The fabrication of final products in sheet plastics are generally performed by means of vacuum and blow forming methods. Now it is considered that if the conventional process for sheet metal press working operations is applied to the forming of sheet plastics, the working cycle will become more efficient, and then it will contribute to the reduction of production costs. In recent years the studies on this subject have been made by some researchers.
The present study deals with the performance of the stretch and deep drawing operations for the hard PVC sheet by means of the similar tooling as is used in sheet metal pressing. For this purpose, first as the fundamental procedure of the forming condtions, several mechanical and forming characteristics were tested, such as the mechanical properties based on the uniaxial tensile testing, the flow and softening properties, using the Koka-type flow tester, the stretch formability, using the Erichsen testing machine provided with a heating unit, and the deep-drawability by means of the cupping apparatus having conical dies.
From the results obtained in these tests, when cylindrical shells are deep-drawn from a flat blank by means of a conical and a flat-formed dies respectively, the maximum successful drawing ratios achieved in a single pressing were examined. In warm press drawing, it was found that the deep-drawability of PVC sheet within the proper forming temperature range from a minimum value of 56°C to about 90°C was preferable. And also, the deformation mechanism in deep-drawing work of PVC sheet could readily be traced in a similar way to the plasticity analysis for sheet metal drawing, then, the forming limit calculated theoretically was shown in satisfactory agreement with the data given by the drawing experiment. In spite of the excellent drawing formabilty, high anisotropy on the radial draw deformation was generated at the cylindrical part, and as a result of the wide allowance of the thickness of PVC sheet the unsteady forming conditions freqently occurred.

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The following conditions that affect the flow properties of blood are discussed in brief from the rheological point of view.
(1) Volume fraction of erythrocytes-hematocrit value: -
The simple Einstein relation between relative viscosity and volume concentration of suspended particles is not valid for blood. The observed relative viscosity is greater than that calculated, owing to the interaction between the erythrocytes and a increase in the effective hematocrit value produced by enclosing and immobilizing of a certain amount of plasma within the collided erythrocytes groups. The asymptotic minimum viscosity of blood is given by a modified Hatschek's equation, over a wide range of hematocrit values.
(2) Temperature: -
The relative viscosity of a disperse system should not be affected by temperature unless the volume fraction and the shape of the dissolved or suspended particle changes. The relative viscosity of blood is, however, affected by temperature. It rises by about 10per cent by decrease in temperature from 37°C to 17°C. This rise is considered to be due to a small increase in the volume of individual erythrocytes, together with a change of shape towards a more spherical and less disc-like form.
(3) Perfusion pressure: -
If the perfusion pressure head is sufficiently large, the rate of flow of blood through a rigid vessel increases in proportion to the increase in the applied pressure head. As the pressure head is lowered, the plotted points indicating the relation between the rate of flow and the applied pressure lie on a smooth curve, which is convex to the pressure axis. The convexily becomes more and more prominent with decrease in the pressure head. Blood, therefore, is not a Newtonian fluid. It will appear to behave as a Newtonian fluid only in the limiting conditions in which the mean shearing stress is quite large and the flow still remains laminar. In order to explain the non-Newtonian flow of blood under low pressure head-the reduction in its apparent viscosity with increase in the shearing stress and rate of shear-the following factors should be taken into account.
(a) Orientation of the erythrocytes. Increase in the rate of shear leads to an increase in the fraction of erythrocytes which are orientated parallel to the flow axis and, as a result, it brings about a decrease in apparent viscosity.
(b) Coherence resistance and marginal slippage layer.“Coherence resistance”between the erythrocytes in addition to the viscous resistance and plug flow of unsheared blood moving down the vessel within a thin, peripheral plasmatic zone under the low pressure head might be responsible for the observed non-Newtonian property of blood. The plasmatic zone is considered to be produced by the wall effect and the axial accumulation of flowing erythrocytes.
(4) The radius of the vessel: -
In a narrow vessel of which radius is less than 300μ, the apparent viscosity of the blood is found to be less than the value observed in larger vessels. The smaller the radius is, the lower becomes the apparent viscosity. This effect (sigma effect) is observed not only in the blood but also in various suspensions in which the suspended particles are large enough to be comparable in size with the radius of the vessel.

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The three components of skeletal muscle fiber, that is, sarcolemma, myofibril and sarcoplasma, different among themselves in their viscoelastic properties, have been separately studied.
A myofibril bundle with properties of living muscle fiber can be separated by removing the sarcolemma of a muscle fiber in liquid paraffine, the smallest sample obtained by this method being about 1μ in diameter.
Myofilaments as thin as 100Å in diameter can be separated by spreading out the myofibril bundle on metal net in air.
The breaking length of a muscle fiber is 180-200% of its resting length, its breaking stress being 0.5∼5×10⁶ dynes/cm².
The ratio of initial elongation to creep by load is a function of the load itself, for example, the maximum of the ratio is 3 to 2, the load and the breaking stress being 1.5×10⁵ and 5×10⁵dynes/cm² respectively.
The thermal expansion coefficient (α) of a muscle fiber of M. sartorius of Bufo is -10^-4∼-10^-5, its absolute value being inversely proportional to its birefringence.
The length-tension diagram of a myofibril bundle coincides with that of intact muscle fiber, as far as the extension is less than 140% of its resting length.
Concerning the time course of creep by loading and the thermo-elasticity, the myofibril bundle and the single muscle fiber resemble each other.
The striated pattern with periodical intervals of about 100Å can be electronmicroscopically observed in the separated myofilament in its resting state.
This periodical intervals increase to 170% of that in its resting state, when the myofilament is extended.
The viscoelasticity of muscle has been discussed on the basis of the results mentioned above and the relevant references.

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The crystalline lens of human eyes plays a major role in their accommodation. It has long been believed that the lens is of an elastic material. This elasticity has been one of the bases of the accommodation theory.
According to Kikkawa and Sato (1963) and Fukuda (1963), the lens is of a viscoelastic material. This conception of the properties of the lens is, however, does not hold with the capacity of human eyes for fast accommodation that is ca. one second. Their observation is quasi-static, their time scale of observation being minutes and hours. So it is more adequate to investigate viscoelastic property on shorter time scale, that is dynamic property, to know the deformation characteristics of the lens.
The viscoelastic property of the crystalline lens has been investigated with a dynamic rheometer (Fukada and Date 1962, manufactured by the Rion Co. Ltd). The elastic modulus and loss tangent of crystalline lens are dependent on the frequency of oscillation and the temperature. There is no large difference between the dynamic property of 0.01cps and 1cps, indicating that the dynamic property of the lens cannot explain human accommodation (Itoi et al., unpublished data).
The deformation process of the human crystalline lens in vivo during the accommodation has been traced with ultrasound echogram and phacometry.
The lens showed viscoelastic characteristics, its stress time curve have shown creep and elastic after-effect. The retardation time was very short as compared with that of lens in vitro. Mizukawa et al. (1960) investigated the accommodation process precisely with their Accommodometer, and found that the refracting power (diopter) of the crystalline lens was a function of time. The dipter-time curve of the lens closely resembled the stress-time curve of any viscoelastic materials, with apparent creep and elastic after-effect (Nakabayashi et al., 1963). Their results are in good accordance with our results obtained from the ultrasound echogram and phacometry.
The source of the difference of rheological property of the lens between in vitro and in vivo is not clear.

