MIATERIALS IENGE& ENGMEERN A ELSEVIE Materials Science and Engineering A317(2001)49-58 ww.elsevier. com/locate/msea Influence of fiber coating thickness on fracture behavior of continuous woven nicalon fabric-reinforced silicon-carbide matrix ceramIc composites JH. Miller a P.K. Liaw b,*. D. Landes Oak Ridge National Laboratory, Oak Ridge, TN 37831-6423, US.A b Department of Material Science and Engineering, The Unirersity of Tennessee, 427-b Dougherty, Knoxville, TN 37966-220 Department of Mechanical Engineering, The Unirersity of Tennessee, Knoxville, TN 37996, US.A Abstract Nicalon"plain-weave fiber fabric-reinforced silicon carbide (Sic) matrix composites with various pyrolytic carbon fiber/matrix interface coating thicknesses have been successfully fabricated by forced chemical vapor infiltration(FCVI) methods. The influence of the carbon interface coating thickness on the fracture behavior of these fiber fabric-reinforced SiC composites has been investigated. Experimental results indicate that fiber coating thickness significantly alters the fracture behavior of Sic omposites. The fracture strength exhibits a maximum as the coating thickness increases. a theoretical model has been developed to simulate the fracture behavior in the Sic composites with varied carbon interface coatings. The model assumes that microcracking, which is due to low matrix toughness, initiates and arrests continuously. The model-predicted fracture behavior compares well with the experimental results. o 2001 Elsevier Science B V. All rights reserved Keywords: Ceramic composites: Interface; Fiber; Fracture: Coating thickness; Silicon carbide 1. Introduction mechanisms is dominant [8-1l] Single fiber level be- havior is becoming well understood [14-22]. The details Woven continuous fiber fabric-reinforced ceramic of the complex interactions among the interface condi- composites(CFCCs) have been the subject of much tion, microcrack initiation and arrest, fiber debond and theoretical modeling in last several years [1-7]. Limited slip and delamination of the fiber fabric plies are still work on the mechanical behavior characterization of being studied [10, 12, 13 woven CFCCs including both experimental and theo- Due to the complexity of the layered woven fiber-fab- retical treatments has been done. The goal of this ric structure present in these composites, bulk com- research has been to()develop and standardize appro- priate test methods; (2) gain a mechanistic understand- posite behavior has not been extensively modeled ing of the complex fracture mechanisms that take place 9,23-251. Steif and Trojnacki([23, 24]developed two similar models, the ' slipping-layers model, and the during the failure of these composites; and (3)provide ' unlayered shear-weak model, for analyzing the flexure some insight on the theoretical modeling of cFcS. behavior of bulk cccs, The basis for these models. as For the most part, woven CFCCs tend to exhibit plastic-like deformation prior to failure, and the expla the names imply, is the fact that laminated CFCCs nations for this behavior are fiber bridging. crack hibit low interlaminar shear strength [9, 10, 23-25 branching, microcracking, delamination, fiber-matrix Ihe ' slipping-layers model[23] assumes a laminated debond and fiber slip, and eventual fiber fracture [8 material whose layers are coupled only by friction 101. Of course, the condition of the fiber-matrix inter- Therefore, once the applied load reaches a certain level, face plays a key role by controlling, which of the above the layers begin to slip relative to each other. The beam then ceases to be a solid beam and becomes a 'stack of Corresponding author. Fax: + 1-423-9744115. discrete beams subjected to the same loads, affecting E-mail address: pliaw@utk.edu(P K. Liaw) each other only by sliding friction 0921-5093/01/S. see front matter o 2001 Elsevier Science B.V. All rights reserved. PI:S0921-509301)01184-4
Materials Science and Engineering A317 (2001) 49–58 Influence of fiber coating thickness on fracture behavior of continuous woven Nicalon® fabric-reinforced silicon-carbide matrix ceramic composites J.H. Miller a , P.K. Liaw b,*, J.D. Landes c a Oak Ridge National Laboratory, Oak Ridge, TN 37831-6423, USA b Department of Material Science and Engineering, The Uniersity of Tennessee, 427-b Dougherty, Knoxille, TN 37966-2200, USA c Department of Mechanical Engineering, The Uniersity of Tennessee, Knoxille, TN 37996, USA Abstract Nicalon® plain-weave fiber fabric-reinforced silicon carbide (SiC) matrix composites with various pyrolytic carbon fiber/matrix interface coating thicknesses have been successfully fabricated by forced chemical vapor infiltration (FCVI) methods. The influence of the carbon interface coating thickness on the fracture behavior of these fiber fabric-reinforced SiC composites has been investigated. Experimental results indicate that fiber coating thickness significantly alters the fracture behavior of SiC composites. The fracture strength exhibits a maximum as the coating thickness increases. A theoretical model has been developed to simulate the fracture behavior in the SiC composites with varied carbon interface coatings. The model assumes that microcracking, which is due to low matrix toughness, initiates and arrests continuously. The model-predicted fracture behavior compares well with the experimental results. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Ceramic composites; Interface; Fiber; Fracture; Coating thickness; Silicon carbide www.elsevier.com/locate/msea 1. Introduction Woven continuous fiber fabric-reinforced ceramic composites (CFCCs) have been the subject of much theoretical modeling in last several years [1–7]. Limited work on the mechanical behavior characterization of woven CFCCs including both experimental and theoretical treatments has been done. The goal of this research has been to (1) develop and standardize appropriate test methods; (2) gain a mechanistic understanding of the complex fracture mechanisms that take place during the failure of these composites; and (3) provide some insight on the theoretical modeling of CFCCs. For the most part, woven CFCCs tend to exhibit ‘plastic-like’ deformation prior to failure, and the explanations for this behavior are fiber bridging, crack branching, microcracking, delamination, fiber–matrix debond and fiber slip, and eventual fiber fracture [8– 10]. Of course, the condition of the fiber–matrix interface plays a key role by controlling, which of the above mechanisms is dominant [8–11]. Single fiber level behavior is becoming well understood [14–22]. The details of the complex interactions among the interface condition, microcrack initiation and arrest, fiber debond and slip, and delamination of the fiber fabric plies are still being studied [10,12,13]. Due to the complexity of the layered woven fiber-fabric structure present in these composites, bulk composite behavior has not been extensively modeled [9,23–25]. Steif and Trojnacki [23,24] developed two similar models, the ‘slipping-layers model’, and the ‘unlayered shear-weak model’, for analyzing the flexure behavior of bulk CFCCs. The basis for these models, as the names imply, is the fact that laminated CFCCs exhibit low interlaminar shear strength [9,10,23–25]. The ‘slipping-layers model’ [23] assumes a laminated material whose layers are coupled only by friction. Therefore, once the applied load reaches a certain level, the layers begin to slip relative to each other. The beam then ceases to be a solid beam and becomes a ‘stack’ of discrete beams subjected to the same loads, affecting each other only by sliding friction. * Corresponding author. Fax: +1-423-9744115. E-mail address: pliaw@utk.edu (P.K. Liaw). 0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 1 1 8 4 - 4
J.H. Miller et al. Materials Science and Engineering 4317(2001)49-58 The unlayered shear-weak model[24] assumes that tensile strength, matrix toughness, and composite the shear stress in the composite cannot increase be- toughness to predict the load yond the shear strength of the composite. Basically, this sponse of a four-point flexure specimen assumption means that the material becomes perfectly plastic once the shear strength is reached. As the ap plied bending load increases, the material develops a 2. Experimental purely plastic region where the transverse shear stresses if calculated by beam theory, would exceed the com- An extensive experimental investigation of the me- posite shear strength. In this region, the shear stresses anical behavior of Nicalon" fiber fabric-reinforced are assumed to remain equal to shear strength, SiC matrix CFCCs with varied pyrolytic carbon fiber causing both the axial and shear stresses in the elastic coatings has been done [9, 10]. Mechanical properties, region(s)of the beam to be greater than that calculated such as the ultimate flexure strength, interlaminar shear stren Based on the concept of utilizing the shear weakness weakness of average fiber coating thickness. An interesting trend layered CFCCs, this paper will examine fiber bridg- w ound in the four-point flexure behavior of these ing, crack branching and deflection, delamination and composites. The ultimate flexure strength exhibited a crack formation and arrest in Nicalon" fiber fabric-re- maximum as the average fiber coating thickness in- inforced silicon carbide(SiC) matrix composites fabri creased. The flexure specimens(3-mm thick by 4-mm cated by forced chemical vapor infiltration(FCVI). A wide by 55-mm long)were cut from the composite disks bulk material behavior model has been developed and using a diamond saw such that the long axis of the bar ed to investigate the feasibility of the assumed roles was parallel to the 0-90 orientation of the top layer of that the above mentioned mechanisms play in the frac he fiber fabric. The plane of the fiber fabric was ture of these composites. This model uses experimental parallel to the top and bottom surfaces of the specimen property data including matrix fracture strength, inter- and were, therefore, perpendicular to plane of the nor laminar shear strength, interfacial shear strength, fiber mal stress, i.e. in-plane bending. The four-point flexure tests were conducted under displacement control, with an outer span of 40 mm, an inner span of 20 mm, and a crosshead speed of 0.508 mm min-l CVI-538[=0.13 u Fig. I shows typical load versus displacement curves Cv-524t=0.27 for composite specimens with varied fiber coating thick- nesses. Samples with no fiber coating exhibited brittle fracture and low strength, but samples with fiber coat ings behaved in an 'elastic-plastic' like manner. The maximum load and crosshead displacement both seem v32=12:mo to go through a maximum as coating thickness in- t=Coating Thickness creases. This trend is better shown in Fig. 2, 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 presents the fracture strength in four-point (ultimate flexure strength)as a function of average fiber Crosshead Displacement (mm) coating thickne Fig. 1. Comparison of four-point flexure curves of samples with The fracture strength exhibits a maximum, as the aried interlayer thickness average fiber coating thickness increases(Fig. 2). With no fiber coating, the material exhibits brittle fracture 500 with a low strength of 85 MPa. The fracture strength ncreases rapidly to 420 MPa at a fiber coating thick- ness of 0.13 um. It then decreases again to 330 MPa at 0. 