ICME Research Proposal to Evaluate Multi-Scale Property Relations for Moisture Absorption of Carbon Fiber Reinforced Plastic Bicycle Wheel
Understanding the formulation, environmental effects and structural properties of the resin system is critical in understanding and building an effective multiscale model of a composite material. In essence, two distinct models must be created and then merged to capture the separate materials that comprise a fiber reinforced plastic composite (FRPC). This proposal summarizes the goals for the Integrated Computations Materials Engineering (ICME) method and provides elementary background information on the organic resin epoxy polymer system commonly utilized in FRPC. This proposal will present a multi-scale internal state variable (ISV) continuum material model. This model will provide a framework that could be used to optimize the resin system and thereby optimize the end-goal composite material. This is exceedingly relevant with the growth of the composite industry as well as the inherent challenges in damage detection due to loading, temperature, and environmental degradation of the resin system.
The ICME method is most easily applied to materials with uniform and simple compositions. With the advent and excitement of advanced materials, there are many opportunities for work to expand little understood relationships and perhaps spring load the concepts of the ICME methods into other branches of materials science . Due to inherent complexity in design, variation in manufacture and difficulty in modeling, little is known comparatively, about the basic mechanical properties of composite materials beyond empirical testing. The field of composites is projected to grow at exponential levels as industry looks for ways of making existing products lighter and stronger. The Aerospace industry is leading the way in much of the research in composites but following closely behind is the automotive and sporting goods industries due to the superior specific strength and stiffness of this class of materials. Despite these advantages, the polymer matrix of the composite material has inherent sensitivities to temperature as well as moisture absorption, which can ultimately lead to reductions in mechanical properties. In a composite material, the bulk of the mechanical properties are derived from the fiber, however, the degradation of the matrix can ultimately result in material failure . Attempting to model a composite material using the ICME method is indeed a lofty goal, however, its relevance cannot be overstated. Factors including fiber weave pattern, type, orientation and fiber volume fraction would all be need to be considered with evaluating the fiber in addition to the effects of the matrix, degree of cross-linking, presence of voids and micro cracks. However, when opening the proverbial can-of-worms, the researcher may find that the properties are better understood using this methodology instead of other material modeling techniques [1, 2]. To begin to create a model for a composite material it is relevant to first model one of the two discrete material systems. As such, the focus of this proposal will be narrowed down to creating a model for the epoxy resin system. Although the bulk of the mechanical properties are derived from the fiber, reduction of properties due to environmental degradation and imperfections in manufacturing processing are more dependent upon the resin matrix .
An important class of resins that to date are predominantly used in composite systems is vinyl esters and specifically epoxies. This class of materials is thermosetting, meaning that crosslinking is present within the polymer structure. Because the mechanical properties are derived by the crosslinking of the material, it is relevant to understand the polymerization process of this class of material. A typical epoxy is shown in Figure 1.0. As can be seen in the below figure, there are two epoxy groups on each monomer which will in turn allow for cross-linking to occur .
Figure 1.0 Typical Epoxy Resin .
The crosslinking of epoxy resin occurs by the reaction with a hardener. The hardener is typically an amine group and acts to open the epoxy ring. Two new bonds are formed in the reaction and the key bond required for cross-linking is the bond between the amine group and the carbon. The amine molecule usually has another amine group on the other end that can react with the second epoxy molecule which in turn allows for cross-linking. The reaction can be seen in greater detail in Figure 2.0 . Understanding this reaction is critical in understanding the superior mechanical properties of an epoxy resin combined with ease of processing when compared to even advanced thermoplastic materials.
Figure 2.0 Epoxy Ring-opening reaction 
As such, the relative concentrations of the epoxy, often referred to as “part A” and the hardener, referred to as “part B” are critical in determining the properties of the final material. If the ratio of materials in not accurate, a material with insufficient material properties would result .
Epoxy Cure and Polymer Weight
The curing profile of the epoxy is also a critical factor in final property determination. Some classes of epoxy are cured at room temperature while others require heat. For example, typical cured epoxies are hard and brittle, but depending on the molecular weight of the polymer different mechanical properties can be achieved. If toughness is a desired property, increasing the length of the polymer chain will increase the toughness but will also decrease the number of crosslinks per unit length. This in turn makes the material less strong, stiff, and also more sensitive to temperature and solvents. As with most classes of materials, there are important trade-offs to consider . Understanding these tradeoffs and capturing them in a multi-scale model can allow for the optimization of the resin system for a given application.
