《纺织复合材料》课程参考文献（Multiscale Modeling and Simulation of Composite Materials and Structures）Chapter 9 Predicting Thermooxidative Degradation and Performance Matrix Composites

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360 G.A.Schoeppner,G.P.Tandon and K.V.Pochiraju or interphase region are a function of the interaction of the fiber and matrix during the manufacturing process,the chemical compatibility of the fiber,and the sizing(if applicable)on the fiber. To deal with the aforementioned complex interactions,modeling is expected to incorporate mechanisms active at multiple scales (constituent, microstructural,lamina,and laminate scales)and multiple domains of res- ponse (chemical,thermal,and mechanical).The motivation is to develop robust,life-performance,prediction modeling capabilities for designers who currently use cost prohibitive experimentally based design allowables and use weight loss to evaluate the thermal-oxidative stability of material systems. In the face of such complexity and lack of knowledge regarding material behavior,industry currently relies on the use of environmental "knockdown factors"for the design of composite aerospace structures which operate in aggressive environments.One of the current methodologies used for determining environmental knockdown factors for designing composite aerospace structures is to determine reduced material allowables for each of the lamina properties (laminate ultimate strengths,notched strengths,fatigue,flexure properties,bearing strengths,etc.)for each of the material forms used in the structure.The material forms may include unitape, woven cloth,fiber preforms with mold filling,etc. The large variety of tests performed on a statistically sufficient number of replicates for the various environmental conditions adds tremendous cost to the materials qualification and design allowables process.In addi- tion,the worst case environmental extreme conditions are typically used for determining reduced materials allowables to help circumvent risk asso- ciated with the variability and inaccurate prediction of service environ- ments.In addition to the environmental knockdown factors,damage tolerance knockdown factors are also applied to the designs.The damage tolerance factors may be determined through damaging full-scale components and testing them for a predetermined number of life cycles in a hot/wet envi- ronment.Using this approach,the end-of-life properties are measured and used in the allowables determination process for designing components. The aerospace engine community (where high-temperature polymer matrix composites(HTPMCs)are most prevalent)often designs to end-of- life properties,and it is accepted that at the end of life for certain lightly I Although fiber-matrix interface and fiber-matrix interphase are often used interchangeably,we formally define the fiber-matrix interface as the two-dimensional surface defined by the common fiber and matrix surfaces.We define the fiber- matrix interphase as the three-dimensional matrix region directly around the fiber that may have properties distinct from the bulk matrix properties

or interphase region1 are a function of the interaction of the fiber and matrix during the manufacturing process, the chemical compatibility of the fiber, and the sizing (if applicable) on the fiber. To deal with the aforementioned complex interactions, modeling is expected to incorporate mechanisms active at multiple scales (constituent, microstructural, lamina, and laminate scales) and multiple domains of response (chemical, thermal, and mechanical). The motivation is to develop robust, life-performance, prediction modeling capabilities for designers who currently use cost prohibitive experimentally based design allowables and use weight loss to evaluate the thermal-oxidative stability of material systems. In the face of such complexity and lack of knowledge regarding material behavior, industry currently relies on the use of environmental “knockdown factors” for the design of composite aerospace structures which operate in aggressive environments. One of the current methodologies used for determining environmental knockdown factors for designing composite aerospace structures is to determine reduced material allowables for each of the lamina properties (laminate ultimate strengths, notched strengths, fatigue, flexure properties, bearing strengths, etc.) for each of the material forms used in the structure. The material forms may include unitape, woven cloth, fiber preforms with mold filling, etc. The large variety of tests performed on a statistically sufficient number of replicates for the various environmental conditions adds tremendous cost to the materials qualification and design allowables process. In addition, the worst case environmental extreme conditions are typically used for determining reduced materials allowables to help circumvent risk associated with the variability and inaccurate prediction of service environments. In addition to the environmental knockdown factors, damage tolerance knockdown factors are also applied to the designs. The damage tolerance factors may be determined through damaging full-scale components and testing them for a predetermined number of life cycles in a hot/wet environment. Using this approach, the end-of-life properties are measured and used in the allowables determination process for designing components. The aerospace engine community (where high-temperature polymer matrix composites (HTPMCs) are most prevalent) often designs to end-oflife properties, and it is accepted that at the end of life for certain lightly 1 Although fiber–matrix interface and fiber–matrix interphase are often used interchangeably, we formally define the fiber–matrix interface as the two-dimensional surface defined by the common fiber and matrix surfaces. We define the fiber– matrix interphase as the three-dimensional matrix region directly around the fiber that may have properties distinct from the bulk matrix properties. 360 G.A. Schoeppner, G.P. Tandon and K.V. Pochiraju

