Fatigue under working stress is a rather complicated problem, but it is very important in practical cases. Study on the fatigue under multiple repeated stress is one of the approaches to the problem.
In this paper are reported the experimental results of multiple repeated stress fatigue test which the authors made recently.
Specimens made of two Al-alloys have been tested by Ono's rotating bending fatigue testing machine. Summary of the results is as follows:
(1) In the case where Al-alloy 52 S is used as the material, and the primary stress is chosen to be 10kg/mm², which is the fatigue strength at N=10⁷, Σn/N is larger than unity.
(2) In the case where Al-alloy is used, and the primary stress is 12kg/mm², Σn/N is nearly equal to unity.
(3) In the case where Al-alloy 17S is used, and the primary and the secondary stresses are 24 and 18kg/mm² respectively, Σn/N is smaller than unity, and when the primary and the secondary stresses are 18 and 24kg/mm² respectively, Σn/N is larger than unity, and sometimes n₂/N₂ is larger than unity.
In this case, nine specimens are used under the same condition, and Levy's method is used to represent the experimental results. It is compared with other conventional methods and the authors consider that the Levy's method is very useful.
(4) Levy's method, however, has an application limit, which is not made clear in Levy's original paper. The authors pointed out this limit.

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In the previous report, the present authors have proposed the following modified Miner's equation for the fatigue-lifes of specimens under varying stress amplitude in two stages.
n₁/N₁+αn₂/N₂=1 (a)
In this paper, they investigated on the value of α and showed that the value of α is the function of the cycle ratio, the stress level of the primary and secondary stress, etc.. Especially, when the secondary stress is higer than the primary one, the value of α could be expressed only by the function of the cycle ratio of the primary stress as follows:
α=1-n₁/N₁ (b)
Moreover, they investigated how the hardness of the specimens varied with the fatigue loading. When the load was transformed from any primary stress level to a higher secondary stress level, the values of hardness on the surface of specimens increased up to a constant value corresponding with the stress level.
But when the secondary stress level is lower than the primary one the value of hardness obtained after the repetition of the primary stress, varied little. And they introduced the equation (b) to approximately show the relation between the fatigue-life and the hardness-variation.

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In the previous paper, we reported on our experiments about the coiled springs of steel wire under pulsating compressive load (mean compressive stress τ_m is equal to stress amplitude τ_a). In the present tests, the fatigue strength and the deformation due to fatigue were obtained with regard to the cases when various mean stresses were applied. Further, the creep deformation under static load was obtained and compared with that under repeated load.
The results were as follows:
(1) A residual shear strain of coiled springs under repeated compressive load was largest in the pulsating test (τ_m=τ_a) and became lower in proportion to an increase of mean stress, but little variation was observed where τ_m/τ_a=0.6.
(2) Fatigue limit (Maximum stress) got higher with an increase of mean stress.
(3) A stress amplitude at endurance limits decreased showing a straight line in accordance with addition of mean stress, and that in a deformation limit did not vary on the whole as if it were constant when τ_m/τ_a=1-0.6, but began to decrease rapidly when mean stress was made beyond such a range.

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We have carried out some torsional fatigue tests, in order to research mainly on the effect of size with large bar type specimens of 50-70mm in diameter and with conventional small specimens of 7mm. The tested materials are 0.2% carbon forged steel, which consists of two charges, one is an acid open furnace steel and the other is an electric furnace steel. As the test results the following aspects were obtained mainly on the size effect.
The fatigue limit of these materials with large specimens fell within the range of 1.36-1.40kg per sq. mm, and was lower as compared with that with small specimens as to both charge steels, that is, 4.9% in the acid open furnace steel and 14.6% in electric furnace steel. It was found that even if the materials are made according to the same order standard and have the same mechanical and chemical properties, the metallurgical procedure of materials gives remarkable effects on the fatige strength, especially on the size effect.

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The distribution of internal stress in the cross section of the decarburized carbon steel bars, which were normalized, quenched and tempered, or shot-peened, were measured.
In this measurement of the internal stress, the dissolution method by acid solution was used in order to remove the outer layers of specimen without any effect of workhardening. The results obtained were as follows:
(1) In the outer portion of both the normalized and the heat-treated specimens, containing the decarburized zone, the internal stress acts as tension. This tensile internal stress gets maximum at the surface layer and sharply decreases towards the center of the specimen, till it vanishes at a certain point, which lies at a depth of around 0.5-1.0mm from the surface, and afterwards changes its sign; this compressive internal stress increases towards the center.
(2) As the depth decarburized increases, each of these maximum tensile internal stress decreases. The maximum value of this tensile stress is about 52kg/mm² in the specimen, when the depth of decarburized layer is 0.15mm, and it reduces almost by half when the depth is 0.5mm. The compressive maximum internal stresses in their center zones are about 3-6kg/mm².
(3) The distribution of internal stress in the quenched and tempered steel bar after decarburizing is similer to that of the normalized one. The surface maximum tensile stress is 35kg/mm² in the specimen having a depth decarburized of 0.15mm, and 15kg/mm² when the depth is 0.5mm. Thus the maximum tensile stress decreases as the depth of decarburized layer increases.
(4) The value of maximum tensile internal stress in the normalized steel bar at each depth decarburized is greater than those of the quenched and tempered bar.
(5) The distribution of internal stress in the shot-peened specimen after decarburization is opposite to that of the above mentioned normalized, or heat treated steel bar.
The value of maximum compressive internal stress at the surface layer increases as the depth decarburized increases. That is 32kg/mm² in the specimen with a depth decarburized of 0.05mm and is 60kg/mm² in the 0.5mm depth specimen.