27 Hm and to 275 MPa at 0.58 um, and then the fracture strength remains at an approximate value of 275 MPa, as the coating thickness increases to 1.27 um [9, 10 Fig. 3a-c are scanning-electron-microscopy (SEM) micrographs of fractured flexure specimens. The micro- 1251.5 graphs show a cross-sectional view of the cracks that Coating Thickness(um) appear on the surface of the fractured flexure samples At a low interlayer thickness of 0.06 um, the failure is Fig. 2. Ultimate flexure strengths of samples with varied interlayer generally controlled by a single, dominant crack propa gating through the matrix normal to the plane of the
50 J.H. Miller et al. / Materials Science and Engineering A317 (2001) 49–58 The ‘unlayered shear-weak model’ [24] assumes that the shear stress in the composite cannot increase beyond the shear strength of the composite. Basically, this assumption means that the material becomes perfectly plastic once the shear strength is reached. As the applied bending load increases, the material develops a purely plastic region where the transverse shear stresses, if calculated by beam theory, would exceed the composite shear strength. In this region, the shear stresses are assumed to remain equal to the shear strength, causing both the axial and shear stresses in the elastic region(s) of the beam to be greater than that calculated by beam theory. Based on the concept of utilizing the shear weakness of layered CFCCs, this paper will examine fiber bridging, crack branching and deflection, delamination, and crack formation and arrest in Nicalon® fiber fabric-reinforced silicon carbide (SiC) matrix composites fabricated by forced chemical vapor infiltration (FCVI). A bulk material behavior model has been developed and used to investigate the feasibility of the assumed roles that the above mentioned mechanisms play in the fracture of these composites. This model uses experimental property data including matrix fracture strength, interlaminar shear strength, interfacial shear strength, fiber tensile strength, matrix toughness, and composite toughness to predict the load versus displacement response of a four-point flexure specimen. 2. Experimental An extensive experimental investigation of the mechanical behavior of Nicalon® fiber fabric-reinforced SiC matrix CFCCs with varied pyrolytic carbon fiber coatings has been done [9,10]. Mechanical properties, such as the ultimate flexure strength, interlaminar shear strength, and toughness, were evaluated as a function of average fiber coating thickness. An interesting trend was found in the four-point flexure behavior of these composites. The ultimate flexure strength exhibited a maximum as the average fiber coating thickness increased. The flexure specimens (3-mm thick by 4-mm wide by 55-mm long) were cut from the composite disks using a diamond saw such that the long axis of the bar was parallel to the 0–90° orientation of the top layer of the fiber fabric. The plane of the fiber fabric was parallel to the top and bottom surfaces of the specimen and were, therefore, perpendicular to plane of the normal stress, i.e. in-plane bending. The four-point flexure tests were conducted under displacement control, with an outer span of 40 mm, an inner span of 20 mm, and a crosshead speed of 0.508 mm min−1 . Fig. 1 shows typical load versus displacement curves for composite specimens with varied fiber coating thicknesses. Samples with no fiber coating exhibited brittle fracture and low strength, but samples with fiber coatings behaved in an ‘elastic-plastic’ like manner. The maximum load and crosshead displacement both seem to go through a maximum as coating thickness increases. This trend is better shown in Fig. 2, which presents the fracture strength in four-point bending (ultimate flexure strength) as a function of average fiber coating thickness. The fracture strength exhibits a maximum, as the average fiber coating thickness increases (Fig. 2). With no fiber coating, the material exhibits brittle fracture with a low strength of 85 MPa. The fracture strength increases rapidly to 420 MPa at a fiber coating thickness of 0.13 m. It then decreases again to 330 MPa at 0.27 m and to 275 MPa at 0.58 m, and then the fracture strength remains at an approximate value of 275 MPa, as the coating thickness increases to 1.27 m [9,10]. Fig. 3a–c are scanning-electron-microscopy (SEM) micrographs of fractured flexure specimens. The micrographs show a cross-sectional view of the cracks that appear on the surface of the fractured flexure samples. At a low interlayer thickness of 0.06 m, the failure is generally controlled by a single, dominant crack propagating through the matrix normal to the plane of the Fig. 1. Comparison of four-point flexure curves of samples with varied interlayer thickness. Fig. 2. Ultimate flexure strengths of samples with varied interlayer thicknesses
J.H. Miller et al. Materials Science and Engineering 4317(2001)49-58 Maximum Tensile Stress Directio given by the appearance of holes in the matrix surface where fibers have been pulled toward the interior of the specimen. The fiber ends are still visible in the surface holes, and the apparent hole depth is small, which is indicative of small fiber displacement When the coating thickness increases to 0. 13 um, as presented in Fig. 3b, small amounts of multiple crack- ing are evident in the matrix, but there is still a single dominant crack. Moderate interface failure takes place, and crack bridging also occurs. In addition, the appar ent hole depth, where fibers that intersect the surface have been pulled to the interior of the specimen, is larger for the 0. 13 um case than for the 0.06 um Also, the dominant crack opening displacement is much larger for the 0. 13 um case. These features give evidence Maximum Tensile Stress Direction of increased fiber pullout over the thinner fiber coating As can be seen in Fig. 3c, at larger fiber coating thicknesses(>0.27 um), there is significant multiple Crack cracking in the matrix and extensive interface failure. It Branching i is interesting that, while the fibers appear to have been bridging appears less in the 0. 27 um case than in the 0. 13 um case. This observation tends to agree with the behavior of the uniform displacement, which goes through a maximum and then decreases 200μm Based on the trend in the experimental flexure results and the cracking observed in the micrographs, it is Maximum Tensile Stress Direction believed that the 'elastic-plastic' failure of these Debond Nicalon" Sic fiber fabric-reinforced Sic matrix com- posites is characterized by matrix microcracking that initiates and continues until the load and overall defect size combination causes a large or macrocrack exten- sion to occur. Further loading beyond the macrocrack extension induces additional microcracking and possi bI rocrack extensions [10]. Cr both for microcracks and macrocracks are assumed to be due to the formation of a delamination caused by crack deflection into an interlaminar shear-weak area To quantify these assumptions, a model has been devel- oped that simulates the failure of a four-point flexure Multiple Matrix Cracking pecten Fig3.(a)SEM micrograph of the side of a fractured flexure bar of 3. Modeling CV1-522 with an interlayer thickness of 0.06 um. Primarily single cracking in both the matrix and fiber bundle regions. (b) SEM A schematic algorithm of the model is presented in micrograph of the side of a fractured flexure bar of CVI-538 with an Fig 4. As shown in the figure, experimental mechanical nterlayer thickness of 0. 13 um. Moderate multiple matrix fracture and interface failure. (c) SEM micrograph of the side of a fractured properties including matrix fracture strength, matrix flexure bar of CV1-524 with an interlayer thickness of 0.27 um and composite (bulk) toughness, interfacial shear Extensive multiple matrix fracture and general interface failure strength, interlaminar shear strength, and Youngs modulus are used in the model. The model calculation maximum tensile stress and through the fiber reinforce- is based on beam theory and fracture mechanics.The ment by progressing along the fiber/matrix interface crosshead displacement is the independent variable with (Fig. 3a). There is indication that some of the fibers loads, stresses(on both net and gross sections), stress have debonded and have been pulled out a short dis- intensity factors, and crack lengths calculated at each tance. Evidence of the minimal fiber debond slip is displacement step
