Phenomenological description of strain rate and temperature‐dependent yield stress of PMMA

Abstract

SYNOPSISA constitutive equation to describe the yield behavior of poly(methy1 methacrylate) (PMMA) is useful not only from the technological point of view, but also for the comprehension of the nonlinear mechanisms acting in the material. In both compression and tension, the yield stress is usually represented as a function of the strain rate at different temperatures. In PMMA and other glassy polymers these curves are related by scaling, that is, they can be matched to form a master curve. Particularly in PMMA the temperature and strain rate dependence of the master curve has been characterized by two different models. The first involves two thermally activated rate processes, one acting only at high strain rates. The second model interprets the yield process as a cooperative movement of several independent structural units, all with the same activation energy. In this article it is demonstrated that only the second phenomenological model is correct because it provides a good fit to the master curve of PMMA both in compression and tension, and verifies the properties of a set of curves related by scaling. Moreover, it is pointed out that the first model leads to severe inconsistencies because it does not consider the nonlinear behavior of PMMA. Finally, the physical parameters obtained (internal stress, activation volume, and enthalpy) are compared with those given in the literature. 0 1995 John Wiley & Sons, Inc. I NTRO DUCT10 NThe dependence of the yield behavior on strain rate and temperature is useful not only to predict simple failure criteria, but to describe the mechanisms acting in a nonlinear isotropic viscoelastic material as well. Particularly, the yield process of glassy polymers has been examined from two different aspects: the molecular and structural theories, and the phenomenological models.The molecular theories assume that the nonrecoverable deformation is due to permanent changes in the polymeric chains. For instance, Robertson' considered that the intramolecular forces were the primary factor for deformation, its rate being a function of temperature. Moreover, Duckett et a1.' modified this theory by including the effect of the hydrostatic pressure. This modified model satisfactorily accounts for the plastic resistance near the CCC 002 1 -8995/95/010055-14 glass transition temperature, but fails at low temperatures over a wide strain-rate range.Some years later, Argon3 developed a molecular theory by assuming that the deformation was a consequence of the formation of a pair of molecular kinks. The energy required to create the kink pair arose from the elastic interactions between molecules ( intermolecular forces ). Argon also suggested that the yield process could not merely evolve through the formation of double kinks, but should require the cooperative change of several adjacent molecular segments. Although this theory turned out to be more relevant at very low temperatures, there are no general physical models to describe the yield behavior over a wide range of both temperature and strain ...

A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures

“…(2)) through transient dip experiments, Brooks et al only needed to consider a horizontal shift [17]. While Povolo and co-workers studied directly the yield stress and showed that the horizontal and vertical shifts are respectively related to the characteristic strain rate _ 3 Ã and to the internal stress s i [15,16]. This later result was found after a very lengthy reasoning method.…”

“…Within the past 10 years, it has been shown, for amorphous polymers by Povolo and co-workers [15,16] and for semi-crystalline polymers by Brooks et al [17], that the two Eyring processes acting in parallel for the description of the yield stress on a wide range of temperatures and strain rates can be substituted with the cooperative model of Fotheringham and Cherry [18,19]. In line with these previous studies, we propose a new formulation of the cooperative model for amorphous polymers with the assumption that yield stress must obey the strain rate/temperature superposition principle of Bauwens-Crowet et al [7].…”

Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: Characterization and modeling of the compressive yield stress

“…Concerning the internal stress, Povolo and Hermida (Povolo and Hermida, 1995;Povolo et al, 1996) proposed a linear dependence of the internal stress with temperature, but they do not have a physical model that can explain it. Nonetheless, we believe that the linear dependence of r i can find some justification in the work of Rault (1998).…”

“…Originally, Cherry (1976, 1978), and Povolo and co-workers (Povolo and Hermida, 1995;Povolo et al, 1996) have not provided any information on the nature of the activation energy of the cooperative model. It is quite remarkable to notice that the b process is also involved in the cooperative process, since it is a physical process that has been identified as a plasticity precursor.…”

“…Although, the scaling properties of the cooperative model have already been studied by Povolo and co-workers (Povolo and Hermida, 1995;Povolo et al, 1996), Richeton et al (2005) have recently proposed a new development which assumes that, independent of the yield stress model, both of the horizontal and vertical shifts have to follow an Arrhenius-like temperature dependence. Subsequently, Richeton et al Fig.…”