Chapter 9:Predicting Thermooxidative Degradation 361 loaded structures,the composites may have cracks.On the other hand,for highly loaded or critical structures,the presence of cracks,even at the end of life,is not accepted.This traditional approach for determining material design allowables,taking into account extremes in-service environments, requires significant testing (cost and schedule).For cost savings and risk mitigation,designers often resort to previously qualified materials,thereby negating the potential benefits of new material advancements.By develop- ing a life prediction/performance modeling capability,the cost and time associated with developing material design allowables can provide oppor- tunities for the insertion of new advanced materials. This chapter focuses on predicting the performance of PMCs in high- temperature environments where thermooxidative conditions are extreme and the material is used near its tolerance limits.For the current design methodology used by aerospace structure designers,composites are con- sidered to be "chemically static,"ignoring the evolution of the chemical/ environmental degradation and nonelastic mechanical response.How- ever,the empirical design allowables are based on the expected end-of life properties by testing specimens that have been aged under representative service environments for the design life. This chapter outlines the current state of the art,the shortcomings of existing capabilities,and future challenges for addressing modeling needs for PMCs in high-temperature oxidative environments.It is believed that the approach presented provides the methodology to accurately model both short-and long-term environmental effects on composite laminates for facilitating design allowables generation (including history-dependent failure prediction)and for predicting life expectancy(degradation state)for fielded composite structures. A valuable resource for understanding the high-temperature behavior of PMCs is the tremendous volume of long-term high-temperature aging data generated in the NASA High-Speed Research (HSR)program.The HSR effort was a national effort to develop the next-generation supersonic passenger jet designed for a 60,000-h life with temperatures approaching 177C.To meet the vehicle requirements,PMCs with high glass transition temperatures T and,thus,high-temperature use capabilities were thermo- mechanically loaded for very long-aging times. The long-term testing conducted in this program demonstrates the challenge of using PMCs in high-temperature environments.An important contribution to understanding the high-temperature performance of the polymer composites evaluated in the program is the use of viscoelastic formulations to model long-term behavior [21,42,49,68,115,116].The assumption inherent in the use of these viscoelastic formulations is that the material is chemically static or the original chemical structure is thermally

loaded structures, the composites may have cracks. On the other hand, for highly loaded or critical structures, the presence of cracks, even at the end of life, is not accepted. This traditional approach for determining material design allowables, taking into account extremes in-service environments, requires significant testing (cost and schedule). For cost savings and risk mitigation, designers often resort to previously qualified materials, thereby negating the potential benefits of new material advancements. By developing a life prediction/performance modeling capability, the cost and time associated with developing material design allowables can provide opportunities for the insertion of new advanced materials. This chapter focuses on predicting the performance of PMCs in hightemperature environments where thermooxidative conditions are extreme and the material is used near its tolerance limits. For the current design This chapter outlines the current state of the art, the shortcomings of existing capabilities, and future challenges for addressing modeling needs for PMCs in high-temperature oxidative environments. It is believed that the approach presented provides the methodology to accurately model both short- and long-term environmental effects on composite laminates for facilitating design allowables generation (including history-dependent failure prediction) and for predicting life expectancy (degradation state) for fielded composite structures. A valuable resource for understanding the high-temperature behavior of PMCs is the tremendous volume of long-term high-temperature aging data generated in the NASA High-Speed Research (HSR) program. The HSR effort was a national effort to develop the next-generation supersonic passenger jet designed for a 60,000-h life with temperatures approaching 177°C. To meet the vehicle requirements, PMCs with high glass transition temperatures Tg and, thus, high-temperature use capabilities were thermomechanically loaded for very long-aging times. The long-term testing conducted in this program demonstrates the challenge of using PMCs in high-temperature environments. An important contribution to understanding the high-temperature performance of the polymer composites evaluated in the program is the use of viscoelastic formulations to model long-term behavior [21, 42, 49, 68, 115, 116]. The assumption inherent in the use of these viscoelastic formulations is that the material is chemically static or the original chemical structure is thermally methodology used by aerospace structure designers, composites are considered to be “chemically static,” ignoring the evolution of the chemical/ environmental degradation and nonelastic mechanical response. However, the empirical design allowables are based on the expected end-of life properties by testing specimens that have been aged under representative service environments for the design life. Chapter 9: Predicting Thermooxidative Degradation 361

