ecture and J Llorca(Editors) Elsevier Science Ltd. All rights reserved FIBER FRACTURE: AN OVERVIEW K.K. Chawla Department of Materials and Mechanical Engineering, University of Alabama at Birmingham, BEC 254, 1530 3rd Avenue S, Birmingham, AL 35294-4461, USA Polymeric Fibers Environmental Effects on Polymeric Fibers Carbon Fibers 5589 Metallic Fibers Glass and Ceramic Fibers 17 Conclusions References 24 Abstract fracture of fibers during processing or in service is generally an undesirable feature fracture in fibers, as in bulk materials, initiates at some flaw(s), internal or on the surface. In general, because of the high surface to volume ratio of fibers, the incidence of a surface flaw leading to fracture is greater in fibers than in bulk materials. Very frequently, a near-surface fiaw such as a microvoid or an inclusion is responsible for the initiation of fracture of fiber. In polymeric fibers, the fundamental processes leading to failure are chain scission and or chain sliding or a combination thereof. Service environment can be a major determining factor in the failure process of fibers. A striking example of this was in the failure of aramid fiber used in the tether rope in space. Metallic fibers represent a relatively mature technology. The surface condition and segregation of inclus the two factors that limit the strength of metallic filaments. Ceramic and silica-based fibers(including optical glass fiber) also have the same crack-initiating flaws as in polymeric and metallic fibers. One major problem in glass fibers is that of failure due to static fatigue. In this paper, examples of fracture in different types of fibers are provided. Some of the possible ways to prevent catastrophic
Fiber Fracture M. Elices and J. Llorca (Editors) 9 2002 Elsevier Science Ltd. All rights reserved FIBER FRACTURE: AN OVERVIEW K.K. Chawla Department of Materials and Mechanical Engineering, University of Alabama at Birmingham, BEC 254, 1530 3rd Avenue S., Birmingham, AL 35294-4461, USA Introduction ..................................... 5 Polymeric Fibers .................................. 5 Environmental Effects on Polymeric Fibers .................. 8 Carbon Fibers .................................... 9 Metallic Fibers ................................... 13 Glass and Ceramic Fibers .............................. 17 Conclusions ..................................... 24 References ...................................... 24 Abstract Fracture of fibers during processing or in service is generally an undesirable feature. Fracture in fibers, as in bulk materials, initiates at some flaw(s), internal or on the surface. In general, because of the high surface to volume ratio of fibers, the incidence of a surface flaw leading to fracture is greater in fibers than in bulk materials. Very frequently, a near-surface flaw such as a microvoid or an inclusion is responsible for the initiation of fracture of fiber. In polymeric fibers, the fundamental processes leading to failure are chain scission and/or chain sliding or a combination thereof. Service environment can be a major determining factor in the failure process of fibers. A striking example of this was in the failure of aramid fiber used in the tether rope in space. Metallic fibers represent a relatively mature technology. The surface condition and segregation of inclusions are the two factors that limit the strength of metallic filaments. Ceramic and silica-based fibers (including optical glass fiber) also have the same crack-initiating flaws as in polymeric and metallic fibers. One major problem in glass fibers is that of failure due to static fatigue. In this paper, examples of fracture in different types of fibers are provided. Some of the possible ways to prevent catastrophic
K.K. Chawla failure in different fibers are pointed out. A considerable amount of progress has been lade in the last quarter of the twentieth century. Keywords Alumina; Aramid; Carbon; Ceramic; Fibers; Metal; Polyethylene; Polymer; Optical
4 K.K. Chawla failure in different fibers are pointed out. A considerable amount of progress has been made in the last quarter of the twentieth century. Keywords Alumina; Aramid; Carbon; Ceramic; Fibers; Metal; Polyethylene; Polymer; Optical; Steel; Tungsten
FIBER FRACTURE: AN OVERVIEW INTRODUCTION fracture of a fiber is generally an undesirable occurrence. For example, during processing of continuous fibers, frequent breakage of filaments is highly undesirable from a productivity point of view. When this happens in the case of spinning of a polymer, ceramic or a glass fiber, the processing unit must be stopped, the mess of the solution or melt must be cleaned and the process restarted. In the case of a metallic filament, a break means that the starting wire must be pointed again, retreaded, and the process restarted. In service, of course, one would like the individual fibers whether in a fabric or in a composite to last a reasonable time Fracture in fibers, as in bulk materials, initiates at some flaw(s), internal or on the surface. In general, because of the high surface to