J.H. Miller et al. / Materials Science and Engineering A317 (2001) 49–58 51 Fig. 3. (a) SEM micrograph of the side of a fractured flexure bar of CVI-522 with an interlayer thickness of 0.06 m. Primarily single cracking in both the matrix and fiber bundle regions. (b) SEM micrograph of the side of a fractured flexure bar of CVI-538 with an interlayer thickness of 0.13 m. Moderate multiple matrix fracture and interface failure. (c) SEM micrograph of the side of a fractured flexure bar of CVI-524 with an interlayer thickness of 0.27 m. Extensive multiple matrix fracture and general interface failure. given by the appearance of holes in the matrix surface where fibers have been pulled toward the interior of the specimen. The fiber ends are still visible in the surface holes, and the apparent hole depth is small, which is indicative of small fiber displacement. When the coating thickness increases to 0.13 m, as presented in Fig. 3b, small amounts of multiple cracking are evident in the matrix, but there is still a single dominant crack. Moderate interface failure takes place, and crack bridging also occurs. In addition, the apparent hole depth, where fibers that intersect the surface have been pulled to the interior of the specimen, is larger for the 0.13 m case than for the 0.06 m case. Also, the dominant crack opening displacement is much larger for the 0.13 m case. These features give evidence of increased fiber pullout over the thinner fiber coating case. As can be seen in Fig. 3c, at larger fiber coating thicknesses (0.27 m), there is significant multiple cracking in the matrix and extensive interface failure. It is interesting that, while the fibers appear to have been debonded and pulled out, the length of the pullout appears less in the 0.27 m case than in the 0.13 m case. This observation tends to agree with the behavior of the uniform displacement, which goes through a maximum and then decreases. Based on the trend in the experimental flexure results and the cracking observed in the micrographs, it is believed that the ‘elastic-plastic’ failure of these Nicalon® SiC fiber fabric-reinforced SiC matrix composites is characterized by matrix microcracking that initiates and continues until the load and overall defect size combination causes a large or macrocrack extension to occur. Further loading beyond the macrocrack extension induces additional microcracking and possibly more macrocrack extensions [10]. Crack arrests, both for microcracks and macrocracks, are assumed to be due to the formation of a delamination caused by crack deflection into an interlaminar shear-weak area. To quantify these assumptions, a model has been developed that simulates the failure of a four-point flexure specimen. 3. Modeling A schematic algorithm of the model is presented in Fig. 4. As shown in the figure, experimental mechanical properties including matrix fracture strength, matrix and composite (bulk) toughness, interfacial shear strength, interlaminar shear strength, and Young’s modulus, are used in the model. The model calculation is based on beam theory and fracture mechanics. The crosshead displacement is the independent variable with loads, stresses (on both net and gross sections), stress intensity factors, and crack lengths calculated at each displacement step. maximum tensile stress and through the fiber reinforcement by progressing along the fiber/matrix interface (Fig. 3a). There is indication that some of the fibers have debonded and have been pulled out a short distance. Evidence of the minimal fiber debond slip is
J.H. Miller et al./ Materials Science and Engineering 4317(2001)49-58 Input of Material Data Kc Matrix =Kc KIc Bulk Composite= K Interlaminar Shear Strength= Tis Initial Crack Length= ao Model calculation Model output Beam The Displacement · Fracture Mechanic Crack Length K1>K? △a=△a (Macrocracking Index Crosshead Displacement No K1>K*? Aa=△a (Microcracking Recalculate Load and Stess Intensity Factor Fig. 4. Schematic algorithm of the four-point flexure model. The model assumes that the specimen has an initial Note that a summary of the symbols used in the rack or defect size of 0.2 mm. This value was chosen model is included in Table because it was roughly the width of a single fiber bundle that could be lying across the thickness direction of the tensile surface of the specimen [9]. The model considers two types of cracking, microcracking and Table I macrocracking. Microcracking occurs when the stress Summary of symbols used in the model the matrix material. Individual microcracks are as- Symbol Description sumed to arrest due to crack deflection caused by the shear weakness of the laminated composite. As a result Initial crack length (0.2 mm) elastic relaxation after microcrack extension does not Aa lways bring the crack tip stress intensity below the Microcracking crack extensio critical toughness of the matrix material. Therefore Position of concentrated load on the crack face(1/2 of the crack length) microcracking is a continuous process that occurs be- Specimen thickness cause the crack tip stress intensity continues to rise. In D fiber diameter other words, the microcracking process does not keep E Young's modulus with the rate of applied load, and the crack tip stress Kic Composite toughness intensity continues to increase even though microcrack- ng is occurring. Eventually, the crack tip stress inten-/* Shear length in macrocracking calculation Shear length in microcracking calculation sity reaches the critical bulk composite toughness and N Fraction of available fibers actually bridging the crack large or macro-cracks result in macrocracking calculation In the model, macrocracking occurs when the crack Fraction of available fibers actually bridging the crack tip stress intensity exceeds the relatively high toughness in microcracking calculation of the bulk composite. Macrocracks are assumed to P Load due to fiber-bridging the crack in the slice P Load due to net section stress on the slice arrest due to crack deflection into interlaminar shear p Load on the slice due to the constraint from the weak areas. As a result, the elastic relaxation following adjacent uncracked material a macrocracking event may bring the crack tip stress Net section stress intensity down below the level of the bulk composite Interlaminar shear strength toughness, but it may still be greater than the low UTSE Fiber strength(2 GPa) Fiber volume fraction (40%) matrix toughness. Therefore, microcracking can and Specimen width does occur in the model after macrocracks form
52 J.H. Miller et al. / Materials Science and Engineering A317 (2001) 49–58 Fig. 4. Schematic algorithm of the four-point flexure model. The model assumes that the specimen has an initial crack or defect size of 0.2 mm. This value was chosen because it was roughly the width of a single fiber bundle that could be lying across the thickness direction of the tensile surface of the specimen [9]. The model considers two types of cracking, microcracking and macrocracking. Microcracking occurs when the stress intensity at the crack tip exceeds the low toughness of the matrix material. Individual microcracks are assumed to arrest due to crack deflection caused by the shear weakness of the laminated composite. As a result, elastic relaxation after microcrack extension does not always bring the crack tip stress intensity below the critical toughness of the matrix material. Therefore, microcracking is a continuous process that occurs because the crack tip stress intensity continues to rise. In other words, the microcracking process does not keep up with the rate of applied load, and the crack tip stress intensity continues to increase even though microcracking is occurring. Eventually, the crack tip stress intensity reaches the critical bulk composite toughness and large or macro-cracks result. In the model, macrocracking occurs when the crack tip stress intensity exceeds the relatively high toughness of the bulk composite. Macrocracks are assumed to arrest due to crack deflection into interlaminar shear weak areas. As a result, the elastic relaxation following a macrocracking event may bring the crack tip stress intensity down below the level of the bulk composite toughness, but it may still be greater than the low matrix toughness. Therefore, microcracking can and does occur in the model after macrocracks form. Note that a summary of the symbols used in the model is included in Table 1. Table 1 Summary of symbols used in the model Symbol Description a Crack length a0 Initial crack length (0.2 mm) a Macrocracking crack extension a* Microcracking crack extension b Position of concentrated load on the crack face (1/2 of the crack length) B Specimen thickness D Fiber diameter E Young’s modulus KIC Composite toughness K Matrix toughness *IC l Shear length in macrocracking calculation l* Shear length in microcracking calculation NF Fraction of available fibers actually bridging the crack in macrocracking calculation N* Fraction of available F fibers actually bridging the crack in microcracking calculation PF Load due to fiber-bridging the crack in the slice P Load due to net section stress on the slice P Load on the slice due to the constraint from the adjacent uncracked material T Net section stress IS Interlaminar shear strength UTSF Fiber strength (2 GPa) F Fiber volume fraction (40%) w Specimen width
