a 1 inch square bar broke under a load of 26 tons, say, while the broken section was only .6 sq. ins. Then the Real Tenacity, as it is sometimes called, is, when thus estimated, But the real load (PF) at the instant of fracture was much less than 26 tons (PE), say only 21 tons, and the real stress only 21/.6 or 35 tons per sq. in. And so it is perhaps on the whole better to say the tenacity or ultimate strength is 26 than 43 tons. There are objections even to regarding 35 tons as the true tenacity. Shape of Specimens.-We said (page 416) that there is a reason for having a fairly long piece of uniform section other than for measurements of extension, and this reason is connected with the question we have just been considering. Suppose, instead of having a long straight part, we make a groove in the specimen piece, as Fig. 316, then we have practically no length at all for extension to take place in; and if we experiment on such a piece we find that it does not draw out at all, but finally breaks across at (k KK, the broken section being very little less than the original one, ¿.e. the original one at KK; the groove is now the bar, the other parts being its ends. Also the breaking load will be found to Fig. 316. be much higher than for a bar of section KK throughout; and consequently the apparent tenacity of the metal will be higher than it would be if obtained by breaking a specimen of the ordinary dimensions. The real tenacity will, however, be found to be much the same as for the ordinary specimen, the whole of the difference in the results appearing to be due to the difference in the broken sections. Now it seems clear that a grooved bar cannot really be stronger than one of uniform section KK-in fact we shall show that for certain kinds of load the grooved bar is actually the weaker, consequently we say, either that the true tenacity should be taken as a measure of the actual strength, to which we have seen there are objections, or better, that specimen pieces should have fairly long parts of uniform sectional area, as we have already stated they now always have. Plastic State-Flow of Metals.-Returning to the consideration of the curve ABCDEF (Fig. 313), we see that up to E it is necessary, in order to produce extension, to continually increase the load and the stress. But after E it appears that a considerable amount of extension can be produced with a decreasing load, which may cause, as we have seen, a constant or slowly increasing stress on the weak section. The metal has now properties directly opposed to its elastic properties. For within the elastic limit strain is proportional to stress, whereas in the present case strain is nearly independent of stress. There are certain materials, e.g. clay, which are practically always in this latter state, for if we press a piece of clay we can change its shape, ¿.e. produce strain, to any extent, by keeping up the pressure long enough, without increasing it at all. Materials of this kind are called Plastic, and a perfectly plastic material would be one in which a given stress could produce any amount of strain, depending only on the time of application. Since the metal appears during EF to be nearly in this condition, we say it is in the plastic state. The change of form produced in the plastic state is often called Flow, and the effect is called the Flow of Metals. This effect is of importance in many industrial occupations, one case which we may mention being the operation of wire-drawing. Here a bar of metal is pulled through a hole of smaller section than the bar, and the metal flows, forming a smaller bar; this process being repeated with continually diminishing sizes of hole, we finally obtain a wire. The effect is complicated by the pressure of the sides of the hole, and so is not a case of simple tension but is similar somewhat to that shown in Fig. 300. The manufacture of lead pipes, or solid-drawn copper pipes, depends on the same phenomenon. Effect of Stress beyond the Elastic Limit.— When a bar is subject to stress within the elastic limit, on removal of the stress the bar returns to its original form, and retains all its original qualities. But if the stress be increased beyond the elastic limit and then removed, the bar in the first place does not return to its original length, but has a permanent increase of length or set; and secondly its properties are altered. Let a bar be stretched, its stress-strain diagram being as in Fig. 317, till the point b is reached. Remove the load, then the bar contracts, and the relation between load and strain is shown by the line ba; Aa shows the amount of permanent set, and ba is almost exactly parallel to AB. Now let the bar be stretched again, when it will extend according to the line ab, and will remain perfectly elastic not only up to the same elastic limit as it originally had, but right up to the point b, and we say the elastic limit is raised up to the stress which was origin ally applied. There will now be a period of imperfect elasticity bc, a new breaking-down point c, and so on, as shown in the figure. The effect can be repeated any number of times, so long as the point E of Fig. 313 has not been reached. Since the elastic limit of a bar can be increased in the above way, it may be thought that the bar is strengthened, and so in a limited sense it is; but for practical use it is not strengthened but weakened, for reasons which we shall now see. A Effect of Impact. We have so far supposed pieces of material to be gradually loaded, but in very many cases the loads which they have to bear in practice will be applied to them suddenly, or may be brought against them with a certain velocity. We will now see what effect this will w have. AB is a rod fastened at A, a weight W encircles the rod, and is let fall from a height on a collar at B. AB will then stretch to a length AB', shown exaggerated; if this be the utmost extension the weight W will then be at rest. Consider now the period from the moment W was let go until it stops at B'. B B R C Fig. 318. Then and Initial K. E. =0, Final K. E. =0. .. Energy exerted _ work done = (by gravity) (against resistance of rod). We will now consider two cases : Case I. When W and h are such that the rod is not stretched beyond the elastic limit. Let R be the final resistance of the bar, i.e. when it is stretched to AB'. Then, setting off B'C = R, and joining BC, BC will be the curve of resistance, since within the elastic limit load varies as strain, and when the load is applied gradually, as in the testing machine, there being no K. E. developed, the load and resistance at every instant balance, therefore resistance varies as strain. ... Work done area of BB'C, =RX BB'. But if A be the sectional area of the bar, an equation which will give us the value of R, and therefore of R/A, the final stress produced, when W and 1⁄2 are given. [Compare with the foregoing chap. xiii. page 271.] One case gives a simple result, viz. when h=0, so that the load is suddenly applied, although not with any initial velocity. or This gives W. AXE R2 .AB, R=2W, so that by sudden application the effect of a load is doubled, and this explains why it is necessary when |