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On the basis of our studies of the mechanochemistry of muscle protein actin, a model is proposed for the motile protein filament. The model consists of a large number of structural units and assemes a straight form, (F)_n, in its stable state. When the filament is subjected to a bending moment, it is bent at one position as a result of the partial breakage of a unit i, F_i→f_i. It is assumed that the reformation, f_i→F_i, takes place impulsively through a process which accompanies an irreversible chemical change in the medium. The active transformation, f_i→F_i, will induce a partial breakage F_j→f_j at another position, because the rapid reformation of the bent filament must be subject to a large viscous friction. It is assumed that, due to the polarity of the filament, the partial breakage, F_j→f_j occurs in a definite direction, j=i+1. The bent will propagate on the filament with the consumption of chemical energy.
A simple hydrodynamic analysis is made for such a motile protein filament in a viscous medium. The calculation is made according to Gray and Hancock. Three typtcal examples are treated; (a) The filament is fixed at one end and bent propagates from the base (b) the filament takes a form of regular polygon, and (c) the filament placed free in the medium.

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The apparatus used in experiment for the present study is a graduated glass tube closed at its top with its bottom end provided with two syringe needles held vertically. A negative pressure has been given through a glass tube by releasing a compressed rubber ball which is joined to the upper side of the tube. The air and the liquid to be tested are drawn in through the top and bottom capillaries respectively into the glass tube. The volume of the liquid thus drawn in measures the value of viscosity.
The formula representing the relation of viscosity and the volume of the liquid drawn in has been determined. In practice, however, the relation has been experimentally determined by measuring the silicone oils with known viscosity. In the present apparatus the diameter and length of the upper capillary is 0.42 and 43mm, and the corresponding quality of lower capillary is 0.67mm and 78mm. The volume of the rubber ball compressed is 18cm³. The diameter and length of graduated glass tube are 4.6 and 65mm.
A range of viscosity from 0.8 to 6.0 centipoise has been covered by this viscometer. The range of viscosity is varied by a suitable choice of dimensions of capillaries. The liquid rises to a certain level and then falls down due to the gravity. The highest level attained is used as the measure of viscosity in the above described calibration curve. The time for liquid flow until the highest level is around 5 seconds.
The difference in density between blood and silicone oil produces only 4% error in the value of viscosity. The correction for the kinetic energy is about 3%.
The error in reproducibility for the repeated measurements is about 1%. The rate of shear in the capillary wall is about 2×10³ sec^-1, which is in the same order as that for the actual blood flow in vessels. The volume of liquid required is only 0.3ml and the measuring time is less than 10 seconds.
The viscosity of whole blood as a function of hematocrit and the viscosity of plasma as a function of protein content have been studied at a temperature of 37°C. The relation between the viscosities of whole blood and plasma and sedimentation rate has been investigated for a number of specimens of human blood.
The viscosity of venous blood in a dog has been measured in vivo by inserting the pointed end of capillary of viscometer into the jugular vein where the intravenous pressure is almost zero. The variation of viscosity of blood in vivo with the injection of aqueous solution of glucose has followed.

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When one makes erythrocyte counts in blood, one may observe irregular darkbright stripes like a gossamer-“Schlieren-effect”-in a mixer. This peculiar phenomenon led us to make experiments to ascertain whether light transparency will change or not according to the state of the erythrocyte suspensions being resting or flowing when light is projected on them. We have found that the transmitted light is more intensive in the flowing state than in the resting state, and one of us (Kuroda) has called this phenomenon“streaming transparency.”
The apparatus for measuring the streaming transparency consists of a Beckman photoelectric spectrophotometer of direct reading type and a chamber with a rotating vessel attached to it, as shown in Fig. 1. The rotating vessel is made of glass and is cylindrical, 8cm in diameter and 1cm in height, as shown in Fig. 2. In the center of the vessel is a glass rod with a small propeller, which is connected with an electric motor with a belt. The erythrocyte suspension is placed in the rotating vessel, and the attenuance (optical density) of the suspension is read at rest and in flow.
The term“degree of streaming transparency”, which is introduced to express the streaming transparency quantitatively, is given by the difference between the attenuance of the resting erythrocyte suspension (A) and that of the flowing erythrocyte suspension (A').
Degree of streaming transparency=A-A'.
The degree of the streaming transparency of the erythrocyte suspension approaches zero when this erythrocyte is completely spherical, while the degree of the streaming transparency becomes larger when the shape of the erythrocyte deviates from the sphere (Tab. 1).
As shown in Fig. 5, the degree of the streaming transparency is remarkably increased with the increasing concentration of erythrocytes. However, at higher concentrations of erythrocytes, the degree of the streaming transparency decreases and becomes negative. This phenomenon, which shows that the light intensity transmitted through the erythrocyte suspensions is smaller in flow than at rest, is termed the“negative streaming transparency.”,
As shown in Fig. 4, at long wave-lengths the degree of the streaming transparency is positive and high and it drops with decreasing wave-length. At 430mμ it is equal to zero, it is negative in the region of Soret band and at shorter wave-lengths it becomes positive again. Fig. 3 shows the light absorption curve obtained with bovine erythrocyte suspension, in which case the absorption band of hemoglobin appears more remarkable in flow than at rest.
In order to explain the cause of the streaming transparency of the erythrocyte suspension, the orientation of erythrocytes in the suspension is first to be considered. Essentially, mammalian erythrocytes are biconcave disc-shaped, and they are distributed in random directions at rests, but when the suspension is allowed to flow in a certain direction, the erythrocytes are arranged in such a direction of to offer the least resistance against flow (Fig.6).
The cause of the streaming transparency may be attributed to the orientation of erythrocytes in flow in such a direction as to take the least resistance against flow, and this streaming transparency is regarded to be in a close relation with the shape of the suspended erythrocytes, the degree of the streaming transparency being zero in the case of spherical erythrocytes. The negative streaming transparency observed is also explained from the light absorption effect and the light scattering effect due to the special orientation of erythrocytes in flow.
The phenomenon of dark and bright stripes of the flowing erythrocyte suspension is considered to be similar to the Schlieren-effect of colloidal solutions. However, streaming transparency is observed, not only in the erythrocyte suspension, but also in suspensions of non-spherical cells

