1997) 481–486. [9] Advanced Ceramics Research, 3292 East Hemisphere Loop, Tucson, AZ 85705-5013, USA. [10] Z.Z. Fang, A. Griffo, B. White, G. Lockwood, D. Belnap, G. Hilmas, J. Bitler, Int. J. Ref. Met. Hard Mater. 19 (2001) 453–458. [11] J.L. Finch, J.M. Staehler, L.P. Zawada, W.A. Ellingson, J.G. Sun, C.M. Deemer, Ceram. Eng. Sci. Proc. 20 (3) (1999) 341–351. [12] R.W. Trice, J.W. Halloran, J. Am. Ceram. Soc. 82 (1999) 2563– 2565. [13] R.W. Trice, J.W. Halloran, J. Am. Ceram. Soc. 82 (1999) 2502–2508. [14] S.Y. Lienard, D. Kovar, R.J. Moon, K.J. Bowman, J.W. Halloran, J. Mater. Sci. 53 (2000) 3365–3371. [15] R.W. Trice, J.W. Halloran, J. Am. Ceram. Soc. 83 (2000) 311–316. [16] M. Tlustochowitz, D. Singh, W.A. Ellingson, K.C. Goretta, M. Rigali, M. Sutaria, Ceram. Trans. 103 (2000) 245–254. [17] D. Singh, T.A. Cruse, D.J. Hermanson, K.C. Goretta, F.W. Zok, J.C. McNulty, Ceram. Eng. Sci. Proc. 21 (3) (2000) 597–604. [18] J.C. McNulty, M.R. Begley, F.W. Zok, J. Am. Ceram. Soc. 84 (2001) 367–375. [19] B.I. Smirnov, Y.A. Burenkov, B.K. Kardashev, D. Singh, K.C. Goretta, A.R. de Arellano-Lopez, Phys. Solid State 43 (2001) 2094–2098. [20] D. Singh, K.C. Goretta, J.W. Richardson Jr., A. de Arellano-Lopez, Scripta Mater. 46 (2002) 747–751. [21] M.Y. He, D. Singh, J.C. McNulty, F.W. Zok, Comp. Sci. 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