In this paper we fiist state the role of the mathematical theory of plasticity in solving the problems concerning various metal forming Processes and then proceed to review the basic rheological behaviours of metals, that is, the plastic flow, instability (i.e., necking and buckling) and fracture, together with their mathematical descriptions. We also discuss critically the tension, compression, torsion and hardness tests, a test under combined stresses, high-speed tests and simulative tests (i.e. the bend test, Erichsen test and conical-cup test) from the viewpoint of testing the rheological behaviours. We describe then various assumptions usually made for the theoretical analysis of forming problems as well as several techniques of experimental analysis, such as the contact stress measurement with pin pickups or with photoelastic tools, strain measurement using a grated metal specimen or a laminated plasticine specimen, and stress analysis from a measured plastic strain distribution.

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The rheological behaviors related to polymer processing have been broadly reviewed. The influence of working conditions on the relationship between the flow and the deformation strain has been experimented mainly in respect of compression, for both the amorphous and the crystalline polymers. In particular, the possibility of cold processing is proposed for the crystalline polymer.
Many non-Newtonian formula in unidirectional flow have been explained, and it is concluded that pseudoplastic flow is likely to be most similar with that of molten polymer. The consistency curves of plastics are useful for practical molding, and are determined on the basis of the flow data obtained from extrusion rheometer. The method of reduced variables is applicable also to the extrusion flow curves of thermorheologically simple materials. On the other hand, the hysteresis effect in extrusion flow curves of crystalline polymers is discussed with melt fracture. Further, the temperature distribution in the radial direction through capillary is theoretically discussed for various non-Newtonian flows of the bosis of thermodynamic cnsideration.
The theoretical analysis of calendering is developed for pseudoplastic flow. The experimental data on Weissenberg's extruder are presented with the theoretical aspect on normal stress effect. Resonable estimation on moldability is discussed, in particular, for injection. The residual stress in the molded products is presented as an important problem in polymer processing, and various testing methods on enviromental stress cracking are compared.

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Some experimental and theoretical considerations have been performed on the packing properties of powderlike materials observed during dry pressing procedure.
Many works have hitherto been reported on the packing characteristics when pressing forces are induced to the powder bed, and then, the relationship between the strain and the compressive stress is represented in a simple hyperbolic curve as illustrated in Figure 3 when fine sorts of powder are used.
However when comparatively stiff kinds of powder possessing low“powder diffusibility1)”are used as raw material, such simple relationship is not obtained, but their relationship between the strain and the compressive stress is observed as many simple hyperbolic curves in a super-positional form as shown in Figure 12.
The mechanism of this phenomenon is thought by the authers as follows; when the compressive force is induced to the packed bed, the bed initially contracts as an elastic body, that is, all the particles of the powder in the bed are contracted elastically mainly in the contact points. This elastically contracted structure is maintained to the point where slippage takes place at the weakest point. Once this slippage takes place, the equilibrium of the whole system is broken, and the slippage flow takes place successively. This slippage flow is observed as plastic deformation of the whole system.
The equilibium is restored for the whole system after the successive processes of plastic deformation have been accomplished. This re-newed equilibrium state means the seoond elastic configuration. Further compressive force deforms the second elastic body, elastically in the first instance, and plastically after slippage is caused. This elastic and plastic deformation observed one after another constitutes successive hyperbolic curvels as illustrated in Figure 12.
When comparativey brittle and crushable kinds of powder are used as raw material, similar successive hyperbolic curves are observed though with linear type in some places as illustruted in Figure 11 and Figure 8. The former figure is the case when fractures take place in the contact points of the powder, and the latter bigure is the case when fractures are pronounced in the whole volume of the powder. The mechanical configuration is changed discontinously or suddenly in both cases, after fractures have taken place.
In the process of plastic deformation, the relationship expressed in equation (1) is established noticeably by many invesigators between the stoain ε and the deformation degrel dl/l3)4)7)11),
ε=∫l'olodl/l=lnl'o/lo (1)
and the relation of equation (6) is also established experimentally between the stress σ and the strain ε4)7)11).
σ=kεn (6)
In the authers theoretical view this equation will be expressed in equation (12),
σ={ec·ε}1+a (12)
where, c is the integral constaut in the mathematical treatment, and a is the factor showing the degree of change of the mechanical structures. This factor is, in the authers' view an important variable in the pressing procedure of powder beds. Some considerations on ec and a are performed based on the experimental observations.