volume ratio of fibers, the incidence of a surface flaw leading to fracture is greater in fibers than in bulk materials Fractography, the study of the fracture surface, of fibers can be a useful technique for obtaining fracture parameters and for identifying the sources of failure. In general, the mean strength of a fiber decreases as its length of diameter increases. This size effect is commonly analyzed by applying Weibull statistics to the strength data. As the fiber length or diameter increases, the average strength of the fiber decreases. It is easy to understand this because the probability of finding a critical defect responsible for fracture increases with size. This behavior is shown by organic fibers such as cotton, aramid, as well as inorganic fibers such as tungsten, silicon carbide, glass, or alumina In this paper, the salient features of the fracture process in different types of fibe lymeric, metallic, and ceramic are described. Points of commonality and difference POLYMERIC FIBERS A very important characteristic of any polymeric fiber is the degree of molecular hain orientation along the fiber axis. In order to get high strength and stiffness in organic fibers, one must obtain oriented molecular chains with full extension. An important result of this chain alignment along the fiber axis is the marked anisotropy in the characteristics of a polymeric fiber. Rigid-rod polymeric fibers such as aramid fibers show very high strength under axial tension. The failure in tension brings into play the covalent bonding along the axis, which ultimately leads to chain scission and/ or chain sliding or a combination thereof. However, they have poor properties under axial compression, torsion, and in the transverse direction. Fig. 1 shows this in a schematic manner. The compressive trength of ceramic fibers, on the other hand is greater than their tensile strength. The compressive strength of carbon fiber is intermediate to that of polymeric and ceramic fibers. This discrepancy between the tensile and compressive properties has been the subject of investigation by a number of researchers(see Chawla, 1998 for details) An example of kinking under compression in a high-performance polymeric fiber derived from rigid-rod liquid crystal is shown in Fig. 2(Kozey and Kumar, 1994) Note that this is a single fiber with preexisting striations on the surface. High-strengtI
FIBER FRACTURE: AN OVERVIEW INTRODUCTION Fracture of a fiber is generally an undesirable occurrence. For example, during processing of continuous fibers, frequent breakage of filaments is highly undesirable from a productivity point of view. When this happens in the case of spinning of a polymer, ceramic or a glass fiber, the processing unit must be stopped, the mess of the solution or melt must be cleaned and the process restarted. In the case of a metallic filament, a break means that the starting wire must be pointed again, rethreaded, and the process restarted. In service, of course, one would like the individual fibers whether in a fabric or in a composite to last a reasonable time. Fracture in fibers, as in bulk materials, initiates at some flaw(s), internal or on the surface. In general, because of the high surface to volume ratio of fibers, the incidence of a surface flaw leading to fracture is greater in fibers than in bulk materials. Fractography, the study of the fracture surface, of fibers can be a useful technique for obtaining fracture parameters and for identifying the sources of failure. In general, the mean strength of a fiber decreases as its length of diameter increases. This size effect is commonly analyzed by applying Weibull statistics to the strength data. As the fiber length or diameter increases, the average strength of the fiber decreases. It is easy to understand this because the probability of finding a critical defect responsible for fracture increases with size. This behavior is shown by organic fibers such as cotton, aramid, as well as inorganic fibers such as tungsten, silicon carbide, glass, or alumina. In this paper, the salient features of the fracture process in different types of fibers, polymeric, metallic, and ceramic are described. Points of commonality and difference are highlighted. POLYMERIC FIBERS A very important characteristic of any polymeric fiber is the degree of molecular chain orientation along the fiber axis. In order to get high strength and stiffness in organic fibers, one must obtain oriented molecular chains with full extension. An important result of this chain alignment along the fiber axis is the marked anisotropy in the characteristics of a polymeric fiber. Rigid-rod polymeric fibers such as aramid fibers show very high strength under axial tension. The failure in tension brings into play the covalent bonding along the axis, which ultimately leads to chain scission and/or chain sliding or a combination thereof. However, they have poor properties under axial compression, torsion, and in the transverse direction. Fig. 1 shows this in a schematic manner. The compressive strength of ceramic fibers, on the other hand, is greater than their tensile strength. The compressive strength of carbon fiber is intermediate to that of polymeric and ceramic fibers. This discrepancy between the tensile and compressive properties has been the subject of investigation by a number of researchers (see Chawla, 1998 for details). An example of kinking under compression in a high-performance polymeric fiber derived from rigid-rod liquid crystal is shown in Fig. 2 (Kozey and Kumar, 1994). Note that this is a single fiber with preexisting striations on the surface. High-strength
