Viscoelastic Response of Glass

According to Partridge [163], toughening is efficient when, by comparison to the neat homopolymer tested under the same conditions, the impact resistance is multiplied by a factor of 10, without losing more than 25% of stiffness. The upper temperature limit for the use of rubber-modified blends is controlled by the matrix melt temperature, Tm, their lower limit by the glass transition temperature, Tg, of the particles. As soon as the viscoelastic response of the latter is too slow to accommodate an external loading, the polymer assumes a glassy state and breaks in a brittle way. 

The viscoelastic response of a sample previously heated to approximately 310°C is shown in Figure 15a. In this case only a single relaxation region exists and this is associated with the glass transition temperature of the fully cured resin formed at 2 C/min. 

In addition to the free volume [36,37] and coupling [43] models, the Gibbs-Adams-DiMarzo [39-42], (GAD), entropy model and the Tool-Narayanaswamy-Moynihan [44—47], (TNM), model are used to analyze the history and time-dependent phenomena displayed by glassy supercooled liquids. Havlicek, Ilavsky, and Hrouz have successfully applied the GAD model to fit the concentration dependence of the viscoelastic response of amorphous polymers and the normal depression of Tg by dilution [100]. They have also used the model to describe the compositional variation of the viscoelastic shift factors and Tg of random Copolymers [101]. With Vojta they have calculated the model molecular parameters for 15 different polymers [102]. They furthermore fitted the effect of pressure on kinetic processes with this thermodynamic model [103]. Scherer has also applied the GAD model to the kinetics of structural relaxation of glasses [104], The GAD model is based on the decrease of the crHiformational entropy of polymeric chains with a decrease in temperature. How or why it applies to nonpolymeric systems remains a question. 

General Regimes of Response. The nonlinear viscoelastic response of polymers, of course, follows some of the same classifications as does the linear response. Hence, the behavior above the glass temperature and into the terminal zone is fluid behavior, and often follows time-temperature superposition. The phenomenology of polymer melts and solutions is commonly described by... 

Below the glass temperatin-e, the nonlinear viscoelastic response of polymeric materials has been much less widely studied than has the behavior of melts and solutions. One reason for this is the lack of an adequate theory of behavior. Therefore the discussion about amorphous materials below the glass tem-peratiu e focuses on recent measin-ements of the nonlinear response as well as... 

It was pointed out in an earlier section that the viscoelastic properties are strongly related to the frictional properties of the polymers. Ferry has described some typical examples of viscoelastic responses of various polymers. The factors upon which the response depends are the molecular weight, the structure (amorphous or crystalline), the test temperature in relation to the glass transition temperature and the type and amount of foreign material which is usually added in commercial preparations for obtaining certain additional desirable properties. 

Ductile deformation requires an adequate flexibility of polymer chain segments in order to ensure plastic flow on the molecular level. It has been long known that macromoleculai- chain mobility is a crucial factor decisive for either brittle or ductile behavior of a polymer [93-95]. An increase in the yield stress of a polymer with a decrease of the temperature is caused by the decrease of macromoleculai chain mobility, and vice versa the yield stress can serve as a qualitative measure of macromolecular chain mobility. It was shown that the temperature and strain rate dependencies of the yield stress are described in terms of relaxation processes, similarly as in linear viscoelasticity. Also, the kinetic elements taking pai-t in yielding and in viscoelastic response of a polymer are similar segments of chains, part of crystallites, fragments of amorphous phase. However, in crystalline polymei-s above their glass transition temperature the yield stress is determined by the yield stress required for crystal deformation... 

General Regimes of Response. The nonlinear viscoelastic response of polymers, of course, follows some of the same classifications as does the linear response. Hence, the behavior above the glass temperature and into the terminal zone is fluid behavior, and often follows time-temperature superposition. The phenomenology of polymer melts and solutions is commonly described by constitutive laws that relate the stress and strain histories to each other (59,69). A brief description of the K-BKZ model (70-72) is provided as it seems to capture most of the behaviors of polymer melts and solutions subjected to large deformations or high deformation rates. At the same time the nonlinear form of the reptation... 

The Knauss-Emri Model. There have been several works in the literature in which volume- or ee-ooZume-dependent clocks were used to describe the nonlinear viscoelastic response of polymeric glasses. The chief success among these is the ICnauss-Emri model (163) in which the reduced time was defined in terms of a shift factor that depended on temperature, stress, and concentration of small molecules in such a way that the responses depended on the free volume induced by each of these parameters. For an isothermal single phase and homogeneous material, the equations are... 

Many potential applications for LFTs require longterm exposure to moderate stresses and temperatures. The thermoplastic matrix of LFTs causes them to be viscoelastic [4]. It can be assumed that the viscoelastic response of the material is totally due to the matrix and not due to the fibers (usually glass or carbon) which are elastic in this regime. Predicting the dimoisional stability of the material in service is an important aspect of materials selection and component design. 

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