Oleg Dmitriev and Sergey Mischenko Tambov State Technical University
Production of composites is a complex, energy-intensive, relatively time-consuming chemical-technological process. Therefore, the issue of increasing intensity of production of composite products is largely linked to the performance of technological operations for composites, such as forming, curing, heat treatment and cooling (Balakirev et al., 1990).
The quality of the thermoset composite products is an integral part of increasing the intensity of the process their of obtaining, which is mainly determined by the properties of the cured material, its macro-and microstructure and geometrical parameters of the finished product. Dependence of the quality of products from the processing parameters is determined mainly by the curing cycle, temperature – conversion of homogeneity, achieved the degree of cure, the degree of thermal degradation of the resin, as well as residual stresses.
The process of curing of thermosetting products of composites accompanied, as a rule, exothermic reaction. Due to the low thermal conductivity of the composites during their curing a significant heterogeneity of the temperature-conversion field perpendicular to layers of prepregs occurs and increases with the thickness of the product. If not optimal temperature-time cycle, this leads to significant overheating of internal layers of material products, the deviation curing degree of polymeric resin from optimal, the destruction of resin, the accumulation of internal stresses that cause the reduction of strength properties of the material, warping of finished product, etc. To remove these deficiencies and thereby improve the product quality indicators can be achieved through optimal assignment of temperature-time cycle of U(t) on the surface of the product (Balakirev et al., 1990).
The principal terms of the optimal technology curing thermoset composites, which provide high quality products on the physical and mechanical properties and greater stability of these properties with respect to time, are as follows (Wu & Joseph, 1990):
– products should be cured on a strictly defined temperature-time cycle;
– compaction pressure should provide the desired resin content and density of the material in the product, as well as of a given thickness;
– in the process of molding products should be provided with the necessary degree of curing resin in the composite;
– product after compaction shall not contain residual stresses greater than the number corresponding to the dynamic equilibrium in the range of operating temperatures and ensures greater stability over time dimensions and mechanical properties of products.
The main parameters of the curing process of composite products are: temperature-time cycle, compaction pressure, the time of its application and duration of the process (Balakirev et al., 1990). Properties of cured polymer composite material depend strongly on the correct choice of these parameters and, consequently, the character of the curing process in time, especially at the initial stage, which lays the desired structure. Therefore, the problem of determining optimal curing cycle of composites is an important and responsible.
The main tasks that must be addressed in the selection of optimal curing of composite, that guaranteed high quality and low unit cost, are (Rosenberg & Enikolopyan, 1978):
– reducing the temperature-conversion of inhomogeneities in the composite;
– reducing the duration of the curing cycle and energy consumption;
– complete curing resin in prepregs;
– compacting of the composite up to the desired thickness of the product.
Until recently, for the choice of curing cycles used empirical methods and curing cycles selected according to the results of lengthy experiments. For example, the authors of works (Rosenberg & Enikolopyan, 1978) selected curing cycles on the basis of the conditions for obtaining maximum strength, finding the dependence of breaking stress in the bending strength of the temperature or pressure. In (Kulichikhin & Astakhov, 1991) curing cycles of products was determined by rheological and dielectric measurements. The author of (Botelho et al., 2001) hold time during the curing thermosetting resins determined by change the viscoelastic properties. In (Stern, 1992), (Aleksashin & Antyufeyev, 2005) curing cycle of products based on epoxy and phenol-formaldehyde epoxy resin was determined by time gelation studied using differential thermal analysis and differential scanning calorimetry. A significant shortcoming of these and many other methods is the need to use samples of small diameter and small thickness, the inability to exert the necessary pressure molding, the absence of rheological characteristics of polymeric binder, etc. Therefore, the results obtained using these methods do not fully correspond to the processes proceeding during cure of materials in real constructions.
The disadvantage of the methods of curing cycles choice is that they basically can be applied to thin-walled products (thickness 1-3 mm), which is implemented a uniform setting of cure on thickness of material, and absolutely can not be applied to thick-walled products (more than 3-5 mm), in which the entire course of the curing process is determined by speed of withdrawal of heat (by thermal conductivity) to be allocated in the exothermic reaction of curing. The curing cycles of thick-walled products usually obtained on base of the curing cycles of thin plates that was obtained empirically. In doing so, the temperature of isothermal hold did not change, and hold time in the press were set to form a linear dependence on the thickness of the product (Dedyukhin & Stavrov, 1976). This method is built without taking into account heat transfer, curing kinetics and processes that related to changes viscosity of resin, which leads to large errors.
The use for this purpose of simple calculation methods, based on the theory of similarity, allowing extrapolate the curing process parameters, found in the same conditions to other conditions of curing. For example, in (Dedyukhin & Stavrov, 1976) obtained a formula for calculation, allowing determine of the hold time of the cure in one-step cycle, depending on temperature molds, taking into account the heating rate and activation energy of resin. However, these formulas do not contain connection the temperature curing cycle and the mechanical characteristics of the material (residual stresses) and do not take into account the possible overheating of internal layers of the product as a result of exothermic effect. Nevertheless, they used to calculate the curing cycles of thick-walled products.
Thus, an analysis of previously used empirical and simple calculation methods revealed the following deficiencies:
a. to determine of the curing cycles of composite required a broad program of experiments;
b. the curing cycles, found to be satisfactory for this material in some conditions, may not be appropriate in other conditions, in particular, when need other thickness of material;
c. these techniques do not guarantee complete and high-quality curing of material by the selected temperature-time curing cycle.
The most complete problem of selection of curing cycle products can be solved through the combined use of optimization methods with the use of mathematical models of thermokinetic curing process and define of mathematical model parameters. This method consists in setting and solving the problem of minimizing a certain criterion of optimality (Afanasyev, 1985). It can help to determine the curing cycle of composite products for any geometrical sizes and shapes.
The first attempts for solving the problem of finding optimal curing of thick-walled products cycle of thermosetting composites were made by the authors of works (Wu & Joseph, 1990), (Frank et al., 1991) and further developed in (Balakirev et al., 1990), (Dmitriev et al., 2009). As a mathematical model in most of these works was used a simplified system of linear differential equations of heat conduction and kinetics without the mass transfer, which limited its use and accuracy of solutions. Strict theory of solutions of such problems are currently not, therefore, in these works have used the approximate methods.
Thus, one can conclude that if there is a large diversity of methods for selecting the curing cycles the majority of them were built on the basis of empirical approaches. In a small number of mathematical methods was used the simplified set of optimization problems, based on a simple linear mathematical models, without taking into account the many phenomena of the process, for example, currents of resin under the pressure, dependence of thermophysical properties on temperature, degree of curing and filling ratio (fraction factor). In addition, almost entirely absent in the tasks of optimizing the recording of pressure forming, determining its magnitude and duration of application.
The aim is to head the prospects of using the method for calculating the optimal curing cycles of large-scale products of polymer composite materials based on mathematical modeling and numerical search of the temperature-time cycle, ensuring the creation of high – quality finished product in the minimal possible time, with minimal power consumption, or with minimal residual stresses.