Stress time anomaly

The idealized laws just reviewed can, however, not describe the behavior of matter if the ratios of stress to strain or of stress to rate of strain is not constant, known as stress anomalies. Plastic deformation is a common example of such non-ideal behavior. It occurs for solids if the elastic limit is exceeded and irreversible deformation takes place. Another deviation from ideal behavior occurs if the stress depends simultaneously on both, strain and rate of strain, a property called a time anomaly. In case of time anomaly the substance shows both solid and liquid behavior at the same time. If only time anomalies are present, the behavior is called linear... 

The analyses of several polymers by dynamic mechanical analysis, DMA, are described in Sect. 4.5 in connection with the brief description of the DMA equipment. It was observed in such experiments that neither the viscosity nor the modulus are constant, as is assumed for the discussion of energy and entropy elasticity, outlined in Sects. 5.6.4 and 5.6.5, respectively. One finds a stress anomaly when the elastic limit of a material has been exceeded and plastic deformation occurs. Other deviations have the stress depend both on strain and rate of strain. Finally, a time anomaly exists whenever the stress/strain ratio depends only on time and not on the stress magnitude. 

Bates 1984 Fredrickson and Larson 1987 Fredrickson andFIelfand 1988). The relaxation of these fluctuations involves collective motion of many molecules, and thus it is slower than the relaxation time of individual molecules. In small-amplitude oscillatory shearing, the fluctuation waveform is deformed, producing a slowly relaxing stress. Presumably, this accounts for (a) the anomalous contribution to G and (b) a similar, but smaller, contribution to G" (Rosedale and Bates 1990 Jin and Lodge 1997). (Similar anomalies are observed in polymer blends.) An asymmetric version of this PEP-PEE polymer that forms cylindrical domains shows an even larger low-frequency anomaly (Almdal et al. 1992). 

Case II Transport. At temperatures well below Tg and at penetrant activities near unity, the initial weight gain is proportional to time rather than to This is termed case II transport (9, JO). A boundary exists between swollen gel and glassy polymer, which advances at constant velocity, independent of the sample thickness. The anomaly is believed to arise because diffusion proceeds more rapidly behind the advancing boundary in the gel phase than the polymer relaxations at the boundary itself (JO). If the penetrant has a sufficiently high activity, the stresses developed at the advancing boundary may be sufficient to cause fracture or crazing of the material. 

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