2
Composite Properties and Behavior

Because composites behave differently than monolithic materials, understanding their properties and behavior in extremes of temperature, stress, and other environmental factors is a great challenge for the engineers who specify their use.

UNDERSTANDING DEGRADATION

Environmental degradation in polymer matrix composites manifests itself in many ways. A multiplicity of mechanisms can degrade performance; degradation can range from a minor loss of stiffness to a worst case of catastrophic and unexpected failure. Changes in a material during service are commonly deemed indicators of degradation. In laminated PMCs, these phenomena can include microcracking, local crazing of polymers in the vicinity of cracks, and localized fiber failures.

It is useful in this discussion to differentiate among damage mechanisms, such as oxidation, time of service, moisture absorption; failure modes, such as fiber delamination or matrix cracking; and stress factors, such as load, temperature, and chemical species available at the surface. A stress factor may or may not precipitate the tensile, shear, or compressive failures of laminates, and the impact of a stress factor depends on loading and environmental conditions. Thus, not all of these obvious damage mechanisms may represent degradation in the sense that they limit performance.

For example, microcracking in laminates is nearly unavoidable, because it is the result of processing at the high temperatures required for polymers and differences in thermal conductivities of the carbon fibers and the polymer matrices. Yet, microcracks at a low density are not necessarily performance-limiting, and their effects are dependent on the application and the evolution of damage. The means for simulating and testing the changes in properties wrought by such mechanisms has been restricted to mechanical tests, which can be relatively insensitive to some types of degradation. For example, environmental effects can manifest in ways other than mechanical performance and may not always be negative. Examples may include surface evolution due to oxidation or moisture, shifts in the glass transition temperature due to elevated temperature or moisture, or cross-linking or chain scission in the polymer due to elevated temperature. In plain terms, the microstructure may evolve in a number of ways before evidencing measurable degradation.

Matrix cracking resulting from a combination of temperature, stress, and/or humidity levels and histories is a good example because it can lead to a reduction in individual ply properties as well as in the laminate properties. However, as is well known in industry, a composite part that has been in service for considerable time invariably contains matrix cracks, but these cracks may contribute little to the measured degradation of the part. Thus, the real challenge is to define and quantify the evolution of the microstructure by measuring the number, distribution, size, origin (interface or matrix), and severity of the cracking that is critical to the performance of the composite structure.



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Going to Extremes: Meeting the Emerging Demand for Durable Polymer Matrix Composites 2 Composite Properties and Behavior Because composites behave differently than monolithic materials, understanding their properties and behavior in extremes of temperature, stress, and other environmental factors is a great challenge for the engineers who specify their use. UNDERSTANDING DEGRADATION Environmental degradation in polymer matrix composites manifests itself in many ways. A multiplicity of mechanisms can degrade performance; degradation can range from a minor loss of stiffness to a worst case of catastrophic and unexpected failure. Changes in a material during service are commonly deemed indicators of degradation. In laminated PMCs, these phenomena can include microcracking, local crazing of polymers in the vicinity of cracks, and localized fiber failures. It is useful in this discussion to differentiate among damage mechanisms, such as oxidation, time of service, moisture absorption; failure modes, such as fiber delamination or matrix cracking; and stress factors, such as load, temperature, and chemical species available at the surface. A stress factor may or may not precipitate the tensile, shear, or compressive failures of laminates, and the impact of a stress factor depends on loading and environmental conditions. Thus, not all of these obvious damage mechanisms may represent degradation in the sense that they limit performance. For example, microcracking in laminates is nearly unavoidable, because it is the result of processing at the high temperatures required for polymers and differences in thermal conductivities of the carbon fibers and the polymer matrices. Yet, microcracks at a low density are not necessarily performance-limiting, and their effects are dependent on the application and the evolution of damage. The means for simulating and testing the changes in properties wrought by such mechanisms has been restricted to mechanical tests, which can be relatively insensitive to some types of degradation. For example, environmental effects can manifest in ways other than mechanical performance and may not always be negative. Examples may include surface evolution due to oxidation or moisture, shifts in the glass transition temperature due to elevated temperature or moisture, or cross-linking or chain scission in the polymer due to elevated temperature. In plain terms, the microstructure may evolve in a number of ways before evidencing measurable degradation. Matrix cracking resulting from a combination of temperature, stress, and/or humidity levels and histories is a good example because it can lead to a reduction in individual ply properties as well as in the laminate properties. However, as is well known in industry, a composite part that has been in service for considerable time invariably contains matrix cracks, but these cracks may contribute little to the measured degradation of the part. Thus, the real challenge is to define and quantify the evolution of the microstructure by measuring the number, distribution, size, origin (interface or matrix), and severity of the cracking that is critical to the performance of the composite structure.

