Stress Evolution during Thermoset Cure
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coefficients of thermal expansion, moduli and characteristic time r for the molecular motions bringing about volume recovery of the epoxy resin system. Other factors influencing the residual stress in the resin include the curing schedule as well as the degree of dimensional constraint to which the resin is subjected. It is very important to understand the state changes which occur during cure of a thermosetting system, because the constitutive equations can be simplified to the corresponding states. A convenient representation of the changes which occur during the cure of a thermosetting system is given by the isothermal time-temperature-transformation (TTT) cure diagram [1]. The diagram, schematically shown in Fig. 1, displays the states and changes of state of the material during isothermal cure as a function of time. The various material states possible include liquid, sol glass, sol/gel/rubber, gel rubber, sol/gel glass, gel glass and char. During isothermal cure, changes occur in the material when a contour separating states is crossed at a given elapsed time. Relevant contours include: microscopic gelation (corresponding to the viscosity rising to the level of a macrogel or the incipient formation of an infinite network of crosslinked polymer molecules), vitrification (corresponding to Tg rising to the cure temperature or involves a transformation from a liquid or a rubber state to a glassy state as a result of an increase in average network molecular weight), devitrification (corresponding to the glass transition temperature decreasing to T,,re because of thermal degradation), and char formation. Both the progress of the isothermal cure process and the state of the material can be clearly represented using these contours in the TYT diagram. If the TTT diagram of one kind of thermosetting material is known, the mechanical behavior of this material can be approximately estimated. For the neat resin system, the curing residual stress 195 Mat. Res. Soc. Symp. Proc. Vol. 515 © 1998 Materials Research Society
before gelation can be neglected because the modulus is then very low. For instance, if Tcure>>Tg,ý, a linear rubbery constitutive relationship can be used to estimate the residual stresses generated during isothermal cure because under this condition the characteristic time r for the molecular motions leading to volume recovery is shorter than the time scale of the experiment. If gelTg< Tcure< Tg•, the epoxy will go through both sot/gel rubbery and sol/gel glass states, and a rather complex viscoelastic constitutive relationship would have to be considered. One important issue during curing arises when the epoxy is in a sol/gel/rubbery or a gel rubbery state, the behavior is very similar to that of a rubber and the Poisson's ratio approaches a value of 0.5. Consequently, the stress increments can reach appreciable values and may generate microcracks if some critical points in the structure are three dimensionally constrained [2]. Therefore, when studying the curing process it is important to know not just
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