An example of injury inflicted in this way is to be found in the method adopted for hooping cast iron tubes cast by Rodman's process. If we take into consideration the undoubted fact of the existence to a considerable extent of useful initial stresses in these tubes, then the hoops should be put on them either with very little shrinkage or none at all, whereas ordnance authorities everywhere have applied to this case methods which are only correct for tubes which are free from initial stresses.Fig. 2
During the process of hooping guns it is very important to know how to take into account the value and mode of distribution of the prejudicial stresses in the inner tube, should such exist. Knowing these stresses, it is possible, by regulating the tension of the hoops, to reduce the compression of the metal at the surface of the bore to the proper extent, thus doing away with the previously existing tension, and by that means removing a source of weakness in the tube. In precisely the same way in the shrinkage of gun hoops attention must be paid to the character and value of the stresses which arise in the course of their manufacture; otherwise it will be impossible to hoop the barrel throughout in a proper manner. If prejudicial stresses exist in the metal of a hoop before it is put in its place, then, when the gun is fired, if it had been shrunk on with the degree of tension usually allowed, the layer situated in the internal radius will be extended beyond admissible limits, thereby causing the resistance of the gun to be less than that prescribed.4
It is evident, from what has been said, that in order to determine precisely the resistance of hollow cylinders to internal pressures, and to make the correct calculations for hooping tubes, it is absolutely necessary to know whether internal initial stresses exist in the tube and in the hoops, and to ascertain what their nature and intensity may be - that is to say, whether they are useful or detrimental; yet it is incontestable that in the construction of modern ordnance no attention has been paid to the investigations indicated. If it be possible to ignore these considerations in the manufacture of guns of small caliber, and where the thickness of metal is not sufficiently great to admit of strongly developed internal stresses, such is by no means the case with the colossal and costly weapons of the present day. In these the thickness of metal in the tube and hoops is very great; hence the extreme probability of very considerable internal stresses developing themselves. That the strength of large guns is often far below that anticipated is demonstrated, year by year, by the repeated cases of failure. Consciousness as to the want of strength in such guns is made evident by the precautionary measures as to their use everywhere adopted.
The heavy artillery produced in the gun factories of Europe is constructed with all the skill, science, and experience which engineers and artillerists can command, and therefore it would seem that instances of defective strength should not arise. Such cases, however, do occur everywhere, and irresistibly give rise to the suspicion that not only is the system of construction of guns of large caliber faulty, but also that the conditions of their manufacture must be considered as defective. Bearing in mind the enormous sums of money expended by every nation in order to secure an armament of completely trustworthy guns, this question demands speedy and searching investigation. The first step in this direction is the study of the internal stresses inherent in the metal; because, if such exist, and are capable of attaining, under certain conditions, considerable magnitudes, then it is absolutely necessary to take advantage of them in order to increase the resistance of the metal, instead of allowing them to act to its detriment.
The study of natural internal stresses is of importance, not only with reference to gun making, but also in respect of other structures where great resistance is required. All have heard of the sudden failure of crank shafts and piston rods, of the bursting of boiler shells and tubes, of the breaking of tires, etc. In the majority of cases the investigations into the causes of such sudden failures have not led to any definite results. It has usually been found that the metal possessed a satisfactory elastic resistance, and satisfied all the conditions set down in the specifications. Had attention been paid during these investigations to the state of the internal stresses in the metal, the cause of unlooked-for accidents might have been explained, and steps would consequently have been taken to avoid them in future.
We are also familiar with the development of considerable internal stresses in various kinds of steel articles which are subjected to hardening and tempering; for example, as dies, tools of various description, sword blades, and thin plates rolled at a low temperature or subjected to cold hammering. In the foundry the appearance of internal stresses is of still more frequent occurrence. The neglect of certain practical rules in casting, and during the subsequent cooling, leads to the spontaneous breakage of castings after a few hours or days, although taken out of the sand apparently perfectly sound. Projectiles for penetrating armor plate, and made of cast steel, as well as shells which have been forged and hardened, and in which the metal possessed an ultimate resistance of over twelve thousand (12,000) atmospheres, with an elastic limit of more than six or seven thousand atmospheres, will crack to a serious extent, and even break up in the lathe, while the recess for the copper ring is being turned out. In shell of this nature, as well as in chilled cast iron shell, the heads are apt to fly off spontaneously either while they are lying in store or during transport.
Such phenomena, it seems to me, demonstrate the existence of internal stresses of considerable magnitude in the metal of the projectiles, and it is highly probable that the manufacture of many articles would have approached nearer to perfection had more attention been bestowed upon the study of the internal stresses which they were liable to. Having thus explained the nature and importance of the subject, I will proceed to describe the experiments which I have made with a view to its illustration. - London Engineer.
Lame holds that in a homogeneous tube subjected to the action of two pressures, external and internal, the difference between the tension and the compression developed at any point of the thickness of the tube is a constant quantity, and that the sum of these two stresses is inversely proportional to the square of the radius of the layer under consideration. Let r, R, and r be the respective radii, p, p1, and p the corresponding pressures, and T, T1, and T, the tensions, then we have:
|T - p = T - p||(1)|
|(T + p)r2 = (T + p)r2||(2)|
|T - p = T1 - p1||(3)|
|(T + p)r2 = (T1 + P1)R2||(4)|
if the radii are known and p and p1 be given, then deducing from the above equations the values T and T1, and also the variable pressure p, we determine -
|T =||p r2(R2 + r2) - p1 R2(r2+r2) |
- - - - - - - - - - - - - -
(R2 + r2)r2
This is the formula of Lame, from which, making p1=0, we obtain the expression in the text.
We must, however, remark that in a built-up hollow cylinder the compression of the metal at the surface of the bore may exceed the elastic limit. This cannot occur in the case of natural stresses.
In certain cases this, of course, may be an advantage, as, for instance, when the inner tube is under injurious initial stresses; but then, in order to be able to apply the necessary shrinkage, we must know the magnitude of these stresses.
When the inner tube is strengthened by means of wire, the initial or natural stresses in the latter may be neglected on account of its thinness; but when the thickness of the hoops is reduced, and the number of layers thereby increased, then the value of the initial stresses in these hoops is a very important factor with respect to the decrease or increase Of the powers of resistance of the gun.