362 G.A.Schoeppner,G.P.Tandon and K.V.Pochiraju recoverable [98].Although these formulations are an important aspect of the overall methodology to model the performance of HTPMCs,a com- prehensive review of such is beyond the scope of the current discussion. The discussion here is limited to modeling the thermooxidative aging of HTPMCs and the role of the various constituents.Although hygrothermal degradation,which is a significant concern for HTPMCs,is not speci- fically addressed here,the methodology described herein can be applied to modeling hygrothermal degradation behavior.As with oxidation,hygro- thermal degradation involves transport and chemical reactions of the polymer with the diffused media.The primary challenge for modeling the coupling of oxidative and hygrothermal degradation of HTPMCs is an understanding of the numerous degradation mechanisms. Several major aging mechanisms that lead to weight loss and damage growth and,hence,degradation of the performance of the polymer resin, fibers,and their composite can be identified.They are: Physical aging.The thermodynamically reversible volumetric response due to slow evolution toward thermodynamic equilibrium is identified as physical aging.The decreased molecular mobility and free-volume reduction lead to strain and damage development in the material. Chemical aging.The nonreversible volumetric response due to chain scission reactions and/or additional crosslinking,hydrolysis,deploy- merization,and plasticization is classified as chemical aging.A dominant chemical aging process for HTPMCs is thermooxidative aging-which is the nonreversible surface diffusion response and chemical changes occurring during oxidation of a polymer (hence a modality of chemical aging).The oxidative aging may lead to either the reduction in molecular weight as a result of chemical bond breakage and loss in weight from outgassing of low molecular weight gaseous species,or chain scission and formation of dangling chains in polymer networks. Mechanical stress-induced aging.Mechanical and thermal fatigue loading cause micromechanical damage growth within the material. The damage evolution,in turn,exacerbates the physical aging and thermooxidative response of the material.This aging mechanism may be the least understood and least modeled by researchers. The capability to predict the performance of HTPMCs for both primary and secondary structural applications is elusive.The highly coupled physi- cal,chemical,and mechanical response of these materials to the extreme hygrothermal environments provides formidable challenges to the com- posite mechanics community.Polymers (in particular amorphous polymers) have been studied from the standpoint of physical aging [98],chemical aging [66],and strain-dependent aging [118].Although models to predict

recoverable [98]. Although these formulations are an important aspect of the overall methodology to model the performance of HTPMCs, a comprehensive review of such is beyond the scope of the current discussion. The discussion here is limited to modeling the thermooxidative aging of HTPMCs and the role of the various constituents. Although hygrothermal degradation, which is a significant concern for HTPMCs, is not specifically addressed here, the methodology described herein can be applied to modeling hygrothermal degradation behavior. As with oxidation, hygrothermal degradation involves transport and chemical reactions of the polymer with the diffused media. The primary challenge for modeling the coupling of oxidative and hygrothermal degradation of HTPMCs is an understanding of the numerous degradation mechanisms. Several major aging mechanisms that lead to weight loss and damage growth and, hence, degradation of the performance of the polymer resin, fibers, and their composite can be identified. They are: – Physical aging. The thermodynamically reversible volumetric response due to slow evolution toward thermodynamic equilibrium is identified as physical aging. The decreased molecular mobility and free-volume reduction lead to strain and damage development in the material. – Chemical aging. The nonreversible volumetric response due to chain scission reactions and/or additional crosslinking, hydrolysis, deploymerization, and plasticization is classified as chemical aging. A dominant chemical aging process for HTPMCs is thermooxidative aging – which is the nonreversible surface diffusion response and chemical changes occurring during oxidation of a polymer (hence a modality of chemical aging). The oxidative aging may lead to either the reduction in molecular weight as a result of chemical bond breakage and loss in weight from outgassing of low molecular weight gaseous species, or chain scission and formation of dangling chains in polymer networks. – Mechanical stress-induced aging. Mechanical and thermal fatigue loading cause micromechanical damage growth within the material. The damage evolution, in turn, exacerbates the physical aging and thermooxidative response of the material. This aging mechanism may be the least understood and least modeled by researchers. The capability to predict the performance of HTPMCs for both primary and secondary structural applications is elusive. The highly coupled physical, chemical, and mechanical response of these materials to the extreme hygrothermal environments provides formidable challenges to the composite mechanics community. Polymers (in particular amorphous polymers) have been studied from the standpoint of physical aging [98], chemical aging [66], and strain-dependent aging [118]. Although models to predict 362 G.A. Schoeppner, G.P. Tandon and K.V. Pochiraju

Chapter 9:Predicting Thermooxidative Degradation 363 the aging response of polymers are available and the fiber response can be assumed to be elementary,the ability to model the thermooxidative aging of the fiber-matrix system (presence of fiber-matrix interface/interphase region complicates the issue with a coupling or sizing agent)is lacking. While the time-dependent physical,chemical,and damage-induced de- gradation mechanisms have been studied for some resin systems,polymer composite thermal oxidation studies from a mechanistic perspective are nascent.Notable exceptions to this are the recent works of the groups of Colin and Verdu [27],Colin et al.[32],Skontorp et al.[97],Wang et al. [1211,and Pochiraju and Tandon [73,741,Tandon et al.[1041,and past work by Wise et al.[125],Celina et al.[22],and McManus et al.[621. Equally important are the experimental characterization efforts by such groups as Bowles et al.[14,19],Tsuji et al.[113],Abdeljaoued [1],Johnson and Gates [49],and Schoeppner et al.[91].However,most literature is confined to thermal oxidation of neat polymer systems and there are limited studies that correlate the thermochemical decomposition of high-temperature polymers to the resulting mechanical performance.Such works include Meador et al.[63-65]and Thorp [107]for PMR-15 high-temperature composites and Lincoln [56]for 5250-4 bismaleimide(BMI)composites. Current emphasis is on the implementation and extension of multiscale models to represent the polymer behavior/properties as a function of the degradation state to include chemical degradation kinetics,micromechanical models with time-dependent polymer constitutive relationships,and ply- level and laminate level models to predict structural behavior.The behavior of the composite will,thus,be dependent on its current chemical,physical. and mechanical state as well as its service history.This multidisciplinary modeling approach will provide generalizable analytical and design tools for realistic prediction of performance,durability,and use life of HTPMCs. The following requirements are identified for the formulation of the predictive thermooxidation models: Appropriate mechanistic and kinetic modeling of polymer environ- mental degradation.For the highly crosslinked polyimide composite of interest,the reactivity of the end cap is often a primary concern [63, 1071.Although the primary,and in some cases secondary,oxidation and hydrolytic degradation mechanisms can be identified,determination of mechanisms up to the final state of degradation is difficult if not impossible.Predicting thermal,physical,and mechanical performance based on the chemical state of the polymer is currently impractical for all but the very simplest of polymer systems.In the absence of this pre- dictive capability,empirical correlation of the chemical state (if known) to mechanical properties is used to help define the constitutive models

