Application of the Theory to Real Materials

load, stress, elastic, material, specimen, yield, strain and fig

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"Yield."-52,

Special interest attaches, for materials such as wrought iron and mild steel, to that part of the stress-strain dia gram which lies just outside the elastic range. Reference to Kirkaldy's diagrams (fig. 1 i) shows that a point (called by A. B. W. Kennedy the "yield-point") is reached, soon after the mate rial has ceased to be elastic, at which the extension increases without any corresponding increase of stress. Somewhat later, the extension becomes less rapid and the stress rises at a fairly regular but gradually decreasing rate. If a lever type of machine is employed, the beam drops when the yield point is reached.

Meanwhile the specimen is seen to under go a considerable change : if scale previously adhered to its surface, this is observed to flake off, in lines inclined at roughly 45° to the direction of pull; if the surface is pol ished, lines appear on it, having the same direction, which can be recognized by touch as steps or ridges. These lines are known as Liiders' lines (W. Liiders, Dingler's Polytech. Journ., vol. 155 [186o], p. 18): their occurrence may be used to determine, without the use of an extensometer, the yield point of a material.

Researches by A. Robertson and G. Cook (Proc. R.S. [A], vol. 88, 1913) have shown that the phenomenon of "yield," thus revealed by early diagrams, is much more complex than those diagrams would suggest, and of the first importance from the practical standpoint. Realizing that its effects would be masked by the inertia of the testing machine as ordinarily employed, these investigators employed the device which is illustrated by fig. 17. Two long rods DD were arranged in parallel with the specimen, so as to share in taking any load applied to the end yokes, Y Y. The loads taken by these rods could be deduced (from a previous calibration) by measuring the elastic strains to which they were subjected : thus, when the total load ap plied to the yokes was known, the load in the specimen could be de duced. Yield of the specimen merely shifted a greater part of the total load on to the rods and since these, on account of their length, remained elastic, there was no sudden increase in their total extension, and consequently no drop of the beam. Accurately cen tral loading of the specimen was ensured by applying the load through hard steel balls, CC, with the aid of special shackles A, B.

The specimens were of ordinary mild steel, annealed (see § 54) to remove any stresses which might have been induced in course of manufacture. The results showed that the stress, on the occur rence of "yield," does not merely remain constant, but actually drops, by an amount which may be as high as 36%. The prac

tical importance of this effect is evident, for it means that the material, within the region of "plastic" strain, can adjust itself in such a manner as to relieve any intense concentration of stress which may have occurred within the elastic range. This property, which is of great value in constructional work, is known as ductility.

Intermittent Loading: Hardening Effect of Permanent Set.-53. Time has another effect of a different and remarkable kind. If, at some point a (fig. 18) in the region of plastic strain, the load is removed, a part of the strain disappears. This part is accordingly termed the "elastic strain" : to a close approximation, it is related with the stress by a linear law, the ratio of stress to elastic strain being, so far as can be ascertained, the ordinary elastic constant of the material. If the load is immediately re placed and then increased in the ordinary way, a new yield-point b is found at or near the stress previously reached. The full line be in fig. 18 shows the subsequent behaviour of the specimen. If on the other hand, some hours are allowed to elapse before the load is replaced, the new yield point appears, not at b, but at a higher stress d. Fracture occurs (at e, fig. 18) under a higher load than before, and at a smaller total extension : we say that a process of hardening has been going on during the interval of rest.

A

similar and even more marked hardening is found to occur when the load, instead of being removed and replaced, is main tained constant for some hours. When loading is resumed, the yield-point is found to be raised very considerably. Fig. 19 ex hibits experiments of this kind, made by J. A. Ewing on speci mens of annealed iron wire : ab shows the result of continuing to load after an interval of 5 minutes, and acd after an interval of 451 hours. (J. A. Ewing, Proc. R.S., 1880.) Annealing.-54. This hardening effect of plastic strain is of great practical importance. When a hole is punched in a plate, the material round its edge is severely distorted by shear, and the consequent hardening of this material is accompanied by a serious decrease in ductility. Consequently, if the plate is strained by tension, concentration of stress, resulting in the formation of cracks, may occur at the edge of the hole. This bad effect of punch ing disappears when a narrow ring of material, immediately sur rounding the hole, is removed by a cutting tool.

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