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Pure glyceryl tristearate was prepared as solid fat particles by complete hydrogenation of olive oil, and pure glyceryl trioleate was prepared as liquid oil by solvent fractionation of olive oil.
The rheological properties of mixtures of these two components were investigated in comparsion with their microstructure revealed by X-ray diffraction. The flow curves of various mixtures were measured by a Weissenberg rheogoniometer and the temperature dependence of viscoelasticity was studied by an forced oscillation apparatus. Two kinds of specimen were prepared. One is a suspension body, that is, simple mixture of triolein and tristearin which is uniformly mixed by stirring it with a glass rod at room temperature, and the other is a molten body, that is, the mixture of tristearin and triolein which is molten at 90°C and recrystallized at 0°C. In each mixture the fraction of tristearin is from 5 to 45% by weight.
All the flow curves for mixtures of 5 to 25% tristearin were typically non-Newtonian. From the relation between the apparent viscosity η and the rate of shear γ, the shear rate dependence of viscocity -(d logη/d log γ) was calculated at a high rate of shear 20sec.^-1 and at a low rate of shear 1 sec.^-1. From the relation between the fraction of tristearin and -(d log η/d log γ), it was observed that the shear rate dependence of viscosity was much larger for the suspension body and at a lower rate of shear. These results suggest that a firm texture is developed in the specimen after the melting of suspension due to the formation of network structure of crystallites of tristearin.
The temperature dependence of dynamic elastic modulus E^* and loss factor tan δ has been measured for mixtures of 25 to 45% tristearin. It has been found that the mixtures of 25 to 40% tristearin show entropy elasticity, that is, the elastic modulus increases with the rise of temperature and that on the other hand, a 45% tristearin mixture shows energy elasticity, that is the elastic modulus decreases with the rise of temperature. It is reasonably assumed that a network structure having crosslinked molecular chains such as exists in rubber in the present mixtures. A number of small crystallites of tristearin would produce the crosslinking points. The molecular weight between crosslinks was tentatively calculated from the elastic modulus at room temperature using Kuhn's theoretical equation for rubber elasticity and found to be in the same order with the molecular weight of tristearin and triolein.
The variation of E^* and tan δ was followed during the heating and cooling at a fixed rate for the same samples. Heat treatment profoundly alters the physical properties of mixtures. After a cycle of heating and cooling, E^* at room temperature increases and tan δ decreases. Observation by X-ray diffraction shows that the degree of crystallinity increases slightly after the heat treatment and also that the habit of crystals changes from β type to β' type. It is seen, however, that log E^* increases almost linearly with the degree of crystallinity for both β and β' types, and that these two lines are almost parallel in the range of crystallinity investigated less than 40%. The value of tan δ is largest at the fraction of tristearin 30 to 35 percent where the rubber-like property is observed most obviously.
The results for the present mixtures where the melting temperatures of two components are far apart would give some useful knowledge to consider the physical properties of more complicate mixures of oils and fats. The network structure formed by the small crystallites and the mobile molecules between them crosslinked by these crystallites would give an interesting model for ellucidating the mechanical properties of ordinary fats.

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The static viscoelasticity and consistency of several processed and natural cheese (Gouda and Cheddar) were measured by means of four kinds of rheometer or consistometer, i.e. parallel plate viscoelastometer, cone-penetrometer, micro-penetrometer and sectilometer.
From the analysis of the results by means of the four-element mechanical model, we obtained the instantaneous elasticity (E₁), retarded viscosity and elasticity (η₂, E₂), flow viscosity (η₃) and retardation time τ for cheese, respectively. The viscosity of cheese ranged from 10⁷ to 10⁸ poises, the shear rigidity ranged from 10⁵ to 10⁶dynes/cm² and the retardation time ranged from 200 to 500sec, at room temperature.
In the cases of viscoelastometer by shear creep and micro-penetration method, both the logarithmic relation between the creep compliance J (t) and the time scale t could be reduced to a master creep curve by the shift along the axis of time scale at the temperature ranging from 5 to 45°C. It is seen, therefore, that the cheese has the behavior of rubbery elasticity and is thermorheologically simple in the narrow range of temperature.
The yield value can be obtained for the same cheese by using a cone-penetrometer which has cones of various angle and weights. The yield value of cheese is about 2×10⁵dynes/cm² at 29°C and is constant independent of cone angle or weights. Cone-penetrometer and sectilometer can not measure the elastic constant, but are useful for measurements of consistency of cheese. Under a certain condition of measurement, both the logarithmic plots of the degree of sectility P_s and micro-penetration P_m are represented by a straight line.

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In order to ascertain the workability of the coating films adhering to a metal-plate, the impact wedge bending test and the cup punching test were carried out with the same specimen at room temperature. During the course of those tests, a great deal of force acting upon the test specimen is produced in the metal-plate, whereby deformation results, and hence it seems most reasonable to conclude that the rupture of the coating films in the case of those tests may be due to their strains produced. The strains of the thin coating films, produced by those tests, are equal to those of the surface of the metal-plate. The results of the two tests were treated by means of dynamic analysis for the strains produced. Thus those two methods of test can be used for the coating films which have the tensile-strain of rupture under 50% limit.
While the impact wedge bending test produces simple tensile strain for the coating film, the cup punching test, on the other hand, simultaneously produces tensile strain in the radius direction and compressive strain in the circumferential direction of the cup, and the magnitudes of those strains at any point of the cup are equal but of opposite signs with each other.
As the results of this analysis, we have found that the ratio of ε_r/ε_t is 1.7∼2.1 for the coating films of phenol resin-epoxy resin-polyvinyl butyral system, where ε_r and ε_t are the limit of the tensile-strains of rupture at the impact wedge bending test and at the cup punching test, respectively. To explain this result, the stress-strain relation of the coating films is treated as an analogous one in the case of an isotropic elastic-body, because at those tests all the cross sections of the broken coating films are perpendicular in respect to the direction of the tensile strain produced, and show a typical pattern of brittle rupture of polymeric materials. Denoting the ratio of the limit of tensile-strains of rupture by y, we can get the following equation:
Y=ε_r/ε_t=2(μ/λ+1)/2(μ/λ+1)+a'
where λ and μ are the constants corresponding to Lamé constant of coating films, a is the ratio of the strains of circumferential direction to the strain of radius direction at two-dimensional deformation, thus a in the case of the cup punching test becomes -1. Assuming Poisson's ratio of the coating films to be ranging from 0.3 to 0.48, an example of applicability of the above equation indicates that y-value becomes ranging from 1.43 to 2.0. From the check described above, a better approximation for y-value is obtained by the use of this equation, although there is no more detail to support that the dynamic equations of an isotropic elastic-body may be used in this case too. Therefore, it appears to be of interest to investigate further the dynamic behavior of the thin coating films adhering to the metal-plate.