spun(dried) Strain of rigid-rod polymeric fibers in tension and compressio show strength under axial tension but have poor properties under axial compression, torsion, an organic fibers fail in <I%. Microbuckling or shear banding responsible for easy failure in compression. The spider dragline silk fiber seems to be an exception to this. In general, highly oriented fibers such as aramid fail in a fibrillar fashion. The term fibrillar fracture here signifies that the fracture surface is not transverse to the axis but runs along a number of planes of weakness parallel to the fiber axis. As the orientation of chains in a fiber becomes more parallel to its axis, its axial tensile modules(E)increases but the shear modulus(G)decreases, i.e. the ratio E/G increases tremendously. During failure involving compressive stresses, fibrillation occurs, which results in a large degree of new surface area. This fibrillation process results in high-energy absorption during the process of failure, which makes these fibers useful for resistance against ballistic penetration Various models have been proposed to explain this behavior of high-performance ers. Fig 3 shows two compressive failure models:(a)elastic microbuckling of poly meric chains; and(b) misorientation. The microbuckling model involves cooperative in phase buckling of closely spaced chains in a small region of fiber. The misorientation model takes into account structural imperfections or misorientations that are invariabl present in a fiber. In the composites literature it has been reported that regions of
K.K. Chawla | ..... | . . J Iteat-treated _ .Heat-treated As spun (dried) ,[/' ~ulated ..... V ............................. , ...................................... , ....................................... ., ....................................... I ........................ ik ............. , Strain ---~- l Fig. 1. Schematic stress-strain curves of rigid-rod polymeric fibers in tension and compression. Such fibers show very high strength under axial tension but have poor properties under axial compression, torsion, and in the transverse direction. organic fibers fail in compression at strains < 1%. Microbuckling or shear banding is responsible for easy failure in compression. The spider dragline silk fiber seems to be an exception to this. In general, highly oriented fibers such as aramid fail in a fibrillar fashion. The term fibrillar fracture here signifies that the fracture surface is not transverse to the axis but runs along a number of planes of weakness parallel to the fiber axis. As the orientation of chains in a fiber becomes more parallel to its axis, its axial tensile modules (E) increases but the shear modulus (G) decreases, i.e. the ratio E/G increases tremendously. During failure involving compressive stresses, fibrillation occurs, which results in a large degree of new surface area. This fibrillation process results in high-energy absorption during the process of failure, which makes these fibers useful for resistance against ballistic penetration. Various models have been proposed to explain this behavior of high-performance fibers. Fig. 3 shows two compressive failure models: (a) elastic microbuckling of polymeric chains; and (b) misorientation. The microbuckling model involves cooperative inphase buckling of closely spaced chains in a small region of fiber. The misorientation model takes into account structural imperfections or misorientations that are invariably present in a fiber. In the composites literature it has been reported that regions of
FIBER FRACTURE: AN OVERVIEW O um An example of kinking under compression in a high-l ance polymeric fiber derived from quid crystal(courtesy of Kozey and Kumar). Higl organic fibers fail in compression at <l%. Microbuckling or shear banding is responsible for easy failure in compression Band of buckled hains/fibrils Fig. 3. Two compressive failure models: (a)elastic microbuckling of polymeric chains; this model involves cooperative in-phase buckling of closely spaced chains in a small region of fiber;( b) misorientation; this model is based on structural imperfections or misorientations that are invariably present in a fiber misorientation in a unidirectional composite lead to kink formation under compressive loading (Argon, 1972). The model shown in Fig. 3b is based upon the presence of such a local misorientation in the fiber leading to kink formation under compression Failure in compression is commonly associated with the formation and propagation of kinks. These kink bands generally start near the fiber surface and then grow to the center of the fiber. It has also been attributed to the ease of microbuckling in such
