a) FIGURE 6-5 (a)Scanning electron micrograph of a maple-derived carbonaceous preform showing porous structure.(M. Singh and ). A. Salem, Mechanical properties and microstructure of biomor hic silicon carbide ceramics fabricated from wood precursors, Journal of the European Ceramic Society, 22, 2002, 2709-2717, Elsevier). (b )SEM micrograph of porous carbon preform made from mahogany wood perpendicular to the growth direction. (M. Singh and J lem, Mechanical properties and microstructure of biomorphic silicon carbide ceramics fabricated from wood pre cursors, Journal of the European Ceramic Society, 22, 2002, 2709-2717, Elsevier). Reprinted with permission from Elsevier. Photo Courtesy of M, Singh, QSS Group, Inc, NASA Glenn Research Center, Cleveland, OH metal matrices). The material incompatibility and the severe processing conditions generally needed for composite fabrication create interfaces that exist in a non-equilibrium state. Thus interface evolution is thermodynamically ordained; however, interface design for properties by processing is essentially an outcome of a variety of kinetic phenomena(reaction kinetics, mass transport etc. ) The nature of the interface that develops in composites during fabrication and subsequent service strongly influences the response of the composite to mechanical stresses and to thermal and corrosive environments. As the inherent properties of the fiber and matrix constituents in a composite are fixed, greatest latitude in designing bulk composite properties realized by tailoring the interface (this is not strictly true, however, because processing conditions that lead to interface development also usually modify both the fiber properties as well as the metallurgy of the matrix). The development of an optimum interfacial bond between the fiber and the matrix is, therefore, a primary requirement for optimum performance of a composite. The nature and the properties of the interface(thickness, continuity, chemistry, strength, and adhesion)are determined by factors both intrinsic to the fiber and matrix materials hemistry, crystallography, defect content), as well as extrinsic to them(time, temperature, pressure, atmosphere, and other process variables). One of the major goals in the study of interfaces in composites is to develop an understanding of and exercise control on the structure chemistry, and properties of interfaces by judicious manipulation of processing conditions, To realize this goal, it is also necessary to develop and use techniques for mechanical, chemical, and structural characterization of interfaces in composites. Considerable progress has been made in aracterizing and understanding interfaces at the microstructural, crystallographic, and atomic Bonding at the fiber-matrix interface develops from physical or chemical interactions, from frictional stresses due to irregular surface topography, and from residual stresses arising from the mismatch of coefficients of thermal expansion(CtE)of the fiber and the matrix materials Composite Materials 407
(a) (b) FIGURE 6-5 (a) Scanning electron micrograph of a maple-derived carbonaceous preform showing porous structure. (M. Singh and J. A. Salem, Mechanical properties and microstructure of biomorphic silicon carbide ceramics fabricated from wood precursors, Journal of the European Ceramic Society, 22, 2002, 2709-2717, Elsevier). (b) SEM micrograph of porous carbon preform made from mahogany wood perpendicular to the growth direction. (M. Singh and J. A. Salem, Mechanical properties and microstructure of biomorphic silicon carbide ceramics fabricated from wood precursors, Journal of the European Ceramic Society, 22, 2002, 2709-2717, Elsevier). Reprinted with permission from Elsevier. Photo Courtesy of M. Singh, QSS Group, Inc., NASA Glenn Research Center, Cleveland, OH. metal matrices). The material incompatibility and the severe processing conditions generally needed for composite fabrication create interfaces that exist in a non-equilibrium state. Thus, interface evolution is thermodynamically ordained; however, interface design for properties by processing is essentially an outcome of a variety of kinetic phenomena (reaction kinetics, mass transport etc.). The nature of the interface that develops in composites during fabrication and subsequent service strongly influences the response of the composite to mechanical stresses and to thermal and corrosive environments. As the inherent properties of the fiber and matrix constituents in a composite are fixed, greatest latitude in designing bulk composite properties is realized by tailoring the interface (this is not strictly true, however, because processing conditions that lead to interface development also usually modify both the fiber properties as well as the metallurgy of the matrix). The development of an optimum interfacial bond between the fiber and the matrix