Polymer matrix composites model

A Unified Approach to Modeling Transport of Heat, Mass, and Momentum in the Processing of Polymer Matrix Composite Materials... 

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

Since the end of the 90 s, our group has been developing a non-empirical kinetic model, named KINOXAM, for the lifetime prediction of polymers and polymer matrix composites in their use conditions. The model is totally open. It is composed of a core, common to all types of polymers, derived from the now well-known closed-loop mechanistic scheme (/). Around this core, various optional layers can be added according to the complexity of oxidation mechanisms and the relationships between the structural changes taking place at the molecular scale and the resulting ones at larger scales (the macromolecular and macroscopic scales). 

The manufacture of polymer matrix composites involves complex chemical and physical changes that must be adequately controlled to produce desirable products. Monitoring techniques and models to correlate monitoring data to improve processing are therefore key aspects to increasing production rates and product quality. 

The scale dependence on strength can be explained by utilizing the point stress failure criterion, that is used with polymer matrix composites [168,169], as well as by considering the statistics offiber strength distribution [148]. These models suggest a characteristic length scale of 0.5 mm over which the stress must exceed the strength of the material in order for failure to initiate. 

Li, S., Thouless, M.D., Waas, A.M., Schroeder, J.A., and Zavattieri, P.D. (2005) Use of a cohesive-zone model to analyze the fracture of a fiber-reinforced polymer-matrix composite. Composites Science and Technology, 65,... 

Li S, Thouless M D, Waas A M, Schroeder J A and Zavattieri P D (2005), Use of Mode-I cohesive-zone models to describe the fracture of an adhesively-bonded polymer-matrix composite. Composite Science and Technology, 65,281-293. 

Roy S, Xu W, Patel S, Case S. Modeling of moisture diffusion in the presence of bi-axial damage in polymer matrix composite laminates. Int J Sol Struct 2001 38 7627-7641. 

For the polymers containing filler that touch each other, the percolation theory has been developed. This assumes a sharp increase in the effective conductivity of the disordered media, polymer matrix composite, at a critical volume fraction of the reinforcement known as the percolation threshold (( )percoi) which long-range connectivity of the system appears. The model that best expresses these aspects is the one created by Vysotsky (Vysotsky and Roldughin 1999), which presumes a percolation network of nanofiller particles inside the polymer matrix as shown in equation (11.10) ... 

Matrix cracking results in reduction in the laminate stiffness and strength. Stiffness reduction in CMCs is greater than that observed in polymer matrix composites due to lower ratio between fibre and matrix moduli. It also affects coefficients thermal expansion and vibration frequencies. A number of models have been suggested to estimate the effect of transverse macrocracks in the 90° plies and matrix cracks bridged by fibres in the 0° plies on the mechanical properties of cross-ply CMC laminates (Pryce and Smith, 1994 Daniel and Anastassopoulos, 1995 Lu and Hutchinson, 1995 Erdman and Weitsman, 1998 Birman and Byrd, 2001 Yasmin and Bowen, 2002 Birman and Weitsman, 2003). 

Bond DA, Smith PA (2006) Modeling the transport of low-moleeular-weight prmetrants within polymer matrix composites. Appl Meeh Rev 59(5) 249-268 Crank J (1980) The mathematies of diffusion, 2nd edn. Oxford UnivCTsity Press, Oxford Weitsman YJ (1991) Moisture in eranposites sorption and damage. In ReifsnidCT KL (ed) Fatigue of composite materials. Elsevier, New York, pp 385-429 Weitsman YJ (2000) Effects of fluids on polymeric eranposites—a review. In Kelly A, Zweben C (editors in Chief) Comprehensive cranposite materials. Talreja R, Manson J-AE (editors). Polymeric matrix composites, vol. 2. Amstradam Elsevier, pp 369—401... 

In polymer matrix composites, there appears to be the optimum level of fiber-matrix adhesion which provides the best mechanical properties. Several models which relate the structure and properties of composites to fiber-matrix interfacial behavior have been proposed based either on mechanical principles with some assumptions made about the level of fiber-matrix adhesion in the composite or have taken a surface chemistry approach in which the fiber-matrix interphase was assumed to be the only factor of importance in controlling the final properties of the composite. Neither effort has had much success. 

In this chapter, the interphase phenomena in the polymer matrix composites at the micro- and nano-scales are briefly reviewed and thdr main differences are discussed. An approach for modeling mechanical properties of continuous macroscopic bodies considering peculiarities brought about by the discrete nature of the matter at the nano-scale is proposed based on the combination of gradient strain elasticity and chain reptation dynamics. 

S. Leigh Phoenix, Modeling the statistical lifetime of glass fiber/polymer matrix composites in tension. Composite Structures, 48(l-3) 19-29,2000. 

The heat transfer model, energy and material balance equations plus boundary condition and initial conditions are shown in Figure 4. The energy balance partial differential equation (PDE) (Equation 10) assumes two dimensional axial conduction. Figure 5 illustrates the rectangular cross-section of the composite part. Convective boundary conditions are implemented at the interface between the walls and the polymer matrix. 

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