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Going to Extremes: Meeting the Emerging Demand for Durable Polymer Matrix Composites Matrix cracking is also a major challenge for computational mechanics and modeling. Identification and quantification of the environmental factors leading to matrix (and/or interfacial) cracking and the subsequent development and implementation of chemical modifications to reduce this cracking may or may not assist the computational effort, but clearly the computational effort would provide benchmarks for the properties required of new materials. It may also help to answer the question, How much cracking is acceptable? Thus it is important to distinguish between changes in material structures that limit performance and changes that do not. At relatively low humidity and static loads, microcracks may not be a significant design factor to prevent failure. At higher humidity and cyclic or dynamic loads, however, the effect of microcracks is greatly magnified, and microcracking emerges as a more significant failure mechanism. As the importance of individual failure mechanisms in failure changes, so does their relative importance. The reasonable subset of mechanisms to consider simultaneously also changes for extreme conditions (see Box 2-1). While it may be interesting to ascertain a number of changes in materials from the nanoscale upward, it is more important to ascertain the mechanisms of failure. The goal is to design PMCs that perform satisfactorily at extreme conditions. However, there are knowledge gaps even for nonextreme conditions at this relatively early stage in the use of composite materials. These gaps widen for extreme conditions. The difficulties in modeling performance and designing to take into account degraded properties are largely due to the issues noted previously—namely, extreme levels of anisotropy, heterogeneity of properties, high homologous temperature behavior of the polymer matrix, and stress transfer factors associated with fiber-matrix interfacial behavior. Additionally, the hierarchical structural levels prevalent in BOX 2-1 Coupling of Mechanisms The slow crack growth phenomenon that plagued the gas pipeline industry about 15 years ago exemplifies the need to understand the interactions between mechanisms. Relatively standard linear elastic fracture mechanics and nonlinear and viscoelastic adaptations that are widely used in the plastics industry were used to devise various tests for fracture toughness for polyethylene polymers to be used in the fabrication of relatively large diameter (e.g., 36 inches) natural gas distribution pipelines. In service, these pipes exhibited slow crack growth, that is, the growth of very long (many inches) cracks over periods of several years. Based on laboratory measurements, the material appeared to have sufficient fracture toughness to preclude the growth of such cracks, even when the pipe was improperly installed in the ground, e.g., by running it over a large rock with a protrusion rather than over a bed of finely crushed gravel. Engineers wondered why the cracks were forming and continuing to propagate for years. Were the fracture toughness tests improperly conducted? Were the theoretical foundations of fracture mechanics unable to predict or account for slow crack growth phenomena in polymers? Was there an alternative fracture toughness test that would explain the slow crack growth data? Was the polyethylene material contaminated? Was the pipe improperly fabricated—that is, did it contain excessive residual stresses due to polymer orientation or “skin” effects? Or did the designers neglect the environmental cracking potential of trace sulfur compounds in natural gas, as was actually the case? In the presence of a small stress concentration, such as a small starter crack, and an applied stress, the trace environmental agent was sufficient to transform a relatively benign crack in an ostensibly tough material into a potentially lethal crack growing at impressively low stress levels and very slow rates! In the absence of a protocol for material degradation at a crack tip resulting from an active chemical species in the presence of an applied far-field stress state, the fracture-mechanics-based testing procedures were useless in predicting performance and gave artificially and erroneously reassuring toughness parameters for the material. It is noteworthy that solvent stress cracking and crazing in polymers is still a subject of active investigation. Polymer matrix composites cannot realistically be expected to be more amenable than the neat polymers themselves to modeling that predicts performance and degradation. Higher performance materials require higher and more insightful levels of understanding because higher performance generally implies a higher potential for loss of that performance.