J.H. Miller et al. Materials Science and Engineering 4317(2001)49-58 P Fig 5 Schematic concept sketch of the micre ing calculation. See Table I for symbol definitions. Note that the model specimen depicted above is oriented the same a cimen with its top surface ottom surface in tension 3. 1. Microcracking Eqs. (1)-3)are the formulas for the resultant loads discussed above. The load on the Aa*-thick slice due to The microcracking is assumed to be triggered when the applied stress, Pa, is the area under the part of the the applied stress intensity factor, Kl, exceeds the low stress distribution curve that falls within the slice(Eq toughness of the matrix material, Kic. The value of Kic (1). Note that w is the overall specimen width such that was taken as 2.5 MPa,/m, which is a literature value w-a is the length of the remaining ligament, and B is for the toughness of the SiC matrix [26]. The length of the specimen thickness(the depth into the paper in Fig the microcrack extension, Aa", is calculated based on 5) equilibrium. Fig. 5 shows schematically the concept of why each microcrack would arrest. Fig 5 presents a specimen loaded in bending prior to Pa=0TAa*B_01 a microcrack extension(the left portion of the figure) and after a microcrack extension(the right portion of The load on the slice that is due to the fibers that are the figure). The model specimen depicted in Fig.5 is being pulled out of the matrix, is equal to the number oriented with the fiber fabric layers parallel to the of fibers bridging the crack multiplied by the tension in compressive(top) and tensile(bottom) surfaces of the each fiber(Eq. (2)). The number of fibers bridging the bar,as is the case in the experimental four-point bend crack is based on the volume fraction of fibers,UF,the tests. Therefore, opening mode crack extensions are diameter of each fiber. D. the area of the crack face backs grow parallel to the fiber fabric layers. Prior to fibers that actually bridge the crack tion of available perpendicular to the fiber fabric plies, while shear (Ad*-thick by B wide), and the fr Due to the crocracking, the specimen has a preexisting crack 0-30-60% layup of the fiber fabric layers [9, 10], roughly length o, which is due to the initial flaw and any prior one-third of the fibers would be aligned to bridge the microcracking and/or macrocracking. After microc- crack. As a result, the value of Ne was assumed to be racking, the crack length, a, has increased by an amount equal to△ai constant and was taken to be 0.3. The physical meaning Aa-thick. This slice is adjacent to e men that is of N, with a value of 0. 3, is that 30% of the fibers Now, consider a slice of the flexure speci ip of the would actually be bridging the crack preexisting crack, and is loaded by the stress distribu- For the microcracking case, each fiber is assumed to tion caused by the applied bending moment, shown in be loaded to 25% of its ultimate tensile strength Fig. 5. The maximum stress on the slice is equal to the (UTSE=2 GPa), during microcrack extension. This maximum net section stress, or. As the microcrack assumption is based on a consideration of the fiber rows, the slice tries to relax elastically, but its relax debond length that could result from an appli Ition is opposed by the fibers that bridge the crack, and tensile stress equal to UTS:/4. Assuming that the ten- the fact that its top surface(represented by the dashed sion in the fiber is opposed by a uniformly distributed line in the left portion of Fig. 5)is still bonded to th shear stress applied to the outer surface of the fiber and rest of the specimen. The fibers that are being pulled equal to the experimentally measured interfacial sliding out of the matrix produce a normal stress on the stress [9, 10, 21], the fiber debond length corresponding and the uncracked material adjacent to the slice to the fiber tensile load of UTSa/4 ranged from 0.05 to duces a shear stress on the top surface of the 0.25 mm. Fiber debond lengths in this range seemed Therefore, the microcrack will arrest when the load reasonable since this was roughly the size of a fiber applied to the Aa*-thick slice prior to microcracking, bundle. Therefore, fiber loading of UTS/4 was used in Pa, is equal and opposite to the opposing loads that are the microcracking calculation due to the fiber bridging, P and the constraint from he adjacent uncracked material, P, (refer to the lower UTS P1 △a*BN portion of Fig. 5)
J.H. Miller et al. / Materials Science and Engineering A317 (2001) 49–58 53 Fig. 5. Schematic concept sketch of the microcracking calculation. See Table 1 for symbol definitions. Note that the model specimen depicted above is oriented the same as the experimental specimen with its top surface in compression and its bottom surface in tension. 3.1. Microcracking The microcracking is assumed to be triggered when the applied stress intensity factor, KI, exceeds the low toughness of the matrix material, K* . The value of IC K*IC was taken as 2.5 MPam, which is a literature value for the toughness of the SiC matrix [26]. The length of the microcrack extension, a*, is calculated based on equilibrium. Fig. 5 shows schematically the concept of why each microcrack would arrest. Fig. 5 presents a specimen loaded in bending prior to a microcrack extension (the left portion of the figure), and after a microcrack extension (the right portion of the figure). The model specimen depicted in Fig. 5 is oriented with the fiber fabric layers parallel to the compressive (top) and tensile (bottom) surfaces of the bar, as is the case in the experimental four-point bend tests. Therefore, opening mode crack extensions are perpendicular to the fiber fabric plies, while shear cracks grow parallel to the fiber fabric layers. Prior to microcracking, the specimen has a preexisting crack length a0, which is due to the initial flaw and any prior microcracking and/or macrocracking. After microcracking, the crack length, a, has increased by an amount equal to a*. Now, consider a slice of the flexure specimen that is a*-thick. This slice is adjacent to the tip of the preexisting crack, and is loaded by the stress distribution caused by the applied bending moment, shown in Fig. 5. The maximum stress on the slice is equal to the maximum net section stress, T. As the microcrack grows, the slice tries to relax elastically, but its relaxation is opposed by the fibers that bridge the crack, and the fact that its top surface (represented by the dashed line in the left portion of Fig. 5) is still bonded to the rest of the specimen. The fibers that are being pulled out of the matrix produce a normal stress on the slice, and the uncracked material adjacent to the slice produces a shear stress on the top surface of the slice. Therefore, the microcrack will arrest when the load applied to the a*-thick slice prior to microcracking, P, is equal and opposite to the opposing loads that are due to the fiber bridging, PF and the constraint from the adjacent uncracked material, P (refer to the lower portion of Fig. 5). Eqs. (1)–(3) are the formulas for the resultant loads discussed above. The load on the a*-thick slice due to the applied stress, P, is the area under the part of the stress distribution curve that falls within the slice (Eq. (1)). Note that w is the overall specimen width such that w−a is the length of the remaining ligament, and B is the specimen thickness (the depth into the paper in Fig. 5). P=Ta*B− T w−a a*2 B (1) The load on the slice that is due to the fibers that are being pulled out of the matrix, is equal to the number of fibers bridging the crack multiplied by the tension in each fiber (Eq. (2)). The number of fibers bridging the crack is based on the volume fraction of fibers, F, the diameter of each fiber, D, the area of the crack face (a*-thick by B wide), and the fraction of available fibers that actually bridge the crack, NF. Due to the 0–30–60° layup of the fiber fabric layers [9,10], roughly one-third of the fibers would be aligned to bridge the crack. As a result, the value of N* was assumed to be F constant and was taken to be 0.3. The physical meaning of N*, with a value of 0.3, is that 30% of the F fibers would actually be bridging the crack. For the microcracking case, each fiber is assumed to be loaded to 25% of its ultimate tensile strength (UTSF=2 GPa), during microcrack extension. This assumption is based on a consideration of the fiber debond length that could result from an applied fiber tensile stress equal to UTSF/4. Assuming that the tension in the fiber is opposed by a uniformly distributed shear stress applied to the outer surface of the fiber and equal to the experimentally measured interfacial sliding stress [9,10,21], the fiber debond length corresponding to the fiber tensile load of UTSF/4 ranged from 0.05 to 0.25 mm. Fiber debond lengths in this range seemed reasonable since this was roughly the size of a fiber bundle. Therefore, fiber loading of UTSF/4 was used in the microcracking calculation. PF=UTSF 4 a*BN* FF (2)
J.H. Miller et al./ Materials Science and Engineering 4317(2001)49-58 It was assumed that only the fibers present in the A*+BAa*+7=0 Aa*-thick slice contribute to the equilibrium of that sice. This assumption was made due to the small value△n*=二B±√B2-4xy of Aa *. It was assumed that Aa* was small enough that fibers bridging the crack in previous crack extensions where would not play a role, i.e. that Aa was small enough not to cause further fiber slipping in fiber bridges from previous crack extensions The shear load produced by the constraint from the djacent uncracked material, P, is assumed to be the OT-UTS BNFUF experimental interlaminar shear strength, tis multiplied by the area in shear(Eq (3). The area in shear is equal 7 =-tis/ to the length of the shear area, /, multiplied by the specimen thickness, B(Fig. 5). The value of /* was 3. 