Epoxy Environmental Modeling
One of the major concerns regarding Fiber Reinforced Polymer composites is the ability of the material to be used in an outdoor environment over prolonged exposure. Thermal aging and moisture deterioration are of relevant concern for nearly every composite material. Absorbed moisture can lead to matrix swelling and UV and elevated temperatures can degrade overall properties over time. Absorbed moisture in turn affects dimensional stability of the finished part as well as the interfacial bonding between the fiber and the matrix which ultimately affects fracture toughness, stiffness, strength, viscoelastic properties and ultimately poor load bearing capability . The ability to model these effects could allow for the development of intelligent inspections schedules of composite parts as well as increase our understanding of the projected lifecycle of the material.
Macroscale ISV Continuum
When compared to metals, the length scales of importance of polymers is similar as well as dependent upon time and temperature. Table 1 lists the length scales of importance for a polymeric system and has been revised from the original table created from a 2012 ICME course to include an examination of the monomer level and the polymer level length scale . By including this additional level, more focus can be made on the monomer chemistry and how the monomer contributes to macroscale properties. For example, the monomer polyethylene is the same in the polymer Low density polyethylene and high density polyethylene. This monomer is the source of many of the great mechanical properties that both polymers share, however, the affect on the polymerization results in a radically different material in terms of toughness and strength. Then, moving up the scale to evaluate the polymer length scale, the focus can be made on crystallinity and density and how these variable contribute to mechanical properties such as yield strength and toughness.
Table 1: Important Length Scales of Polymers  ThermoSetting Polymers • Structures • Continuum Element • Fibers • Hard Phases • Entanglements • Crosslinks • Polymers • Monomers • Molecules • Atoms • Electrons
Upon evaluation of the work done in ICME, comparatively little has been done regarding polymers and this is not surprising. The level of complexity from the molecular level and onto discrete regions of crystallinity and surrounding amorphous regions explain the inherent scope and time constraints due to the need of modeling larger volumes of material . A macroscale description is therefore difficult to develop due to the underlying micromechanisms involved and their dependence on temperature, strain rate and stress state and a variety of other factors. In order for a model to be accurate it must thereby be comprehensive and capture the complexity necessary to model the details from all the various length scales and all the interactions involved. This model must capture amorphous material properties that will be decidedly different from crystalline regions and includes chain slippage, entanglements, void formation and growth, and chain rupture [1, 3, 4].
Requirements of the structure must be understood and defined in order to understand lower scales. Structural characteristics related to solid mechanics such as elastic modulus, creep, and environmental effects would be necessary inputs for an effective structural scale model. For Epoxy, the following characteristics would be needed to understand the macroscale properties: elastic modulus, strain rate effects, density, temperature dependence of properties, bonding and mobility defined by plastic deformation, particle-polymer interaction, and particle-crack interactions. Because the environmental effects related to the performance of the material are significant it will be relevant to capture effects such as temperature and humidity and how these affect macroscale properties. Failure to incorporate temperature dependence, for example, would severely limit the usability and robustness of the model. This information is found and carried through the multiscale model [1, 2, 3].
There is much interest and study in the field of fracture mechanics for epoxy. Fracture mechanics scale modeling needs to include how particles and voids interact. This link is found on the lower length scale. The relevance of modeling this behavior is the ability to fit and validate the model to a large body of research available in the literature [1, 5].
Microscale finite element simulations (FEA) are important to quantify how particles, voids, and the surrounding material matrix interact. Overall, the molecular structure of epoxy is amorphous which does in some cases minimize the complexity of the material model by not having to consider regions of high crystallinity. Being able to accurately model the void interaction in the material is of high interest for Epoxy and its role as the matrix in a composite system [1, 3,].
A coarse-grained model can be used to simulate an epoxy system for molecular dynamics simulations. In this model, it has been shown that epoxy can be modeled and the model is capable of being optimized to fit thermochemical properties of epoxy. Crystallographic slip between the amorphous and crystalline regions of polymers plays a large role in the fracture behavior of polymers. Much like dislocations in metals, crystalline regions can dislocate and glide past amorphous regions, usually when a preferred slip direction. The preferred slip direction can be found using molecular simulations on the chain tilt interface region and can be used to predict tensile failure of the epoxy system [1, 6].
At the atomic nanoscale much information can be gleaned for quantification and understanding of polymer fracture behavior. Existing literature has found success in using the Reactive Force Field (ReaxFF) to represent hydrocarbon materials and specifically Epoxy . Research has found good correlation with using ReaxFF to understand molecular dynamics that result in mechanical behavior which correlates well with experimental data. The interface energy output of this step passes on as inputs to microscale FEA simulations. Molecular interactions like chain entanglement, deformation induced chain alignment, and chain rupture can be passed directly to the ISV continuum model [1, 7, 8].
At the electronic scale the density functional theory (DFT) can be used to calculate the lattice parameter and elastic constants of epoxy. DFT calculations are used as input fields for atomistic potential functions at the next level of the model. DFT has been successfully employed to model the polymer structure and conformations of many materials and is effective at describing chain stiffness, polymer concentration, and short chain molecules [1, 9].