is, therefore, a primary requirement for optimum performance of a composite. The nature and the properties of the interface (thickness, continuity, chemistry, strength, and adhesion) are determined by factors both intrinsic to the fiber and matrix materials (chemistry, crystallography, defect content), as well as extrinsic to them (time, temperature, pressure, atmosphere, and other process variables). One of the major goals in the study of interfaces in composites is to develop an understanding of and exercise control on the structure, chemistry, and properties of interfaces by judicious manipulation of processing conditions. To realize this goal, it is also necessary to develop and use techniques for mechanical, chemical, and structural characterization of interfaces in composites. Considerable progress has been made in characterizing and understanding interfaces at the microstructural, crystallographic, and atomic levels. Bonding at the fiber-matrix interface develops from physical or chemical interactions, from frictional stresses due to irregular surface topography, and from residual stresses arising from the mismatch of coefficients of thermal expansion (CTE) of the fiber and the matrix materials. Composite Materials 407
Both the fiber and matrix characteristics as well as the interface characteristics control the physical, mechanical, thermal, and chemical behavior of the composite. As an example, consider fracture behavior of a composite in which fibers are the strengthening phase. The fracture in the composite can proceed at the interface, through the matrix, or through the reinforcement depending on their respective inherent mechanical properties and the defect population. If the matrix is weak relative to the fiber and the interface, it will fail by the usual crack nucleation and growth mechanism. If the matrix and the interface are strong, the load is transferred across the interface to the reinforcement, which will provide strengthening until a threshold stress reached at which the composite will fail. Similarly, electrical, thermal, and other properties of a composite are determined by the properties of the fiber, matrix, and the interface Purely physical interactions( e.g, dispersion forces and electrostatic interactions) seldom ominate the interface behavior in composites. USually, some chemical interaction between fiber and matrix aids interface growth and determines the interface behavior. Chemical inter- actions may involve adsorption, impurity segregation, diffusion, dissolution, precipitation and reaction layer formation. These interactions are abruptly terminated at the conclusion of com- posite fabrication, which renders the interface inherently unstable. Driven by a need for these compositional and structural transformations at the interface continue after fabrication,usually with sluggish kinetics, via reaction paths that may involve intermediate non-equilibrium phases Chemical interactions between the fiber and the matrix not only determine the interface proper es and behavior, but may also modify the properties of the fiber and the metallurgy of the matrix. For example, the extent of fiber strength degradation and loss of age-hardening response because of chemical reactions in metal-matrix composites are directly related to the extent of interfacial reactions as reflected in the size of the reaction zone at the interface. The loss of age-hardening response is because of loss of chemically active solutes in the fiber-matrix reactions. It is, there fore, very important to control the processing conditions to design the interface for properties with minimum fiber degradation and little alterations in the metallurgy of the matrix. Because the rate of chemical reaction can be characterized in terms of temperature-dependent rate con- stants and activation energies, fundamental insights into the mechanisms of strength-limiting interfacial reactions can be derived Besides chemical interactions between the fiber and the matrix, the thermoelastic compatib ity between the two is important, particularly if the fabrication and/or service involves significant temperature excursions. a large mismatch between the coefficients of thermal expansion(Cte) of the fiber and the matrix can give rise to appreciable thermoelastic stresses which may affect the adhesion at the interface. For example, these stresses can give rise to interfacial cracking if he matrix cannot accommodate these stresses by plastic flow. In such a case, stress-absorbing intermediate compliant layers are deposited at the interface to promote compatibility and reduce the tendency for cracking by reducing the CTE mismatch-induced stresses Such layers may also provide protection to the reinforcement against excessive chemical attack in reactive matrices A careful control of the fabrication conditions can enhance the interface strength without excessive fiber degradation. Usually, a moderate chemical interaction between fiber and matrix improves the wetting, assists liquid-state fabrication of composite, and enhances the strength of the interface, which in turn facilitates transfer of extermal stresses to the strengthening agent, i. e, the fiber. But an excessive chemical reaction would degrade the fiber strength(even though the interface strength may be high)and defeat the very purpose for which the fibers were incorporated in the monolith. In contrast, if toughening rather than strengthening is the objective, as in brittle 408 MATERIALS PROCESSING AND MANUFACTURING SCIENCE