2. Macrocracking considered as a constant and was set equal to 0.05 mm The choice of this value was based on the assumption The condition for macrocracking is met, when the K, that the length of the area in shear should be similar to level exceeds, Kic, the fracture toughness of the com- the fiber debond length and on the same order of posite or bulk material. The critical toughness value for magnitude as the length of a microcrack extension. macrocracking was taken to be equal to the experimen Preliminary calculations made during the development tally measured toughness from the chevron-notch of this model indicated that the magnitude of a microc- toughness tests [9, 10]. Similar to the microcracking rack extension fell between 0.01 and 0.10 mm. As a case, the macrocrack will arrest, when equilibrium is result, the value of 0.05 mm seemed to be a reasonable met among(I)the applied stress on a slice of a speci men Aa-thick loaded in bending, just prior to cracking P=1 (3)(2)the resultant loads associated with the fiber bridging in the wake of the crack; and (3) the shear stress on the Eq(4)is the condition of equilibrium for the Aa* top surface of the slice(represented by the dashed line thick slice, i.e. the force balance among the applied in the left portion of Fig. 6) due to the constraint stress-induced load prior to cracking, and the fiber provided by the adjacent uncracked material. Refer to bridging and constraint loads after cracking. Eq. (5)is Fig. 6 for a schematic sketch of this concept. Also, note the result of substituting Eqs. (1)-(3)into Eq (4)and that the symbols used in the macrocracking analysis are rearranging the terms. the same as those used in the microcracking case, with P。=P2+PF the exception that the superscript ised to denote microcracking has been omitted for the macrocracking △a*2+a1 BNAUF-Aa*-TIs/*=0 case. In addition, recall that a summary of the symbols used in this paper is included in Table 1 Fig. 6, which is very similar to Fig. 5, shows a Notice that Eq. (5)is in the standard form of the specimen loaded in bending prior to a macrocrack quadratic equation, and therefore, the value of the extension(the left portion of the figure), and after a microcrack extension, Aa", that produces the equi- macrocrack extension(the right portion of the figure) librium condition described by Eq. (5)can be calcu- Prior to macrocracking, the specimen has a preexisting lated, as shown in Eqs.(6)and(7) crack that was produced by prior microcracking and PF Fig. 6 Schematic concept sketch of the macrocracking calculation. See Table I for symbol definitions. Note that the model specimen depicted above is oriented the same as the experimental specimen with its top surface in compression and its bottom surface in tensio
54 J.H. Miller et al. / Materials Science and Engineering A317 (2001) 49–58 It was assumed that only the fibers present in the a*-thick slice contribute to the equilibrium of that slice. This assumption was made due to the small value of a*. It was assumed that a* was small enough that fibers bridging the crack in previous crack extensions would not play a role, i.e. that a* was small enough not to cause further fiber slipping in fiber bridges from previous crack extensions. The shear load produced by the constraint from the adjacent uncracked material, P is assumed to be the experimental interlaminar shear strength, IS multiplied by the area in shear (Eq. (3)). The area in shear is equal to the length of the shear area, l*, multiplied by the specimen thickness, B (Fig. 5). The value of l* was considered as a constant and was set equal to 0.05 mm. The choice of this value was based on the assumption that the length of the area in shear should be similar to the fiber debond length and on the same order of magnitude as the length of a microcrack extension. Preliminary calculations made during the development of this model indicated that the magnitude of a microcrack extension fell between 0.01 and 0.10 mm. As a result, the value of 0.05 mm seemed to be a reasonable choice. P=ISl*B (3) Eq. (4) is the condition of equilibrium for the a*- thick slice, i.e. the force balance among the applied stress-induced load prior to cracking, and the fiber bridging and constraint loads after cracking. Eq. (5) is the result of substituting Eqs. (1)–(3) into Eq. (4) and rearranging the terms. P=P+PF (4) − T w−a a*2+ T−UTSF 4 BN* FF −a*−ISl*=0 (5) Notice that Eq. (5) is in the standard form of the quadratic equation, and therefore, the value of the microcrack extension, a*, that produces the equilibrium condition described by Eq. (5) can be calculated, as shown in Eqs. (6) and (7). a*2+a*+=0 (6) a*= −2−4 2 (7) where = − T w−a (8) =T−UTSF 4 BN* FF (9) = −ISl* (10) 3.2. Macrocracking The condition for macrocracking is met, when the KI level exceeds, KIC, the fracture toughness of the composite or bulk material. The critical toughness value for macrocracking was taken to be equal to the experimentally measured toughness from the chevron-notch toughness tests [9,10]. Similar to the microcracking case, the macrocrack will arrest, when equilibrium is met among (1) the applied stress on a slice of a specimen a-thick loaded in bending, just prior to cracking; (2) the resultant loads associated with the fiber bridging in the wake of the crack; and (3) the shear stress on the top surface of the slice (represented by the dashed line in the left portion of Fig. 6) due to the constraint provided by the adjacent uncracked material. Refer to Fig. 6 for a schematic sketch of this concept. Also, note that the symbols used in the macrocracking analysis are the same as those used in the microcracking case, with the exception that the superscript ‘*’ used to denote microcracking has been omitted for the macrocracking case. In addition, recall that a summary of the symbols used in this paper is included in Table 1. Fig. 6, which is very similar to Fig. 5, shows a specimen loaded in bending prior to a macrocrack extension (the left portion of the figure), and after a macrocrack extension (the right portion of the figure). Prior to macrocracking, the specimen has a preexisting crack that was produced by prior microcracking and Fig. 6. Schematic concept sketch of the macrocracking calculation. See Table 1 for symbol definitions. Note that the model specimen depicted above is oriented the same as the experimental specimen with its top surface in compression and its bottom surface in tension.
J.H. Miller et al./ Materials Science and Engineering 4317(2001)49-58 macrocracking. After macrocracking, the crack length The expression for Pr, seen in Eq (13), is very similar a, has increased by an amount equal to Aa. to the microcracking case(Eq(3). The only difference Similar to the microcracking analysis, consider a slice is that / the length of the area in shear, has been of the flexure specimen that is Aa-thick, prior to the replaced by l, but this is a difference in name only. The macrocrack extension. This slice is adjacent to the tip length of the area in shear on the top surface of the of the preexisting crack, and is loaded by the stress Aa-thick slice, l, was assumed to be equal to /", the distribution induced by the applied bending moment, length of the shear area used in the microcrack shown in Fig. 6. The maximum stress on the slice is calculat equal to the maximum net section stress, or. As the P=τ macrocrack grows, the slice tries to relax elastically, but its relaxation is opposed by the fibers that bridge the Eq(14)represents the equilibrium expression for the rack, and the fact that its top surface(represented by macrocracking case the dashed line in the left portion of Fig. 6) is still P。=Pt+P (14) bonded to the rest of the specimen. Therefore, the macrocrack will arrest when the load applied to the Aa-thick slice prior to macrocracking, Pa, is equal and △a(ar- UTSENFUE)△a-(rs+ UTSENFDFa) opposite to the opposing loads that are due to fiber bridging, P and the constraint from the adjacent un cracked material, Pr (refer to the lower portion of Fig Substituting Eqs.(11)-(13)into Eq.(14) yields Eq 6) (15), which is analogous to Eq. (5)in the microcracking The expression, Pa, for the macrocracking case(Eq calculation. Notice that Eq. (15)is also in the standard (11))is identical to that used in the microcracking case form of the quadratic equation. Therefore, it can be (Eq. (1), with the exception that the crack extension, solved, as shown in Eqs.(16)and(17) △a*, has been replaced by△a x△a2+B△a+?=0 (16) P=-△aB △a2B (11) B±√B2 The expression for PF shown in Eq (12), is some- where what different from the microcracking case(Eq.(2)) The difference is due to some slightly different assump- a (18) tions for the macrocracking case. First, it was assumed hat all the fibers that bridge the crack contribute to the B=0r-UTSENFU equilibrium of the Aa-thick slice, i.e. all fibers in the area between the crack tip and the tensile surface of the (Isl+ UTSENEDFa) specimen played a role in the crack arrest. This behav The preceding discussion details the way in which the ior was assumed because of the relatively large value of concept of shear weakness was used to predict the crack Aa. The assumption was that Aa was large enough that arrest length for both microcracking and macrocrack slipping would occur in all fiber bridges over the entire ing. Following is a discussion of the calculation of the length of the crack. This idea is represented in Fig. 6 by stress intensity factor that was compared with the criti- showing the load due to fiber bridging being distributed cal toughnesses, which sets the criterion to trigger either over the entire crack length (lower middle portion of microcracking or macrocracking the figure). The horizontal lines on the crack face represent the distributed load due to the fiber bridging, 3.3. Stress intensity calculation while the load arrow labeled, PF, is the resultant of the distributed load In this model, it was assumed that the stress intensity Pp-UTS(a+△a)BNFF (12) factor applied to the crack tip, KI, consisted of t me contributions; KIM from an applied moment on the Second, for the macrocracking analysis, it was a cracked specimen, and Ki sumed that the fibers are loaded to 100% of their the face of the crack that was due to the fiber brid g breaking strength, rather than the value of 25% used in load, PF Fig. 7 shows schematically the loading condi the microcracking analysis. And lastly, to account for tions for both contributions. Fig. 7a presents a speci- fiber fracture during crack growth, the fraction of men with a crack of length, a, loaded by a crack available fibers that actually bridge the crack, Ne, was opening moment. Fig. 7b exhibits a specimen loaded by assumed to decrease as the crack grew. The model a concentrated force on the crack face. For the purpose assumes that No decreases linearly from NF=NF=0.3 of the present analysis, it was assumed that the applied to Ne=0, as a/w increases from 0 to I bending loads caused the crack opening moment, and
