Engineering aspects of fatigue

6.11.2 Engineering aspects of fatigue

In laboratory testing of materials the stress system is usually simplified, and both the Woehler and push–pull types of test are in common use. The results are usually plotted on the familiar S–N curve (i.e. stress versus the number of cycles to failure, usually plotted on a logarithmic scale). Ferritic steels may be considered to exhibit a genuine fatigue limit with a fatigue ratio S/TS ≈ 0.5. However, other materials, such as aluminum- or copper-based alloys, certainly those of the age-hardening variety, definitely do not show a sharp discontinuity in the S–N curve. For these materials no fatigue limit exists and all that can be specified is the endurance limit at N cycles. The importance of the effect is illustrated by the behavior of commercial aluminum-based alloys containing zinc, magnesium and

copper. Such an alloy may have a TS of 617 MN m −2 but the fatigue stress for a life of 10 8 cycles is

only 154 MN m −2 (i.e. a fatigue ratio at 10 8 cycles of 0.25).

The amplitude of the stress cycle to which the specimen is subjected is the most important single variable in determining its life under fatigue conditions, but the performance of a material is also greatly affected by various other conditions, which may be summarized as follows:

1. Surface preparation. Since fatigue cracks frequently start at or near the surface of the com- ponent, the surface condition is an important consideration in fatigue life. The removal of machining marks and other surface irregularities invariably improves the fatigue properties. Putting the surface layers under compression by shot peening or surface treatment improves the fatigue life.

Mechanical properties I 373

2. Effect of temperature. Temperature affects the fatigue properties in much the same way as it does the tensile strength (TS); the fatigue strength is highest at low temperatures and decreases gradually with rising temperature. For mild steel the ratio of fatigue limit to TS remains fairly constant at about 0.5, while the ratio of fatigue limit to yield stress varies over much wider limits. However, if the temperature is increased above about 100 ◦

C, both the tensile strength and the fatigue strength of mild steel show an increase, reaching a maximum value between 200 and 400 ◦

C. This increase, which is not commonly found in other materials, has been attributed to strain ageing.

3. Frequency of stress cycle. In most metals the frequency of the stress cycle has little effect on the fatigue life, although lowering the frequency usually results in a slightly reduced fatigue life. The effect becomes greater if the temperature of the fatigue test is raised, when the fatigue life tends to depend on the total time of testing rather than on the number of cycles. With mild steel, however, experiments show that the normal speed effect is reversed in a certain temperature range and the number of cycles to failure increases with decrease in the frequency of the stress cycle. This effect may be correlated with the influence of temperature and strain rate on the TS. The temperature at which the tensile strength reaches a maximum depends on the rate of strain, and it is therefore not surprising that the temperature at which the fatigue strength reaches a maximum depends on the cyclic frequency.

4. Mean stress. For conditions of fatigue where the mean stress, i.e. N a f = (σ max +σ min )/2,

does not exceed the yield stress σ y , then the relationship N a f = const.,

≈ 10 5 cycles, i.e. N less than the knee of the S–N curve, where a

known as Basquin’s law, holds over the range 10 2 to

10 and N f is the number of cycles to failure. For low cycle fatigue

y , then Basquin’s law no longer holds, but a reasonable relationship

p N b f b =D = const., (6.60) p is the plastic strain range, b ≈ 0.6 and

D is the ductility of the material. If the mean stress becomes tensile a lowering of the fatigue limit results. Several relationships between fatigue limit and mean stress have been suggested, as illustrated in Figure 6.68a. However, there is no theoretical reason why a material should follow any given relationship and the only safe rule on which to base design is to carry out prior tests on the material concerned to determine its behavior under conditions similar to those it will meet in service. Another common engineering relationship frequently used, known as Miner’s concept of cumulative damage, is illustrated in Figure 6.68b. This hypothesis states that damage can be expressed in terms of the number of cycles applied divided by the number

to produce failure at a given stress level. Thus, if a maximum stress of value S 1 is applied to a specimen for n 1 cycles which is less than the fatigue life N 1 , and then the maximum stress is reduced to a value equal to S 2 , the specimen is expected to fail after n 2 cycles, since according to Miner the following relationship will hold:

n 1 / N 1 +n 2 / N 2 (6.61)

374 Physical Metallurgy and Advanced Materials

Gerbers parabolic

Goodman’s

Stress (MN m relation

Stress (tons in

N 1 Limiting stress amplitude N 2

Mean stress

Cycles (N)

(b) Figure 6.68 Fatigue relationships.