FIBER FRACTURE: AN OVERVIEW Fig. 2. An example of kinking under compression in a high-performance polymeric fiber derived from rigid-rod liquid crystal (courtesy of Kozey and Kumar). High-strength organic fibers fail in compression at strains < 1%. Microbuckling or shear banding is responsible for easy failure in compression. Fig. 3. Two compressive failure models: (a) elastic microbuckling of polymeric chains; this model involves cooperative in-phase buckling of closely spaced chains in a small region of fiber; (b) misorientation; this model is based on structural imperfections or misorientations that are invariably present in a fiber. misorientation in a unidirectional composite lead to kink formation under compressive loading (Argon, 1972). The model shown in Fig. 3b is based upon the presence of -such a local misorientation in the fiber leading to kink formation under compression. Failure in compression is commonly associated with the formation and propagation of kinks. These kink bands generally start near the fiber surface and then grow to the center of the fiber. It has also been attributed to the ease of microbuckling in such
KK Chawla fibers as well as to the presence of microvoids and the skin-core structure of these fibers. It should be pointed out that poor properties in shear and compression are however, also observed in other highly oriented polymeric fibers such as polyethylene and poly(p-phenylene benzobisoxazole)or PBO fibers, which are not based on rigid-rod polymers. A correlation between good compressive characteristics and a high glass transition temperature(or melting point) has been suggested(Northolt, 1981; Kozey and Kumar, 1994) Thus, with the glass transition temperature of organic fibers being lower than that of inorganic fibers, the former would be expected to show poorer properties in compression. For aramid and similar fibers, compression results in the formation of kink bands leading to eventual ductile failure. Yielding is observed at about 0.5%o strain. This is thought to correspond to a molecular rotation of the amide carbon-nitrogen bond from the normal extended trans configuration to a kinked configuration Tanner et 1986). This causes a 45 bend in the chain, which propagates across the unit cell, the microfibrils and a kink band results in the fiber Efforts to improve the compressive properties of rigid-rod polymer fibers have involved introduction of cross-linking in the transverse direction. There is a significant effect of intermolecular interaction or intermolecular cross-link strength. a polymeric fiber(PIPD)with a compressive strength of 1.6 GPa has been reported (Jenkins et al., 2001). This high compressive strength is ascribed to bi- directional, intermolecular hydrogen bonding. A high degree of intermolecular covalent cross-linking should result in higher compressive strength, as compared to systems in which only hydrogen bonding is present (Jenkins et al., 2001). However, cross-linking may also result in lower tensile strength and increased brittleness of the fiber. Cross- linking by thermal treatment may result in the development of internal stresses. Other cross-linking methods(e. g. via radiation) should be explored in greater detail. One would expect radiation to result in a different cross-linked structure than that obtained by thermal treatment. Here it is instructive to compare the behavior of some carbon fibers. Highly graphitic, mesophase pitch-based fibers show a fibrillar fracture and poor compressive properties. PAN-based carbon fibers, which have some linking of the graphitic planes in the transverse direction, show better properties in compressic not a very fibrillar fracture. Of course metallic and ceramic fibers show brillation during a tensile or compressive failure Environmental Effects on Polymeric Fibers Environmental factors such as humidity, temperature, pH, ultraviolet radiation, n affect the strength and the fracture process in polymeric fibers. Natural polymeric fibers are more susceptible to environmental degradation than synthetic polymeric fibers. Cellulose is attacked by a variety of bacteria, fungi, and gae Micro-organisms use cellulose as a food source. Natural fibers based on protein such as wool, hair, silk, etc, can also be a food source for micro-organisms, but such fibers are more prone to degradation due to humidity and temperature. Polymeric fibers, natural or synthetic, undergo photo degradation when exposed to light (both visible and ultraviolet). Physically this results in discoloration, but is also accompanied by a