Both the fiber and matrix characteristics as well as the interface characteristics control the physical, mechanical, thermal, and chemical behavior of the composite. As an example, consider the fracture behavior of a composite in which fibers are the strengthening phase. The fracture in the composite can proceed at the interface, through the matrix, or through the reinforcement depending on their respective inherent mechanical properties and the defect population. If the matrix is weak relative to the fiber and the interface, it will fail by the usual crack nucleation and growth mechanism. If the matrix and the interface are strong, the load is transferred across the interface to the reinforcement, which will provide strengthening until a threshold stress is reached at which the composite will fail. Similarly, electrical, thermal, and other properties of a composite are determined by the properties of the fiber, matrix, and the interface. Purely physical interactions (e.g., dispersion forces and electrostatic interactions) seldom dominate the interface behavior in composites. Usually, some chemical interaction between fiber and matrix aids interface growth and determines the interface behavior. Chemical interactions may involve adsorption, impurity segregation, diffusion, dissolution, precipitation and reaction layer formation. These interactions are abruptly terminated at the conclusion of composite fabrication, which renders the interface inherently unstable. Driven by a need for these interactions to proceed to completion and the interface to approach thermodynamic equilibrium, compositional and structural transformations at the interface continue after fabrication, usually with sluggish kinetics, via reaction paths that may involve intermediate non-equilibrium phases. Chemical interactions between the fiber and the matrix not only determine the interface properties and behavior, but may also modify the properties of the fiber and the metallurgy of the matrix. For example, the extent of fiber strength degradation and loss of age-hardening response because of chemical reactions in metal-matrix composites are directly related to the extent of interracial reactions as reflected in the size of the reaction zone at the interface. The loss of age-hardening response is because of loss of chemically active solutes in the fiber-matrix reactions. It is, therefore, very important to control the processing conditions to design the interface for properties with minimum fiber degradation and little alterations in the metallurgy of the matrix. Because the rate of chemical reaction can be characterized in terms of temperature-dependent rate constants and activation energies, fundamental insights into the mechanisms of strength-limiting interracial reactions can be derived. Besides chemical interactions between the fiber and the matrix, the thermoelastic compatibility between the two is important, particularly if the fabrication and/or service involves significant temperature excursions. A large mismatch between the coefficients of thermal expansion (CTE) of the fiber and the matrix can give rise to appreciable thermoelastic stresses which may affect the adhesion at the interface. For example, these stresses can give rise to interfacial cracking if the matrix cannot accommodate these stresses by plastic flow. In such a case, stress-absorbing intermediate compliant layers are deposited at the interface to promote compatibility and reduce the tendency for cracking by reducing the CTE mismatch-induced stresses. Such layers may also provide protection to the reinforcement against excessive chemical attack in reactive matrices during fabrication and service. A careful control of the fabrication conditions can enhance the interface strength without excessive fiber degradation. Usually, a moderate chemical interaction between fiber and matrix improves the wetting, assists liquid-state fabrication of composite, and enhances the strength of the interface, which in turn facilitates transfer of external stresses to the strengthening agent, i.e., the fiber. But an excessive chemical reaction would degrade the fiber strength (even though the interface strength may be high) and defeat the very purpose for which the fibers were incorporated in the monolith. In contrast, if toughening rather than strengthening is the objective, as in brittle 408 MATERIALS PROCESSING AND MANUFACTURING SCIENCE
