RESEARCH INTO THE FATIGUE OF METALS

Issued by British Information Services – The Certificated Engineer March 1966

The phenomenon of fatigue failure in metals is still incompletely understood and several of its aspects are being investigated at the National Engineering Laboratory in Britain. 

The phenomenon of metal fatigue was first observed and studied well over a century ago and has since been the subject of intensive and systematic research, particularly in the past 20 years. Nevertheless, most failures of metal components or structures which occur at room temperatures may be attributed to some aspect of fatigue.

Some of these failures are due to the lack of precise knowledge of the service-loading conditions. However, where these are accurately known, there remains the problem of predicting the endurance under such conditions, which may involve widely varying stress amplitudes. A study of this problem, known as cumulative fatigue damage, forms part of the research programme at the National Engineering Laboratory (N.E.L.).

Even where the fatigue loading is known to be of constant amplitude, the prediction of endurance is still complicated by the existence of stress concentrations or of fretting conditions. Many failures are caused by the lack of application of existing knowledge of the effects of notches in fatigue; thus, stress concentrations may be a consequence of poor detail design or of manufacturing techniques which provide an inadequate surface finish. The large reduction in plain fatigue strength owing to fretting conditions is possibly less widely appreciated; this topic is also being studied extensively at the N.E.L.

The sophisticated design methods now employed in the aircraft industry, incorporating "fail-safe" structures, render catastrophic failure by fatigue infrequent in this field; however, a correspondingly greater interest has been aroused in the behaviour of a propagating fatigue crack. Thus, in many instances it may be just as important to know whether a fatigue crack will grow to dangerous proportions between routine inspections, as to prevent its initiation. Extensive investigation of crack propagation forms the third major field of study in the fatigue research programme at the N.E.L.

Cumulative Damage

One of the problems facing the designer of a component subjected to fatigue loading is that, while the amplitudes of the fatigue stresses in service will probably vary considerably during the life of the component, most of the data in the literature refer to tests conducted at a constant stress-amplitude. As it is not always feasible to test trial components under simulated service conditions, some method must be employed of estimating the endurance under variable-stress conditions, from the constant stress-amplitude data. The well-known linear cumulative damage hypothesis, as stated by Palmgren and Miner, may be written

where n is the number of cycles at a given stress and N is the number of cycles to failure at that stress in a constant-amplitude test. Although widely used because of its simplicity, this rule is known to be inexact and may give dangerously optimistic life predictions, especially for complex stress spectra. In other cases, life predictions from this rule are unduly conservative, resulting in heavier structures than necessary. The avoidance of such over-design is particularly important in the field of aircraft design, where weight-saving is vital. In general, this rule is an over-simplification of the problem, making no allowance for the effects of residual stresses or the interaction between high and low stress levels.

Rotating-bending fatigue tests at the N.E.L. on mild steel and aluminium alloy specimens subjected to repeated linearly increasing and decreasing stress blocks, support the concept of 'hypothetical' stress/ endurance curves which may be used instead of the conventional SIN curve, together with a linear damage accumulation law, to make allowance for the various effects that the Palmgren-Miner rule ignores. This concept was developed in the work of Freudenthal and of Corten and Dolan and their associates, but still requires further experimental verification. The work at the N.E.L. shows in particular that, for cumulative damage tests on mild steel specimens (although not for aluminium alloy), only stress cycles below 80 per cent of the fatigue limit may be considered non-damaging, whereas the Palmgren-Miner rule implies that all stresses of amplitude less than the fatigue limit may be neglected. This work is being extended to more complex stress spectra, including random amplitude stress cycles, and to other materials.

Crack Propagation

The variation of the service stress is only one of the many complications that arise in the prediction of the life of an actual component, and which limit the usefulness of a knowledge of only the plain fatigue properties of the material. In some cases, the catastrophic failure of a component, particularly in aircraft structures, may depend less on the cyclic stress required to initiate a crack than on that required to cause the crack to grow. Thus, parameters describing the behaviour of a fatigue crack are essential to a complete understanding of the fatigue phenomenon.

An extensive programme has been carried out at the N.E.L. on the determination of the laws governing the rate of crack growth and of the cyclic stress required to cause a crack of a given length to grow. Fatigue cracks have been grown from a small central slit in sheets ten inches wide and 0.125-inch-thick, subjected to a wholly tensile loading cycle, T +-ơ. It has been found that the initial crack growth rate (when the crack length is less than one-eighth of the sheet width) satisfies an equation

where ± ơ = alternating stress based on the gross cross-sectional area of the sheet, in tons/inch2 , 1 = crack length, in inches, N = number of cycles, in millions (106), and A = a material constant which for some materials depends on the value of the mean stress, T, that is A = P + QT. Values of P and Q are given in Table I.