8 K.K. Chawla fibers as well as to the presence of microvoids and the skin-core structure of these fibers. It should be pointed out that poor properties in shear and compression are, however, also observed in other highly oriented polymeric fibers such as polyethylene and poly(p-phenylene benzobisoxazole) or PBO fibers, which are not based on rigid-rod polymers. A correlation between good compressive characteristics and a high glass transition temperature (or melting point) has been suggested (Northolt, 1981; Kozey and Kumar, 1994). Thus, with the glass transition temperature of organic fibers being lower than that of inorganic fibers, the former would be expected to show poorer properties in compression. For aramid and similar fibers, compression results in the formation of kink bands leading to eventual ductile failure. Yielding is observed at about 0.5% strain. This is thought to correspond to a molecular rotation of the amide carbon-nitrogen bond from the normal extended trans configuration to a kinked configuration Tanner et al., 1986). This causes a 45 ~ bend in the chain, which propagates across the unit cell, the microfibrils, and a kink band results in the fiber. Efforts to improve the compressive properties of rigid-rod polymer fibers have involved introduction of cross-linking in the transverse direction. There is a significant effect of intermolecular interaction or intermolecular cross-linking on compressive strength. A polymeric fiber (PIPD) with a compressive strength of 1.6 GPa has been reported (Jenkins et al., 2001). This high compressive strength is ascribed to bidirectional, intermolecular hydrogen bonding. A high degree of intermolecular covalent cross-linking should result in higher compressive strength, as compared to systems in which only hydrogen bonding is present (Jenkins et al., 2001). However, cross-linking may also result in lower tensile strength and increased brittleness of the fiber. Crosslinking by thermal treatment may result in the development of internal stresses. Other cross-linking methods (e.g. via radiation) should be explored in greater detail. One would expect radiation to result in a different cross-linked structure than that obtained by thermal treatment. Here it is instructive to compare the behavior of some carbon fibers. Highly graphitic, mesophase pitch-based fibers show a fibrillar fracture and poor compressive properties. PAN-based carbon fibers, which have some linking of the graphitic planes in the transverse direction, show better properties in compression and not a very fibrillar fracture. Of course metallic and ceramic fibers show little fibrillation during a tensile or compressive failure. Environmental Effects on Polymeric Fibers Environmental factors such as humidity, temperature, pH, ultraviolet radiation, and micro-organisms can affect the strength and the fracture process in polymeric fibers. Natural polymeric fibers are more susceptible to environmental degradation than synthetic polymeric fibers. Cellulose is attacked by a variety of bacteria, fungi, and algae. Micro-organisms use cellulose as a food source. Natural fibers based on protein such as wool, hair, silk, etc., can also be a food source for micro-organisms, but such fibers are more prone to degradation due to humidity and temperature. Polymeric fibers, natural or synthetic, undergo photo degradation when exposed to light (both visible and ultraviolet). Physically this results in discoloration, but is also accompanied by a
FIBER FRACTURE. AN OVERVIEW worsening of mechanical characteristics. A striking example of environmental leading to failure of aramid fiber was the failure of the tether rope for a satellite in space. The rope made of aramid fiber failed because of friction leading to excessive static charge accumulation,which led to premature failure of the tether rope and the loss of an ein a multifilament yarn or in a braided fabric, frictional force in the radial direction holds the fibers together. Such interfiber friction is desirable if we wish to have strong yarns and fabrics. However there are situations where we would like to have a smooth fiber surface. For example, for a yarn passing round a guide, a smooth fiber surface will be desirable. If the yarn surface is rough, then a high tension will be required, which, in turn, can lead to fiber breakage. In general, in textile applications, friction characteristics can affect the handle, feel, wear-resistance, etc. In fibrous composites, the frictional characteristics of fiber can affect the interface strength and toughness CARBON FIBERS Carbon fibers are, in some ways, similar to polymeric fibers while in other ways they are similar to ceramic fibers. A characteristic feature of the structure of all carbon fibers is the high degree of alignment of the basal planes of graphite along the fiber axis The degree of alignment of these graphitic planes can vary depending on the precursor used and the processing, especially the heat treatment temperature used. Transmission electron microscopic studies of carbon fiber show the heterogeneous microstructure of arbon fibers. In particular, there occurs a pronounced irregularity in the packing of graphitic lamellae as one goes from the fiber surface inward to the core or fiber axis The graphitic basal planes are much better aligned in the near-surface region of the fiber, called the sheath. The material inside the sheath can have a radial structure or an irregular layer