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The dependence of the peeling strength on the peeling rate is treated in this paper rheologically. First we showed experimentally that the time-temperature superposition principle is applicable to the S-type curve of the peeling strength vs, the rate for the amorphous polymer films (Vinylite) of various plasticizer (DBP) contents above glass transition temperature (T_g). The dependence of the shift factor a_T on the temperature obeyed the W. L. F. equation giving reference temperature T_s considerably lower than T_g+50^°, where T_g is measured dilatometrically. This means that the fractional free volume at T_g is larger than 0.025, in our case showing 0.037. This discrepancy is explained by the theory of Ferry and Stratton on the increase of fractional free volume due to the extension of polymers of Poisson's ratio less than 1/2. The apparent activation energy at T_s evaluated from the dependence of log a_T on temperature, are 46.5-33kcal/mol for samples of plasticizer contents 0-40%, which are reasonable values for the viscous flow of the polymer segments. From these experimental results we conclude that the dependence of the peeling strength on the rate is substantially rheological in character, and that the course of peeling is not governed by the electrostatic mechanism as proposed by Deryagin et al.
Secondly, we derived a theoretical formula relating to the peeling strength to the rate of peeling in adhesive tapes, assuming that the adhesive layer is deformed locally only at the peeling end, and its rhelogical behavior is described by the simple Voigt model. It is also assumed for simplicity that the shape of the bend at the peeling end is regarded as a part of a circle of radius R, which is determined by the peeling force P as R=√E_oI/P, and that the deformation is vertical to the adherend surface. If the peeling proceeds steadily with velocity v, we may represent the initial and proceeding stage after time t of peeling with two circles whose centers are at (O, R) and (vt, R). Then the elongation of the adhesive layer at the origin, y, is given as a function of v, R, and t, with its time derivative, dy/dt, as a function of v, R, and y. Introducing this into Voigt's equation and integrating the equation dW=fdy from f=0 to f=f_b where f_b means the critical surface force, we obtain work of deformation, W_d, at the adhesion break. In the work of deformation, elastic energy W_e must be reserved. Put W_d'=W_d-W_e, then the sum of W_a, work of adhesion, and W_d' equals to the work done by the applied force, that is W_a+W_d'=P(1-cosθ), where θ is peeling angle. Carrying necessary calculation with some reasonable approximations, we obtain the following equation in the case of L-peeling (θ=π/2),
P-C₁P^1/4v+C₂P^1/2v²=W_a,
C₁=2√2h^1/2/3(E_oI)^1/4·(f_b/E)^3/2η,
C₂=2/(E_oI)^1/2(η/E)²f_b,
where E_o is Young's modulus of polymer film which determines the curvature at the peeling end, I, its moment of inertia, h, the thickness of the adhesive layer, η and E, viscosity coefficient and Young's modulus of the adhesive. This equation represents well the S-type curve of logP vs.

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The investigation of the variation problem in mechanical systems has two purposes. One of them is to find out the variation principle as a fundamental principle of mechanical system, and the other is to build up a technique of obtaining an approximate solution of the equation of motion. In the case of the conservation system, these two viewpoints fortunately stand together. In the case of viscoelastic material, on the other hand, it is not possible to make the variation problem as the basis of mechanics. In fact, since the stress in such a system is not the conserving force, we cannot get the variation function in a closed form. However, making use of a suitable technique for the variation of the parameters, we have been enabled to establish the variation method, on the basis of the so-called Hamilton's principle of mechanics for the purpose of finding the approximate solution of the equation of motion.
Hamilton's principle in our case is written as
∫_t∫_v[1/2ρδr²-Sp(σ_E·δe_E)+ρK_E·δr]dtdV+∫_t∫_SF_E·δrdtdS=0
in the Euler form, and
∫_t∫_V0[1/2ρ₀δr²-Sp(σ_L·δe_L)+ρ₀K_L·δr]dtdV₀+∫_t∫_S0F_L·δrdtdS₀=0
in the Lagrange form. Here σ is the stress tensor, e the strain tensor (=a⁺·a/2 in Lagrange system, a: the displacement tensor), ρ the density, K the volumic force acting on the unit mass of the sample, and F the surface force acting on the boundary of the sample.
In further treatment, we must use a suitable model describing the mechanical behavior of the sample. In the viscoelastic material it is supposed that there exists energy-storing mechanism as well as energy-dissipative mechanism. For each mechanism we suppose the displacement tensor and the stress tensor, a₁ and σ₁, and a₂ and σ₂, respectively, in addition to the observable ones, a and σ. As the viscoelastic model, we define the three dimensional Voigt model by the relation (in E-system)¹⁾
a=a₁=a₂ and σ=σ₁+σ₂,
and the Maxwell model by
δa·a^-1=δa₁·a₁^-1+δa₂·a₂^-1 and σ=σ₁=σ₂.
Introducing the stored energy density w(e₁), we have the following variation functions:
a) The Voigt model.
I_E^(V)=∫_t∫_V[1/2ρr²-W_E(e)-Sp[(a^-1·σ_{E, 2})_c·a]+ρK_E·r]dtdV-∫_t∫_SF_E·r dtdS
in E-system, and
I_L^(V)=∫_t∫_V0[1/2ρ₀r²-W_L(e)-Sp[(σ_{L, 2})_c·e_L]+ρ₀K_L·r]dtdV₀-∫_t∫_S0F_L·r dtdS₀
in L-system.
b) The Maxwell model.
I_E^(M)=∫_t∫_V[1/2ρr²-W_E(e₁)-Sp[(a₂^-1·σ_E)_c·a₂]+ρK_E·r]dtdV-∫_t∫_SF_E·r dtdS