J.H. Miller et al. / Materials Science and Engineering A317 (2001) 49–58 55 macrocracking. After macrocracking, the crack length, a, has increased by an amount equal to a. Similar to the microcracking analysis, consider a slice of the flexure specimen that is a-thick, prior to the macrocrack extension. This slice is adjacent to the tip of the preexisting crack, and is loaded by the stress distribution induced by the applied bending moment, shown in Fig. 6. The maximum stress on the slice is equal to the maximum net section stress, T. As the macrocrack grows, the slice tries to relax elastically, but its relaxation is opposed by the fibers that bridge the crack, and the fact that its top surface (represented by the dashed line in the left portion of Fig. 6) is still bonded to the rest of the specimen. Therefore, the macrocrack will arrest when the load applied to the a-thick slice prior to macrocracking, P, is equal and opposite to the opposing loads that are due to fiber bridging, PF and the constraint from the adjacent uncracked material, P (refer to the lower portion of Fig. 6). The expression, P, for the macrocracking case (Eq. (11)) is identical to that used in the microcracking case (Eq. (1)), with the exception that the crack extension, a*, has been replaced by a. P=TaB− T w−a a2 B (11) The expression for PF shown in Eq. (12), is somewhat different from the microcracking case (Eq. (2)). The difference is due to some slightly different assumptions for the macrocracking case. First, it was assumed that all the fibers that bridge the crack contribute to the equilibrium of the a-thick slice, i.e. all fibers in the area between the crack tip and the tensile surface of the specimen played a role in the crack arrest. This behavior was assumed because of the relatively large value of a. The assumption was that a was large enough that slipping would occur in all fiber bridges over the entire length of the crack. This idea is represented in Fig. 6 by showing the load due to fiber bridging being distributed over the entire crack length (lower middle portion of the figure). The horizontal lines on the crack face represent the distributed load due to the fiber bridging, while the load arrow labeled, PF, is the resultant of the distributed load. PF−UTSF(a+a)BNFF (12) Second, for the macrocracking analysis, it was assumed that the fibers are loaded to 100% of their breaking strength, rather than the value of 25% used in the microcracking analysis. And lastly, to account for fiber fracture during crack growth, the fraction of available fibers that actually bridge the crack, NF, was assumed to decrease as the crack grew. The model assumes that NF decreases linearly from NF=N* F=0.3 to NF=0, as a/w increases from 0 to 1. The expression for P, seen in Eq. (13), is very similar to the microcracking case (Eq. (3)). The only difference is that l*, the length of the area in shear, has been replaced by l, but this is a difference in name only. The length of the area in shear on the top surface of the a-thick slice, l, was assumed to be equal to l*, the length of the shear area used in the microcrack calculation. P=ISlB (13) Eq. (14) represents the equilibrium expression for the macrocracking case. P=P+PF (14) − T w−a a2 (T−UTSFNFF)a−(ISl+UTSFNFFa) =0 (15) Substituting Eqs. (11)–(13) into Eq. (14) yields Eq. (15), which is analogous to Eq. (5) in the microcracking calculation. Notice that Eq. (15) is also in the standard form of the quadratic equation. Therefore, it can be solved, as shown in Eqs. (16) and (17). a2+a+=0 (16) a= −2−4 2 (17) where = T w−a (18) =T−UTSFNFF (19) = −(ISl+UTSFNFFa) (20) The preceding discussion details the way in which the concept of shear weakness was used to predict the crack arrest length for both microcracking and macrocracking. Following is a discussion of the calculation of the stress intensity factor that was compared with the critical toughnesses, which sets the criterion to trigger either microcracking or macrocracking. 3.3. Stress intensity calculation In this model, it was assumed that the stress intensity factor applied to the crack tip, KI, consisted of two contributions; KIM from an applied moment on the cracked specimen, and KIF from a concentrated load on the face of the crack that was due to the fiber bridging load, PF. Fig. 7 shows schematically the loading conditions for both contributions. Fig. 7a presents a specimen with a crack of length, a, loaded by a crack opening moment. Fig. 7b exhibits a specimen loaded by a concentrated force on the crack face. For the purpose of the present analysis, it was assumed that the applied bending loads caused the crack opening moment, and
J.H. Miller et al./ Materials Science and Engineering 4317(2001)49-58 Fig. 7. Schematic concept sketch of stress intensity geometries. (a)k due to an applied moment. (b)k due to a load on the crack face. See table I for symbol definitions. Note that the model specimen depicted above is oriented the same as the experimental specimen with its top surface in compression and its bottom surface in tension the resultant of the distributed load due to fiber bridg- ig. ll exhibits the experimental and model-pre- ing(PF from above)gave the concentrated load on the dicted ultimate flexure strengths over a wide range of crack face. Since the fiber bridging opposed the crack interlayer thicknesses. The predicted ultimate flexure opening, the applied Ki at the crack tip was assumed to strengths were found to be in good agreement with the be given by Eq(21) experimental results. In other words, the model-pre- K=KIM-K listed values follow the same trend as the experimental (21) results, both increase rapidly from approximately 280 where 300 MPa at an interlayer thickness of about 0.03 um to KI IM一 (22) the maximum of 380-420 MPa at a coating thickness around 0. 15 um. Then, the experimental and model- predicted ultimate flexure strengths decrease to 330 MPa at 0. 25 um and to 275 MPa at 0.6 um 6、2mx2)am(0g23+019 cos(/2)(a/w -Model Prediction (23) (b/a)\a =1.3-0.3 25) Cv-526 Coating Thickness=0.03 um EqS.(22)-(2 handbook stress intensity solu- tions [27, 28]. In Eqs.(24)and(25), PF is the resultant load due to fiber bridging(from Eq. (12)), and b is the distance between the specimen surface and the line of Fig 8. Experimental and model-predicted load vs crosshead displace. action of the force applied to the crack face. In the case ment curves for CVl-526 of this model, b was arbitrarily taken to be one-half of the crack length(b=a/2), as shown in Fig. 7 500 --Model Prediction 4. Results and discussion Experimental and model-predicted load versus dis- placement curves for three specimens of different inter- face coating thicknesses are exhibited in Figs. 8-10 10 represent coating thicknesses of0.03,0.13 and 0.27 um, respectively. All three figures show that oating Thickness =0.13 Hm there is a good agreement between the experimenta curve and the model prediction. Each four-point flexure curve exhibits an initial linear elastic behavior. followed Crosshead Displacement(mm) by'plastic-like'behavior, and an eventual sharp drop in Fig 9. Experimental and model-predicted load vs crosshead displace- ment curves for CvI-538
56 J.H. Miller et al. / Materials Science and Engineering A317 (2001) 49–58 Fig. 7. Schematic concept sketch of stress intensity geometries. (a) K due to an applied moment. (b) K due to a load on the crack face. See Table 1 for symbol definitions. Note that the model specimen depicted above is oriented the same as the experimental specimen with its top surface in compression and its bottom surface in tension. the resultant of the distributed load due to fiber bridging (PF from above) gave the concentrated load on the crack face. Since the fiber bridging opposed the crack opening, the applied KI at the crack tip was assumed to be given by Eq. (21). KI=KIM−KIF (21) where KIM= M Bw3/2 f a w (22) f a w =62 tan(/2)(a/w) cos(/2)(a/w) 0.923+0.199 1−sin 2 a w 4 (23) and KIF= 2 a PF B 1 1−(b/a) 2 f b a (24) f b a =1.3−0.3b a 5/4 (25) Eqs. (22)–(25) are handbook stress intensity solutions [27,28]. In Eqs. (24) and (25), PF is the resultant load due to fiber bridging (from Eq. (12)), and b is the distance between the specimen surface and the line of action of the force applied to the crack face. In the case of this model, b was arbitrarily taken to be one-half of the crack length (b=a/2), as shown in Fig. 7. 4. Results and discussion Experimental and model-predicted load versus displacement curves for three specimens of different interface coating thicknesses are exhibited in Figs. 8–10. Figs. 8–10 represent coating thicknesses of 0.03, 0.13, and 0.27 m, respectively. All three figures show that there is a good agreement between the experimental curve and the model prediction. Each four-point flexure curve exhibits an initial linear elastic behavior, followed by ‘plastic-like’ behavior, and an eventual sharp drop in load. Fig. 11 exhibits the experimental and model-predicted ultimate flexure strengths over a wide range of interlayer thicknesses. The predicted ultimate flexure strengths were found to be in good agreement with the experimental results. In other words, the model-predicted values follow the same trend as the experimental results, both increase rapidly from approximately 280– 300 MPa at an interlayer thickness of about 0.03 m to the maximum of 380–420 MPa at a coating thickness around 0.15 m. Then, the experimental and modelpredicted ultimate flexure strengths decrease to 330 MPa at 0.25 m and to 275 MPa at 0.6 m. Fig. 8. Experimental and model-predicted load vs. crosshead displacement curves for CVI-526. Fig. 9. Experimental and model-predicted load vs. crosshead displacement curves for CVI-538.