ceramic-matrix composites, then creation of a weak rather than strong interface is desired so tha ck deflection and frictional stresses during sliding of debonded fibers will permit realization of toughness. In such ing by strong chemical can induce too high a bond strength, which will, in turn, confer poor tought Thus, a delicate balance between several conflicting requirements is usually necessary to tailor the interface for a specific application with the aid of surface-engineering and processing science Fiber Strengthening with a fiber residing in a matrix, the length of the fiber limits the distance over which bonding and load transfer are possible For effective composite strengthening, the fiber must have a minimum critical length, Ic; fibers shorter than this length do not serve as load-bearing constituents. This critical length is ord Tc where d is the fiber diameter, af is the fracture strength of the fiber, and te is the fiber-matrix bond strength. The critical length, Ic, is on the order of a few millimeters for most composites Thus, for effective strengthening, the actual fiber length must exceed a few millimeters.In continuous fiber-reinforced composites, the tensile strength and the elastic modulus are strongly anisotropic. Usually, the strength of the composite along the fiber length(longitudinal strength) follows a simple rule of mixture(ROM), i.e., Oc Ve of +Vm Om, where om and of are the strength of the matrix and reinforcement, respectively, and Vt and Vm are the fiber and matri volume fractions. For composites reinforced with discontinuous, aligned fibers with a uniform distribution in the matrix and with the fiber length, L, greater than the critical length Lc,the omposite strength, ocd, along the longitudinal direction is =of vf +σm(1-Vf) (6-2) If the fiber length is smaller than the critical length, then o d is given from Ve+om(1-vt (6-3) phere d is the fiber diameter, and t is the shear stress at the fiber surface, which for a plastically deformable matrix such as metals is the yield strength of the matrix, and for a brittle matrix (ceramics or polymers), is the frictional stress at the interface. Calculations based on Equation [6-2] show that for aligned, discontinuous fibers with I>lc, the loss in composite's strength relative to the case of continuous fibers will not be appreciable provided the stress concentration at the ends of the short fibers is negligible The elastic modulus of a continuous fiber-reinforced composite along the longitudinal(fibe direction is given from the following ROM relationship Ec= vref vmer here Em and Et are the Young's moduli of the matrix and reinforcement, respectively,and Ve and Vm are the volume fractions of the fiber and the matrix, respectively. The composite Composite Materials 409
ceramic-matrix composites, then creation of a weak rather than strong interface is desired so that crack deflection and frictional stresses during sliding of debonded fibers will permit realization of toughness. In such a case, recipes designed to improve the wetting by strong chemical reactions can induce too high a bond strength, which will, in turn, confer poor toughness on the composite. Thus, a delicate balance between several conflicting requirements is usually necessary to tailor the interface for a specific application with the aid of surface-engineering and processing science. Fiber Strengthening With a fiber residing in a matrix, the length of the fiber limits the distance over which bonding and load transfer are possible. For effective composite strengthening, the fiber must have a minimum critical length,/c; fibers shorter than this length do not serve as load-bearing constituents. This critical length is crfd lc = 2rc (6-1) where d is the fiber diameter, af is the fracture strength of the fiber, and rc is the fiber-matrix bond strength. The critical length, lc, is on the order of a few millimeters for most composites. Thus, for effective strengthening, the actual fiber length must exceed a few millimeters. In continuous fiber-reinforced composites, the tensile strength and the elastic modulus are strongly anisotropic. Usually, the strength of the composite along the fiber length (longitudinal strength) follows a simple rule of mixture (ROM), i.e., ac = Vf crf + Vrn am, where am and crf are the strength of the matrix and reinforcement, respectively, and Vf and Vm are the fiber and matrix volume fractions. For composites reinforced with discontinuous, aligned fibers with a uniform distribution in the matrix and with the fiber length, l, greater than the critical length lc, the composite strength, aca, along the longitudinal direction is ( /c) O'cd = O'f gf 1 -- ~ -{- O'm(l - gf) (6-2) If the fiber length is smaller than the critical length, then Crcd is given from lrc O'cd = ---5- gf + O'm(1- Vf) t/ (6-3) where d is the fiber diameter, and rc is the shear stress at the fiber surface, which for a plastically deformable matrix such as metals is the yield strength of the matrix, and for a brittle matrix (ceramics or polymers), is the frictional stress at the interface. Calculations based on Equation [6-2] show that for aligned, discontinuous fibers with 1 > lc, the loss in composite's strength relative to the case of continuous fibers will not be appreciable provided the stress concentration at the ends of the short fibers is negligible. The elastic modulus of a continuous fiber-reinforced composite along the longitudinal (fiber) direction is given from the following ROM relationship: Ec = Vf Ef + Vm Em (6-4) where Ern and Ef are the Young's moduli of the matrix and reinforcement, respectively, and Vf and Vrn are the volume fractions of the fiber and the matrix, respectively. The composite Composite Materials 409
modulus, Ect, transverse to the fiber direction is given from a relationship reminiscent of the electrical resistance of parallel circuit: Ve Vn Ect es For discontinuously reinforced composites, KEr vr+ Em Vr (6-6) where K is called the fiber efficiency factor, and its value depends on the modulus ratio, (Ef/Em); for most cases K is in the range 0.1-0.6. These relationships apply to situations where fiber-matrix interface is devoid of reaction layers, such as in polymer-matrix composites Polymer-Matrix Composites Matrix Fiber-reinforced polymers are widely used as structural materials for relatively low-temperature use. Generally, polymers have lower strength and modulus than metals or ceramics but they are hore resistant to chemical attack than metals. Figure 6-6 displays a schematic comparison of the strength characteristics of ceramics, metals, polymers, and elastomers. Prolonged exposure to UV light and some solvents can, however, cause polymer degradation. Polymers are giant chainlike molecules or macromolecules, with covalently bonded carbon atoms as the backbone of the chain. Small-chain, low-molecular-weight organic molecules( monomers)are joined together via the process of polymerization, which converts monomers to polymers. Polymerization occurs either through condensation or through addition of a catalyst In condensation polymerization, Ceramics Elastomers Strain FIGURE 6-6 Comparison of idealized stress-strain diagrams for metals, amorphous polymers, and elastomers.(BS. Mitchell, An Introduction to Materials Engineering and Science for Chemical and Materials Engineers, Wiley-Interscience, Hoboken, NJ, 2004, p. 469) 410 MATERIALS PROCESSING AND MANUFACTURING SCIENCE
modulus, Ect, transverse to the fiber direction is given from a relationship reminiscent of the electrical resistance of parallel circuit: 1 Vf Vm = ~ (6-5) Ect Ef Em For discontinuously reinforced composites, Ecd -- KEf Vf + EmVm (6-6) where K is called the fiber efficiency factor, and its value depends on the modulus ratio, (El/Em); for most cases K is in the range 0.1-0.6. These relationships apply to situations where the fiber-matrix interface is devoid of reaction layers, such as in polymer-matrix composites. Polymer-Matrix Composites Matrix Fiber-reinforced polymers are widely used as structural materials for relatively low-temperature use. Generally, polymers have lower strength and modulus than metals or ceramics but they are more resistant to chemical attack than metals. Figure 6-6 displays a schematic comparison of the strength characteristics of ceramics, metals, polymers, and elastomers. Prolonged exposure to UV light and some solvents can, however, cause polymer degradation. Polymers are giant, chainlike molecules or macromolecules, with covalently bonded carbon atoms as the backbone of the chain. Small-chain, low-molecular-weight organic molecules (monomers) are joined together via the process of polymerization, which converts monomers to polymers. Polymerization occurs either through condensation or through addition of a catalyst. In condensation polymerization, l / Ceramics ~o Conventional plastics Elastomers Strain FIGURE 6-6 Comparison of idealized stress-strain diagrams for metals, amorphous polymers, and elastomers. (B. S. Mitchell, An Introduction to Materials Engineering and Science for Chemical and Materials Engineers, Wiley-lnterscience, Hoboken, NJ, 2004, p. 469). 410 MATERIALS PROCESSING AND MANUFACTURING SCIENCE