the aging response of polymers are available and the fiber response can be assumed to be elementary, the ability to model the thermooxidative aging of the fiber–matrix system (presence of fiber–matrix interface/interphase region complicates the issue with a coupling or sizing agent) is lacking. While the time-dependent physical, chemical, and damage-induced degradation mechanisms have been studied for some resin systems, polymer composite thermal oxidation studies from a mechanistic perspective are nascent. Notable exceptions to this are the recent works of the groups of Colin and Verdu [27], Colin et al. [32], Skontorp et al. [97], Wang et al. [121], and Pochiraju and Tandon [73, 74], Tandon et al. [104], and past work by Wise et al. [125], Celina et al. [22], and McManus et al. [62]. Equally important are the experimental characterization efforts by such groups as Bowles et al. [14, 19], Tsuji et al. [113], Abdeljaoued [1], Johnson and Gates [49], and Schoeppner et al. [91]. However, most literature is confined to thermal oxidation of neat polymer systems and there are limited studies that correlate the thermochemical decomposition of high-temperature polymers to the resulting mechanical performance. Such works include Meador et al. [63–65] and Thorp [107] for PMR-15 high-temperature composites and Lincoln [56] for 5250-4 bismaleimide (BMI) composites. Current emphasis is on the implementation and extension of multiscale models to represent the polymer behavior/properties as a function of the degradation state to include chemical degradation kinetics, micromechanical models with time-dependent polymer constitutive relationships, and plylevel and laminate level models to predict structural behavior. The behavior of the composite will, thus, be dependent on its current chemical, physical, and mechanical state as well as its service history. This multidisciplinary modeling approach will provide generalizable analytical and design tools for realistic prediction of performance, durability, and use life of HTPMCs. predictive thermooxidation models: – Appropriate mechanistic and kinetic modeling of polymer environmental degradation. For the highly crosslinked polyimide composite of interest, the reactivity of the end cap is often a primary concern [63, 107]. Although the primary, and in some cases secondary, oxidation and hydrolytic degradation mechanisms can be identified, determination of mechanisms up to the final state of degradation is difficult if not impossible. Predicting thermal, physical, and mechanical performance based on the chemical state of the polymer is currently impractical for all but the very simplest of polymer systems. In the absence of this predictive capability, empirical correlation of the chemical state (if known) to mechanical properties is used to help define the constitutive models. The following requirements are identified for the formulation of the Chapter 9: Predicting Thermooxidative Degradation 363

364 G.A.Schoeppner,G.P.Tandon and K.V.Pochiraju Polymer constitutive models that incorporate the chemical,thermal, and deformation state and history dependence.Linear viscoelastic constitutive models have been successfully used to model the physical aging of the polymer phase of polymer composites used in high- temperature environments.Beyond physical aging,accounting for the effects of chemical aging(oxidative and nonoxidative)in a constitutive model requires path/history-dependent relationships.Constitutive models and/or empirically derived correlations that account for the dominant behavior of the material provide alternatives to models that can predict performance based on the chemical degradation state. Integrated mechanistic models that explicitly represent fiber-matrix phases and interfaces to predict lamina properties.The highly critical fiber-matrix interface/interphase region may govern the oxidative beha- vior of HTPMCs,but significant challenges exist in measuring properties of the interphase region.Prediction of strength/failure requires know- ledge of the constituent properties,including strength and toughness as a function of the degradation state or aging history.It is beyond current modeling capabilities to predict mechanical properties based on the chemical state of the polymer.For lack of a robust constitutive model,simplifying assumptions regarding the history-dependent pro- perties can be made as a first-order approximation to predict the material behavior. Structural laminate models with lamina property descriptions and dis- crete ply representations for laminate and composite failure modeling under history-dependent environmental service loads.As for the micro- mechanical scale in which the fiber,matrix,and interphase regions are represented explicitly,the residual stresses on the ply-level and lami- nate level scales play a critical role in the thermal oxidation process. Accurate representation of the free-edge interlaminar stresses in multi- directional composites,taking into account stress-assisted diffusion,is essential for accurately modeling the oxidation-susceptible free surfaces. Experimental validation of the simulation and transition into designer assistance tools and property databases.To transfer the prediction methodology from scientists to designers,a new generation of tools that incorporate the simulation methods and experimental databases needs to be developed.To facilitate adoption of the tools by designers, any such development must be in collaboration with the practitioners from the airframe and propulsion segments of the aerospace industry. This methodology of tool development in collaboration with design practitioners was used in the DARPA Accelerated Insertion of Materials-Composite(AIM-C)program [82]

