FATIGUE OF METALS, a generic term denoting all phenomena associated with the behaviour of metals subjected to repetitions of a range of stress. The term, however, is more gener ally applied to the progressive deterioration, leading to ultimate fracture, caused by repetitions of a cycle of stress, the maximum stress of the cycle being numerically less than that stress which causes failure on a single application. Fracture by fatigue can be caused by repeated cycles of direct, bending, torsional, or combined stresses, and is accelerated by the presence of shock conditions or surface defects, sudden discontinuities of section, etc., which create local concentrations of stress.
Three Types of Stresses.—Cyclical variations of stress can be divided into three main types : Alternating stresses (maximum and minimum stress of cycle differ in sign), pulsating stresses (stresses vary from zero to maximum value) and fluctuating stresses (vary in magnitude but not in sign). Any stress cycle is defined numer ically by the expression where M is the average stress, and R is the range of stress (algebraic difference of maximum and minimum stresses). Fatigue range or limiting range (R) is the greatest range of stress which can be applied for an indefinitely great number of repetitions without causing fracture. Endurance, under a given range of stress, is the number of repetitions neces sary to cause fracture.
In 1849 Jones and Galton investigated the behaviour of cast iron bars subjected to pulsating bending strains. Fracture occur red in less than 1 oo,000 strainings when the range of strain ex ceeded one-third of the static ultimate deflection. The endurance decreased at an increasing rate with increased ranges of strain. Bars which had been partially fatigued suffered no loss in static ultimate strength. Somewhat similar tests, on a wrought-iron built-up girder, were made by Fairbairn in 186o–I. The loading was applied with shock. Fairbairn's conclusions confirmed those of the earlier workers and also pointed to the existence of a definite fatigue range for metals. These conclusions received further support from the experiments of Wohler (1871), in which, for the first time, strict attention was paid to the magnitude of the applied stresses. Wohler used iron and steel subjected to cycles of direct, bending, and torsional stresses.
Subsequent to these early classical investigations, the fatigue of metals has formed the subject of several hundreds of independ ent researches. The main objects of these investigations and the conclusions drawn from the results are briefly summarised below. (Except where otherwise stated, the remarks apply only to tests conducted at air temperature.) Evidence of a Limiting Range of Stress.—The results of a series of endurance tests, where any one type of straining action and a constant value of the mean stress of the cycle are employed, show that the endurance (N) to fracture increases at an increasing rate as the range of stress (S) decreases. A curve connecting S and N tends to become parallel to the N axis. It is regarded as established that, in the case of ferrous metals, the S/N curve has become parallel to the N axis at values of N of or reversals, and remains so for the maximum endurances investi gated (Io$ to cycles). This is also true for some of the pure metals and non-ferrous alloys. Tests on some non-ferrous metals and alloys, however, have shown fractures to occur after several hundred millions of reversals, although, at these endurances, the slope of the S/N curve is very small. In general, sound metals appear to possess a definite limiting range of stress Two relations have been suggested, both of which can be expressed by the formula — RLR(I-M) R where is the limiting range when M is the corresponding value of the mean stress ; RLR is the limiting range when M=o, f is the static ulti mate strength of the metal, and x has the value of I or 2. Some experimental results agree with one of these relations, others conform to neither. For cycles of direct stresses, the linear relation is generally a safe rule between the limits of M=o and M=IR. Some experiments employing torsional stresses have shown that the value of is not altered appreciably by wide variations in the value of M.
Effect of Frequency of Cycle (F) on Limiting Range is now established that a constant value of is obtained at frequencies up to 5,000 cycles per minute. Tests made on copper, iron, and mild steel at frequencies of 3,000, 30,000, and 6o,000 cycles per minute gave progressively greater values of at the higher frequencies.
Under repetitions of the limiting range, or a numerically inferior range, a state is ultimately reached when no further plastic strain occurs ; approximate elasticity only results as strain hysteresis can be detected. These natural elastic limits are not related to the primitive, or original, elastic limits of the material. When the applied range of stress exceeds the limiting range, plastic def or mation generally occurs until the cracking stage is reached.
Effect on Limiting Range of Temperature of Test.— Available data relate only to reversed stresses (M=o). The limit ing range is largely unaffected in value until temperatures of about 400°C. are reached. At higher temperatures de creases, the rate of decrease varying with different metals. The effect of elevated temperatures on is not, in general, as marked as on the static ultimate strength under prolonged load ing; e.g., the values of -RL for four steels and one non-ferrous alloy, at various temperatures between 550°C. and 750°C., have been found to be equal to, or greater than, the static strength (under prolonged loading) at the same temperatures.
Effect of Repeated Stresses on Microstructure of Metals. —Repeated stresses applied to crystalline aggregates cause slip bands to appear on the surfaces of favourably orientated crystals. If is not exceeded, this local action ceases after a certain number of repetitions and the metal becomes strain-hardened. Under repetitions of greater stress ranges, microscopic cracks are initiated in the regions of maximum slip, and fracture is caused by propagation of these cracks throughout the metal. Even in ductile materials, the process of initiation and propagation of these cracks may be so highly localised that the appearance of fracture is one usually associated with that of brittle materials. Precisely similar surface phenomena are exhibited by single metallic crystals subjected to repeated stresses, suggesting that fatigue failure is essentially a process of deterioration of crystal line material and that the chief effect of the inter-crystal bound aries in aggregates is to inhibit slip due to the change in orienta tion of neighbouring crystals.
A fundamental theory of fatigue has yet to be advanced. The attrition theory (Ewing and Humfrey) is not supported by the results of recent research. A number of theories have been based on the assumption (Beilby) that plastic strain in metals a change from the crystalline to the amorphous state on the surfaces of slip. The manner in which the fatigue crack is ini tiated has not been explained satisfactorily. The results of experi ments on single crystals (Gough, Hanson, and Wright) suggest that the effect of slip is to produce local distortions within the crystal, thus setting up internal stresses which, under repetitions of stress ranges, lead to the disruption of inter-atomic bonds and the initiation of cracks. The breaking-up, under strain, of a crystal grain into a number of crystallites of slightly varying orientations is an alternative hypothesis which is consistent with observed facts. Little doubt exists that, in some manner, fatigue failure is the direct result of local plastic deformation, and it seems highly improbable that fatigue would occur in a material which is truly elastic.
The importance of an understanding of fatigue phenomena in its relation to industry cannot be over-estimated. Those machine and structural components whose working conditions can be so adjusted as to exclude the possibility of fatigue failure constitute a very small minority. The whole trend of development of modern engineering lies in the direction of the employment of higher working stresses, speeds, and temperatures. These consider ations, together with the necessities of eliminating unnecessary material—to reduce first cost—and the reduction of the weight power factor—which has become of prime importance since the advent of aircraft—tend to make the static strength properties of metals (except at elevated temperatures) of less relative im portance than their fatigue properties. A conservative estimate of failures in modern engineering practice attributes 8o% of such failures to fatigue. As fatigue failures are usually unaccompanied by any marked preliminary warnings, a deplorable loss of life has often resulted. See METALLOGRAPHY; METALLURGY; MA TERIALS, STRENGTH OF.