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Assuming that the elastic displacement of a material particle is expressible by the displacement from θ_eⁱ to Θ^j in general curvilinear coordinate system or that from x_eⁱ to Xⁱ in Cartesian coordinate system, the contravariant component of the elastic strain tensor will be defined by
ε^ij=1/2(∂Θⁱ/∂x_e^α∂Θ^j/∂x_e^α-∂Θⁱ/∂Xβ∂Θ^j/∂Xβ) (1)
The contravariant component of the actual strain rate tensor will be given by
f^ij=1/2(V^i/j+V^j/i) (2)
where Vⁱ represents the contravariant component of velocity vector and V^i/j denotes the contravariant differentiation of Vⁱ by Θ^j.
We assume that the stress tensor τ is a function of both the elastic strain tensor ε and the actual strain rate tensor f, and may be expressible as a polynomial in ε and f. If the material is isotropic in its rest state, this relation must be invariant to the transformation of the coordinate system. Then, considering the symmetric property of τ, the relation will be written as follows:
τ=(-P+a₀)1+α₁ε+α₂f+α₃ε²+α₄f²+α₅(εf+fε)+α₆(ε²f+fε²)+α₇(εf²+f²ε)+α₈(ε²f²+f²ε²) (3)
where P is the hydrostatic pressure, 1 is the metric tensor and α₀, α₁, …… α₈ are polynomials of ten invariants such as t_rε, t_rε², t_rε³, t_rf, t_rf², t_rf³, t_rεf, t_rε²f, trεf² and t_rε²f². Considering that the principal axes of ε are equivalent to those of τ but not to f, Eq. (3) will be reduced to
τ=(-p+α₀)1+α₁ε (4)
This equation assures the coincidence of the principal axes of τ with those of ε in every case, but in some cases it may happen that the principal axes of the other term of Eq. (3) become equal to those of τ. In simple shearing flow, such term is α₇(εf²+f²ε). Then, Eq. (3) will be
τ=(-p+α₀)1+α₁ε+α₇(εf²+f²ε) (5)
which may be expressed in terms of the contravariant components of tensors as follows:
τ^ij=(-P+α₀)G^ij+α₁ε^ij+α₇(εⁱ_αf_βαfβj+fⁱ_αf_β;αεβj) (6)
The applications of our theory to simple shearing flow and steady flow through pipe have been made with satisfactory results; especially it has been shown that two normal stresses in the direction perpendicular to the stream are equivalent to each other.

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A new approach to problems of the so-called inter-chain relaxation is presented and the dependence of viscosity of polymer Melts on molecular weight, M, is discussed. In the measurement of steady viscosity, the time scale of observation is generally long. Hence the intra-chain motion with shorter relaxation times will relax almost completely and reach a state of dynamic equilibrium, while the inter-chain relaxation mechanism of longer time scale may still be effective. In the present theorry, each chain molecule is expressed only by the position of its center of mass and its velocity. The intermolecular force between the two molecules is assumed to be the sum of two kinds of force: the one is a force derived from potential like that in simple liquids, and the other is a frictional force due to the entanglements between the two molecules. On the basis of the transport theory of liquids by Born and Green, the general expression of viscosity is derived from the fundamental equation for the velocity distribution function of a molecule. The expression is factorized into some factors such as mutual potential, friction constant.
The M dependence of each factor is roughly estimated under the following assumptions; (i) each chain molecule is composed of N freely orienting segments, (ii) the spacial distribution of segments of a molecule is Gaussian about its center of mass since an applied velocity gradient is very small, (iii) the mutual potential energy between the two segments is approximated by a three dimensional square well potential, (iv) the effective friction constant between the two molecules is proportional to the co-volume occupied in common by them, and (v) the equilibrium distribution function for the two molecules is approximated in a simple form.
In conclusion we obtain the viscosity η as follows:
η=AN+BN³,
where A and B are constants independent of N, and it is expected that A>>B. This theoretical prediction agrees semi-quantitatively with the experiment.

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The investigations about the steady shear viscosity of non-Newtonian flow in concentrated polymer solutions have been reported by Porter et al. and Ozaki et al. Log viscosity versus log molecular weight relations obtained by Porter et al. and by Ozaki et al, are those at constant shear stresses and at constant rates of shear, respectively.
In the results obtained by Porter et al., the slope of log η"log M relation becomes smaller as the shear stress increases in the region of molecular weight higher than a critical value M_c as is shown in Fig. 1.
On the other hand, the slopes of log η"log M relation obtained by Ozaki et al. are 3.4 in the region of molecular weight lower than a second critical value M'_c (>M_c) which depends on shear rate γ₀ and <3.4 (nearly 2) in the region of molecular weight higher than M'_c as is shown in Fig. 2.
Since the concentrated polymer solution spreads a network structure crosslinked temporarily by the entanglement of polymer molecules, it is desirable to make clear the viscosity versus molecular weight relations by making use of the theory of network structure.
In § 2 the linear theory of viscoelasticity of network structure is reported in a reformed formalism. When we consider a polymer molecule in the network structure, the aggregation of the remaining molecules could be considered to be a sort of viscoelastic medium. When a part of polymer molecule between the adjacent crosslinkages termed chain, a chain in a molecule has the viscoelastic effects on other chains in the same molecule through the viscoelastic medium, so that the system corresponds to a model composed of interacting Rouse model. The viscoelastic interactions between the chains in a, molecule. though they seems intra-molecular interactions, are due to the average inter-molecular interactions induced by the motion of the viscoelastic medium. By using the above model we obtain the slip equation (2.17) and the stress (2.2'), where <γ_i> and <D_i> contained in τ_i are viscous and elastic effects in the i-th normal coordinate and are given by (2.19). For continuous distribution of relaxation times, the slip equation and the stress are written as (2.21), which are the expressions in the linear theory.
In order to investigate the non-Newtonian effect on viscosity, the linear theory is extended by introducing the parameters depending on the shear stress or rate, and we assume the phenomenological relations (3.1), where α and β are parameters characterizing the elastic and the viscous effects and functions depending only on the shear stress. In non-Newtonian flow, the stress and the slip equation are given by (3.2) and (3.3), respectively. τ_α is the critical relaxation time corresponding to the movement of molecule having molecular weight M_c, τ_β being the maximum relaxation time.
For steady flow the stress is given by (4, 2), where γ_o is the shear rate and ν is the number of chains in the unit volume. The log η-log M relation at constant shear stress is given by (4.3'), where M_s (=M_c) is the molecular weight of chain. From (4, 3'), β is determinable as a parameter depending on shear stress from the experimental results obtained by Porter et al. The experimental data show that as the shear stress increases β decreases from 2.5 to 0.
On the other hand β is a function of shear rate and molecular weight, since the shear stress is a function of molecular weight M and shear rate γ_o.

