Doi and Edwards (DE) proposed that the relaxation of entangled linear polymers under large deformation occurs in two steps: the fast chain contraction (via the longitudinal Rouse mode of the chain backbone) and the slow orientational relaxation (due to reptation). The DE model assumes these relaxation processes to be independent and decoupled. However, this decoupling is invalid for a generalized convective constraint release (CCR) mechanism that releases the entanglement on every occasion of the contraction of surrounding chains. Indeed, the decoupling does not occur in the sliplink models where the entanglement is represented by the binary interaction (hooking) of chains. Thus, we conducted primitive chain network simulations based on a multichain sliplink model to investigate the chain contraction under step shear. The simulation quantitatively reproduced experimental features of the nonlinear relaxation modulus G(t,γ). Namely, G(t,γ) was cast in the time-strain separable form, G(t,γ)=h(γ)G(t) with h(γ)=damping function and G(t)=linear modulus, but this rigorous separability was valid only at times t comparable to the terminal relaxation time, although a deviation from this form was rather small (within ±10%) at t>τ(R) (longest Rouse relaxation time). A molecular origin of this delicate failure of time-strain separability at t∼τ(R) was examined for the chain contour length, subchain length, and subchain stretch. These quantities were found to relax in three steps, the fast, intermediate, and terminal steps, governed by the local force balance between the subchains, the longitudinal Rouse relaxation, and the reptation, respectively. The contributions of the terminal reptative mode to the chain length relaxation as well as the subchain length/stretch relaxation, not considered in the original DE model, emerged because the sliplinks (entanglement) were removed via the generalized CCR mechanism explained above and the reformation of the sliplinks was slow at around the chain center compared to the more rapidly fluctuating chain end. The number of monomers in the subchain were kept larger at the chain center than at the chain end because of the slow entanglement reformation at the center, thereby reducing the tension of the stretched subchain at the chain center compared to the DE prediction. This reduction of the tension at the chain center prevented completion of the length equilibration of subchains at t∼τ(R) (which contradicts to the DE prediction), and it forces the equilibration to complete through the reptative mode at t≫τ(R). The delicate failure of time-strain separability seen for G(t,γ) at t∼τ(R) reflects this retarded length equilibration.
Damping functions of entangled polymers for shear, uniaxial, biaxial, and planar deformations, as well as normal stress ratios for shear deformations, were obtained from Brownian simulations making use of the primitive chain network model. To investigate the effect of the force balance over the entanglements and of the convective constraint release mechanism, comparisons with predictions of earlier theories and with experimental data in the literature were performed. It was found that the obtained damping functions are close to the three-chain theory [Marrucci, Greco, and Ianniruberto, Macromol Symp, 158, 57 (2000)] suggesting that the force balance is a dominant correction over the basic Doi-Edwards theory as compared with the effect of convective constraint release. Furthermore, the predicted normal stress ratio in shear, i.e., a quantity very sensitive to the different assumptions, is in good agreement with experiments, suggesting that the combination of force balance, convective constraint release, and other relaxation modes, as accounted for through the primitive chain network model, is quite acceptable.
In general, clothing pressure is measured using a sensor set on the surface of a human body or dummy, and it is not possible to measure clothing pressure without the sewing process. We have developed a numerical-analysis-based technique to simulate clothing pressure without having to sew the cloth into clothes. We presupposed that clothing made of knitted fabric was applied to a mannequin in close contact with its surface. Based on this simulation, this paper proposes a model for fabric deformation, by extension applicable to large deformation, with anisotropy and non-linearity taken into account. In this model, the fabric is separated into isotropic and anisotropic elements, and non-linearity is assigned to both the isotropic and anisotropic elements. Furthermore, to use this model, we propose a method for fitting the knitted fabric tightly to a human body model while sewing the knitted fabric model reflecting the paper pattern. To prevent excessive extension of the knitted fabric model reflecting the paper pattern during the process of fitting, we adopted the two-step fitting method involving application of the fabric to a temporary human body model (intermediary) followed by its application to a formal human body model. The clothing pressure values calculated with this method were very close to the actually measured values using a rigid mannequin.
In order to solve the problem of the bowing phenomenon in the tentering process of film, the stretching and thermosetting conditions were examined with a poly (ethylene terephthalate) film. The simulated and experimental results confirmed that decreasing or preventing the transmission to the next thermosetting zone of the longitudinal force generated by the transverse stretching, and then restretching the film in the thermosetting zone, effectively reduces the bowing distortion. The following effects were observed ( 1 ) Once the film is cooled after stretching it in a tenter, the different patterns of its deformation behavior can be obtained. The bowing distortion changes remarkably with the temperature of film and the length of the cooling zone. ( 2 ) When the temperature of the cooling zone is not higher than the glass transition point, the effect of the cooling zone in reducing the bowing distortion is at its maximum. The longer the cooling zone is, the less the bowing distortion becomes. However, it becomes almost constant when the length of the cooling zone is at least twice the width of the film. ( 3 ) When the cooling zone is set up between the stretching and thermosetting zones, the bowing distortion is almost independent of the thermosetting temperature.
SYNOPSISThe bowing phenomenon throughout a tenter was experimentally observed with a pilot plant of successive biaxial stretching. The observed results were compared with simulated ones, by which the deformation behaviors of film in a tenter were predicted, with the assumption that the film was homogeneous isotropic, homogeneous anisotropic, heterogeneous isotropic, or heterogeneous anisotropic for a two-dimensional elastic body with an FEM. Comparatively good agreement between the simulated and observed results was obtained for a heterogeneous anisotropic elastic body with an initial mesh, involving in advance a plastic deformation part.
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