The study of the cyclic stress required to grow a crack has been carried out by testing plate specimens 2.1 inches wide and 0.25-inch-thick which incorporate two coplanar edge cracks. For zero mean load conditions it was found that whether a crack grows depends on the parameter ơ31. If this parameter has a value greater than a material constant, C, then the crack with grow; if ơ31 is less than C, the crack remains dormant. Values of C have been determined for several materials and are also given in Table I. Work has begun on determining the effect of mean stress on the value of C.

The effect of environment on the initiation and propagation of fatigue cracks in mild steel has been studied by testing specimens immersed in oil or water or coated in butyl rubber. It was found that such environments have little effect on the initiation of a crack but can have a profound effect on its propagation. This work is to be extended to other materials whose C values have been determined.

Some studies of crack initiation and propagation are also being carried out on sheet specimens subjected to fluctuating tensile loads of such magnitude that failure occurs after a small number of cycles. These sheet specimens contain either a central hole or two edge notches, and the elastic-plastic stress and strain distribution at the notch are studied by using a photoelastic surface-coating technique. The growth of the fatigue crack through the local plastic region at the notch is of particular interest.

These photoelastic-coating techniques have been used extensively to study the deformation around cracks in the crack-propagation work on various sheet materials described previously. The strains in the local plastic region around the tip of the crack were found to be higher than those predicted by elastic theory. For all the nine materials tested except mild steel, the elastic-plastic maximum shear strain (γ) distribution around a crack in a wide sheet could be estimated, during loading, from the equation

where E is the modulus of elasticity, Es the secant modulus corresponding to γ1 and γ0 the elastic solution for the maximum shear strain. It is expected that this equation should apply to all materials having a monotonically increasing tensile stress strain curve.

Fretting

It is known that. serious reductions in the fatigue strength of a material may result from fretting conditions as shown in Fig. 3. Fretting is damages caused by surfaces rubbing together under a small-amplitude oscillatory motion. Shallow cracks form at the edges of micro-welds between the fretting surfaces relatively early in the life, even under low fatigue stress in the body of the material. Some of these cracks coalesce to form pits, thus releasing metal particles which may subsequently oxidise to give an abrasive product, causing much of the wear. If the fatigue stress in the. body of the specimen is sufficiently high, the small, oblique, surface cracks will propagate through the material. Atmospheric corrosion enhances this propagation and possibly also the initial crack formation. The nature of the fretting process, the effect of various parameters on the fretting-fatigue strength of structural materials, and the use of anti-fretting coatings are being investigated at the N.E.L.

It has been found that the fretting amplitudes causing the greatest fatigue damage are in the range of plus or minus 0.00015 Inch to about plus or minus 0.0.005 Inch, and that substantial improvement in fatigue strength is gained if fretting amplitude is reduced below 0.0001 inch. This surface slip will not occur where the product of normal load and coefficient of friction exceeds the tangential force. Thus, in joints such as pin-joints a sufficient interference between the pin and the hole increases the load normal to the interface. Similarly, in joints where the relative deformation is not too large a high coefficient of friction is advantageous. In some joints where one component is clamped against another. It is possible to reduce slip by increasing the flexibility of one component in the tangential direction, and thus enabling the differential strain to be taken up by elastic deformation without requiring unduly high contact pressures. However, large contact spans mean that more deformation must be accommodated and make it very difficult to prevent surface slip. If appreciable surface slip does occur, then fatigue strength decreases with increase of contact pressure. It has also been shown that fretting has its greatest effect when its direction coincides with that of the cyclic stress.

The fretting-fatigue strengths of both En26 alloy steel and L65 aluminium alloy decrease rapidly with increasing tensile mean stress. At high mean stress the amplitude of the fretting movement is particularly critical for En26 steel. Under low mean stress it is found that the fretting-fatigue strength of En26 steel (67 tons/inch2 tensile strength) is like that of mild steel (24 tons/inch2 tensile strength). This is explained by the very similar crack propagation behaviour of these two steels (see Table I).

An extension of this work of immediate practical application is the determination of the fatigue strength of pin-joints. Previous work at the N.E.L. has shown that the fatigue strength of pin-joints in light alloy material is greatly increased by using a suitable degree of interference between the steel pin and the light alloy plate, thus inhibiting surface slip and fretting. Further tests on plates of three steels give similar results. Clearance fits are also found to give some improvement over neat-fitted pins, owing to elimination of contact, and therefore fretting, at the sides of the hole where the stresses are highest.

Concluding Remarks

The previous paragraphs have described in some detail several of the major research projects being carried out at the N.E.L. on fatigue of metals. Much other work in this field is proceeding concurrently, including the fatigue testing of actual components for industry. Such tests have included rotating-bending fatigue tests on full-scale railway wheel and axle assemblies, and fatigue tests on a rear-axle casing of a commercial road vehicle.

On the other hand, the fatigue programme is balanced by fundamental research into the mechanisms of fracture from the metallurgical or metal-physics viewpoints, including studies of cyclically strained material using the techniques of thin-film electron microscopy.

This paper is published by permission of the Director of the National Engineering Laboratory, Department of Scientific and Industrial Research.