– Polymer constitutive models that incorporate the chemical, thermal, and deformation state and history dependence. Linear viscoelastic constitutive models have been successfully used to model the physical aging of the polymer phase of polymer composites used in hightemperature environments. Beyond physical aging, accounting for the effects of chemical aging (oxidative and nonoxidative) in a constitutive model requires path/history-dependent relationships. Constitutive models and/or empirically derived correlations that account for the dominant behavior of the material provide alternatives to models that can predict performance based on the chemical degradation state. – Integrated mechanistic models that explicitly represent fiber–matrix phases and interfaces to predict lamina properties. The highly critical fiber–matrix interface/interphase region may govern the oxidative behavior of HTPMCs, but significant challenges exist in measuring properties of the interphase region. Prediction of strength/failure requires knowledge of the constituent properties, including strength and toughness, as a function of the degradation state or aging history. It is beyond current modeling capabilities to predict mechanical properties based on the chemical state of the polymer. For lack of a robust constitutive model, simplifying assumptions regarding the history-dependent properties can be made as a first-order approximation to predict the material behavior. – Structural laminate models with lamina property descriptions and discrete ply representations for laminate and composite failure modeling under history-dependent environmental service loads. As for the micromechanical scale in which the fiber, matrix, and interphase regions are represented explicitly, the residual stresses on the ply-level and laminate level scales play a critical role in the thermal oxidation process. Accurate representation of the free-edge interlaminar stresses in multidirectional composites, taking into account stress-assisted diffusion, is essential for accurately modeling the oxidation-susceptible free surfaces. – Experimental validation of the simulation and transition into designer assistance tools and property databases. To transfer the prediction methodology from scientists to designers, a new generation of tools that incorporate the simulation methods and experimental databases needs to be developed. To facilitate adoption of the tools by designers, any such development must be in collaboration with the practitioners from the airframe and propulsion segments of the aerospace industry. This methodology of tool development in collaboration with design practitioners was used in the DARPA Accelerated Insertion of Materials – Composite (AIM-C) program [82]. 364 G.A. Schoeppner, G.P. Tandon and K.V. Pochiraju

Chapter 9:Predicting Thermooxidative Degradation 365 For those steps described above where prediction capability is lacking, experimental/empirical means must be used to represent the behavior of the material.It is these empirical relationships that preserve the capability to make predictions on how materials will behave when mechanistic models are not available.Experimental validation of predictive models for a given geometric scale provides a basis for building models at higher geometric scales.As an example,polymer constitutive models can be validated by testing neat resin polymers but validation of such models on the lamina or laminate scale is not viable.This is due to the fact that fibers mask the polymer degradation behavior particularly for the fiber-dominated composite properties.Additionally,fibers can exacerbate some degradation mechanisms of polymer due to the introduction of fiber-matrix residual stresses and the introduction of fiber-matrix interface/interphase. The multiscale modeling levels and the vital links between the various model levels are illustrated in Fig.9.1.This description of the hierarchical scheme is an idealized representation of the methodology needed to mechanistically model the behavior of PMCs in aggressive environments. In particular,a kinetic description of the polymer phase of the material is necessary when the materials are subjected to or susceptible to chemical changes or degradation. Chemical Degradation Constituents Interface Characteristics Micromechanics Ply-level Analysis Fig.9.1.Multiscale modeling levels The primary focus of the discussion in this work is on predicting isothermal-oxidative aging of unitape laminates with particular focus on the composites using PMR-15 high-temperature polymer.Additionally,the reinforcement is limited to polyacrylonitrile (PAN)-based carbon fibers. PMR-15 is a widely used addition polyimide with a maximum service temperature of approximately 288C.Among the class of high-temperature polymers are the bismaleimides,Avimid-N,thermosetting polyimides (AFR700B,LARC RP46),and phenylethynyl-terminated polyimides (PETI-5,AFR-PE-N)resin systems.Each of these material systems has unique degradation reactions,mechanisms,and kinetics particular to their chemical structure.Although experimental observations and predictions of the behavior of PMR-15 neat resin and composites are not necessarily representative of the behavior of these other high-temperature polymer