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Going to Extremes: Meeting the Emerging Demand for Durable Polymer Matrix Composites many high-performance PMCs make the simultaneous allowance for degradation at each structural level and the assignment of relative importance to each possible failure mode a daunting task. This is a challenge to multiscale modeling from a computational standpoint and is compounded when mechanistic or physical factors are considered. Investigation of the traditional methods of monitoring structural health, both in the laboratory and in applications, may also lead to new understanding. Updated experimental methods may also be needed to understand the underlying methods of degradation. In any new framework, well-studied failure mechanisms—such as microcracking, fracture, delamination, statistical fiber failure, creep, and fatigue—must be restudied to determine their relative importance at high temperature and high humidity, for both static and cyclic loads. In addition, data supporting an understanding of the combined effect of key failure mechanisms, or at least of an important subset of such mechanisms, are critically needed to validate these investigations. CURRENT MODELING METHODOLOGY Work in composite damage is voluminous and is anchored in several different academic disciplines, largely based on mechanism of interest (see Appendix D). More than 6,000 papers concerned with composite damage have been published in scientific and engineering journals since 1955; the vast majority focus on single mechanisms, conditions, or applications (see Table 2-1). And, although literally hundreds of models of composite damage have been developed over the last six decades, only a few have been fully implemented in commercial FEA codes. To date, none apparently incorporates a materials processing history (Appendix E). The propensity to focus on specific failure mechanisms can be attributed to three factors: (1) the scholarly imperative to focus on single mechanisms to produce broadly applicable, archival results that can be more readily validated even in a small set of conditions; (2) the paucity and inaccessibility of data on materials that have failed in real applications (such data might be able to verify one or more simultaneous failure mechanisms); and (3) the confounding effects of multiple failure mechanisms within a system, which make results even more application-dependent and specific, and also likelier to be subject to proprietary protection by the institution or company that generated them. Indeed, truly sufficient scrutiny of failure mechanisms carries three independent burdens: (1) the cost of generating a wide range of diagnostics on materials before, during, and after processing and through the service life and of spanning optical, mechanical, and chemical assays; (2) the potential cost of legal liability for findings of failure mechanisms not uncovered or even postulated prior to construction of the failed components or during their initial testing and use; and (3) the protection of sensitive or proprietary information, either for national security or for competitive advantage. When the damage product is obvious, as it is in matrix cracking, it is possible to define protocols and perform calculations to ascertain the degree to which various cracks can form and grow while still maintaining structural integrity. When the damage product is the degradation and weakening of material in the immediate vicinity of a crack tip and in the presence of an applied load, the protocols have yet to be established and the calculations are at best crude. The tendency for cracks to form is further affected by changes to such matrix properties as the glass transition temperature or the surface energy that may be attributed to environmental conditions. Much remains to be done before high-performance PMCs can be certified by appropriate models and computations for long-term applications under extreme environmental conditions. An understanding of mechanisms, as well as of chemical kinetics and other phenomena, is a TABLE 2-1 Papers Published in Selected Composite Areas, 1955-2004 Number of Papers Search Keywords 6,940 composite* and damage 2,035 composite* and (temperature or therm*) and damage 466 composite* and micromechanic* and damage NOTE: Asterisks indicate wild card characters used in Boolean searches. SOURCE: Science Citation Index, at <http://www.isiknowledge.com>. Accessed February 2005.

