Present-day constitutive equations, including the rate-dependent model of Carreau and the deformation-dependent model of Yamamoto, can be classified according to the dependences of Lkn and τkn-1 on certain tensor invariants. Here Lkn, and τkn-1 are the rate of creation of network strands and the probability of the disappearance of junctions, respectively, as defined by Lodge. A new constitutive equation is presented here, in which Lkn depends on the invariant of relative strain and τkn-1, on that of rate of strain. The applicability of integral type constitutive equations, including the new one presented here, is examined by comparing their predictions with the experimental results on the non-linear and unsteady response of concentrated polymer solutions. The non-linear viscoelastic phenomena examined are steady-shear flow, stress-overshoot, interrupted flow, stress relaxation under large strain, two-step stress relaxation, stress relaxation after cessation of steady flow, and stress relaxation after stress development. By using constitutive equations having memory functions whose relaxation time depends on the rate of strain, the experimental results can be explained fairly well, except for the two-step stress relaxation. On the other hand, the model with strain-dependent relaxation time does explain the two-step relaxation qualitatively, although it does not satisfactorily explain the results of interrupted flow, stress relaxation under large strain, and stress relaxation after cessation of steady flow. It was found that no constitutive equation of the integral type can consistently describe stress relaxation under large strain and two-step stress relaxation.
The dynamic and thermal properties of silk fibroin of various conformations (random coil, α-form, and β-form) were investigated. Samples of silk fibroin films and well-oriented β-forms of degummed silk, raw silk, and silk gut were used. The temperature dependence of dynamic modulus (E') for random coil, α-form, and β-form of silk fibroin film was measured. Below 100°C, E' decreased with increasing temperature. This is probably due to the evaporation of water contained in the samples. Above 150°C, E' decreased. The decrease may be caused by molecular motion of the main chains or by the partial decomposition of silk fibroin. E' for silk fibroin in the random coil conformation increased around 180°C. This increase is considered to be due to the crystallization of the silk fibroin. For the degummed silk, raw silk, and silk gut, E' decreased slowly up to about 160°C. The loss tangent increased slowly up to about 100°C, being due to the evaporation of water in the random coil, α-form, and β-form samples. The random coil sample showed a dispersion peak at around 180°C, which is caused by the crystallization of silk fibroin. The loss tangent increased in α-form and β-form samples at 150°C. This is caused by the molecular motion of main chains or the partial decomposition of silk fibroin. For the degummed silk, raw silk, and silk gut, a dispersion peak was observed at 265, 265, and 250°C, respectively. The decomposition peak in DTA curve appeared at 290, 294, and 296°C for the random coil, α-form, and β-form, respectively. For the random coil, the exthothermic peak appeared at 218°C, which is caused by β-form crystallization. The decomposition peak in the raw silk, degummed silk, and silk gut appeared at 376, 393 and 310°C, respectively.
The hydrostatic extrusion of several polymer samples, i. e., polyethylene, polypropylene, nylon 6, polycarbonate, polytetrafluoroethylene, polyoxymethylene and poly (4-methyl-1-pentene), was studied employing a 500 ton hydrostatic extrusion press whose maximum extrusion pressure is 15000kg/cm2. Preliminary attempts were made to extrude polymer melt by this hydrostatic extruder. A billet of polyethylene (15mm in diameter) and the pressure medium (castor oil) were pre-heated to 110°C to facilitate the melting of polymer at extrusion. It could be assumed that the preheated polyethylene would become molten due to the heat evolved during extrusion. The billet was extruded under a pressure of 7500kg/cm2 through a die hole 1mm in diameter. The extrusion ratio was as large as 225, and the shear stress was about 2×109 dynes/cm2. The extrudate was granular and no continuous product was obtained. It was postulated that the extrudate was kept in a molten state for a considerable long period of time after extrusion because of the depression of the melting point due to extrusion. Extrusion under a pressure of 3000kg/cm2, using a die with a hole 2mm in diameter, gave a melt-fractured product. Extrusion experiments are being continued to eliminate the factors hindering stable extrusion. The relation between the extrusion pressure P and the extrusion ratio R in the hydrostatic extrusion of polymer solids can be given in a manner similar to metal extrusion by P=alnR+b where a is the slope of the P vs. lnR plot and thus gives a measure of the increase in pressure required for an increase in extrusion ratio and b is a constant characteristic of the sample. Values of a for the polymer samples were compared with those for metal samples. The a-value of polyethylene is near that of aluminum, while the a-value of nylon 6 is similar to that of copper. However, the polymer samples have only limited ductilities, and there is no definite relation between a-value and ductility. Nylon 6, having a comparatively large a-value (3.77 tons/cm2), is much more ductile than polytetrafluoroethylene with a smaller a-value (0.85 ton/cm2). The production of cracked or fractured extrudates of polymers would be due to the swelling in radial direction and various irregular deformations during extrusion. In other words, the viscoelastic behavior of polymers is responsible for the abnormal extrusion. The P vs. ΔV/V plots of polymers are generally time-dependent and it was found that the compression curve in the equilibrium state is markedly different from those obtained at any finite rates of compression. On the contrary, no time-dependent effect was observed in the compression of molten n-paraffin. The plot in the equilibrium state and the plots at any rates of compression overlapped perfectly with each other. The polyethylene sample obtained by hydrostatic extrusion displayed a uniaxial orientation, but no indication of selective uniplanar orientation was found at the surface of the extrudate. This is very different from the structure of samples made by the cold-extrusion method which, like metal extrusion, gives extrudates with uniplanar orientation. To prevent radial expansion on extrusion, the polymer was enclosed in a thick-walled sheath of metal and then subjected to hydrostatic extrusion. The metal-clad billet of polymer thus prepared yielded a satisfactory extrudate at an extrusion ratio at which the bare polymer billet gave a fractured product. The sample of polypropylene made from aluminum-clad billet at an extrusion ratio of 6.83 under a hydrostatic pressure of 3700kg/cm2 showed a higher transparency and a higher density than the ordinary sample.
The flow characteristics of a general purpose polystyrene (PSGP: Styron 683) mixed with 20 and 30wt% short glass fibers (diameter=10μ, length=ca. 3mm) are compared with those of PSGP itself. The flow characteristics of a base polymer (BP) composed of 50wt% of a general purpose polystyrene (PSGP: Dialex HF55-344) and 50wt% high impact polystyrene (HIPS: Dialex HT88) and, mixed with 1, 5 and 10wt% short vinylon fibers (diameter=ca. 20μ, length=ca. 3mm) are compared with those of the base polymer itself. It is especially interesting that the non-Newtonian flow behavior index decreases for the glass fiber mixed polymer while it increases for the vinylon fiber mixed one. This is probably due to a difference of the flexibility of the mixed fibers.