For those steps described above where prediction capability is lacking, experimental/empirical means must be used to represent the behavior of the material. It is these empirical relationships that preserve the capability to make predictions on how materials will behave when mechanistic models are not available. Experimental validation of predictive models for a given geometric scale provides a basis for building models at higher geometric scales. As an example, polymer constitutive models can be validated by testing neat resin polymers but validation of such models on the lamina or laminate scale is not viable. This is due to the fact that fibers mask the polymer degradation behavior particularly for the fiber-dominated composite properties. Additionally, fibers can exacerbate some degradation mechanisms of polymer due to the introduction of fiber–matrix residual stresses and the introduction of fiber–matrix interface/interphase. The multiscale modeling levels and the vital links between the various model levels are illustrated in Fig. 9.1. This description of the hierarchical scheme is an idealized representation of the methodology needed to mechanistically model the behavior of PMCs in aggressive environments. In particular, a kinetic description of the polymer phase of the material is necessary when the materials are subjected to or susceptible to chemical changes or degradation. Fig. 9.1. Multiscale modeling levels The primary focus of the discussion in this work is on predicting isothermal-oxidative aging of unitape laminates with particular focus on the composites using PMR-15 high-temperature polymer. Additionally, the reinforcement is limited to polyacrylonitrile (PAN)-based carbon fibers. PMR-15 is a widely used addition polyimide with a maximum service temperature of approximately 288°C. Among the class of high-temperature polymers are the bismaleimides, Avimid-N, thermosetting polyimides (AFR700B, LARC RP46), and phenylethynyl-terminated polyimides (PETI-5, AFR-PE-N) resin systems. Each of these material systems has unique degradation reactions, mechanisms, and kinetics particular to their chemical structure. Although experimental observations and predictions of the behavior of PMR-15 neat resin and composites are not necessarily representative of the behavior of these other high-temperature polymer Chapter 9: Predicting Thermooxidative Degradation 365

366 G.A.Schoeppner,G.P.Tandon and K.V.Pochiraju material systems,the modeling methodology and procedures for deter- mining material parameters may be directly applicable to predicting their behavior.On the other hand,the observed behavior of other high-temp- erature material systems can deviate significantly from PMR-15 and such deviations will be noted when appropriate.Current polymer and polymer matrix composite modeling approaches for chemical and physical aging,as well as the modeling process for predicting thermooxidative degradation, are discussed in the following sections. 9.1.1 Physical Aging of Polymers and PMCs At temperatures below a polymer's glass transition temperature(T),the material is in a nonequilibrium state and undergoes a time-dependent re- arrangement toward thermodynamic equilibrium.During this rearrangement (relaxation)toward the equilibrium state,there are time-dependent changes in volume,enthalpy,and entropy,as well as mechanical properties and this is known as physical aging.Physical aging is characterized by changes in stiffness,yield stress,density,viscosity,diffusivity,and fracture energy (toughness)as well as embrittlement in some polymeric materials.The physical aging rate depends on the distance the aging temperature is from the material's T Therefore,the closer the aging temperature to the T,the greater the polymer molecular mobility and the greater the relaxation rate, while the driving force defined as the entire path to the equilibrium state, decreases. Practical considerations of physical aging only become important when aging temperatures are near the T.Physical aging is a reversible process known to be easily altered with stress and temperature.For high-temperature PMCs that are used at temperatures near the material's Ts,physical aging may dramatically affect the time-dependent mechanical properties (creep and stress relaxation)and rate-dependent failure processes [56].For highly crosslinked polyimide systems,it is difficult to separate the physical aging from chemical aging effects when conducting tests near the Ts because the aging effects are coupled.Whereas in some simple polymer systems, physical aging can be reversed by heating the polymer above the Te and quenching,heating highly crosslinked polymers above the Te induces chemical aging,thereby,altering the thermodynamic equilibrium state. Earlier studies on the effects of physical aging on polymer composite behavior were conducted by Sullivan [99],McKenna [59],and Waldron and McKenna [118].The majority of the reported work on predicting the long-term performance of PMCs in high-temperature environments is limited to physical aging models and the use of linear viscoelastic and

material systems, the modeling methodology and procedures for determining material parameters may be directly applicable to predicting their behavior. On the other hand, the observed behavior of other high-temperature material systems can deviate significantly from PMR-15 and such deviations will be noted when appropriate. Current polymer and polymer matrix composite modeling approaches for chemical and physical aging, as well as the modeling process for predicting thermooxidative degradation, are discussed in the following sections. 9.1.1 Physical Aging of Polymers and PMCs At temperatures below a polymer’s glass transition temperature (Tg), the material is in a nonequilibrium state and undergoes a time-dependent rearrangement toward thermodynamic equilibrium. During this rearrangement (relaxation) toward the equilibrium state, there are time-dependent changes in volume, enthalpy, and entropy, as well as mechanical properties and this is known as physical aging. Physical aging is characterized by changes in stiffness, yield stress, density, viscosity, diffusivity, and fracture energy (toughness) as well as embrittlement in some polymeric materials. The physical aging rate depends on the distance the aging temperature is from the material’s Tg. Therefore, the closer the aging temperature to the Tg, the greater the polymer molecular mobility and the greater the relaxation rate, while the driving force defined as the entire path to the equilibrium state, decreases. Practical considerations of physical aging only become important when aging temperatures are near the Tg. Physical aging is a reversible process known to be easily altered with stress and temperature. For high-temperature PMCs that are used at temperatures near the material’s Tg, physical aging may dramatically affect the time-dependent mechanical properties (creep and stress relaxation) and rate-dependent failure processes [56]. For highly crosslinked polyimide systems, it is difficult to separate the physical aging from chemical aging effects when conducting tests near the Tg because the aging effects are coupled. Whereas in some simple polymer systems, physical aging can be reversed by heating the polymer above the Tg and quenching, heating highly crosslinked polymers above the Tg induces chemical aging, thereby, altering the thermodynamic equilibrium state. Earlier studies on the effects of physical aging on polymer composite behavior were conducted by Sullivan [99], McKenna [59], and Waldron and McKenna [118]. The majority of the reported work on predicting the long-term performance of PMCs in high-temperature environments is limited to physical aging models and the use of linear viscoelastic and 366 G.A. Schoeppner, G.P. Tandon and K.V. Pochiraju

