Very few structures operate at a ‘static’ stress (Figure 1), where the stress on the structure is constant. Most structures, such as airplanes or bicycles, are subjected to repeat (‘cyclic’) and varying stresses, and this cyclic stressing can lead to cracking. These varying stresses can cause cracks, and the cracks can cause failures.
|Figure 1. Cyclic Stresses cause Fatigue.|
You can perform a simple experiment on fatigue. You cannot fail a paper clip by simply pulling it to failure, as it is too strong under a single (‘static’) load. But it is very weak under a small repeated (cyclic) bending load:
- take a paper clip;
- bend it repeatedly;
- it fails (separates) in a few bends (the repeated bending is your cyclic load).
You have initiated a crack in the paper clip, and it has grown to failure because of your repeated bending. The paperclip’s ‘fatigue life’ or ‘endurance’ is the number of times (‘cycles’) you have bent it before failure.
Problems with structures subjected to cyclic stresses were identified 150 years ago. As iron and steel structures came into widespread use, engineers were faced with failures occurring well below the tensile strength of the materials. The materials were ductile (could deform), but the failures exhibited little or no ductility (no deformation). The world became aware of ‘metal fatigue’.
The structures that were failing had been subjected to repeated stressing (cyclic stresses). The static or peak stress was not sufficient to fail the structure, but these cyclic stresses were sufficient. Hence, engineers had to understand these failures, and the effect of these cyclic stresses.
Metal fatigue was reported by railroad engineers in the 1880’s. A number of accidents involving failed train axles led engineers to describe the parts as being ‘tired’, or ‘fatigued’. Most of the early failures had developed in machine parts which were subjected to high frequency repeated loading.
The first commercial jet airplane (the Comet) failed in the early 1950s due to fatigue around its square-shaped windows. A combination of poor design and bad manufacturing led to many deaths.
Today, ‘fatigue’ is defined as : ‘process of development of or enlargement of a crack as a result of repeated cycles of stress’. These repeated cycles of stress can either:
- initiate (create) and grow a crack in a structure; or,
- grow an existing crack.
These fatigue mechanisms can lead to failure.
The Three Stages of Fatigue
Fatigue is made up of three stages: initiation; propagation; and, failure. When I have no macroscopic defects present, the fatigue life consists of about 90% ‘initiation’ of a crack, and about 10% ‘propagation’ of a crack. When I have a macroscopic defect (e.g. a crack) present, most of the fatigue life is propagation.
Even small macroscopic defects (such as those in a weld) will have negligible cycles to initiation.
Fatigue Assessment using ‘S-N’ Curves
We know that fatigue is made up of three stages: initiation; propagation; and, failure. All these stages can be described by a cyclic stress (S) versus number of cycles (N) to failure curve (the ‘S-N’ curve), Figure 2, provided the existing defects in the structure are ‘insignificant’ (small); for example, they are all within quality control levels.
The S-N curve is obtained experimentally, for the specific material, environment, loading, and structure shape, and there are examples in the literature; for example, Reference 2.
We obtain a ‘fatigue life’ from the S-N curves: this is the number of cycles the material can withstand, before failure, at a specified stress range.
The S-N curves are ‘log-log’ plots. We use log-log plots to allow us to fit the wide range of cycles (N) we are interested in – typically between 1000 and 100,000 cycles. We also need a wide range for our cyclic stress range to accommodate the varying stresses experienced by various structures. We could not fit this wide range of data on a simple linear-linear graph.
|Figure 2. The ‘S-N’ Curve for Fatigue Assessment.|
The S-N curves are sensitive to many parameters (e.g., the mean stress in the stress cycle). The stress range has the greatest effect on fatigue life, but other parameters, such as the environment, have an effect.
The fatigue life of metals decreases when they are exposed to a corrosive environment, Figure 3. This ‘corrosion fatigue’ is usually called ‘environmentally-assisted cracking’ (EAC). It is caused by the combined actions of cyclic loading and a corrosive environment. The fatigue life of a pipeline in water and seawater can be recovered, more or less, by correct application of cathodic protection.
|Figure 3. Effect of Environment on Fatigue Life.|
Fatigue Assessment using Fracture Mechanics
S-N curves can be applied to ‘defect-free’ materials that have been produced to an acceptable standard. We cannot use S-N curves if we have a pre-existing defect, such as a crack. We must use fracture mechanics methods (e.g. ) to assess pre-existing defects.
Pipelines and Fatigue
Pipelines are subjected to cyclic stresses due to:
- internal pressure variations, caused by changing demands for the product;
- changes in temperatures (these changes will cause the pipeline to expand or contract, and this leads to changes in stresses);
- external loads, such as traffic loading over a buried pipeline, or movement on a seabed from sea currents).
These cyclic stresses can:
- create and grow cracks;
- cause existing cracks in the pipeline to grow; or,
- cause other defects such as gouges or dents, to crack, and grow these new cracks.
Pipelines sometimes fail due to fatigue, and these failures are usually associated with pre-existing defects in welds, or damage in the pipeline such as dents.