Vol. 18, No. 8 (1962)
1962, 18 (8): 379-391. doi: 10.7498/aps.18.379
Torsional fatigue experiments were carried out on 99.6% commercial aluminum and 99.99% high-purity aluminum (annealed and cold-worked). The shape and the area of the hysteresis loop (stress versus strain) after various stress cycles N were determined, from which the energy loss△E in each cycle and the maximum torque Tm of the specimen were calculated. The △E-N curves and Tm-N curves were analyzed and different stages of the curves were correlated with the results of metallographic observations on the specimen surface during the process of fatigue. It is then concluded that, in the initial stage of fatigue loading, the basic process that gives rise to the change of △E and Tm is the pinning of dislocations by the vacancies generated during fatigue and this occurs as a bulk effect. Later on, the localized coarse slip regions appearing in the specimen give rise to an extra energy loss △E, but have only an insignificant effect on Tm. Consequently, the changes of Tm and △E in this stage no longer correspond to each other. Such an analysis may clarify many of the dis-crepencies reported in the literature concerning the results of observation on the change of △E and Tm (representing a change in hardness) during fatigue.Assuming the curves experimentally observed to be a summation of the effects given rise by these two processes (a bulk process and a localized process), and taking into account that the contributions from these two processes on △E and Tm vary with the fatigue amplitude, the condition of specimen treatment (annealed or cold-worked), and the impurity content of the specimen, the shape and the position of the numerous experimental curves of △E-N and Tm-N can be interpreted satisfactorily. However, the validity of this viewpoint needs further experimental verification.
1962, 18 (8): 392-399. doi: 10.7498/aps.18.392
Fatigue experiments under constant torsional strain were carried out with an Al-4% Cu alloy. The energy loss △E was found to decrease to about zero in the initial stage of experiment, and to rise again after a certain number of cyclic loading. Results of metallographic observation showed that corresponding to the up-rise of △E, the slip regions became suddenly localized. These observations confirmed our previous assumption that the appearance of localized coarse slip regions is one of the basic processes giving rise to △E. Under fatigue loading, the maximum torque Tm was found to rise in the initial stage of experiment. It reached a maximum value and maintained there for a certain number of cyclic loading, after which a sudden drop occurred, and this drop corresponded to the up-rise of △E. Such an occurrence seems to be an indication of the sudden un-pinning of those dislocations which were pinned during the initial stage of fatigue loading. It is contemplated that the process of pinning of dislocations may be due to the nucleation of clusters of copper solute atoms drawn from the Cottrell atmosphere formed during the initial stage of experiment, along certain favorable sections of the dislocations, in consequence of which other sections of the dislocations were subsequently unpinned from copper solute atoms. As the clusters grow up in size, the length of the un-pinned dislocation segments increases until a certain critical value is reached, at which an avalanche occurs and numerous dislocations are produced. Such a happening results in a sudden drop of Tm and leads to the formation of localized slip regions which give rise to an up-rise of △E.
EFFECT OF AGING, INTERMITTENT LOADING AND RE-SOLUTION TREATMENT UPON THE FATIGUE BEHAVIOR OF ALUMINUM-COPPER ALLOYS
1962, 18 (8): 400-410. doi: 10.7498/aps.18.400
A study was made on the effect of various treatments upon the energy loss △E and the maximum torque Tm in aluminum-copper alloys containing 1%, 2% and 4% copper under fatigue loading. Metallographic observations were made correspondingly.Experiments made with Al-1% Cu alloy showed that when the applied torsional strain is large, the shapes of the △E and Tm curves are similar to that of high-purity aluminum and commercial aluminum. However, when the torsional strain is small, or when the specimen was aged at room temperature before the fatigue experiment, the shapes of the △E and Tm curves are similar to those of Al-4% Cu alloy. These results can all be interpreted in terms of the interaction between solute atoms and dislocations.Experiments on intermittent loading were made on Al-1% Cu and Al-2% Cu alloys. The results confirmed the viewpoint that the up-rise of △E in the later stage of fatigue experiment are due to the occurrence of coarse slip bands in the specimen, and is not due to the softening of the specimen associated with over-aging.Re-solution treatments were made in fatigue experiments of Al-4% Cu alloy. Judging from the behavior exhibited by the △E and Tm curves after each treatment, the conclusion may be drawn that the fatigued specimen can be made to recover to its original condition if the specimen is treated immediately after the up-rise of △E. However, if the specimen is treated a while after the up-rise of △E, the fracture of the specimen is sped up because of the occurrence of fatigue cracks in the specimen.Two conclusions having practical significance can be made on the basis of our experimental results: (1) It is possible to detect the formation of initial fatigue cracks through the method of measuring △E, because the occurrence of coarse slip bands is a prelude of crack formation; (2) it is possible to delay the occurrence of coarse slip bands and thus to raise the fatigue life through the method of alloying and heat treatment.
1962, 18 (8): 411-421. doi: 10.7498/aps.18.411
【Abstract】In this paper the author has made a complete topological analysis on a machine oscillation problem governed by a third order nonlinear differential equation of the following form: A(d3δ)/(dt3)+(d2δ)/(dt2)-Acotδ(dδ)/(dt)(d2δ)/(dt2)+((PiA)/M)cotδ+Csin2δ)(dδ)/(dt)+Bsinδ-(Pi)/M=0 and has suggested a simple graphical method for the system performance computation. A numerical example is given for illustration.