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Going to Extremes: Meeting the Emerging Demand for Durable Polymer Matrix Composites critical missing link. These mechanisms allow making a connection between material evolution and environmental factors. Because extreme environments introduce additional mechanisms, it is key to understand which features or necessary elements of fundamental degradation (or evolution mechanisms) we need to capture in modeling, as well as how to model them. One of the most important considerations is that PMCs are a structure rather than a monolithic material. This means that the microstructural evolution must be understood, from design, to processing, to installation, and throughout (but not limited to) the PMC component’s service life. STATE OF MODELING The models typically used to address material degradation and failure can be broadly classified. While it is not possible here to thoroughly review these models, some of the most common types of models for the alteration, response, and failure of materials include the following: Phenomenological models may be the largest group of models. They correlate operating conditions with tabulated life data. Such data may be cycles to failure, time to failure, or stiffness change to failure. Because the models fit data to empirical observations and have no rigorous physical basis, their results cannot be extrapolated to other materials or other conditions. Phenomenological failure criteria are sometimes used to provide metrics for such correlations—for instance, energy or yield1 functions with characteristic material parameters that may depend on time-dependent (or cycle-dependent) characterizations.2-5 Fatigue modeling, for example, generally relies on this approach.6 Strain-based estimation methods7 and stiffness change methods8,9 are also common. Time-temperature and aging time superposition methods are also used.10,11 A few models are supported by analysis that attempts to account specifically for energy dissipation.12-15 Models employing tensorial strength parameters16 may be thought of 1   R.M. Guedes. 2004. An energy criterion to predict delayed failure of multi-directional polymer matrix composites based on a non-linear viscoelastic model. Composites Part A—Applied Science and Manufacturing 35(5):559-571. 2   H.F. Brinson. 1999. Matrix dominated time dependent failure predictions in polymer matrix composites. Composite Structures 47(1-4):445-456. 3   Y.T. Yeow. 1978. The Time-Temperature Behavior of Graphite/Epoxy Laminates. Ph.D. thesis, Virginia Polytechnical Institute. 4   Y.T. Yeow, D.H. Morris, and H.F. Brinson. 1979. The time-temperature behavior of a unidirectional graphite/epoxy laminate. Composite Materials: Testing and Design (5th Conference), STP 674, Philadelphia, Pa., pp. 263-281. 5   M. Reiner and K. Weissenberg. 1939. A thermodynamic theory of the strength of materials. Rheology Leaflet 10:12-20. 6   R. Talreja. 2000. Fatigue of polymer matrix composites. Comprehensive Composite Materials, C. Zweben and A. Kelly, eds. New York, N.Y.: Elsevier. 7   J. Petermann and K. Schulte. 2002. Strain based service time estimation for angle-ply laminates. Composites Science and Technology 62(7-8):1043-1050. 8   A.W. Wharmby and F. Ellyin. 2002. Damage growth in constrained angle-ply laminates under cyclic loading. Composites Science and Technology 62(9):1239-1247. 9   R. Talreja. 1985. Fatigue of Composite Materials. Technical University of Denmark, Lyngby. 10   Y. Miyano, M. Nakada, and N. Sekine. 2004. Accelerated testing for long-term durability of GFRP laminates for marine use. Composites Part B—Engineering 35(6-8):497-502. 11   R.D. Bradshaw and L.C. Brinson. 1997. Physical aging in composites: An analysis and method for time-aging time superposition. Polymer Engineering and Science 37:31-44. 12   C. Hiel. 1983. The Non-linear Viscoelastic Response of Resin Matrix Composites. Ph.D. thesis, University of Brussels. 13   C. Hiel, A.H. Cardon, and H.F. Brinson. 1983. The non-linear viscoelastic response of resin matrix composites. Composite Structures, I.H. Marshall, ed. London and New York: Applied Science, pp. 271-281. 14   O.S. Bruller. 1973. The energy balance of a viscoelastic material. International Journal of Polymer Materials 2:137-148. 15   O.S. Bruller. 1981. Energy-related failure criteria of thermoplastics. Polymer Engineering and Science 21(3):145-150. 16   S.W. Tsai and E.M. Wu. 1971. General theory of strength for anisotropic materials. Journal of Composite Materials 5:58-80.