there occurs a stepwise reaction of molecules, and in each step a molecule of a simple compound nerally water, forms as a by-product. In addition to polymerization, monomers can be joined to form a polymer with the help of a catalyst without producing any by-products. For example, the linear addition of ethylene molecules(CH2)results in polyethylene, with the final mass of polymer being the sum of Linear polymers consist of a long chain, often coiled or bent, of atoms with attached side groups(e.g, polyethylene, polyvinyl chloride, polymethyl metacrylate or PMMA). Branched polymers consist of side-branching of atomic chains. In cross-linked polymers, molecules of one chain are bonded(cross-linked) with those of another, thus forming a three-dimensional network Cross-linking hinders sliding of molecules past one another, thus making the polymer strong and rigid. Ladder polymers form by linking linear polymers in a regular manner; ladder polymers are more rigid than linear polymers. Figure 6-7 illustrates these different types of polymers Unlike pure metals that melt at a fixed temp polymers show a range of temperature over which crystallinity vanishes on heating On cooling, polymer liquids contract just as metals do. In the case of amorphous polymers, this co on continues below the melting point, Tr of crystalline polymer to a temperature, Tg, called the glass transition temperature, at which the supercooled liquid polymer becomes extremely rigid owing to extremely high viscosity. The structure of the polymer below Tg is essentially disordered, like that of a liquid. Figure 6-8 shows he changes in the specific volume as a function of temperature in a polymer. Many physical properties such as viscosity, heat capacity, modulus, and thermal expansion change abruptly at Tg. For example, Figure 6-9 displays the variation of the natural logarithm of elastic modulus as a function of temperature; the transitions from the glassy to rubbery, and rubbery to fluid states are accompanied by discontinuities in the modulus. The glass transition temperature, Tg, is a function of the structure of the polymer; for example, if a polymer has a rigid backbone structure and/or bulky branch groups, then Tg will be quite high. The glass transition phenomenon is also observed in amorphous ceramics such as glasses. Glasses have a mixed ionic and covalent … FIGURE 6-7 Molecular chain configurations in polymers: (a)linear, (b) branched, (c)cross linked, and (d) ladder.(KK Chawla, Composite Material-Science& Engineering, Springer-Verlag, New York, NY, 1987, p. 59) Composite Materials 411
there occurs a stepwise reaction of molecules, and in each step a molecule of a simple compound, generally water, forms as a by-product. In addition to polymerization, monomers can be joined to form a polymer with the help of a catalyst without producing any by-products. For example, the linear addition of ethylene molecules (CH2) results in polyethylene, with the final mass of polymer being the sum of monomer masses. Linear polymers consist of a long chain, often coiled or bent, of atoms with attached side groups (e.g., polyethylene, polyvinyl chloride, polymethyl metacrylate or PMMA). Branched polymers consist of side-branching of atomic chains. In cross-linked polymers, molecules of one chain are bonded (cross-linked) with those of another, thus forming a three-dimensional network. Cross-linking hinders sliding of molecules past one another, thus making the polymer strong and rigid. Ladder polymers form by linking linear polymers in a regular manner; ladder polymers are more rigid than linear polymers. Figure 6-7 illustrates these different types of polymers. Unlike pure metals that melt at a fixed temperature, polymers show a range of temperatures over which crystallinity vanishes on heating. On cooling, polymer liquids contract just as metals do. In the case of amorphous polymers, this contraction continues below the melting point, Tm, of crystalline polymer to a temperature, Tg, called the glass transition temperature, at which the supercooled liquid polymer becomes extremely rigid owing to extremely high viscosity. The structure of the polymer below Tg is essentially disordered, like that of a liquid. Figure 6-8 shows the changes in the specific volume as a function of temperature in a polymer. Many physical properties such as viscosity, heat capacity, modulus, and thermal expansion change abruptly at Tg. For example, Figure 6-9 displays the variation of the natural logarithm of elastic modulus as a function of temperature; the transitions from the glassy to rubbery, and rubbery to fluid states are accompanied by discontinuities in the modulus. The glass transition temperature, Tg, is a function of the structure of the polymer; for example, if a polymer has a rigid backbone structure and/or bulky branch groups, then Tg will be quite high. The glass transition phenomenon is also observed in amorphous ceramics such as glasses. Glasses have a mixed ionic and covalent J (b) (a) (c) (d) FIGURE 6-7 Molecular chain configurations in polymers: (a) linear, (b) branched, (c) crosslinked, and (d) ladder. (K. K. Chawla, Composite Material- Science & Engineering, Springer-Verlag, New York, NY, 1987, p. 59). Composite Materials 411