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Fatigue phenomena of tire cords are usually described by the S-N diagram as in the case of metals. The fatigue life increases as the static load decreases. The logarithm of fatigue life is related linearly to the static load above a limiting value of the static load, but when the static load decreases beyond the limiting value the linear relation does not hold, and the fatigue life increases so rapidly that it takes a very long time to measure that.
Tire cords are so designed that each constituting cord (1650 den/2) is not subjected to a load above 1kg when the tires are in running state, and naturally, it is desirable that experimental observations should be performed under a load of about 1kg. However, practical measurements have hitherto been made under loads above 1kg, and the fatigue life under lower loads has been estimated by extraporating the linear part in the S-N diagram. Such a procedure may results in a error because the S-N diagrams for various kinds of cords are not parallel with each other, and also the linear relation does not hold under lower loads. Thus, the true fatigue life under running states should be measured only experimentally.
The authors have tried to make a flexing fatigue tester of rotary type and made it possible to measure the fatigue life of various kinds of tire cords under a load of 1kg (per a cord). Further, they have obtained the so-called “master curve” from the present data and also from that obtained by the apparatus reported in Part 1 of this series, making comparisons among the S-N diagrams under a load ranging from 0.25 to 3.0kg per a cord.
The results obtained are as follows: The textile cord does not show a clear fatigue limit, and the slope of the linear part in the S-N diagram depends on the sort of the fiber and also on the manufacturing conditions (As already reported in Part 2 of this series). The slope of the linear part in the S-N diagram may be explained by considering the tensile recovery of the fiber. The tensile recovery of a fiber which has been allowed fully to relax when manufactured is nearly 100% in fairly a wide range of extension, but decreases when the extension exceeds some limit. On the contrary, the fiber which has been stretched strongly in spinning process shows rather a low tensile recovery under a small elongation, which does not decrease much under a large elongation. The Topfam spinning rayon belongs to the former and the BX to the latter.
If the fatigue of fiber arises from consumption of external energy, the fatigue may not occur in a range of the tensile recovery of 100%, but may increase as the tensile recovery decreases. The fatigue life of the fiber whose tensile recovery varies much with increasing elongation varies widely. From this we may explain the fact that the S-N diagram of the Topfam spinning rayon has a less steep and that of BX has a steeper slope.

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We examined by electronimage and Fisher Sub-Sieve Sizer (F.S.S.), how precipitation conditions and chemical composition of carbonates for receiving tube cathode influence the shape and size of particles.
a) Particle size of single carbonates (BaCO₃, SrCO₃, CaCO₃)
CaCO₃ particles were largest and BaCO₃ particles were smallest under the same precipitation conditions.
CaCO₃ and SrCO₃ particles precipitated by (NH₄)₂CO₃ were larger than CaCO₃ and SrCO₃ particles precipitated by Na₂CO₃, while BaCO₃ particles were not so much influenced by precipitant as CaCO₃ and SrCO₃.
b) Particle shape of single carbonates (BaCO₃, SrCO₃, CaCO₃)
CaCO₃ particles had an influence on precipitant type, while BaCO₃ and SrCO₃ particles were not so much influenced as CaCO₃.
c) Particle size of double carbonates
Particle size of co-precipitated Ca-Ba and Ca-Sr system was larger than that of Ba-Sr system under the same precipitation conditions and this tendency was most remarkable in the case of particles precipitated by (NH₄)₂CO₃. On the other hand, Ba-Sr system was not so much influenced by precipitant type.
d) Particle shape of double carbonates
The chemical composition had no influence on particle shape of Ba-Sr system, while that of Ca-Ba and Ca-Sr system was sensitive to Ca content.
e) Particle size of triple carbonates
Particle size increased with the increase of Ca content. Particles precipitated by Na₂CO₃ decreased with the increase of temperature, while particles precipitated by (NH₄)₂CO₃ rapidly decreased with the increase of temperature up to 50°C, slowly decreased at 50-70°C and increased above 70°C. The concentration of nitrates solution had not so much influence as the precipitation temperature. The particle size of carbonates precipitated by Na₂CO₃ was smaller than the particles precipitated by (NH₄)₂CO₃ under the same conditions.
f) Particle shape of triple carbonates
The relation between the chemical composition and particle shape of triple carbonates was closer than the relation between those of double carbonates.
In the case of (NH₄)₂CO₃, the following shape transition was observed, that is to say, spheroidal shape was found at a precipitation temperature of 40-50°C, fan shape was found at 50-80°C and needle shape was found above 80°C. While in the case of Na₂CO₃, the greater part of carbonates were needle at 40°C and all parts of them were needle above 40°C.
g) Effects of pH on particle size
Effects of pH of nitrates solution on particle size were studied by adding acetic acid to nitrates solution before precipitation process. In this manner a significant difference of particle size was recognized when the fraction of acetic acid was above 0.08mol.
h) Density of carbonate crystal
The density of co-precipitated double and triple carbonates were about 2.8-3.9gr/cm³.
i) Ball-milling effects
Ball-milling effects were examined. Fan shape particles were easily crushed in comparison with needle type and were sufficiently crushed for 15 hours.
j) Sprayed coating density
The relation between the size and shape of carbonates and the density of the sprayed carbonates coating were examined about various carbonates without ball-milling, but in this case the provided solvents and binder were the same.
In the case of same particles shape, coating density decreased with the increase of particle size.

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