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Going to Extremes: Meeting the Emerging Demand for Durable Polymer Matrix Composites as phenomenological models; though their generic tensorial forms are based on strength-of-materials considerations, the fitted variables are generally load-specific. Statistical models interpret data sets to establish probabilities of failure at various applied conditions, significance of data samples and predictions, confidence intervals, design allowables, or reliability estimates. Because this approach requires large data sets for the exact event, material, and conditions, it is not predictive. It is also very expensive and slow and can only generate relevant results after the fact. Essentially every prime contractor designs on the basis of allowables that are set from statistical analysis of data. The analysis methods are well established, typically based on Weibull statistics and incorporating a mechanistic model for damage coalescence,17 and effective in the presence of a robust and relevant data set. Mechanical models attempt to represent durability as a mechanical process—that is, in terms of balance of forces, mass, momentum, energy; transport; and constitutive equations. Macroexamples are structural analysis methods such as fracture mechanics, strain energy release methods, and some energy dissipation schemes.18-20 These include composite-specific models, such as those for statistical fiber breakage,21 matrix microcracking,22 or interfacial failure.23 Indeed, some of these phenomena are often relatable to more complex loading conditions, including fatigue.24 Microexamples include dislocation or slip models (and diffusion models in some cases) that represent discrete defects at the microlevel.25,26 Thermodynamic models are representations of life in terms of thermodynamic state variables (sometimes called internal state variables and often called damage parameters) that are associated with homogenized, continuum representations of physical degradation. The process is usually called damage mechanics. These methods have the advantage of addressing material state changes as dissipative thermodynamic processes and the disadvantage of being based on homogenized representations of the physics and mechanics that do not retain specific properties of mechanisms of damage or failure. Strength-based versions of the method bridge the gap between mechanics and materials, and some versions have been modified to include micromechanics of discrete behavior of heterogeneous phases in composites.27-30 Classical strength of materials models employ traditional, yield-based failure criteria, e.g., Tresca or von Mises limits,31 on composite laminates, using different yield criteria for matrix- or 17   A.M. Sastry and S.L. Phoenix. 1994. Shielding and magnification of loads in elastic, unidirectional composites. SAMPE Journal 30(4):61-67. 18   J.L. Rebiere and D. Gamby. 2004. A criterion for modelling initiation and propagation of matrix cracking and delamination in cross-ply laminates. Composites Science and Technology 64(13-14):2239-2250. 19   O. Attia, A.J. Kinloch, and F.L. Matthews. 2001. Modelling the fatigue life of polymer-matrix fibre-composite components. Composites Science and Technology 61(15):2273-2283. 20   C. Bathias. 1991. Fracture and fatigue of high-performance composite-materials-mechanisms and prediction. Engineering Fracture Mechanics 40(4-5):757-783. 21   C. Zweben. 1994. Is there a size effect in composites? Composites 25(6):451-454. 22   J.A. Nairn and S. Hu. 1994. Damage Mechanics of Composite Materials, R. Talreja, ed. Amsterdam: Elsevier, pp. 187-243. 23   L.T. Drzal, M.J. Rich, M.F. Koenig, and P.F. Lloyd. 1983. Adhesion of graphite fibers to epoxy matrices. 2. The effect of fiber finish. Journal of Adhesion 16(2):133-152. 24   A.L. Highsmith and K.L. Reifsnider. 1982. Stiffness reduction mechanisms in composite material. Damage in Composite Materials, ASTM STP 775:103-117. 25   K.L. Reifsnider. 1994. Modeling of the interphase in polymer-matrix composite-material systems. Composites 25(7):461-469. 26   S. Suresh. 1991. Fatigue of Materials. Cambridge, U.K.: Cambridge University Press. 27   S.R. Patel and S.W. Case. 2000. Durability of a graphite/epoxy woven composite under combined hygrothermal conditions. International Journal of Fatigue 22(9):809-820. 28   K.L. Reifsnider and S.W. Case. 2002. Damage Tolerance and Durability of Material Systems. New York, N.Y.: Wiley Interscience. 29   N. Himmel. 2002. Fatigue life prediction of laminated polymer matrix composites. International Journal of Fatigue 24(2-4):349-360. 30   R. Talreja. 1990. Internal variable damage mechanics of composite materials. Yielding, Damage and Failure of Anisotropic Solids, J. P. Boehler, ed. London: Mechanical Engineering Publications, pp. 509-533. 31   L.J. Hart-Smith. 1998. Predictions of the original and truncated maximum-strain failure models for certain fibrous composite laminates. Composites Science and Technology 58(7):1151-1178.