J.H. Miller et al. Materials Science and Engineering 4317(2001)49-58 was investigated by Lara-Curzio, Ferber, and Lowden 3.50----Model Prediction [21], but was not considered as part of this model. Also, multiple cracking was found to be present in the failure of these composites [9, 10], and no attempt was made to account for this mechanism. In addition fibers that do not run along the length of the specimen are not considered by this model. It was assumed that the role these fibers play is small. And finally, this model as- sumes a straight-through crack, which is not the case given the complexity of the woven structure of the composite In order to have a complete understanding of the Crosshead Displacement(mm) effect that the fiber coating thickness has on the frac Fig. 10. Experimental and model-predicted load vs. crosshead dis- ture behavior of these composites, a better understand placement curves for CVI-524 ing of the complex fiber-coating-matrix interaction during fracture is required. This research did not ad- dress those very complex mechanisms in detail. The -o-Model Prediction point of this research was to evaluate the feasibility of predicting bulk composite behavior from simplified as- sumptions of the micro-mechanisms found to take place Even with these limitations, the model does provide some insight into the possible failure mechanisms that are important in thes lte predicted load versus displacement curve is of the same 0.25 0.5 0.75 I 1.25 1.5 shape and on the same order of magnitude as the oating Thickness (um) experimental curve, indicates that the assumed cracking Fig. Il. Experimental and model-predicted ultimate fle and arresting mechanisms are feasible over a range of coating thickness from 0 to 1. 27 um. The agreement between the model predictions and 5. Concluding remarks the experimental measurements in Figs. 8-10 is the A model was developed based on the assumption most significant in terms of the shape of the four-point that the failure of woven CFCCs is controlled by flexure load versus displacement curves rather than the continuous microcrack initiation and arrest. followed maximum load values. The similarity in the shape of by eventual macrocracking. The model simulates the the load versus displacement curve between the experi- four-point flexure behavior of CFCCs by treating the mental measurement and the model prediction demon- crosshead displacement as an independent variable and strates the model's ability to predict the failure calculating loads, stress intensity factors, and crack mechanisms. According to the model, the ' plastic-like behavior is due to continuous initiation and arrest of lengths based on the crosshead displacement, beam theory, and fracture mechanics. In the model, microc microcracks, while the sharp decease in load from the racking is assumed to initiate due to the low toughness maximum is caused by the formation of a large macro- of the matrix, and arrest due to fiber bridging and slip crack. In addition, the model predicts that further and crack deflection. The fiber bridging and slip result cracking occurs following the macrocracking from a low level of interfacial strength. The crack event deflection occurs because of the interlaminar shear The model appears to work relatively well, but it weakness of the layered woven CFCC. Macrocracking loes have several limitations. The model does not is predicted, when the toughness of the bulk composite de explicitly show the dependence of fracture behavior on is exceeded fiber coating thickness. Instead, the fiber coating thick Overall the agreement between the experimental and ness effect presents itself in the results of the model, model-predicted curves was good. This trend indicates because the experimental properties used in the model that the assumptions about the fracture mechanisms in calculation, interlaminar shear strength and bulk com- these composites are feasible. As a result it is con posite toughne functions of fiber coating thick- cluded that the failure mechanism of Nicalon"SiC fiber ness. Another limitation of the model is that it does not fabric-reinforced SiC matrix composites is characterized account for the fiber debonding stress. Fiber debonding by matrix microcracking that is triggered by the low
J.H. Miller et al. / Materials Science and Engineering A317 (2001) 49–58 57 Fig. 10. Experimental and model-predicted load vs. crosshead displacement curves for CVI-524. was investigated by Lara-Curzio, Ferber, and Lowden [21], but was not considered as part of this model. Also, multiple cracking was found to be present in the failure of these composites [9,10], and no attempt was made to account for this mechanism. In addition, fibers that do not run along the length of the specimen are not considered by this model. It was assumed that the role these fibers play is small. And finally, this model assumes a straight-through crack, which is not the case given the complexity of the woven structure of the composite. In order to have a complete understanding of the effect that the fiber coating thickness has on the fracture behavior of these composites, a better understanding of the complex fiber-coating–matrix interaction during fracture is required. This research did not address those very complex mechanisms in detail. The point of this research was to evaluate the feasibility of predicting bulk composite behavior from simplified assumptions of the micro-mechanisms found to take place in this composite material. Even with these limitations, the model does provide some insight into the possible failure mechanisms that are important in these composites. The fact that the predicted load versus displacement curve is of the same shape and on the same order of magnitude as the experimental curve, indicates that the assumed cracking and arresting mechanisms are feasible. 5. Concluding remarks A model was developed based on the assumption that the failure of woven CFCCs is controlled by continuous microcrack initiation and arrest, followed by eventual macrocracking. The model simulates the four-point flexure behavior of CFCCs by treating the crosshead displacement as an independent variable and calculating loads, stress intensity factors, and crack lengths based on the crosshead displacement, beam theory, and fracture mechanics. In the model, microcracking is assumed to initiate due to the low toughness of the matrix, and arrest due to fiber bridging and slip, and crack deflection. The fiber bridging and slip result from a low level of interfacial strength. The crack deflection occurs because of the interlaminar shear weakness of the layered woven CFCC. Macrocracking is predicted, when the toughness of the bulk composite is exceeded. Overall the agreement between the experimental and model-predicted curves was good. This trend indicates that the assumptions about the fracture mechanisms in these composites are feasible. As a result, it is concluded that the failure mechanism of Nicalon® SiC fiber fabric-reinforced SiC matrix composites is characterized by matrix microcracking that is triggered by the low Fig. 11. Experimental and model-predicted ultimate flexure strengths over a range of coating thickness from 0 to 1.27 m. The agreement between the model predictions and the experimental measurements in Figs. 8–10 is the most significant in terms of the shape of the four-point flexure load versus displacement curves rather than the maximum load values. The similarity in the shape of the load versus displacement curve between the experimental measurement and the model prediction demonstrates the model’s ability to predict the failure mechanisms. According to the model, the ‘plastic-like’ behavior is due to continuous initiation and arrest of microcracks, while the sharp decease in load from the maximum is caused by the formation of a large macrocrack. In addition, the model predicts that further microcracking occurs following the macrocracking event. The model appears to work relatively well, but it does have several limitations. The model does not explicitly show the dependence of fracture behavior on fiber coating thickness. Instead, the fiber coating thickness effect presents itself in the results of the model, because the experimental properties used in the model calculation, interlaminar shear strength and bulk composite toughness, are functions of fiber coating thickness. Another limitation of the model is that it does not account for the fiber debonding stress. Fiber debonding