structure, sometimes termed the onion skin structure. The radial core and well aligned sheath structure is more commonly observed in mesophase-pitch-basec carbon fibers. A variety of arrangement of graphitic layers can be seen in different fibers. In very general terms, the graphitic ribbons are oriented more or less parallel to he fiber axis with random interlinking of layers, longitudinally and laterally (Jain and Abhiraman, 1987; Johnson, 1987; Deurbergue and Oberlin, 1991). Fig. 4 shows a two- dimensional representation of this lamellar structure called turbostratic structure. Note the distorted carbon layers and the rather irregular space filling. The degree of alignment of the basal planes increases with the final heat treatment temperature. Examination of lattice images of the cross-section of carbon fiber shows essentially parallel basal planes in the skin region, but extensive folding of layer planes can be seen in the core region is thought that this extensive interlinking of lattice planes in the longitudinal direction is responsible for better compressive properties of carbon fiber than aramid fibers. In spite of the better alignment of basal planes in the skin region, the surface of carbon fibers can show extremely fine scale roughness. A scanning electron micrograph of pitch-based carbon fibers is shown in Fig. 5. Note the surface striations and the roughness at a microscopic scale
FIBER FRACTURE: AN OVERVIEW worsening of mechanical characteristics. A striking example of environmental leading to failure of aramid fiber was the failure of the tether rope for a satellite in space. The rope made of aramid fiber failed because of friction leading to excessive static charge accumulation, which led to premature failure of the tether rope and the loss of an expensive satellite. In a multifilament yarn or in a braided fabric, frictional force in the radial direction holds the fibers together. Such interfiber friction is desirable if we wish to have strong yarns and fabrics. However, there are situations where we would like to have a smooth fiber surface. For example, for a yarn passing round a guide, a smooth fiber surface will be desirable. If the yarn surface is rough, then a high tension will be required, which, in turn, can lead to fiber breakage. In general, in textile applications, frictional characteristics can affect the handle, feel, wear-resistance, etc. In fibrous composites, the frictional characteristics of fiber can affect the interface strength and toughness characteristics. CARBON FIBERS Carbon fibers are, in some ways, similar to polymeric fibers while in other ways they are similar to ceramic fibers. A characteristic feature of the structure of all carbon fibers is the high degree of alignment of the basal planes of graphite along the fiber axis. The degree of alignment of these graphitic planes can vary depending on the precursor used and the processing, especially the heat treatment temperature used. Transmission electron microscopic studies of carbon fiber show the heterogeneous microstructure of carbon fibers. In particular, there occurs a pronounced irregularity in the packing of graphitic lamellae as one goes from the fiber surface inward to the core or fiber axis. The graphitic basal planes are much better aligned in the near-surface region of the fiber, called the sheath. The material inside the sheath can have a radial structure or an irregular layer structure, sometimes termed the onion skin structure. The radial core and well aligned sheath structure is more commonly observed in mesophase-pitch-based carbon fibers. A variety of arrangement of graphitic layers can be seen in different fibers. In very general terms, the graphitic ribbons are oriented more or less parallel to the fiber axis with random interlinking of layers, longitudinally and laterally (Jain and Abhiraman, 1987; Johnson, 1987; Deurbergue and Oberlin, 1991). Fig. 4 shows a twodimensional representation of this lamellar structure called turbostratic structure. Note the distorted carbon layers and the rather irregular space filling. The degree of alignment of the basal planes increases with the final heat treatment temperature. Examination of lattice images of the cross-section of carbon fiber shows essentially parallel basal planes in the skin region, but extensive folding of layer planes can be seen in the core region. It is thought that this extensive interlinking of lattice planes in the longitudinal direction is responsible for better compressive properties of carbon fiber than aramid fibers. In spite of the better alignment of basal planes in the skin region, the surface of carbon fibers can show extremely fine scale roughness. A scanning electron micrograph of pitch-based carbon fibers is shown in Fig. 5. Note the surface striations and the roughness at a microscopic scale