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Going to Extremes: Meeting the Emerging Demand for Durable Polymer Matrix Composites fiber-dominated behavioral directions. These approaches are a subset of phenomenological approaches and are readily able to incorporate results of micromechanical models. Chemical models represent degradation processes as rate equations. The most common is the Arrhenius equation, which is cast in various forms to describe time-dependent failure, such as in creep rupture. The well-known principle of time-temperature superposition is one manifestation of this approach and is valid when all relaxation processes exhibit the same relative change with temperature.32 Advantages of the approach are simplicity and explicit temperature dependence. Disadvantages include the fact that the approach is generally phenomenological and empirical and does not involve physical observables at intermediate times before failure. Chemical degradation, such as oxidation, has been explicitly incorporated into some such treatments.33 Atomistic models describe polymers at the fully detailed level of atoms and molecules. While this is currently daunting in terms of the time needed for computation, significant progress is being made with coarse-graining approaches and combining atomistic approaches into multiscale models.34 Bridging scale methods that link, for example, molecular dynamic simulations with finite element simulations could be one way of incorporating mechanistic-level information. The rapid advances in several areas of atomistic modeling of polymers and composites will likely play a significant role in the discovery of new materials and their application.35 Environmental models are an important additional layer of modeling that takes a material's response to the environment into account. Such a response might be the absorption and desorption of moisture or the transport of dissolved substances (such as oxygen or other chemical species) from the surface to the interior of the composite. This class of models is itself divisible into thermodynamic, chemical, and mechanical models and even "industrial" approximations (or rules of thumb). The simplest and best developed of these are the moisture absorption models. It is important to note that a material's response to the environment cannot be modeled until the interaction with the environment is understood and incorporated adequately into the model. In spite of the success of some of these models, several barriers remain to reducing reliance on knockdown factors (see Box 2-2). Even with the success of models such as strain-invariant failure theory (SIFT),36 which has shown ability to predict failure under simple loadings accurately,37 knockdown factors are still used in conjunction with this theory in predicting fatigue lifetime (absent the data needed to provide validation). Also, none of these approaches are fully mechanistic: Each is built around specific representations of degradation and failure mechanisms that are discretely described in time and space. 32   It is important to note that any changes in the stress transfer mechanism with temperature render this relationship invalid. Thus, semicrystalline polymers almost never exhibit such validity. Conversely, amorphous rubbery polymers often do exhibit valid time-temperature superposition. Amorphous glassy polymers often appear to exhibit such validity over relatively narrow ranges of frequency or timescale, typically three to four decades. Observations over longer timescales often show divergence from these predictions. Any extrapolations of failure lifetime data made using time-temperature superposition should be viewed with extreme caution, especially for semicrystalline or amorphous glassy polymers. 33   K.T. Gillen and M. Celina. 2000. The wear-out approach for predicting the remaining lifetime of materials. Polymer Degradation and Stability 71(1):15-30. 34   W.K. Liu, E.G. Karpov, S. Zhang, and H.S. Park. 2004. An introduction to computational nanomechanics and materials. Computational Methods in Applied Mechanical Engineering 193:1529-1578. 35   S.C. Glotzer and W. Paul. 2002. Molecular and mesoscale simulation of polymers. Annual Review of Materials Research 32:401-436. 36   T.E. Tay, S.H.N. Tan, V.B.C. Tan, and J.H. Gosse. 2005. Damage progression by the element-failure method (EFM) and strain invariant failure theory (SIFT). Composites Science and Technology 65:935-944. 37   In a hat-stiffened panel under tension and compression, for example, SIFT recently predicted failure within 10 percent of actual, representing an improvement over the 50 percent margin provided by classical solutions of a decade ago. From R.J. Meilunas. 2004. Accelerated insertion of materials–Composites program: Methodology and toolset. Presentation at the Defense Manufacturing Conference, Las Vegas, Nev.