Figure 3 presents a summary of the various length scales and bridge relationships that would be desirable to capture the continuum that describes the process, performance, and design interactions present in the overlap of materials science, manufacturing, and engineering . Figure 2 has been developed and modified after a proposed modeling strategy presented in a course covering ICME concepts and case studies .
Figure 3: Multiscale Modeling of Epoxy as Resin in Composite System .
In conclusion, developing a multiscale model for Epoxy would serve to be incredibly relevant and further the knowledge base of the role that Epoxy plays in a composite system. Since the composites industry is projected to grow at an increasingly high rate and become more commonplace within the automotive industry, having an ability to understand the process, structure, property relationship within the material system will be of utmost importance . The task of creating a robust and accurate multiscale model for a composite system will of course be dependent on the suitability and accuracy of the resin model. Modeling the effects of temperature, strain rate, moisture uptake kinetics, and degradation behavior will be critical to understand the overall system [11 – 16]. The motivation of such a model is apparent when considering the challenges of inspecting composite structures and the difficulty in detecting damage. Creating a model that can be used to predict how the material will perform over time when exposed to environmental stressors can help spring load not only the composites industry but also the ICME method applicability [1, 10].
- ↑ 1. Horstemeyer, M. 2018, Integrated Computational Materials Engineering. Wiley, New Jersey.
- ↑ 2. Narteh, A., Watson, D. et. Al “Properties of Carbon, E-Glass, and Hybric E-Glass/Carbon Fiber Reinforced Polymer Composites Exposed to Seawater Conditioning”. Conference Proceedings SAMPE 2018.
- ↑ 3. Strong, B. 2006, Plastics: Materials and Processing. Pearson Prentice Hall, New Jersey.
- ↑ 4. 2019, “ICME Category: Polymers”. From https://icme.hpc.msstate.edu/mediawiki/index.php/Category:Polymers
- ↑ 5. Sutton, S. “Fatigue Crack Propagation in an Epoxy Polymer,” Engineering Fracture Mechanics, Volume 6, Issue 3, October 1974, Pages 587-594, IN23-IN24, 592.
- ↑ 6. Yang, S., Cui, Z, Qu, J., “A Coarse-Grained Model for Epoxy Molding Compound,” Journal of Physical Chemistry, Volume 118, Issue 6, 2014, 1660- 1669.
- ↑ 7. Odegard, G., Jensen, B., Gowthan, S., Wu, J., He, J., Zhang, Z. “Predicting Mechanical Response of Crosslinked Epoxy using ReaxxFF”, Chemical Physics Letters. 2013.
- ↑ 8. S Nouranian, MA Tschopp, SR Gwaltney, MI Baskes, and MF Horstemeyer, “An Interatomic Potential for Saturated Hydrocarbons Based on the Modified Embedded-Atom Method”, Physical Chemistry Chemical Physics 16 (13) (2014):6233-6249.
- ↑ 9. Zhauyang, W., Ning, N., Zhang, L., “Density Functional Theory of Polymer Structure and Conformations” Polymers, April 2016.
- ↑ 10. Gibson RF, “A review of recent research on mechanics of multifunctional composite materials and structures”, Composite Structures, 92, 2010, pp. 2793–2810
- ↑ 11. Sayer M, Bektaş NB, Demir E, Çallioğlu H, “The effect of temperatures on hybrid composite laminates under impact loading”, Composite Part B: Engineering, 43(5), 2012, pp. 2152–2160.
- ↑ 12. Surathi P, Karbhari VM, “Hygrothermal effects on durability and moisture kinetics of fiberreinforced polymer composites”, Project SSR, University of California SDDoSE, Services, CDoTDoE Department of Structural Engineering, University of California, San Diego, 2006
- ↑ 13. Kootsookos A, Mouritz AP, “Seawater durability of glass- and carbon-polymer composites”. Composites Science and Technology, 64, 2004 pp. 1503–1511.
- ↑ 14. Prian L, Barkatt A, “Degradation mechanism of fibre-reinforced plastics and its implications to predictions of long-term behavior”, Journal of Materials Science, 34, 1999, pp. 3977–3989.
- ↑ 15. Rao RMVGK, Chanda M, Balasubramanian N. “Factors affecting moisture absorption inpolymer composites Part II: Influence of external factors”. Journal of Reinforced Plastic Composite, 3: 1984 pp.246–53.
- ↑ 16. Rao RMVGK, Balasubramanian N, Chanda M, “Factors affecting moisture absorption in polymer composites Part I: Influence of internal factors”, Journal of Reinforced PlasticComposite, 3: 1984: 232–245.