Two effects acting on fatigue properties of copper were investigated; the surface damage such as intrusion-extrusion and the internal structure induced. The former effect was examined by repetition of electro-polishing the surface layer and cyclic stressing. The fatigue life can be prolonged unexpectedly by such processes, but the damaged layer increases in thickness at the later stages of operation and eventually a fracture occurs. If the amount of polish is increased at these stages so as to remove perfectly this layer, an infinite extension of the life seems to be expected. In specimens fractured, the more cells and dipoles were observed than in the ordinary fatigued specimens. These structures seem to play a part in increasing the crack growth rate. An attempt has been made to present a dislocation model for the crack growth at the 1st stage of fatigue, in which dipole dislocations play an important role.

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Non-uniform deformation of an elastic, strain-hardening block caused by plane-strain compression is analyzed, using the finite element method. The surface of the block is supposed to stick on a rigid tool. Deformation at rather early stage is analyzed for 6 cases concerning height to width ratio of the block, h₀. As the result, it becomes clear that the bulge on the free surface is single when h₀<2 but is double when h₀>2, that the load of compression increases as h₀ becomes smaller, and that the pressure is larger at the center than near the edge only when h₀ is small. Moreover, it is made clear that the plastic zone grows from the surface to the center when h₀ is small, from the center to the surface when h₀ becomes a little larger and from two points inside the block to the surface when h₀ is so large that double bulge yields, and so on.

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Finite element method is applied to the theoretical analysis of plane-strain compression of an elastic, plastic strain-hardening block under general conditions of lubrication, and deformations are pursued from elastic through partially plastic to fully plastic stages. The relative slip-ratio proposed and evaluated in Part 2 of our series of papers is used as the boundary condition instead of the friction coefficient which is often used in conventional treatments. As the result, it becomes clear (i) that the bulge of the free surface is single when the height to width ratio of the block h₀<2 and is double when h₀>2 in all conditions of lubrication, (ii) that relationship between the compression ratio and load is affected largely by h₀ and the condition of lubrication, (iii) that the initiation of the first yield is delayed but the attainment of a fully plastic state is accelerated by improvement of the condition of lubrication, and (iv) that plastic zones grow differently according to the value of h₀.

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Formerly, the authors analyzed non-uniform plastic deformation of a cylinder that was caused by friction on cylinder-tool interface in axial compression, using the calculus of variation. In this report, shape of bulge, deformation in the body, load, distributions of vertical pressure, of tangential stress and of friction coefficient on the cylinder-tool interface, etc. are calculated again, improving the former method of calculation. Next, various experiments are performed to prove the theoretical results, and to get further knowledge about friction. The experimental results agree qualitatively with the theoretical ones. As the result, it becomes clear that double bulge yields when height of the cylinder is large, that distribution of pressure is much affected by its height, that friction coefficient increases from the center to the edge, that friction coefficient can be investigated both by oblique type pin method, by measuring contact ratio of the surface, etc.

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Non-uniform deformation of an elastic, strain-hardening circular cylinder in axial compression is analyzed by the finite element method. Deformation is pursued from elastic through partially plastic to totally plastic stages, allowing for the finite deformation or geometrical change of the material coordinates. As the boundary conditions, the experimentally determined values of the slip-ratio which was proposed by the authors are used instead of the conventional friction coefficient. Calculations of 23 cases are performed for various combinations of lubrication and height to diameter ratio. As the result, the followings have become clear: shape of bulge of the free side surface, relation between the load and the compressive strain, distribution of normal pressure and tangential stress together with the friction coefficient on the boundary surface, mean friction coefficient, patterns of appearance, growth of plastic zones, etc. These results are qualitatively in agreement with the theoretical results which were presented in Part 1 of this series of investigation; i.e. the results obtained by applying variational principle. Agreement with the experimental observations is also satisfactory.

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Concerning the out-of-plane twist-bending vibration of a ring of rectangular cross section, an analytical expression of the natural frequency is given by the theory of a circular arc bar for the region of small length-to-diameter ratios, whereas for the region of large ratios another one is given by the Rayleigh's theory of inextensional vibrations of a shell. However, those two formulae are both invalid in the middle range of the ratios. Especially from a practical point of view, the present paper proposes an approximate formula which is applicable over the entire range of length-to-diameter ratios, This formula is obtained by combining the two previous formulae appropriately on the assumption of an analogy to a single-degree-of-freedom system of a mass and two springs in series, which depends not so much on a mathematical procedure as on an intuitional consideration.

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This paper is concerned with the investigation on the entrance loss which occurs in a radial turbulent flow between parallel discs. Because the theoretical determination of the entrance loss is almost impossible, the author has constituted an empirical equation by using nondimensional quantities - the space between the discs, the radius of rounded corner at entry boundary etc.- which have large influences on the entrance loss. This equation will be usefull for the solution of practical problems.

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Pulsating air flow in a diesel engine air-charging system caused by the opening and closing of the scavenging ports produces surging phenomena which are considerably different in their characteristics from those observed in the ordinary, steady flow blower system. By substituting a simple model for the engine air-charging system, the authors analyzed the surging phenomena through theoretical calculations and determined the effects of each model element on the surging. A series of experiments were then made to verify the validity of the analytical calculation method adopted. A good agreement was observed between the results of calculations and experiments, and it was found that a simplified theoretical calculation neglecting the influence of the pressure waves in the air duct of the air-charging system could serve as an effective means to deal with the surging phenomena where the air duct was comparatively short in length as that of the diesel engine.

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