KK Chawla Fig. 4. A two-dimensional representation of the lamellar structure(or fiber. The cross-section of carbon fiber has essentially parallel basal plane folding of layer planes can be seen in the core region. It is thought that planes in the longitudinal direction is responsible for better compress aramid fibe A carbon fiber with a perfectly graphitic structure will have the theoretical Young modulus of slightly over 1000 GPa. In practice, however, the Young modulus is about 50% of the theoretical value in the case of PAN-based carbon fiber and may reach as much as 80% of the theoretical value for the mesophase-pitch-based carbon fiber. The rength of carbon fiber falls way short of the theoretical value of 180 GPa(Reynolds, 981). The practical strength values of carbon fiber may range from 3 to 20 GPa. The main reason for this is that while the modulus is determined mainly by the graphitic crystal structure, the strength is a very sensitive function of any defects that might be present, for example, voids, impurities, inclusions, etc. The strength of carbon fiber thus depends on the gage length, decreasing with increasing gage length. This is because the probability of finding a defect in the carbon fiber increases with its gage length Understandably, it also depends on the purity of the precursor polymer and the spinning nditions. A filtered polymer dope and a clean spinning atmosphere will result in a higher strength carbon fiber for a given gage length Following Huttinger(1990), we can correlate the modulus and strength of carbon fiber to its diameter. One can use Weibull statistics to analyze the strength distribution in brittle materials such as carbon fiber. As mentioned above, such brittle materials show a size effect, viz the experimental strength decreases with increasing sample size. This is demonstrated in Fig. 6, which shows a log-log plot of Youngs modulus as a function
10 K.K. Chawla Fig. 4. A two-dimensional representation of the lamellar structure (or turbostratic structure) of a carbon fiber. The cross-section of carbon fiber has essentially parallel basal planes in the skin region, but extensive folding of layer planes can be seen in the core region. It is thought that this extensive interlinking of lattice planes in the longitudinal direction is responsible for better compressive properties of carbon fiber than aramid fibers. A carbon fiber with a perfectly graphitic structure will have the theoretical Young modulus of slightly over 1000 GPa. In practice, however, the Young modulus is about 50% of the theoretical value in the case of PAN-based carbon fiber and may reach as much as 80% of the theoretical value for the mesophase-pitch-based carbon fiber. The strength of carbon fiber falls way short of the theoretical value of 180 GPa (Reynolds, 1981). The practical strength values of carbon fiber may range from 3 to 20 GPa. The main reason for this is that while the modulus is determined mainly by the graphitic crystal structure, the strength is a very sensitive function of any defects that might be present, for example, voids, impurities, inclusions, etc. The strength of carbon fiber thus depends on the gage length, decreasing with increasing gage length. This is because the probability of finding a defect in the carbon fiber increases with its gage length. Understandably, it also depends on the purity of the precursor polymer and the spinning conditions. A filtered polymer dope and a clean spinning atmosphere will result in a higher strength carbon fiber for a given gage length. Following Htittinger (1990), we can correlate the modulus and strength of carbon fiber to its diameter. One can use Weibull statistics to analyze the strength distribution in brittle materials such as carbon fiber. As mentioned above, such brittle materials show a size effect, viz., the experimental strength decreases with increasing sample size. This is demonstrated in Fig. 6, which shows a log-log plot of Young's modulus as a function
FIBER FRACTURE: AN OVERVIEW Fig. 5. A scanning electron ph of pitch-based carbon fibers. Note the surface striations and the a6.0 In d (um) Fig. 6. A log-log plot of modulus of the commer I caTbon f odulus as a function of carbon fiber diameter for three different carbon curves follow the expression(E/Eo)=(do/d) where E is Young,s fiber of diameter d while Eo is the theoretical Young modulus and do is the fiber diameter coresponding to Eo. The exponent, n obtained from the slope of the straight lines in this figure is about 1.5, and is independent of the fiber type of carbon fiber diameter for three different commercially available carbon fibers. The curves in this figure are based on the following expression (E/E0)=(do/d)
FIBER FRACTURE: AN OVERVIEW 11 Fig. 5. A scanning electron micrograph of pitch-based carbon fibers. Note the surface striations and the roughness at a microscopic scale. Fig. 6. A log-log plot of Young's modulus as a function of carbon fiber diameter for three different carbon fibers (after Htittinger, 1990). The curves follow the expression (E/Eo)= (do~d) n where E is Young's modulus of the commercial carbon fiber of diameter d while E0 is the theoretical Young modulus and do is the fiber diameter corresponding to E0. The exponent, n obtained from the slope of the straight lines in this figure is about 1.5, and is independent of the fiber type. of carbon fiber diameter for three different commercially available carbon fibers. The curves in this figure are based on the following expression: (E/Eo) -- (do/d)" (1)