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It has been pointed out by several authors that in some polymeric substances there exists an interesting relation between steady viscosity and dynamic viscosity, namely that the velocity gradient dependence of steady viscosity is similar to the angular velocity dependence of dynamic viscosity, at least in the range of a long time scale¹⁾. There have been made many experiments that show the relation quantitatively
η(κ=γω)=η'(ω), 1<γ<2 (1)
where η (κ) denotes the steady shear viscosity as a function of velocity gradient κ and η' (ω) denotes the dynamic viscosity as a function of angular velocity ω. In this paper we shall consider such a relation phenomenologically by making use of the three dimensional Maxwell model described in the previous report³⁾. Denoting the observable displacement tensor and the internal strain tensor by a and λ, respectively, we have the fundamental equation of our Maxwell model:
dλ/dt=da/dt·a^-1·λ+λ·a^+-1·da⁺/dt+(dλ/dt)^* (2)
where (dλ/dt)^* is the term due to the dissipation mechanism.
Attending to the non-negativity of the dissipation energy -(1/2)Sp[(dλ/dt)^*·λ^-1·σ] (σ is the stress tensor), we assume the dissipation term in the form
(dλ/dt)^*=-β/1+θ(1+θλ)·(λ-1)=-β[1+φ(λ-1)]·(λ-1) (3)
with two constant parameters β>0 and θ≥0 or φ=θ/(1+θ). On the other hand, the stress tensor σ may be written in the following form attending to the condition σ_e=σ-P1→0 for λ→1:
σ_e=G[1+ν(λ-1)]·(λ-1) (4)
where ν is a constant parameter which may be non-negative in high-polymeric system consisting of the so-called Langevin chains. From Eqs. (3) and (4), we have
(dλ/dt)^*=-β/G[σ_e+Gφ(1-ε)(λ-1)·(λ-1)] (5)
where ε=ν/φ gives non-linearity between the dissipation term and the stress. The dissipation term may increase more rapidly than the stress with increasing strain, so that we assume 0≤ε≤1.
In Figs. 1∼3 we can find the velocity gradient dependence of the viscosity coefficient for a series of values of the parameters φ and ε. In these figures the curves denoting as“Dynamic”show the dynamic viscosity vs. angular velocity relation for which the abscissa should be read as the value of the reduced angular velocity ω/β instead of the reduced velocity gradient κ/β. These figures show that the rather strange relation, Eq (1) is qualitatively reproduced by our non-linear model. In the case of φ=1, we have η'(ω=κ)=η(κ), irrespective of the value of ε.
In Figs. 4∼6 is shown the normal stress difference
Δ₁σ=σ₁₁+σ₂₂-2σ₃₃ (6)
which is measurable directly by the so-called Weissenberg rheogoniometer of cone and plate type. This behavior is qualitatively in good agreement with the experimental results obtained by several investigators⁴⁾.

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The steady-flow and dynamic properties of polyethylene melts measured with a rotating cylinder type rheometer have been compared with the current theories and existing data on the relation between the steady-flow and dynamic viscosities. Contrary to the prediction of DeWitt, the dynamic viscosity η' vs. angular frequency (ω) curve decreases earlier than does the apparent viscosity η_a vs. rate of shear (D) curve, and these curves cannot be superposed by simple shifting along the abscissa. Pao's theory is not necessarily be applicable to our experimental results: the dynamic fluidity J"ω (J" is the loss compliance) vs. ω curve is not always the same as the apparent fluidity 1/η_a vs. D curve. The empirical law originated by Cox and Merz fits very well to our results, and the η_a vs. D curve coincides very well with the |η^*| vs. ω curve, where |η^*| is the absolute value of complex viscosity. Nevertheless, the consistency η_c or the differential viscosity η_d is not the same as η', contrary to Strella's theory. Our finding might closely be connected with the essential difference in linearity between the steady-flow and the dynamic behavior.

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Viscoelastic measurements were made of a molten“amorphous”polypropylene obtained by extracting it from isotactic polypropylene with hot ether. The results indicate the existence of a kind of physical (crystalline) crosslinks that connect molecules in the specimen in its molten state. The crosslinks are removed by raising the temperature or by giving it a large deformation.
The dynamic rigidity G' and viscosity η' as functions of frequency were measured at various temperatures with a rotational elastoviscometer of cone-and-plate type. The experimental results are that i) G' and η' observed at each frequency become lower with increasing temperature, and that ii) the frequency variation of G' at 129 and 135°C is expressed as G'∝ω² in the frequency range used, as is demanded by Rouse theory. The method of reduced variables can be applied to the two curves, giving 12kcal/mol as the apparent activation energy consistent with the value obtained from the steady-state viscosity data in the same temperature range. The exponent is less than 2 at lower temperatures, and the G' curve at each temperature levels off at lower frequencies, thus suggesting the existence of plateau. As the temperature is raised, η' becomes less dependent on frequency until it is wholly independent of frequency at 125°C. The method of reduced variables can not be applied to the present case in general.
Creep measurements as well as dynamic ones were made of the same specimen before and after it was given a large deformation by rotating the plate of the cone-and-plate viscometer ten times. As a result of the large deformation, it was found that the creep compliance J(t) was increased at 91°C and the retarded elastic compliance J(t)-t/η was decreased. If the retarded elasticity function ψ(t)=[J(t)-t/η]/J_d is plotted against the time logarithmically, it is seen that the large deformation given beforehand makes the subsequent retarded elastic deformation occur faster, i.e. makes the retardation times become shorter (J_d=the steady state compliance). It was also observed that G' and η' were decreased at 75°C by the previous deformation.
It has been reported that non-Newtonian flow of molten polymers is observed when the molecular weight exceeds the critical molecular weight M_c. M_c of polypropylene is inferred to be larger than or comparable with the molecular weight of our specimen 2×10₄. Nevertheless, at temperatures lower than 125°C, our experimental results, for example the decrease of η' with increasing frequency, show the existence of large molecules with very long relaxation times. It is very probable that our specimen is composed of randomly coiled molecular chains, some of which are connected to each other by a kind of crosslinks. Some of the segments with stereoregular sequence remaining eventually in this extracted specimen tend to array themselves side by side, thus forming embryonic crystallites which serve as crosslinks. The crystallites melt at higher temperatures and are destroyed by a large deformation, and the apparently large molecules are separated into intrinsic small molecules.

