Plastic flow modeling in glassy polymers

Abstract

Glassy amorphous and semi-crystalline polymers exhibit strong rate, temperature, and pressure dependent polymeric yield. As a rule of thumb, in uniaxial compression experiments the yield stress increases with the loading rate and applied pressure, and decreases as the temperature increases. Moreover, by varying the loading state itself complex yield behavior can be observed. One example that illustrates this complexity is that most polymers in their glassy regimes (i.e., when the temperature is below their characteristic glass transition temperature) exhibit very pronounced yield in their uniaxial stress stress-strain response but very nebulous yield in their uniaxial strain response. In uniaxial compression, a prototypical glassy-polymer stress-strain curve has a stress plateau, often followed by softening, and upon further straining, a hardening response. Uniaxial compression experiments of this type are typically done from rates of 10{sup -5} s{sup -1} up to about 1 s{sup -1}. At still higher rates, say at several thousands per second as determined from Split Hopkinson Pressure Bar experiments, the yield can again be measured and is consistent with the above rule of thumb. One might expect that that these two sets of experiments should allow for a successful extrapolation to yet higher rates. A standard means to probe high rates (on the order of 105-107 S-I) is to use a uniaxial strain plate impact experiment. It is well known that in plate impact experiments on metals that the yield stress is manifested in a well-defined Hugoniot Elastic Limit (HEL). In contrast however, when plate impact experiments are done on glassy polymers, the HEL is arguably not observed, let alone observed at the stress estimated by extrapolating from the lower strain rate experiments. One might argue that polymer yield is still active but somehow masked by the experiment. After reviewing relevant experiments, we attempt to address this issue. We begin by first presenting our recently developed glassy polymer model. While polymers are well known for their non-equilibrium deviatoric behavior we have found the need for incorporating both equilibrium and non-equilibrium volumetric behavior into our theory. Experimental evidence supporting the notion of non-equilibrium volumetric behavior will be summarized. Our polymer yield model accurately captures the stress plateau, softening and hardening and its yield stress predictions agree well with measured values for several glassy polymers including PMMA, PC, and an epoxy resin. We then apply our theory to plate impact experiments in an attempt to address the questions associated with high rate polymer yield in uniaxial strain configurations.