Application of the Theory to Real Materials

Relation Between Safe Range and Mean

As suming that a limiting range exists for reversed stresses, the ques tion arises, how is it affected by the imposition of a mean stress M? In other words, what is the relation between R and M, for safe ranges of stress? Before this question can be answered, it is evident that a very large amount of data must be accumulated ; Gough, who has analysed carefully such results as are available, regards the problem as still unsolved. Two forms of "law" have been pro posed which seem fairly satisfactory, namely, the "modified Goodman law" and "Gerber's parabolic law." According to the modified Goodman law, where R is the safe range corresponding to a mean stress M, is the safe range when M=0 and f is the ultimate strength of the material. According to Gerber's law, Gerber's law is closely satisfied by the experiments of Wohler and Bauschinger and, less closely, by Haigh's results for mild steel. Goodman's law applies to Haigh's experiments on naval brass, in cases where the mean stress was tensile. (Cf. Gough, op. cit., Chap. IV.) Influence of Frequency.-67. This again is a question de manding a great accumulation of experimental results. Tests by B. Hopkinson (Proc. Roy. Soc., vol. 86, 1911) and Stanton in dicate that a slight increase in endurance accompanies a rise in frequency. Under reversed stresses, the limiting ranges of stress for a certain mild steel were found to be: ± tons/sq.in. (Stanton machine: 1,000/1,30o r.p.m.) ± tons/sq.in. (Wailer machine: 2,200 r.p.m.) tons/sq.in. (Hopkinson machine: 7,000 r.p.m.) C. F. Jenkin (Proc. Roy. Soc., vols. 103, 1923 and 109, 1925) has developed apparatus by which fatigue tests can be conducted at speeds up to 20,000 cycles per second. His work is still in prog ress, but so far his results confirm the conclusion that increased speed has at all events no deleterious influence.

Much information is now available regarding the behaviour of engineering materials under imposed stresses of various kinds.

But much still remains to be done : (I) in developing rules for design which shall be applicable to "compound" fatigue stresses; (2) in correlating the fatigue properties of a material with "static" properties such as its elastic limit, yield stress or ultimate strength, or with the results of "impact" or "hardness" tests; (3) in explaining the inner mechanism of fatigue.

The

last of these problems comes within the scope of the third section of this article. All three are discussed at considerable length (although, necessarily, without very conclusive results) in the treatise by Gough to which reference has been made above.

Impact Tests.--69.

Fatigue tests are concerned with the slow cumulative effect of stress-cycles which could be imposed thousands or even millions of times without producing rupture. At the other end of the scale of practical conditions, we have to consider the possibility that a material may be broken by shock —that is, by intense stresses maintained for an infinitesimal period of time.

To investigate "toughness," or resistance to shock, is the pur pose of impact tests. They usually involve the breaking of a specimen of standardized form (it is commonly notched, in order to secure a concentration of stress at one section) by means of a falling weight : the energy absorbed in this process is taken as a figure of merit for the material. Unfortunately, they have

been developed largely by empirical methods—mainly because little is known of the stresses which obtain during impact. The shape of the notch, the velocity of striking, even the shape of the striker, appear to affect the results, which are not easy to interpret by a dimensional law, even when specimens of the same material and geometrical form are employed, differing only in respect of size (cf. R. V. Southwell, Aeronautical Research Committee, R. and M. 732, 1921). Thus it is difficult to compare results obtained by different methods or on different i and the subject cannot be briefly summarized. The reader is re ferred to Batson and Hyde, Mechanical Testing, vol. i (1922), or to Timoshenko and Lessels,Applied Elasticity, Chap. XIV. Hardness Tests.-7o. In us ing the term "hardness," we may be thinking of resistance to in dentation, of resistance to abra sion, or of ability to retain a cut ting edge. These properties are not identical, and each calls for a separate test. We shall here con fine attention to various forms of indentation test. (Cf. Timo shenko and Lessels, op.cit., Chap. XV.) A measure of resistance to indentation may be obtained by applying a standard pressure to two crossed specimens of the same material and measuring the indentation thus produced. Reaumur (1722) used right-angled prisms and measured the depth of the indentation; Foppl used circular cylinders (figure 27b) and measured the superficial area; Haigh used square prisms (fig. 27c).

Brinell (Proc. Inter. Ass. Test. Math., 1901) proposed a test which has since come into very general use. A hard steel ball is forced into the material under a standard pressure, and the di mensions of the indentation are measured. This test is practically convenient, in that it can be imposed without damage on a finished engineering component ; moreover it appears to determine, with some accuracy, the ultimate strength which may be expected of the material when exposed to an ordinary tensile test. Subsequent work by Meyer (Zeitsch. d. Ver. deutsch. lug., p. 645, Batson (Proc. Inst. Mech. Eng., 1923) and Devries (Proc. Am. Soc. Test. Math., vol. XI.) has shown that standardization of the test conditions is important : Brinell suggested a ball of to mm. diameter, and a standard pressure of 3,00o kg. for hard and of 500 kg. for soft materials.

71. Dynamic tests of a similar nature have been proposed. In the scleroscope test, hardness is measured by the height of rebound of a small diamond-pointed hammer which is allowed to fall through a standard distance : an advantage is offered in that there is no permanent indentation.

Reaumur also tested hardness by using the material to scratch a standard bar of increasing hardness from one end to the other. Turner (Proc. Birm. Phil. Soc., vol. V. 1887) reversed the process, employing a standardized diamond point to scratch the material under test, and measuring the load which this point must carry in order to produce a visible scratch. Martens, Hadfield and Han kins have contributed to the development of this test, and have investigated the correlation of "scratch hardness" with "Brinell hardness" (cf. Timoshenko and Lessels, loc. cit.).