Application of the Theory to Real Materials

A modified form of this machine, employed by T. E. Stanton and R. Batson (Brit. Ass. Report, 1916) enables torsional stresses to be superposed.

"Specific Stress" and "Specific Strain."-62. It is important to distinguish between the conditions imposed by different ma chines, because these largely influence the behaviour of the material. Thus the machine just described applies a definite bend ing-moment (that is, practically speaking, a definite stress), inde pendent of the strains which the material may undergo ; we describe such conditions as specific stress. In other machines a definite strain is imposed, independent of the stress-distribution which may result through plastic distortion of the specimen ; we describe such conditions as specific strain. In other machines, again, the conditions are such that the stress either increases or diminishes as the strain increases.

This variation in the conditions of test has its counterpart

in 'A. Wohler, Zeitschr. f. Bauwesen, vols. 8-20 (1860-70). An account is given in Engineering, vol. II (1871).

actual practice : thus a connecting-rod is exposed to conditions of specific stress, and the valve springs of an internal combustion engine to conditions of "specific strain." The Variable Factors in Fatigue. Nomenclature.-63. Even when the stress imposed is the simplest possible,—namely, simple tension,—it is evident that many variable factors are in volved. First, the stress may vary between any two limits. Using positive and negative signs to denote tension and compression, we write and pm,.. for the highest and lowest tensions which are imposed ; we term the "upper" or "superior" limit of stress, and the "lower" or "inferior" limit. The "total range of stress" (R), and the "average" or "mean stress" of the cycle (M), are then defined by the relations R=Pmax• and the stress-cycle may be concisely described as the cycle In an "alternating stress" test, M is zero and the stress fluc tuates between equal and opposite limits.

Again, the stress may fluctuate between specified limits at dif ferent speeds If T is the time (in secs.) taken by one complete stress cycle, the number of cycles per second is given by n= and is termed the "frequency" of the test.

Further, the stress may fluctuate with time, during one stress cycle, according to any imposed relation. This relation ought always to be specified in describing the results of tests, in order to make the conditions precise ; but little information is available at present regarding its importance.

Endurance Tests, and the "S-N Curve."-64.

The aim of fatigue tests is to determine, for a definite stress-cycle applied at a definite frequency, the number of cycles which a material can sustain without fracture. This number (N) is termed the "endurance." In a test under alternating stress, the cycles may (subject to the remark at the end of the last paragraph) be taken to be defined by , the greatest (numerical) value of the stress S. We 2 seek by experiment to relate S with the endurance N, and the curve which gives this relation is termed an "S-N curve." Fig. 26, by T. E. Stanton and J. R. Pannell (Proc. Inst. Civ. Eng., vol. 188, 1911-12), in tests of mild steel, shows typical results. It will be seen that the plotted points lie more or less evenly on a curve which appears to become parallel with the N axis when the num ber of reversals to fracture is large. The last point on the dia gram relates to a specimen which was still unbroken after lc) mil lion reversals of stress. We say that the test has been carried out "on a io million reversals basis"; and on this basis we may express the results by saying, either (a) that the endurance limits of stress are -±12.75 tons/sq.in. or (b) that the limiting range, for reversed stresses, is 25.5 tons/sq.in.

65.

Evidently, if the true curve does in fact become horizontal, there is a limiting range of stress below which fracture will not. occur for any number of reversals, however large. It is not pos sible to decide this question positively, since we can, in practice, impose only a limited number of stress-cycles. (The greatest numbers imposed in any recorded test would appear to be 202 millions : the specimen, tested by J. E. Howard under reversed bending—Proc. Inter. Assoc. Test. Mat., 1909 Congress.—was not broken.) But the weight of evidence appears to show that limiting ranges of stress do exist, and that they can be found, with all the accuracy required for practical purposes, by endurance tests on a I reversals basis. Gough, who has done much to elucidate this question, emphasizes that tests on a one million reversals basis are practically worthless.