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Going to Extremes: Meeting the Emerging Demand for Durable Polymer Matrix Composites BOX 2-2 Knockdown Factors Knockdown factors are commonly used to estimate properties of PMCs at use conditions. Typically, a first step is testing of as-manufactured (pristine) PMCs. Next, similar PMCs are exposed to, say, elevated temperatures, thermal cycling, and/or damage (e.g., cutting a hole) and then are retested. The ratio of conditioned (or damaged) to pristine property establishes a knockdown factor, also called the knockdown. The knockdown then would be applied across the board to the property. For example, the knockdown at room temperature could be applied across the entire use range. Different properties are typically tested for different conditions. For example, materials would be tested in a condition that attacks the matrix in compression because this is often a critical property and is highly matrix-dependent. However, there is no set method for establishing knockdowns. The application may suggest that testing for some extreme conditions is warranted. For example, if a part will see temperatures of 475°F for 500 hours of its life, that may warrant conditioning the samples for 500 hours at 475°F before testing. Knockdowns are also determined for subelement or component testing. Many projects—especially military projects—have specific damage-tolerance specifications. For example, a material might have to withstand a tool weighing 10 pounds dropped from 3 feet, which is simulated by a 1-inch diameter spherical impactor. In this case, a subcomponent or component would be damaged accordingly, then tested to the limit load or other load required by the specification. Note that a limit load is the largest load a part would see in normal use. An ultimate load is typically a defined value, normally 1.5 times the limit load. In addition, none of these approaches are robust enough to provide specific guidance to manufacturing that will result in PMCs with improved durability, nor can they provide guidance for the knowledge-based design that is the basis for the engineering used by most original equipment manufacturers today. The approaches are also not truly multiphysical38 in that all of the related balance equations and constitutive equations are solved as coupled field equations for the specific boundary conditions and applied conditions required for the materials. Reducing dependence on knockdown factors in lifetime estimation will not require anything so grand as development of completely interlinking and multiscale models for a large variety of materials. Indeed, the recent exercise that compared leading failure theories in laminated PMCs39 revealed that the head-to-head comparison of models thought of as classical show wide variation in both their predicted failures and in their correlation with experimental results, when the results are plotted as points on traditional failure envelopes with axes of principal stresses or strains. Furthermore, the closing recommendations of the group that conducted the worldwide failure exercise40 specifically point out the serious challenges remaining in extending any of these models to extreme conditions, in applying these approaches to multiaxial loads and different environments, and in coupling models. The physics of specific failure mechanisms or interactions with the environment remain unknown. Some current testing practices have proven inadequate: For example, a thick, flat test sample may show only limited material degradation in a given environment because the interior material (in the absence of micro- or other cracking) is not exposed to the environment. A thin, curved, microcracked component will not behave like the test sample (see Box 2-3). Conversely, this effect can be beneficial—if an oxide skin forms on the surface of exposed parts, the structural response can be much better than the response of the bulk material because most of the structure does not see the environment. 38   Multiphysics implies interactions among a range of physical phenomena—for example, viscous, turbulent, thermal, chemical, mechanical, electromagnetic, or plasma processes. 39   World-wide failure exercise on failure prediction in composites. 2002. Composites Science and Technology 62:1479. 40   P.D. Soden, A.S. Kaddour, and M.J. Hinton. 2004. Recommendations for designers and researchers resulting from the world-wide failure exercise. Composites Science and Technology 64(3-4):589-604.

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Going to Extremes: Meeting the Emerging Demand for Durable Polymer Matrix Composites BOX 2-3 Cryogenic Conformal Fuel Tanks Cryogenic fuel tanks have traditionally been egg-shaped bottles fabricated of welded titanium. However, with the cost of placing material in orbit roughly $10,000 per pound, a strong incentive has emerged to reduce vehicle weight and increase payload space on reusable space launch vehicles. One way to increase space is to reduce the envelope allocated to the fuel tanks by having them conform to the shape of the aeroshell; they are then known as conformal fuel tanks (Figure 2-3-1). In metallic systems, it is difficult to fabricate a structure with a sharp radius and compound curvature. Polymer matrix composites allow doing this, and their use in conformal composite fuel tanks offers lower weight and lower cost fabrication. The X-33 program entailed a one-fourth scale unmanned prototype of a reusable launch vehicle. A conformal, lightweight, full-scale, honeycomb core sandwich composite tank with carbon-fiber-reinforced epoxy face sheets and a Nomex nonperforated core was fabricated, filled with liquid hydrogen, and tested at NASA's Marshall Space Flight Center under external load. The tank, which previously had been tested unloaded at temperature, passed all load conditions without leaking but failed in one quadrant (lobe) during the liquid hydrogen dump when the tank warmed to −73°C. The core debonded from the inner face sheet with its outer face sheet intact. Post-test analysis showed the tank's inner face sheet exhibited microcracks, which allowed hydrogen gas to leak from the tank into the core cells during and after the fill cycle. The gas became trapped in each core cell and liquified. Cryopumping caused even more gas to penetrate and liquefy. As the liquid hydrogen was dumped out of the tank, the temperature and pressure in the core cells slowly rose as the liquid hydrogen in the cells gasified. When the temperature reached -73°C, cell pressure was sufficient to overcome the adhesive bond and delaminate the inner face sheet. The microcracking resulted from the differences in coefficient of thermal expansion between the carbon fiber and the epoxy matrix. During fabrication, the epoxy matrix is cross-linked and solidified at 350°F. When cooled, the matrix cannot contract because of the presence of the carbon fibers. Consequently, stresses are built up in the matrix that cannot be relieved; thus, the matrix either cracks, exacerbated at cryogenic temperatures, or the residual strength is lowered sufficiently so that microcracking occurs under relatively mild external stress conditions. It is likely the failure could have been prevented if a predictive model was available to forewarn of the potential presence of microcracking and reveal the critical flaw geometry. FIGURE 2-3-1 Cryogenic conformal fuel tank.

