Cure modeling

Model Networks. Constmction of model networks allows development of quantitative stmcture property relationships and provide the abiUty to test the accuracy of the theories of mbber elasticity (251—254). By definition, model networks have controlled molecular weight between cross-links, controlled cross-link functionahty, and controlled molecular weight distribution of cross-linked chains. Sihcones cross-linked by either condensation or addition reactions are ideally suited for these studies because all of the above parameters can be controlled. A typical condensation-cure model network consists of an a, CO-polydimethylsiloxanediol, tetraethoxysilane (or alkyltrimethoxysilane), and a tin-cure catalyst (255). A typical addition-cure model is composed of a, ffl-vinylpolydimethylsiloxane, tetrakis(dimethylsiloxy)silane, and a platinum-cure catalyst (256—258). 

Using both condensation-cured and addition-cured model systems, it has been shown that the modulus depends on the molecular weight of the polymer and that the modulus at mpture increases with increased junction functionahty (259). However, if a bimodal distribution of chain lengths is employed, an anomalously high modulus at high extensions is observed. Finite extensibihty of the short chains has been proposed as the origin of this upturn in the stress—strain curve. 

Figure 8. Influence of the reaction rate constants on the isocyanate and hydroxyl decrease during curing model calculations.

Addition-cured model systems, of silicone networks, 22 569 Addition-curing silicones, 22 35 Addition-fragmentation mechanism, of chain- transfer (CT) agents, 23 383-384... 

The objective of the Springer KBES is twofold To ensure a high-quality part in the shortest autoclave curing cycle duration. This KBES is similar to QPA in that sensor outputs are combined with heuristics not with an analytical curing model. The rules for compaction dictate that dielectrically measured resin viscosity be held Constant during the First temperature hold in the autoclave curing run. The autoclave temperature is made to oscillate about the target hold temperature in an attempt to attain constant viscosity. Full pressure is applied from the cure cycle start. 

For use in a strategy such as SHMPC, a model must also be relatively small because it must provide real-time output in an on-line application. In a batch process, such as autoclave curing, model output must be available before the process moves into its next phase (i.e., before the next measurement is recorded). This requirement for real-time models in an on-line application limits the types of models that can serve in SHMPC. 

Mallow, A., Muncaster, F., Campbell, F. Science Based Cure Model for Composites, American Society for Composites, First Technical Conference, Dayton, OH, Oct. 1986... 

Probably the first major publication of a process model for the autoclave curing process is one by Springer and Loos [14]. Their model is still the basis, in structure if not in detail, for many autoclave cure models. There is little information about results obtained by the use of this model only instructions on how to use it for trial and error cure cycle development. Lee [16], however, used a very similar model, modified to run on a personal computer, to do a parametric study on variables affecting the autoclave cure. A cure model developed by Pursley was used by Kays in parametric studies for thick graphite epoxy laminates [18]. Quantitative data on the reduction in cure cycle time obtained by Kays was not available, but he did achieve about a 25 percent reduction in cycle time for thick laminates based on historical experience. A model developed by Dave et al. [17] was used to do parametric studies and develop general rules for the prevention of voids in composites. Although the value of this sort of information is difficult to assess, especially without production trials, there is a potential impact on rejection rates. 

Mixing activated cure materials such as polyurethanes will instantly start releasing exothermic heat after the mixture of its two components has occurred. The Castro-Macosko curing model, a second order reaction kinetic, accurately fits this behavior and is written as [44],... 

Since non-isothermal cure is of practical importance in cure control, one would like to extend the cure model to include non-isothermal cure kinetics. This modification is shown below ... 