Chapter 9:Predicting Thermooxidative Degradation 367 time-temperature superposition models [21].Inherent in the use of physical aging models is the assumption that the aging process is thermoreversible, therefore nonreversible chemical aging cannot be properly modeled using this approach.That is,the effects of irreversible processes,e.g.,chemical decomposition,hydrolytic degradation,oxidation,etc.,are neglected in these models or are assumed to be implicitly accounted for in determining the physical aging parameters.However,chemical aging can be the primary life-limiting degradation process for HTPMCs used at temperatures near their T.Neglecting the modeling of the chemical degradation for com- posites in an oxidative environment will likely result in inaccurate and nonconservative predictions of performance. 9.1.2 Chemical Aging of Polymers and PMCs Chemical aging,unlike physical aging,is typically not thermoreversible. Hydrolysis (the chemical reaction of the polymer with water)and oxi- dation(the chemical reaction of the polymer with oxygen)are the primary forms of chemical degradation in HTPMCs.The chemical changes occurring during oxidation include chemical bond breaks that result in a reduction in molecular weight,mechanical response changes,and a local loss of mass associated with outgassing of oxidation byproducts.Although the rate of oxidative chemical reactions is,in part,governed by the avail- ability of reactive polymer,the oxygen concentration,and the reaction temperature for high Ts glassy polymers,the rate of oxidation can be greater than the rate of diffusion of oxygen into the polymer.For such circum- stances,the oxidative process is diffusion rate limited.Diffusion rate-limited oxidation of neat polymer specimens typically results in the development of an oxidative layer or graded oxidative properties near the free surfaces of the specimen.Within the oxidized region of the polymer,it is typical that the tensile strength,strain to failure,flexural strength,density,and toughness decrease while the modulus increases.The effect of oxidation on changes in the Ts is dependent on the specific polymer system.Some polymers initially have a decrease and then an increase in T3,others may have only a decrease,and still others may only have an increase in T.This may be due to competing chemical and physical aging phenomenon [56]or differences in the oxidation reaction mechanisms.Since HTPMCs typi- cally operate at temperatures near their initial design T3,any changes in the local or global T can have detrimental effects on performance. Determination of the primary,secondary,and tertiary chemical degrada- tion mechanisms in high-temperature polyimide composites is an extremely challenging task [92]but can yield substantial benefits for designing new

time–temperature superposition models [21]. Inherent in the use of physical aging models is the assumption that the aging process is thermoreversible, therefore nonreversible chemical aging cannot be properly modeled using this approach. That is, the effects of irreversible processes, e.g., chemical decomposition, hydrolytic degradation, oxidation, etc., are neglected in these models or are assumed to be implicitly accounted for in determining the physical aging parameters. However, chemical aging can be the primary life-limiting degradation process for HTPMCs used at temperatures near their Tg. Neglecting the modeling of the chemical degradation for composites in an oxidative environment will likely result in inaccurate and nonconservative predictions of performance. 9.1.2 Chemical Aging of Polymers and PMCs Chemical aging, unlike physical aging, is typically not thermoreversible. Hydrolysis (the chemical reaction of the polymer with water) and oxidation (the chemical reaction of the polymer with oxygen) are the primary forms of chemical degradation in HTPMCs. The chemical changes occurring during oxidation include chemical bond breaks that result in a reduction in molecular weight, mechanical response changes, and a local loss of mass associated with outgassing of oxidation byproducts. Although the rate of oxidative chemical reactions is, in part, governed by the availability of reactive polymer, the oxygen concentration, and the reaction temperature for high Tg glassy polymers, the rate of oxidation can be greater than the rate of diffusion of oxygen into the polymer. For such circumstances, the oxidative process is diffusion rate limited. Diffusion rate-limited oxidation of neat polymer specimens typically results in the development of an oxidative layer or graded oxidative properties near the free surfaces of the specimen. Within the oxidized region of the polymer, it is typical that the tensile strength, strain to failure, flexural strength, density, and toughness decrease while the modulus increases. The effect of oxidation on changes in the Tg is dependent on the specific polymer system. Some polymers initially have a decrease and then an increase in Tg, others may have only a decrease, and still others may only have an increase in Tg. This may be due to competing chemical and physical aging phenomenon [56] or differences in the oxidation reaction mechanisms. Since HTPMCs typically operate at temperatures near their initial design Tg, any changes in the local or global Tg can have detrimental effects on performance. Determination of the primary, secondary, and tertiary chemical degradation mechanisms in high-temperature polyimide composites is an extremely challenging task [92] but can yield substantial benefits for designing new Chapter 9: Predicting Thermooxidative Degradation 367