J.H. Miller et al. Materials Science and Engineering 4317(2001)49-58 matrix toughness. Then, with continued microcracking [4P.k Liaw, N. Yu, D K. Hsu, N. Miriyala,V Saini, LL and increases in load, a large crack extension occurs C.J. McHargue, R.A. Lowden, J. Nucl. Mater (219) The large macrocrack is triggered by the bu 93-100 com- posite toughness being exceeded. Further microcracking [C.H. Hsueh, J. Am. Ceram. Soc. 71(6)(1988)490-493. [6 C.H. Hsueh, Mater. Sci. Eng. A123(1990)I-ll and macrocracking can follow after the initial macroc [7R.J. Kerans, Scr. Metall. 31(8)(1994)1079-1084 racking event [8R.A. Lowden, Characterization and control of the fiber/matri interface in ceramic matrix composites. ORNLTM-1 1039 Acknowledgements 9 J H. Miller, Fiber coatings and the fracture or of a woven ntinuous fiber fabric-reinforced ceramic composite, M s.The- The University of Tennessee, Knoxville, The authors would like to thank r.A. Lowden J C. [0J H. Miller, R.A. Lowden, P K. Liaw, Met. Tr Mclaughlin, N L. Vaughn, O.J. Schwarz, D P Stinton, (1998), submitted for publication. and T.M. Besmann for their invaluable help in con- [II] C.H. Hsueh, P F. Becher, P. Angelini, J. Am. Ceram Soc. 71 ducting this research. This research was performed in cooperation with the University of Tennessee, [12 T Isikawa, T w. Chou, J. Mater. Sci. 17(1992)3211-3220 Knoxville, under contract 1lX-SN191V with Lockheea' [13]R N. Singh, S.K. Reddy, J. Am. Ceram. Soc. 79(1)(1996) 137-147. Martin Energy Research Corporation and is sponsored [14] C.H. Hsueh, Mater Sci Eng A145(1991)135-142 by the US Department of Energy, Assistant Secretary [15] C.H. Hsueh, Mater Sci Eng A145(1991)143-150 for Conservation and Renewable Energy, Office of [6] C H Hsueh, Mater. Sci Eng A54(1992)25-32 Industrial Technology, Industrial Energy Division, un- [7 C.H. Hsueh, Mater. Sci. Eng. A 165(1993)189-195 der contract DE-ACo5-84oR21400 with Lockheed [18 D.R. Mumm, K.T. Faber, Acta Metall. 43(3)(1995)1259-1270 [19] T.A. Parthasarathy, D B. Marshall,RJ. Kerans, Acta Metall. 42 Martin Energy Research Corporation. P K. Liaw is (11)(1994)3773-3784. very grateful for the financial support of National [20]O. Sbaizero, E. Lucchini, J.Eur. Ceram Soc. 16(1996)813-818 Science Foundation (DMi-9724476 and EEC-9527527) [21] E. Lara-Curzio, M.K. Ferber, R.A. Lowden, Ceram. Eng. Sci with Dr d.R. durham and m.f. poats. as contract Proc.15(1994) monitors, respectively [22]X. Aubard, Composites Sci. Technol. 54(1995)371-378. [ P.S. Steif, A. Trojnacki, Int. J. Solids Struct. 30(10)(1993) 1355-1368 24 P.S. Steif, A. Trojnacki, Int. J. Solids Struct. 30(10)(1993) References 1369-1378 25P.s. Steif, A. Trojnacki, J. Am. Ceram. Soc. 77(1)(1994) P.K. Liaw, D K. Hsu, N. Yu, N. Miriyala, V. Saini, H Measurement and prediction of composite stiffness mo [26RW. Hertzberg, Deformation and Fracture Mechanics of En Symposium on High Performance Composites, TMS eering Materials, Wiley, New York, 1989 dale,PA,1994,pp.377-395 27T. L. Anderson, Fracture Mechanics, Fundamentals and Appli- [2]PK.Liaw,JoM47(10)(1995)29 tions, CRC Press, Boca Raton, FL, 1995 3 w. Zhao, P K. Liaw, D.C. Joy, Ceram. Eng. Sci. Proc. 18(3) [28 H. Tada, P C. Paris, G.R. Irwin, The Stress Analysis of Cracks (1997)295-303 Handbook. Paris Productions. St. louis. 1985
58 J.H. Miller et al. / Materials Science and Engineering A317 (2001) 49–58 matrix toughness. Then, with continued microcracking and increases in load, a large crack extension occurs. The large macrocrack is triggered by the bulk composite toughness being exceeded. Further microcracking and macrocracking can follow after the initial macrocracking event. Acknowledgements The authors would like to thank R.A. Lowden, J.C. Mclaughlin, N.L. Vaughn, O.J. Schwarz, D.P. Stinton, and T.M. Besmann for their invaluable help in conducting this research. This research was performed in cooperation with the University of Tennessee, Knoxville, under contract 11X-SN191V with LockheedMartin Energy Research Corporation and is sponsored by the US Department of Energy, Assistant Secretary for Conservation and Renewable Energy, Office of Industrial Technology, Industrial Energy Division, under contract DE-AC05-84OR21400 with LockheedMartin Energy Research Corporation. P.K. Liaw is very grateful for the financial support of National Science Foundation (DMI-9724476 and EEC-9527527) with Dr D.R. Durham and M.F. Poats, as contract monitors, respectively. References [1] P.K. Liaw, D.K. Hsu, N. Yu, N. Miriyala, V. Saini, H. Jeong, Measurement and prediction of composite stiffness moduli, in: Symposium on High Performance Composites, TMS, Warrendale, PA, 1994, pp. 377–395. [2] P.K. Liaw, JOM 47 (10) (1995) 29. [3] W. Zhao, P.K. Liaw, D.C. Joy, Ceram. Eng. Sci. Proc. 18 (3) (1997) 295–303. [4] P.K. Liaw, N. Yu, D.K. Hsu, N. Miriyala, V. Saini, L.L. Snead, C.J. McHargue, R.A. Lowden, J. Nucl. Mater. (219) (1995) 93–100. [5] C.H. Hsueh, J. Am. Ceram. Soc. 71 (6) (1988) 490–493. [6] C.H. Hsueh, Mater. Sci. Eng. A123 (1990) 1–11. [7] R.J. Kerans, Scr. Metall. 31 (8) (1994) 1079–1084. [8] R.A. Lowden, Characterization and control of the fiber/matrix interface in ceramic matrix composites, ORNL/TM-1 1039, 1989. [9] J.H. Miller, Fiber coatings and the fracture behavior of a woven continuous fiber fabric-reinforced ceramic composite, M.S. Thesis, The University of Tennessee, Knoxville, 1995. [10] J.H. Miller, R.A. Lowden, P.K. Liaw, Met. Trans. Mater. (1998), submitted for publication. [11] C.H. Hsueh, P.F. Becher, P. Angelini, J. Am. Ceram. Soc. 71 (11) (1988) 929–933. [12] T. Isikawa, T.W. Chou, J. Mater. Sci. 17 (1992) 3211–3220. [13] R.N. Singh, S.K. Reddy, J. Am. Ceram. Soc. 79 (1) (1996) 137–147. [14] C.H. Hsueh, Mater. Sci. Eng. A145 (1991) 135–142. [15] C.H. Hsueh, Mater. Sci. Eng. A145 (1991) 143–150. [16] C.H. Hsueh, Mater. Sci. Eng. A154 (1992) 125–132. [17] C.H. Hsueh, Mater. Sci. Eng. A 165 (1993) 189–195. [18] D.R. Mumm, K.T. Faber, Acta Metall. 43 (3) (1995) 1259–1270. [19] T.A. Parthasarathy, D.B. Marshall, R.J. Kerans, Acta Metall. 42 (11) (1994) 3773–3784. [20] O. Sbaizero, E. Lucchini, J. Eur. Ceram. Soc. 16 (1996) 813–818. [21] E. Lara-Curzio, M.K. Ferber, R.A. Lowden, Ceram. Eng. Sci. Proc. 15 (1994) 989. [22] X. Aubard, Composites Sci. Technol. 54 (1995) 371–378. [23] P.S. Steif, A. Trojnacki, Int. J. Solids Struct. 30 (10) (1993) 1355–1368. [24] P.S. Steif, A. Trojnacki, Int. J. Solids Struct. 30 (10) (1993) 1369–1378. [25] P.S. Steif, A. Trojnacki, J. Am. Ceram. Soc. 77 (1) (1994) 221–229. [26] R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Wiley, New York, 1989. [27] T.L. Anderson, Fracture Mechanics, Fundamentals and Applications, CRC Press, Boca Raton, FL, 1995. [28] H. Tada, P.C. Paris, G.R. Irwin, The Stress Analysis of Cracks Handbook, Paris Productions, St. Louis, 1985.
