Inner Structure of Metals Problems of Elastic Failure and of Fatigue 72

"Amorphous" Theory.-75.

The "amorphous theory of metals," first propounded by G. T. Beilby and developed by W. Rosenhain (Beilby, Aggregation and Flow of Solids, 1921, p. 123), seeks to explain, in conformity with these observations, the phe nomena of "strain hardening" (§ 53). It can be shown that the process of polishing develops on the surface of metals a thin layer of "amorphous" (or structureless) material; and it is assumed that slipping at the internal surfaces of a crystal has a similar effect. The amount of amorphous material will increase with the intensity of the stress applied : it is assumed that this material is at first mobile (that is, offers little resistance to further distor tion), but afterwards sets like cement, and is then hard and elastic.

Effects of Fatigue.-76.

Ewing and Humphrey (see Phil. Trans. R.S., 1903) employed the microscope to examine the pro cess by which metals break through "fatigue" when subjected to repeated reversals of stress. The first sign of fatigue was the appearance of slip lines on one or more crystals in the region of '1173-76 have been based, by permission, on the article written by Sir J. A. Ewing for the nth edition.

greatest stress : these become more distinct and tend to broaden, developing finally into cracks which can be identified as such because they do not disappear when the surface is repolished. Once a crack has formed it quickly spreads, and finally the speci men breaks with a sharp fracture.' X-Ray Examination of Crystals.-77. For the microscope, as we have seen, the crystal grain is the ultimate unit. But the methods of X-ray analysis, developed by W. H. and W. L. Bragg (see CRYSTALLOGRAPHY), have enabled the study of inner struc ture to be carried much further, since they reveal the structure of the individual crystal ; and a further stimulus to research in this field has resulted from the discovery, by H. C. Carpenter, C. F. Elam and others (see METALLURGY), of methods whereby single crystals of aluminium and other metals can be produced in sizes such that they can be subjected to ordinary engineering tests. At the hands of G. I. Taylor, C. F. Elam (Proc. R.S. [A], vol. 102, pp. 643-67, 1923) and others, these tests have provided a satisfactory explanation of the manner in which crystals distort under steady or fluctuating loads.

78. The stress which a single crystal can withstand without suffering permanent distortion is markedly low as compared with the strength of the crystalline aggregate. It thus appears that we must look to the crystal boundaries (where the atoms presumably have a more random distribution, owing to conflict between re quirements of adjoining crystal "lattices") for an explanation of the relatively high resistance which the aggregate can oppose. This view is supported by the fact that increased strength accompanies a reduction in the size of the crystal grains, under the influences of hardening processes such as heat treatment or "cold work." It remains for further investigation, using the more powerful methods which are now available, to give precision to ideas which have helped, in the past, to correlate the phenomena of plastic distortion and fatigue.

Current Views on Elastic Failure and Fatigue.-79.

A. A. Griffith (Phil. Trans. R.S. [A], vol. 221, pp. 163-198, 1920) has been led, by discrepancies between theory and experiment in regard to concentration of stress in the neighbourhood of scratches or flaws, to propound a theory of rupture (for brittle materials) which takes account of the surface-energy generated in the forma tion of cavities. He has verified the consequences of his theory by producing fibres of fused silica which exhibit strength of a quite abnormal order.

This work is quoted as exemplifying the new outlook which has been made possible by recent advances in physics : it is to microscopical, chemical and X-ray investigations that engineers are looking for a solution of the ultimate problems of elastic failure and fatigue. But understanding of the properties of ma terials contributes only to one side of the general problem of engineering design ; and the practical rule, that working stresses must be kept within the elastic limits, is not likely to lose its validity. The other side of the problem is the calculation of stress, and stresses, in a crystalline aggregate, can only be determined in statistical fashion. So tests of the older type, on specimens large in comparison with the crystalline structure, have not ceased to be useful, nor reached the limits of their development.

(R. V. S.)