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In the processing of thermoplastic polymers, materials are to be deformed in the very state of melts. From this point of view, thorough studies on polymer melts are necessary to understand the flow phenomena of melts in the practical processing. We have been investigating the capillary flow phenomena of polymer melts by means of a kind of rheometer which is a screw extruder modified to measure the relation between pressure and flow rate in wide range.
Each polymer has its distinctive features in the flow phenomena differing from those in other polymers, such as flow properties, entrance pressure loss or end effects correction factor, melt fracture and Barus effect. For instance, the flow property of high-density polyethylene is not in a single curve but in two seperated curves, one corresponding to the lower shear rate region with smooth extrudates, and the other corresponding to the higher shear rate region with melt fracture.
In Fig. 1 is shown the typical relation between the pressure and the flow rate obtained in the case of various length nozzles with the same diameter. With increasing pressure in the experiment, a little wavy roughness is recognized on the surface of extrudates from S point on figure. Further increase of pressure causes a sudden jump of flow rate, and at the same point (F point in Fig. 1) melt fracture is recognized and some decrease of pressure follows this discontinuity. Consequently, two values of flow rate exist under the same pressure in the transient region.
Figs. 2, 3, 4 show the flow properties of high-density polyethylene which are independent of nozzle dimensions below F point but dependent on nozzle diameter above F point.
If we presume that the jump of flow rate of high-density polyethylene is caused by slippage at capillary wall, the equation (4) gives successfully the slippage velocity at wall which is independent of nozzle diameter and the function of only shear stress at wall as shown in Fig. 7 and equation (10).
Not so many reports on the flow properties of high-density polyethylene have yet been published, but they will be important along the development of the resin. And there remain now many unsolved problems in the field of the flow phenomena of polymer melts for investigation.

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In applications of a previously reported theory to a preliminary study about rheological characteristics of the filler-reinforced rubber vulcanizate, an analysis of abnormally large hystersis loops in extension cycles has been attempted here, based on a simple assumption for the rate of change in the adhered state between the filler and the chain molecules of the rubbery medium. In the previous model in Fig. 2, as soon as the specimen is extended to an extension ratio α in the direction of z-axis, a portion of the rubbery medium contacted with the point P₀ on the surface of the dsphere moves to the point P on the surface of a cavity determined by γ in the previous theory, and then the portion P moves gradually toward the limit position P_∞ on the surface of an equilibrium cavity γ_∞ determined by α. The transfer of P is caused by the disconnection of adhered chains around the previous position P₀, and when the strain energy of the medium is exhausted owing to the disconnection, P tends to the terminus P_∞. When the disconnection proceeds from the original surface-density of adhered chains g_f0 to the effective one g_f=g_f0 cosΘunder a constant extension α, let it be assumed that the cap of d-sphere around the z-axis with an area S₀(1-cosΘ), (S₀=2πd²) is growing bald like an egg, as seen in Fig. 2. In j th course of the extension cycle, let the zone of d-sphere located between the two small circles which are placed at respective angle Θ_j0 and Θ_j∞ with z-axis be bald as seen in Fig. 2. While, when the extended specimen tends to relax, the area S₀cosΘ' of a portion of the spherical surface in contact with the medium within a definite small distance increases, and the quick readhesion in a portion of the disconnected chains is possible within this area; perhaps most of the physical adhesions and some of chemical ones may be readhered. From the previous theory, the size of a cavity γ is determined by that of perfect non-adhesion γ_II and also the degree of adhesion (1-ζ) according to the formula γ-1=(γ_II-1)ζ. It should be noted that though γ(α(t), t) is the function not only of an extension history α(t) but also a time t, γ_II(α(t)) is the function only of α(t), accordingly γ_II(α) is an equilibrium quantity under the constant α. If the surface-density g_f=g_f^(m)(1-ζ) in the previous theory be approximated by the effective one g_f, an important relation cosΘ=(1-ζ)/(1-ζ₀) is obtained, where g_f^(m) denotes the surface-density of perfect adhesion and (1-ζ₀) is given by the virgin density g_f0=g_f^(m)(1-ζ₀).
Based on this picture, let us assume the rate of disconnection, [d(1-ζ_j)/dt]_d, and that of read-hesion, [d(1-ζ_j)/dt]_r, in jth course of extension cycles is described respectively as following schema:
[d(1-ζj)/dt]_d_??_{the area of a zone S₀(cosΘ_j-cosΘ_j∞) of d-sphere}
×{the size of a cavity (γ_II-1) of the perfect non-adhesion
under an instantaneous value of α(t)}, (Eq. (3.2) cf.)

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In a previous theory expounded by one of the authors on the mechanical and optical analysis of the filler reinforced rubber vulcanizates, the degree of adhesion (1-ζ) was treated as a fixed parameter. When the specimens containing the filler of higher concentration are extended, the degree of adhesion (1-ζ) decreases and the remarkable relaxation (softening) appears in the specimens as shown in Fig. 1.
Under the rate theory explained in the paper preceding this report, the hysteresis loops in extension cycles for filler-reinforced vulcanized rubbers are analysed as follows.
The present specimens are natural rubber vulcanizates corporated alternately with one of the three species of carbon black, i.e. ISAF (Intermediate Super-Abrasion Furnace), HAF (High Abrasion Furnace), or SRF (semi-reinforcing furnace) and of the two species of non-black, i.e. Hi-Sil (silica) or CaCO₃ (calcium carbonate), all these five sorts with various concentrations of X=0 (pure vulcanizate), 0.05, 0.1, 0.15, 0.2, 0.25, (here X denotes the volume ratio of filler to rubber examined). Each specimen was extended to the maximum extension ratio α_m=2 for the 1st cycle; for the 2nd, α_m=3 and so on. The experimental curves of tension in each extension course, namely α_m=2, 3, 4 and 5, are shown in Figs. 2-11. Moreover, the experimental and, theoretical hysteresis curves for α_m=3 (48sec) and α_m=4 (72sec) in the case of X=0.1 or X=0.2 are shown in Figs. 12-17. Most of the curves for various α_m and X are omitted here.
It has been proved that according to the above analysis, the hysteresis loops containing the Mullins effect in the filled specimen can be analysed by means of the present theory based on the rate processes, but the details in the phenomena must be expected in future studies. Especially precise examinations of the elementary process in rheology, for instance, about stress relaxation, creep and the rate of recovery and so on, must be made quantitatively and these experiments are now being prepared.

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The effect of mastication on the crystallization of rubberlike polymer in the elongated state was studied by the stress relaxation method at low temperature.
Pale crepe of natural rubber was selected as the sample of this experiment. This sample (3±0.01g) was masticated in the internal mixer at 20°C in the oxygen atmosphere (in air). The mastication time was varied between 0.5∼5min. The masticated rubber was sheeted by the open roll, and the test strips (with breadth 1cm, length 3cm, thickness ca. 1.5∼2mm) were cut out from this sheet.
The stress relaxation of these samples was studied by relaxometer at -23, -12, -2°C. For the comparison, the data at 50, 70°C were also taken. For the period from the attachment of the sample on the cramp to the start of the measurement, it is naturally assumed for the sample to be crystallized. This crystallinity for this period, however, is considered to be negligible for the long measurement time.
The tendency of the stress relaxation curves of the masticated rubber was independent of the relaxation temperature. That is, the more heavily the sample was masticated, the lower the initial stress was and the higher the relaxation rate was (Fig. 1 and Fig. 2). This tendency was not changed in the elongation between 15∼150%.
The effect of the variation of temperature on the stress relaxation was studied for the sample masticated for the same time. The higher the temperature of the measurement was, the lower the initial stress was, and the slower the relaxation rate was (Fig. 3 and Fig. 4).
From these results, the factor due to the crystallization and the factor due to the intermolecular folw are thought to effect the relaxation phenomena of these masticated rubbers at low temperature. The crystallization of the masticated rubber seems to be remarkably interfered with by the molecular chain ends which was produced by the chain scission of molecules in mastication.

