Extension of flat films uneven in thickness and lying on the (x, y) plane is analysed mathematically. Constitutive models assumed are isothermal Newtonian fluids and rubber-like elastic solids. Governing equations reduce to the Cauchy-Riemann equations when the material is Newtonian fluid and the film is uniform in thickness. Many unusual modes of extension exist in this case. In both cases of Newtonian fluids and rubberlike elastic solids, governing equations reduce to readily solvable ordinary differential equations when the extension is axisymmetrical. Conditions of wrinkle free extension are introduced. Numerical solutions are obtained for the general extension of the films of rubber-like elastic solids.
The viscosity and viscoelasticity of a molten liquid crystal pitch were investigated by a cone-plate type rheometer at various temperatures. The molten material's viscous behavior was characterized by WLF-type temperature-dependence and pseudo-plastic flow. Furthermore, the material's viscoelastic behavior was marked by two relaxation mechanisms at different angular frequencies. The mechanism with a longer relaxation time was observed in the lower angular frequency. It was presumed that this was due to some higher order structures in the liquid crystal pitch resulted from the dependences of the dynamic storage modulus on the temperature, the shear history and the degree of the heat treatment etc. The other mechanism with a shorter relaxation time, τ, was observed in the higher angular frequency that corresponded to the glass transition. To investigate the effect of τ on the property of carbon fiber, the spinning process of the pitch fiber was simulated. It was found that the Deborah number ND, defined by the ratio of τ to the representative time scale of the spinning process tr, determined the preferred orientation and crystallinity of the pitch fiber and the carbon fiber.
The stress relaxation and simultaneous birefringence variation were measured for bisphenol A polycarbonate over the glassy to the rubbery plateau regions. The measurements were performed at various temperatures of 142 to 156°C over the time range of 0.4 to 2000 s. Results of relaxation measurements were consistent with those of dynamic measurements with respect to the birefringence as well as the stress in the framework of linear viscoelasticity. A modified stress-optical rule was applied to the results of relaxation measurements. This rule was earlier proposed to replace the stress-optical rule which was suitable only in the rubbery and the terminal flow regions. The relaxation modulus, E (t), was separated into two component functions, ER(t) and EG(t). In constructing master curves of ER(t) and EG(t) with the method of reduced variables, their shift factors were found to have different temperature dependence. This result can account for the break down of time-temperature superposition principle for E (t) reported by several investigators. The present modified stress-optical rule was more convenient in several ways compared with the similar modifications proposed earlier by Priss et al. and Read.
Effects of process variables and material properties on melt spinning of pitches have been studied based on simulation using governing equations by Kase and Matsuo. It is shown that the tension F in a filament depends on spinning conditions as well as viscosity of pitch in the form of F∝μ0W1/6ƒ1(v0, vL, vA)/ƒ2 (T0, Ts, TA, E). Here, W, v0, vL and vA are, mass flow rate, velocity at the spinnerette, winding speed and cross-flow air velocity respectively, and T0, Ts and TA denote temperatures at the spinnerette, at the solidification point and of air. Temperature dependence of viscosity is simplified by an Arrhenius type equation with a pre-exponential factor μ0 and a flow activation energy E. To improve spinnability, the maximum tensile stress σL should be decreased by increasing W, T0 and TA or by decreasing vL, vA, Ts, μ0, and E. In other words, slower cooling of the filament with larger diameter for a pitch with smaller activation energy is preferable to better spinnability. Effects of these factors on diameter, temperature and strain rate of the spinning filament are also discussed.
Pulse Strain Method for viscoelastic measurements is presented, which is based on the Raised Cosine Pulse Method (RCP Method). According to the RCP Method, frequency dependence of complex shear modulus is given by the Fourier transform of shear stress as the response to a pulse strain of cosine type. However, frequency range of observation is limited to only 1 or 2 decades in lower region of fundamental frequency of applied pulse strain. To expand the frequency range, we have modified the RCP Method using Rectangular Pulse Strain, which includes high-frequency components (RAP Method). Comparison among the RCP Method, RAP Method and conventional dynamic methods was made on a 20% polystyrene solution in diethylphthalate. In the case of the RAP Method, frequency range was expanded to higher frequencies of fundamental frequency of applied pulse strain compared with the RCP Method. Computer simulation of Pulse Strain Method was made to know the requirements for further expansion of frequency range. The shear stress as the response to pulse strain was calculated for a Maxwell model using the Boltzmann superposition principle, and then complex shear modulus was calculated from Fourier transform of pulse strain and shear stress. The obtained shear modulus from simulation was compared with the theoretical value. It has been shown that resolution and response time of a torque transducer are important to make the best use of Pulse Strain Method. The requirements for a torque transducer are as follows, resolution is 1/10000, and response time is 0.1 ms.
Flow patterns and fiber orientations in the two-dimensional contraction and expansion flows of fiber suspensions are calculated using Dinh-Armstrong model. The assumption that all fibers lie tangent to a streamline is excluded from the present calculation. Therefore the Jeffery's equation is integrated along a streamline to obtain the fiber orientation. The flow pattern of fiber suspension is different from that of Newtonian fluid : a vortex near the corner in the suspension flow becomes larger than that in the Newtonian flow. The dependence of the vortex length on a parameter α, which is a characteristic parameter of fiber suspensions, and on Reynolds number is discussed. In the contraction flow, fibers lie tangent to a streamline in the main flow, but not in the vortex region. In the expansion flow, however, fibers rotate along a streamline, so fibers do not lie tangent to a streamline even in the main flow. Furthermore, stress-relief-mechanism causes increase of the vortex in both flows.
A mechanism of chain slippage across the entanglement link is adopted to describe the early stage behavior in the stress relaxation of concentrated polymer systems. The chain slippage in the postulated mechanism occurs due to the equilibration of natural monomer (Rouse bead) densities between the primitive segmental units. It is shown that the process X introduced by Lin can be confirmed theoretically and that it partially contributes to the reduction of stress discrepancy between the processes A and B of Doi.