368 G.A.Schoeppner,G.P.Tandon and K.V.Pochiraju polyimides that are less susceptible to degradation.The primary and secondary oxidation mechanisms for PMR-15 were determined by Meador et al.[63-65]in a series of tests on model compounds.It was determined that the nadic end group,in which the aliphatic carbons are consumed during oxidation,is the primary rapid mechanism for weight loss.The second,longer-term mechanism is the oxidation of the diamine bridging methylene to the carbonyl group.As part of a separate effort,Thorp [107] determined that the nadic end group is also responsible for the primary hydrolytic degradation mechanism.Similar types of studies have led to the development of polyimides with a more thermally stable phenylethynyl end group as a replacement for the degradation-susceptible nadic end group. These new material developments include the family of phenylethynyl- terminated polyimides such as NASA's PETI resins [47]and the Air Force-developed AFR-PE-N resins that are more thermally stable than PMR-15[123]. 9.1.3 Mechanical Stress-Induced Aging Elevated temperatures can have a dominating effect on the strength and stiffness of HTPMCs [76],and the strength and stiffness at the operating temperature are primary considerations for selecting suitable materials for a given application.Primary consideration is also given to the long-term durability of the material in the elevated temperature environment.The effects of long-term mechanical loading on PMCs at elevated temperatures are manifested in the creep-relaxation response (viscoelastic-plastic beha- vior)and the load-induced damage developed under thermomechanical cyclic loading.Often a linear elastic representation of the fiber-dominated composite properties is sufficient,while various time-dependent linear and nonlinear viscoelastic-plastic models [85,86]may be needed to represent the resin-or matrix-dominated properties for high-temperature appli- cations.Additionally,there is a strong coupling between chemical aging and the damage development due to the changes in stiffness,strength,and toughness that occur during long-term aging. For the purpose of the discussion here,mechanical stress-induced aging is associated with stress-assisted diffusion and aging as well as thermo- mechanical-induced damage or cracking.The development of damage in HTPMCs exacerbates the chemical and physical aging by introduction of stress concentrations that accelerate physical aging effects and exacerbates the chemical aging by introducing pathways for oxidants and other agents to advance deeper into the material.Damage typically takes the form of matrix cracks and fiber-matrix interface debonds,with the micromechanical

polyimides that are less susceptible to degradation. The primary and secondary oxidation mechanisms for PMR-15 were determined by Meador et al. [63–65] in a series of tests on model compounds. It was determined that the nadic end group, in which the aliphatic carbons are consumed during oxidation, is the primary rapid mechanism for weight loss. The second, longer-term mechanism is the oxidation of the diamine bridging methylene to the carbonyl group. As part of a separate effort, Thorp [107] determined that the nadic end group is also responsible for the primary hydrolytic degradation mechanism. Similar types of studies have led to the development of polyimides with a more thermally stable phenylethynyl end group as a replacement for the degradation-susceptible nadic end group. These new material developments include the family of phenylethynylterminated polyimides such as NASA’s PETI resins [47] and the Air Force-developed AFR-PE-N resins that are more thermally stable than PMR-15 [123]. 9.1.3 Mechanical Stress-Induced Aging Elevated temperatures can have a dominating effect on the strength and stiffness of HTPMCs [76], and the strength and stiffness at the operating temperature are primary considerations for selecting suitable materials for a given application. Primary consideration is also given to the long-term durability of the material in the elevated temperature environment. The effects of long-term mechanical loading on PMCs at elevated temperatures are manifested in the creep–relaxation response (viscoelastic–plastic behavior) and the load-induced damage developed under thermomechanical cyclic loading. Often a linear elastic representation of the fiber-dominated composite properties is sufficient, while various time-dependent linear and nonlinear viscoelastic–plastic models [85, 86] may be needed to represent the resin- or matrix-dominated properties for high-temperature applications. Additionally, there is a strong coupling between chemical aging and the damage development due to the changes in stiffness, strength, and toughness that occur during long-term aging. For the purpose of the discussion here, mechanical stress-induced aging is associated with stress-assisted diffusion and aging as well as thermomechanical-induced damage or cracking. The development of damage in HTPMCs exacerbates the chemical and physical aging by introduction of stress concentrations that accelerate physical aging effects and exacerbates the chemical aging by introducing pathways for oxidants and other agents to advance deeper into the material. Damage typically takes the form of matrix cracks and fiber–matrix interface debonds, with the micromechanical 368 G.A. Schoeppner, G.P. Tandon and K.V. Pochiraju

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