(a)

5. Environment. Fatigue occurring in a corrosive environment is usually referred to as corrosion fatigue. It is well known that corrosive attack by a liquid medium can produce etch pits which may act as notches, but when the corrosive attack is simultaneous with fatigue stressing, the detrimental effect is far greater than just a notch effect. Moreover, from microscopic obser- vations the environment appears to have a greater effect on crack propagation than on crack initiation. For most materials even atmospheric oxygen decreases the fatigue life by influencing the speed of crack propagation, and it is possible to obtain a relationship between fatigue life and the degree of vacuum in which the specimen has been held.

It is now well established that fatigue starts at the surface of the specimen. This is easy to understand in the Woehler test because, in this test, it is there that the stress is highest. However, even in push–pull fatigue, the surface is important for several reasons: (1) slip is easier at the surface than in the interior of the grains, (2) the environment is in contact with the surface and (3) any specimen misalignment will always give higher stresses at the surface. Accordingly, any alteration in surface properties must bring about a change in the fatigue properties. The best fatigue resistance occurs in materials with

a worked surface layer produced by polishing with emery, shot-peening or skin-rolling the surface. This beneficial effect of a worked surface layer is principally due to the fact that the surface is put into compression, but the increased TS as a result of work hardening also plays a part. Electropolishing the specimen by removing the surface layers usually has a detrimental effect on the fatigue properties, but other common surface preparations such as nitriding and carburizing, both of which produce a surface layer which is in compression, may be beneficial. Conversely, such surface treatments as the decarburizing of steels and the cladding of aluminum alloys with pure aluminum increase their susceptibility to fatigue.

The alloy composition and thermal and mechanical history of the specimen are also of importance in the fatigue process. Any treatment which increases the hardness or yield strength of the material will increase the level of the stress needed to produce slip and, as we shall see later, since the fundamental processes of fatigue are largely associated with slip, this leads directly to an increase in fatigue strength. It is also clear that grain size is a relevant factor: the smaller the grain size, the higher is the fatigue strength at a given temperature.

The fatigue processes in stable alloys are essentially the same as those of pure metals but there is, of course, an increase in fatigue strength. However, the processes in unstable alloys and in materials exhibiting a yield point are somewhat different. In fatigue, as in creep, structural instability frequently leads to enhancement of the fundamental processes. In all cases the approach to equilibrium is more

Mechanical properties I 375 complete, so that in age-hardening materials, solution-treated specimens become harder and fully aged

specimens become softer. The changes which occur are local rather than general, and are associated with the enhanced diffusion brought about by the production of vacancies during the fatigue test. Clearly, since vacancy mobility is a thermally activated process, such effects can be suppressed at sufficiently low temperatures.

In general, non-ferrous alloys do not exhibit the type of fatigue limit shown by mild steel. One exception to this generalization is the alloy aluminum/2–7% magnesium/0.5% manganese, and it is interesting to note that this alloy also has a sharp yield point and shows Lüders markings in an ordinary tensile test. Accordingly, it has been suggested that the fatigue limit occupies a similar place in the field of alternating stresses to that filled by the yield point in unidirectional stressing. Stresses above the fatigue limit readily unlock the dislocations from their solute atom atmospheres, while below the fatigue limit most dislocations remain locked. In support of this view, it is found that when the carbon and nitrogen content of mild steel is reduced, by annealing in wet hydrogen, striking changes take place in the fatigue limit (Figure 6.5) as well as in the sharp yield point.