Resin Flow Models

In the past, various resin flow models have been proposed [2,15-19], Two main approaches to predicting resin flow behavior in laminates have been suggested in the literature thus far. In the first case, Kardos et al. [2], Loos and Springer [15], Williams et al. [16], and Gutowski [17] assume that a pressure gradient develops in the laminate both in the vertical and horizontal directions. These approaches describe the resin flow in the laminate in terms of Darcy s Law for flow in porous media, which requires knowledge of the fiber network permeability and resin viscosity. Fiber network permeability is a function of fiber diameter, the porosity or void ratio of the porous medium, and the shape factor of the fibers. Viscosity of the resin is essentially a function of the extent of reaction and temperature. The second major approach is that of Lindt et al. [18] who use lubrication theory approximations to calculate the components of squeezing flow created by compaction of the plies. The first approach predicts consolidation of the plies from the top (bleeder surface) down, but the second assumes a plane of symmetry at the horizontal midplane of the laminate. Experimental evidence thus far [19] seems to support the Darcy s Law approach. 

In overcoming the shortcomings of the earlier models, Dave et al. [21,22] proposed a comprehensive three-dimensional consolidation and resin flow model that can be used to predict the following parameters during cure (1) the resin pressure and velocity profiles inside the composite as a function of position and time, (2) the consolidation profile of the laminate as a function of position and time, and (3) resin content profile as a function of position and time. 

A generalized three-dimensional resin flow model has been developed that employs soil mechanics consolidation theory to predict profiles of resin pressure, resin flow velocity, laminate consolidation, and resin content in a curing laminate. 

Resin flow models are capable of determining the flow of resin through a porous medium (prepreg and bleeder), accounting for both vertical and horizontal flow. Flow models treat a number of variables, including fiber compaction, resin viscosity, resin pressure, number and orientation of plies, ply drop-off effects, and part size and shape. An important flow model output is the resin hydrostatic pressure, which is critical for determining void formation and growth. 

In the past, various resin flow models have been proposed (2, 15-19). Two main approaches to predicting resin flow behavior in laminates have been suggested in the literature thus far. In the first case, Kardos et al.2), Loos and Springer15), Williams et al.16) and Gutowski17) assume that a pressure gradient develops in the laminate both in the vertical and horizontal directions. These approaches describe the resin flow in the laminate in terms of Darcy s Law for flow in porous media, which requires knowledge of the fiber network permeability and resin viscosity. Fiber... 

Hou (1986) presented a resin-flow model for long-fibre-reinforced-composite prepreg lamination processing. The model includes the following chemorheological model ... 

In typical RTM applications, in-plane part dimensions are much larger than its thickness. Thus, as will be studied in this chapter, many resin flow models in the literature are based on the assumption that there is no significant transverse flow which simplifies the modeling to a 2D flow in the in-plane directions, and only a shell mold cavity is used for the solution domain. 2D flow assumption is violated when ... 

The flow along the fiber direction can be modeled as a channel flow (the viscous flow between two parallel plates). Loss and Springer (29) validated thermomechanical models, including the chemorheological behavior of resin and resin flow models. 

For thick epoxy laminates processed in the autoclave, voids once formed and stabilized can only be removed by dissolution or by resin flow. Furthermore, resin gradients are deleterious to structural laminates. These two key phenomena make an understanding of resin transport vital to the development of any processing model. 

This model can also provide resin pressure gradients, resin flow rates, consolidation profiles, and, when combined with the void model, void profiles at any point in the laminate. 

Models of the intimate contact process that have appeared in the literature are commonly composed of three parts or submodels. The first submodel is used to describe the variation in the tow heights (surface waviness or roughness) across the width of the prepreg or towpreg. The second submodel, which is used to predict the elimination of spatial gaps and the establishment of intimate contact at the ply interfaces, relates the consolidation pressure to the rate of deformation of the resin impregnated fiber tow and resin flow at ply surface. Finally, the third submodel is the constitutive relationship for the resin or resin-saturated tow, which gives the shear viscosity as a function of temperature and shear rate. 

Several viscosity and kinetic models, and experimental procedures for developing these models, are available for a number of commercially available resin systems [1-5]. These models allow insight into autoclave process decisions based on changes in resin viscosity and kinetic behavior and can be used to determine hold temperatures and durations that allow sufficient resin flow and cross-linking to avoid over bleeding, exotherms, and void formation. 

Resin flow and pressure distributions are among the most challenging aspects of the autoclave process cycle to model. Accounting for tooling and bagging variations, such as inner bag... 

Experimental studies, such as those to be discussed in Section 10.2.5, have been key to demonstrating the validity of these flow models. Many of the more sophisticated models [3,6,8] have shown to follow the resin flow process accurately. These models are extremely useful for choosing material systems and for determining optimum pressure cycles and bagging procedures. 

Heat transfer models of the autoclave process are the most accurate and well understood of all the process models. Much of this understanding is because the models are so easily verified through thermocouple measurements. Thermocouples are the most common part-sensing technique used in production. The challenging aspects are the incorporation of the affects of resin flow, resin kinetics, and autoclave position on heat transfer properties. The importance of incorporating resin kinetic models is to properly predict conditions that may lead to exotherms, especially for thick laminates [17]. 

Two matrix flow submodels have been proposed the sequential compaction model [15] and the squeezed sponge model [11], Both flow models are based on Darcy s Law, which describes flow through porous media. Each composite layer is idealized as a fiber sheet surrounded by thermoset resin (Fig. 13.9). By treating the fiber sheet as a porous medium, the matrix velocity iir relative to the fiber sheet is given as (Eq. 13.5) ... 

The fabrication of composite laminates having a thermosetting resin matrix is a complex process. It involves simultaneous heal, mass, and momentum transfer along with chemical reaction in a multiphase system with time-dependent material properties and boundary conditions. Two critical problems, which arise during production of thick structural laminates, are the occurrence of severely detrimental voids and gradients in resin concentration. In order to efficiently manufacture quality parts, on-line control and process optimization are necessary, which in turn require a realistic model of the entire process. In this article we review current progress toward developing accurate void and resin flow portions of this overall process model. 

Very briefly, the Dave model considers a force balance on a porous medium (the fiber bed). The total force from the autoclave pressure acting on the medium is countered by both the force due to the spring-like behavior of the fiber network and the hydrostatic force due to the liquid resin pressure within the porous fiber bed. Borrowing from consolidation theories developed for the compaction of soils 22 23), the Dave model describes one-dimensional consolidation with three-dimensional Darcy s Law flow. Numerical solutions were in excellent agreement with closed-form solutions for one- and two-dimensional resin flow cases in which the fiber bed permeabilities and compressibility, as well as the autoclave pressure, are all held constant21). 

Dave, R., Kardos, J. L., and Dudukovic, M. P. A Mathematical Model for Resin Flow During Composite Processing , submitted to Polymer lomp. 

Blest et al. (1999) examine the modelling and simulation of resin flow, heat transfer and curing of multilayer composite laminates during autoclave processing. An empirical cure equation is used ... 

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