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Going to Extremes: Meeting the Emerging Demand for Durable Polymer Matrix Composites The framework for all theories currently utilized to predict failure conditions (e.g., loads, lifetimes) is phenomenological, with the attendant limitations. Thus, strain invariant failure theory is nothing more than an appropriate and proper framework in which to describe strains in three dimensions within an inhomogeneous and anisotropic material. Within this framework, it may be possible to analyze failure data obtained with a particular composite stacking sequence subjected to a particular set of stress components and then transfer that analysis in a solid-mechanics-based way to another composite stacking sequence with a different set of stresses. Thus, the SIFT method is useful for exploiting the maximum information from the failure data for any particular composite system, provided that the constituents are unchanged, the processing is unchanged, and environmental factors do not induce a new failure mechanism. SIFT is therefore not a failure theory but a failure analysis protocol. Modularized models in validated combinations of models for specific materials systems, particularly in extreme environments, are clearly needed. There are presently two overarching barriers to developing such a suite of tools. First, there are not enough materials history and databases to independently validate such models for real materials systems. Secondly, the method of model implementation in various commercial finite element codes, analytical solutions, and proprietary codes used by industry precludes easy transition from one model or scale to another. There are a number of specific barriers and challenges to the refinement of these theories so as to take into account the environment: Material properties are irretrievably linked to process history, and process history is expensive to track. The importance of process history is certainly not a new concept in materials design and use, given that we have been engineering the micro- and nanostructure of metals since the Bronze Age. However, the complexity and cost for multiphase materials are much greater, since the process histories of the components must be learned, along with the process history of the composite. The extrapolation of test conditions is problematic. Because conditions alter the mechanisms of failure, it is not always possible to extrapolate composite response based on a single model. Failure criteria are largely mechanical. Structural finite element analyses are generally employed by the end users of advanced materials to predict material response at some point in the lifetime. Mechanisms that are not linked repeatably and reliably to significant alterations in stress distributions are not readily tracked with these tools. So-called knockdown factors can mask the real mechanisms. Used to reduce the rated loads or other service conditions of a material based on usage, knockdown factors can be inaccurate or even misleading; more importantly, they do not result in new knowledge useful in design of improved materials. Models not readily implemented within a structural analysis framework will be shelved. Multivariate models that give no independent verification for each parameter are unlikely to be used widely, particularly if they are not readily implemented in a structural finite element code. Finite element analysis (FEA) is used to track not only stress distribution and evolution but also thermal and environmental history; as such, it is the gateway to analysis by end users. Simply put, if a model cannot be seamlessly incorporated into this framework, it is difficult to use. Models often require the sensing of alterations, which can be a tremendous challenge. Numerous environmental situations and applications exist for which the identification of damage (and its subsequent modeling) is not nearly as obvious as it is with matrix cracking, making the identification and evaluation of the relevant computational mechanics issues difficult if not impossible. In such cases, the chemical, materials, and mechanics perspectives remain inextricably linked to one another, and an interdisciplinary effort is essential for problem recognition and remediation. Degradation mechanisms need to be understood and modeled at the mechanistic level; phenomenological models cannot extend beyond the database and cannot be used for knowledge-based (e-engineering) design and manufacturing. See Box 2-3 for a pertinent example. Degradation, for the purposes of this report, can be defined as any process that changes the local stress/strain state or the local state of a material component. Mechanistic degradation must be based on physical measurables—that is, there must be many variables such as temperature, strain, microstructure,

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Going to Extremes: Meeting the Emerging Demand for Durable Polymer Matrix Composites or other state variables that change in a measurable way as degradation alters properties such as stiffness and strength. This change in properties, in turn, determines the performance of the material element, and when that performance falls below acceptable levels, it delimits life. In certain copolymers, for example, the microstructure can change dramatically (the matrix and distributed phases can be inverted, for example) as a function of hydration and temperature, greatly altering stiffness, fracture strain and stress, creep rates, and failure times. The precise (and robust) correlation of that microstructure with the resulting full complement of properties and performance is a continuing challenge.