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[in Japanese]

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Though a number of investigations have hitherto been reported of the gaskets of several materials used in the machine parts to be tightened, i.e. piping, vessel etc., they are considered to be insufficient for design purposes. In this paper, therfore, the authors have studied experimentally the gasket factor for asbestos-joint sheet gasket under internal fluid pressure up to 20Kg/cm², with water and machine oil for fluid. From the results, the authors found various factors influencing the gasket factor, and the following facts have been confirmed.
1) The relation between the gasket stresses and internal pressures is shown to be in a definite equation.
2) The gasket factors are shown to have constant value regardless of the kind of internal fluid or its pressure, or of the gasket size.
3) The gasket factor increases slightly proportionally with the thickness of gasket, but it is negligibly small.
4) The gasket factor decreases with the increment of the width of the gasket and it can be expressed by the following experimental formula;
m=sb^-k
in which m is the gasket factor, b is the width of the gasket, and s and k are the factors dependent on the kind of internal fluid.
5) When the internal fluid is machine oil, the gasket factor is smaller than when it is water, by about 0.6.

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In the previous paper of the authors, experimental and analytical studies were made on the influencing factors in asbestos-joint sheet gasket affecting the tightening characteristics under the pressure of internal fluid up to 20Kg/cm². In the present paper, the authors propose an empirical formula regarding the relation between the gasket factor and leak pressure. And the authors made further analytical discussions in the paper about the condition in which the internal diameter of gasket was of constant quantity in the influencing factors and the width and thickness were of variable quantity, and the internal fluids applied were water and machine oil.
In the present paper, experimental and analytical studies were made under the condition in which all the width and the internal diameter are of variable quantities and the internal pressure applied ranges between 1 to 60Kg/cm². The specimens tested in our experiments are asbestos-joint sheet, synthetic rubber and vinyle chloride gaskets.

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The present writers have investigated the accelerated testing for predicting the fatigue limit of hard drawn steel wire by means of stepwise load increase test with Haigh-Robertson wire fatigue testing machine, and have cleared the simplified method for predicting the fatigue limit with only one loading rate.
The principal results of this investigation can be summarized as follows:
1) The modified Prot method that takes the exponent n=0.40 in equation σ_R=σ_W+k·αⁿ, produces better agreement with conventional Wöhler fatigue limit than does the original Prot method based n=0.50.
2) Stepwise load increase test using four loading rates with three specimens can reduce the fatigue testing time to one third as compared with conventional Wöhler procedure.
3) Simplified method for predicting the fatigue limit with only one loading rate can be performed by increasing the division plate reading of head stock by 0.1 degree to every 50000 cycles until the specimen (l=150d) breaks down. The starting stress is taken about 10% lower than the experientialy expected fatigue limit. For 0.6% carbon hard drawn steel wire, if the mean value of the stresses at failure for three specimens is divided by 1.09, a value close to Wöhler fatigue limit, with an error less±3.2%, may be obtained. The testing time can be reduced to one sixth as compared with that of conventional Wöhler procedure.

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Many investigations of fatigue of metals under actual stresses have been carried out recently. Most of them have been done in the case where only the amplitudes of repeated stresses are varying with time. In the case of actual stress spectra of machine members, however, not only the amplitudes of repeated stresses but also the mean stresses fluctuate, and extremely complicated stress patterns are repeated.
As one of the investigations of those phenomena, the fatigue tests of the low-carbon steels have been carried out by the authors in the case where the repeated bending stress amplitudes are constant and the mean bending stresses fluctuate cosinusoidaly with time.
In order to analyze the varying stress spectra, and to discuss the strength and lives of metal members under those fluctuating stresses, it is necessary to measure the values of actual stresses induced on the test piece, For this purpose, the bending moments applied on the test pieces have been measured from the elastic strain of the driving shaft or of the jaw gripping of the test piece with the electrical resistance strain meter, the electromagnetic oscillograph, and the vacuum tube volt meter.
Besides in order to examine the patterns of the repeated stresses, they have been monitored with the synchroscope, then it is ascertained that those patterns are exactly sinusoidal, and it is also ascertained with electromagnetic oscillograph that the mean stresses fluctuate surely cosinusoidaly with time.
As the results of the tests, it has been made clear that, in the case of the repeated bending stresses with the varying mean bending stresses, the endurance limits and the fatigue lives of the repeated bending stresses are considerably reduced in comparison with those in the case of the repeated bending stresses with the constant mean bending stresses.

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Standard compaction tests have been performed for sandy soil which is mixed with two kinds of cement. Mixed materials are the normal Portland cement and the blast-furnace slag cement, the amount of which is 6% weight of sand for both cases.
During the compaction and the curing of such cement-treated sandy soil mixtures, about 1 or 2% of water is consumed for the cement hydration. This is a characteristic phenomenon in soil stabilization by cement.
During the undrained triaxial compression tests, the behaviours of the pore water pressure in the specimens have been measured to obtain the shear strength parameters in terms of the effective stress. The general pattern of the pore pressure-strain curves indicates that the pore pressure rises up to the peak value as the shear strain increases and that when the failure occurs it turns to decrease gradually to the negative value. The values of shear strength parameters obtained in a series of these tests are φ'=30°∼50°and c'=3∼13kg/cm².

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