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In order to clarify the relaxation phenomena of crystalline phase in semicrystalline polymer, temperature dependence of complex dynamic modulus at frequencies of 3.5, 11 and 110c/s was measured for a mat of single crystals of polyethylene over a temperature range from -160°C to 120°C.
The single crystals prepared from 0.03% xylene solution of fractionated Marlex 9 (Mv=520000) were so laminated as to lay their surfaces in parallel to each other by rapid filtration, and pressed at room temperature to form a film of about 100μ thickness. The structure of a single crystal and the layered structure of single crystals within the film, which was used for the viscoelastic measurements, were examined by means of electron microscope and X-ray diffraction technique.
The temperature dependence of dynamic loss molulus E" at three different frequencies within the crystalline dispersion region, which was obtained by applying the stress in perpendicular direction to the molecular chain axis, were replotted as function of frequency at various temperatures. By making the curve at 80°C standard, and shifting the curves at various temperatures horizontally along the frequency axis, a master curve of E" as a function of angular frequency was obtained. The relaxation spectrum at 80°C was calculated from this master curve by using Alfrey's zeroth order approximation; H_l (log τ)=4.6/π^-1 E" (log 1/ω). From the measurements on reproducibility of the temperature dependence of E" performed by repeating the cycles of heating and cooling, it is confirmed that the effect of the changes in crystalline structure on the relaxation spectrum for crystalline absorption is negligible below 110°C. The slope of the relaxation spectrum is about -1/5 at a longer time side and about 1/3.5 at a shorter time side, and both of them are broader than those observed for the primary dispersion region of non-crystalline phase.
The temperature dependence of the shift factor obtained for composing the master curve of E" is divided into two regions of different activation energies. This fact suggests that the relaxation mechanism of the crystalline dispersion can be classified into two different modes. Taking it into consideration that the activation energy of the crystalline dispersion below 70°C, 16.2Kcal/mole, is comparable to that of the secondary dispersion due to the local relaxation of the frozen main chains in the non-crystalline region and in the defective region within the crystal, the relaxation mechanism of this dispersion is reasonably ascribed to the occurence of the local torsional or twisting motion of main chains in the crystal lattice around their molecular axis. This dispersion is named here β_c dispersion.
The activation energy of the crystalline dispersion above 70°C, 43.7Kacl/mole, is larger than that for β_c dispersion. On the other hand, the fact that the lamella thickness of the single crystal of polyethylene thickens considerably above 110°C, suggests that the migrational motion of the molecular chains in the crystal lattice along the c-axis can occur in such a higher temperature region. Taking these facts into consideration, the relaxation mechanism of this dispersion can be ascribed to the large motion of the molecular chains in the crystal lattice, such as the migrational motion along the c-axis, and resembles that of the primary dispersion (α_a dispersion) in respect to the occurence of large motion of molecular chains. This dispersion is named here α_c dispersion.

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Crystalline polymers show non-linear viscoelastic properties at very low excitations compared with amorphous polymers. It is very difficult to discuss the non-linear viscoelasticity generally, However, the degree of non-linearity has been defined at the temperature region where the dispersion due to crystal is important, as a result of considerations based on simple mechanical model and phenomenological method. The temperature dependency of this degree of non-linearity has been examined by making experiments of stress relaxation for high and low density polyethylenes and polyethylenet erephthalate. The result is that the degree of non-linearity is related to the dispersions closely, that is, the degree of non-linearity has larger values at the starting points of each dispersion. These facts suggest that the interaction between different dispersions will be the main factor for the non-linear viscoelastic mechanism.

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Extensive studies of viscoelastic properties of high-polymeric materials have necessitated the development of an apparatus which can measure full-automatically the viscoelastic functions of the materials, such as complexdynamic modulus, relaxation modulus, and creep compliance, over the range of frequency (time) and temperature as wide as possible.
In this paper, the apparatus which has been designed and constructed by the authors for such multiple purposes as above under tensile deformation will be discussed. The apparatus can also be used for simpleshear deformation of the testspecimen by a slight modification of the specimen jaws.
The apparatus has servo-mechanism which can control the static strain or stress of the testspe cimen constant during the forced vibration for dynamic measurements. This servo-mechanism of keeping the static condition of the specimen constant is very important for successful measurement of dynamic properties automatically and is also helpful for making the apparatus multi-versatile in uses as follows:
a. Dynamic experiment under constant static tension.
b. Dynamic experiment under constant static deformation.
c. Stress relaxation experiment.
d. Strain creep experiment.
e. Constant rate deformation and cyclic deformation.
The essential point for measuring full-automatically the viscoelastic functions, such as dynamic modulus as functions of frequency and temperature, is to obtain the stress and strain amplitudes and their phase difference as directreading quantities. By means of this apparatus these purposes have been satisfactorily attained within the range of frequency from 1 to 100 cps and of temperature from -60 to 200°C.
The limitation of frequency range coverable depends mainly upon the technique for detecting the error of the phase difference so fine as less than 0.1 degree: i.e., its lowest limit is to be determined by the capacity for the directreading of the three quantities, of such electrical analogue technique as adopted here, and its highest limit by the relation of measuring frequency with resonance frequency of the apparatus, especially of the stress detector (4000 cps), and with the geometrical dimension of the specimen for longitudinal wave propagation. The lowest limit of measurable frequency can be expanded in some extent as low as 0.01 cps by analyzing manually the stress and strain waves recorded, however electrical-digital technique may be recommendable and will be discussed in the following paper.
The limitation of temperature range coverable, especially of lowest limit, depends on the technique of cooling the testspecimen and will be easily improved by changing the technique of circulating dryice-methanol mixture to that of blowing dry air cooled by liquid nitrogen.
Illustrations are given of the experimental results on the frequency dependence of complex dynamic tensile modulus (C.D.T.M.) for three kinds of epoxy resin at 25°C., the temperature dependence of C.D.T.M. for atactic polyvinyl alcohol at 1, 10 and 100 cps, and the frequency dependence of C.D.S.M. of a polyvinyl chloride foam, which was obtained full-automatically at various temperatures.

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