K.K. Chawla where E is Youngs modulus of the commercial carbon fiber of diameter d while Eo is the theoretical Young modulus and do is the fiber diameter corresponding to Eo. The exponent, n obtained from the slope of the straight lines in Fig. 6 is about 1.5, and is independent of the fiber type. It would appear that these fibers would attain their theoretical value of modulus at a diameter of about 3 um If we perform a similar analysis with respect to the tensile strength of carbon fit we can wnt where o is the strength of a fiber with a diameter d, while oo is the higher strength of a fiber with a smaller diameter, do Now the theoretical strength of a crystalline solid, oo is expected to be about 0. 1 Eo (Meyers and Chawla, 1999), i.e. in this case oo= 100 GPa. For this value of ao, the exponent n in Eq. 2 is between 1.65 and 2(Meyers and Chawla, 1999). This means that in order to obtain a strength of 100 GPa, the diameter of the carbon fiber must his do value corresponding to strength is less than the do value corresponding to the theoretical modulus. The strengtH corresponding to a 3 um diameter carbon fiber from Eq. 3 will be between 12 and 18 GPa, an extremely high value. This can be understood in terms of the heterogeneous structure of carbon fiber. Recall from our discussion above that the near-surface region of a carbon fiber has more oriented basal planes than in the core. As we make the fiber diameter smaller, essentially we are reducing the proportion of the core to the near-surface region The fracture in carbon fibers is attributed to the presence of discrete flaws on the fiber surface and within it. Most of the volumetric defects in carbon fibers originate from the rganic inclus (2)organic inclusions (3)irregular voids from rapid coagulation (4)cylindrical voids precipitated by dissolved gases These defects get transformed during the high-temperature treatment into diverse perfections. Basal-plane cracks called Mrozowski cracks represent the most important type of Aaw that limit the tensile strength of carbon fibers. These occur as a result of anisotropic thermal contractions within the ribbon structure on cooling down from high-temperature treatment(>1500C). These cracks are generally aligned along the fiber axis. Their presence lowers the tensile strength of the fiber by providing easy crack nucleation sites. The fiber elastic modulus, however, is unaffected because the elastic strains involved in the modulus measurement are too small. Surface flaws can also limit the tensile strength of the carbonized fibers Oxidation treatments tend to remove surface defects and thus increase the strength levels of the fib It should be mentioned that compressive strength of carbon fiber is low compared to its tensile strength. The ratio of compressive strength to tensile strength for carbon fibers may vary anywhere between 0. 2 and 1(Kumar, 1989). High-modulus PAN-based fiber. A crack initiates on the tensile side and propagates across the fiber John
12 K.K. Chawla where E is Young's modulus of the commercial carbon fiber of diameter d while E0 is the theoretical Young modulus and do is the fiber diameter corresponding to E0. The exponent, n obtained from the slope of the straight lines in Fig. 6 is about 1.5, and is independent of the fiber type. It would appear that these fibers would attain their theoretical value of modulus at a diameter of about 3 ~m. If we perform a similar analysis with respect to the tensile strength of carbon fibers, we can write: (cr/cr0) = (do~d) n (2) where cr is the strength of a fiber with a diameter d, while cr0 is the higher strength of a fiber with a smaller diameter, do. Now the theoretical strength of a crystalline solid, or0 is expected to be about 0.1 E0 (Meyers and Chawla, 1999), i.e. in this case or0 = 100 GPa. For this value of cr0, the exponent n in Eq. 2 is between 1.65 and 2 (Meyers and Chawla, 1999). This means that in order to obtain a strength of 100 GPa, the diameter of the carbon fiber must be reduced from d to do 1500~ These cracks are generally aligned along the fiber axis. Their presence lowers the tensile strength of the fiber by providing easy crack nucleation sites. The fiber elastic modulus, however, is unaffected because the elastic strains involved in the modulus measurement are too small. Surface flaws can also limit the tensile strength of the carbonized fibers. Oxidation treatments tend to remove the surface defects and thus increase the strength levels of the fiber. It should be mentioned that compressive strength of carbon fiber is low compared to its tensile strength. The ratio of compressive strength to tensile strength for carbon fibers may vary anywhere between 0.2 and 1 (Kumar, 1989). High-modulus PAN-based carbon fibers buckle on compression, forming kink bands at thinner surface of the fiber. A crack initiates on the tensile side and propagates across the fiber (Johnson