Takuji Yamaguchi

Inverse Transformation of the Schapery's Superposition Principle for Nutting Model

The constitutive equation of Schapery, which describes the stress in terms of strain history under uniaxial deformation, is transformed into an equation for expressing the strain with the aid of the method of undetermined coefficients and multipliers. For simplicity, it is assumed that the relaxation modulus is proportional to some powers of time and strain (Nutting model). The functional form of strain equation as well as the coefficients and multipliers are assigned so as to express stress relaxation and creep rigorously. The derived equation has a modified form of another equation of Schapery, which describes the strain in terms of stress history under uniaxial deformation. The obtained equation can be used to predict the strain under the continuous and monotonous stress history, for example loading at constant stressor strain-rate. However, if the stress history or its derivative has discontinuity, such as in two step stress-relaxation (creep) and stress relaxation after stop of slow loading, the equation fails to express the strain at a given time.

EFFECT OF DRAW RATIO ON NONLINEAR VISCOELASTIC BEHAVIORS OF DRAWN LOW DENSITY POLYETHYLENE FILMS

The one-step stress relaxation and stress-strain curve (s-s curve) under a constant rate of elongation are measured for drawn low density polyethylene films in the nonlinear strain range at 20°C, and effects of the draw ratio on the behavior are investigated.Stress relaxation of films at low draw ratios D=1.2_??_2 is remarkable and the rate of stress relaxation decreases with increasing strain. For undrawn (D=1) and highly drawn films (D=3_??_5), the stress relaxation is slight compared with films at low draw ratios, and the rate of stress relaxation is nearly independent of strain. Therefore, the relaxation modulus of undrawn and highly drawn films is factorized into time and strain factors, but at low draw ratios this is not the case. However, master curves of films at low draw ratios from time-strain reduced model (model III) are also not so smooth as that of highly drawn films.Generally, the nonlinearity of drawn films in the stress relaxation is weaker than that of undrawn films. Relaxation modulus at each strain decreases at initial drawing and then rapidly increases with increasing draw ratio.The s-s curves of highly drawn films at low strain rates are nearly linear. As strain rates become high, deviation of the s-s curve from linear theory increases. Generally, the calculated s-s curves from superposition principle of model III agree with the observed curves. However, the calculated s-s curves of highly drawn films at low strain rates, are lower than the observed curves, because non-linearity in calculation is overestimated in spite of nearly linear in the observed s-s curves. At high strain rates the calculated s-s curves of films at low draw ratios are greater than the observed curves. The causes of this result are considered as follows: (1) neglecting effect of strain rate on non-linearity in calculation, (2) numerical error introduced by calculation from extrapolated master relaxation curve.

EFFECTS OF TEMPERATURE AND STRAIN RATE ON THE TENSILE BEHAVIOR OF POLYETHYLENE FILMS

Stress-strain curves for polyethylene films have been measured at various temperatures from 20 to 100 C under different rates of extension over a range of 3.5 decades. Applicability of different superposition principles (model I, II and III) defined in the previous paper to non-linear stress-strain curves has been investigated.Generally, non-linearity in stress-strain curve decreases with increasing temperature and increased with increasing strain rate. The non-linearity of low density polyethylene is weaker than that of high density polyethylene.Seemingly, effects of time t and strain e on stress σ are factorizable so that the secant modulus K (t, e)=σ (t)/e equals f (e) H (t). Therefore the master curve of log K reduced to any strain e0 can be composed by only vertical shift in log K-log t plots, However, the relaxation modulus at 1% strain calculated from the equation Er (t, e)=K (t, e) [1+(dlog K (t, e)/dlog t)] does not agree with the observed values in the previous paper. Therefore, the superposition principle of model I is not applicable to the case of a constant rate of elongation for polyethylene.In the theory of model III, if the reduced factor ae (e) for master relaxation curve satisfies certain conditions, the master curve of secant modulus can be composed and log ae (e) is obtained from the following equation: where log be, is the horizontal shift factor for the master curve of log K. But the calculated values from above equation do not agree with observed values in the previous paper. Then stress-strain curves are directly calculated from the superposition principle. Generally, the predicted values from model III agree with observed curves compared to other models. However, appreciable differences between theory and experiment exist at 60_??_80°C as the strain rate increases. The cause of this disagreement is to be sought in neglecting the effect of strain rate on non-linearity in calculation.Master curves of the secant modulus at each same strain reduced to 20°C are composed by only horizontal shift. Temperature dependences of shift factor log aT are qualitatively similar to those of log aT used to compose master relaxation curves in the previous paper. However, apparent activation energies are unreasonably large as compared with the prevailing data.

A Study on the Weldability of Fiber Glass Reinforced Polyethylene (Part 1)

In the previous report, an experimental study of the molding properties of fiber glass reinforced polyethylene was described. The present report explains the weldability of fiber glass reinforced polyethylene by ultrasonic welding.Fiber glass reinforced polyethylene used for experimental study had a low density polyethylene as the matrix, random mat of glass fiber as reinforcing agent.Ultrasonic welder used for this experiment was made by Seidenshiya-Denshi-Kogyo Co. Ltd., its frequency being 20 KHz and power 1000W. Ultrasonic welding seems to be made in the following way. Bonding surfaces of the to plastics were placed close to each other to the extent of bonding free among polymer being influencial by heat softening melt phenomena caused by ultrasonic vibration of plastics. That is to say, ultrasonic heating effect is considered to be initiated both by heat, due to internal strain caused by compressive vibration, and by crashing effect, due to heat only near the bonding surface caused by the strong stress of surface introduced by crashing between the little gap of bonding surface. We continued the experiment under the assumption that polyethlene bonding at the fiber glass reinforced polyethlene boundary surface proceed by heat from the inner parts of plastics caused by ultrasonic vibration and by heat of the surface, and that the caolscence is made in accordance with the progress of mutual diffusion of glass fiber caused by static load.The following summary can be made from the results of the present experiment. Ultrasonic welding produced good results when glass content was small. Good weld had nearly the same strength of fiber glass reinforced polyethylene base material, by the mutual diffusion of glass fiber.

A Study on the Weldability of Textile

Conventional sewing process has been one of the hindrances in development of textile gathering materials as industrial materials.Synthetic fiber, most of which are of thermo-polymer, has made startling progress recently; hence there is a possibility that the conventional cutting and sewing processes are replaced with melt-cutting and welding processes.This report treats weldability and comments on microstructure and macroproperties of the weld achieved by ultrasonic welding method on flat woven cloth of 6-nylon as textile gathering materials, whose fineness was represented by 912 denier warps and 895 denier woofs, while density was 28 warps and 29 woofs per inch. In other words, (i) relationship between welding conditions (welding pressure, ultrasonic acting time) and strength of the weld;(ii) relationship between shape of the weld (shape of anvil) and welding joint strength;(iii) relationship between heat effect by X-ray diffraction and change in microstructure of the nylon woven cloth;and(iv) change in structure of woven cloth at the section of the weld, as observed by microscope are discussed in the report, and possibility of weld of textile gathering materials is looked for.The following summary can be made from the results of the present experiments. The possibility seems to have been found out to weld the nylon cloth, maintaining the properties as fiber and, obtaining necessary.The weld done with the type V anvil has stable structure and higher strength at the place of the weld.