Of course, it should be noted that cure conversion or kinetic models themselves should be accurately determined, because they must be used in parallel with cure models of chemoviscosity. There are essentially two forms of kinetic model used to describe thermoset curing reactions, namely empirical and mechanistic models. Empirical models assume an overall reaction order and fit this model to the kinetic data. This type of model provides no information on the kinetic mechanisms of the reaction, and is predominantly used to provide models for industrial samples. Mechanistic models are derived Irom an analysis of the individual reactions involved during curing, which requires detailed measurements of the concentrations of reactants, intermediates and products. Essentially, mechanistic models are intrinsically more complex than empirical models however, they are not restricted by compositional changes, as are empirical models. Typical kinetic models used in the analysis of thermosetting chemical reactions are listed in Table 4.2. 

Cure modelling of polyester pultrusion systems was carried out by Ng and Manas Zloczower (1989). A mechanistic model that couples free-radical polymerization and diffusion control (Section 1.2.3) was used for the cure kinetics and is shown here ... 

Three-dimensional analyses of heat transfer and cure in pultrusion of epoxy-resin composites have been examined by Chachad et al. (1995, 1996) and Liu et al. (2000). Carlone et al. (2006) review finite-difference and finite-element process models used for predicting heat transfer and cure in pultrusion. In this work they recommend the following empirical nth-order cure model for predicting cure kinetics of epoxy-resin composites, which is then coupled to the system s energy balance to predict thermal properties and cure conversion ... 

Nichetti (2003, 2004) examined the use of a cure model to predict mechanical properties of isothermally vulcanized moulded items. 

Ultraviolet processing has been restricted to lab-scale studies however, many authors have examined kinetic cure modelling of these systems during the development of new UV-cure materials. 

Lee and Cho (2005) developed a cure model for UV nano-imprinting. It was shown via fibre-optic FTIR techniques (as developed by Decker and Moussa (1990)) that the degree of cure had an exponential relation to the UV-irradiation time, power and temperature. 

Little process modelling has been developed due to the low industrial usage of y-irradiation processing for reactive polymers. However, many researchers are examining cure models for promising materials. 

Tang et al. (2004) presented a cure model that captures transient, thermal and chemical effects that are ignored in typical threshold-based models. This new model incorporates as inputs photoinitiation rates, reaction rates, diffusion and temperature distributions, and is able to determine the spatial and temporal distributions of monomer and polymer concentrations, molar masses, crosslink densities and degree of cure. 

Cole et al. (2001) reviewed physical models for most stages of the microlithography process. For the curing stage, they state that there has been no recent development of cure models since the work of Dill (1975). Dill (1975) presented models that incorporate both light absorption and photopolymer cure kinetics modelling, as shown by the following equations ... 

Nonisothermal flow of a curing model liquid in a flat slit is discussed in Refs. [88, 89] as applied to the casting of rubber stock under the conditions of airing. 

As seen in Figure 2.26, the Tg — x data obtained from the residual cure (MT)DSC experiments are well described by the optimised Tg— x relationship [Eq. (27)] of the diffusion-controlled cure model (Tg is the solid line and Tga is the dashed line). The departure of the experimental data from the continuous dashed line is due to the effect of increasing crosslinking beyond the gel point. The conversion at gelation correlates well with the value of 25% measured with dynamic rheometry (using the criterion G = G ). 

Table 3.5 Cure model parameters for unsaturated polyester and vinyl ester...

The cycle time is the total of the three stages mold preparation and preform preparation, mold filling and resin cure. Mold filling time is predicted by using the flow models. Cure model is used to determine the degree of resin cure and if a database is available which relates the degree of cure to the mechanical properties, the user can decide when to demold the part. 

Flow and cure models require important material properties as input. These are permeability of the fiber preform and reaction kinetics of the resin, respectively. The accuracy of the models depends on the accuracy in characterizing these properties. 

Empirical resin cure models have been formulated for various resin systems. The heat generation due to the cure reaction, 5 may be linearly related to the rate of the reaction, R as follows ... 

Michaud, D. J., Beris, A. N. and Dhurjati, P. S. (2002), Thick-sectioned RTM composite manufacturing. Part I In situ cure model parameter identification and sensing . Journal of Composite Materials, 36(10), 1175-1199. 

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