Fig. C-9. Typical S-N Fatigue Curve
Fig. C-9. Typical S-N Fatigue Curve
The fatigue strength, or fatigue life, is the number of cycles to failure at a specified stress level. Normally, the fatigue strength increases as the static tensile strength increases. For example, high strength steels heat treated to over 200 ksi yield strengths have much higher fatigue strengths than aluminum alloys with 70 ksi yield strengths. A comparison of the S-N curves for steel and aluminum are shown in Fig. C.11. Note that steel not only has a higher fatigue strength than aluminum, it also has what is called an endurance limit. In other words, below a certain stress level, the steel alloy will never fail. On the other hand, aluminum does not have a true endurance limit. It will always fail if tested to a sufficient number of cycles. Therefore, the fatigue strength of aluminum is usually reported as the stress level it can survive at a large total number of cycles, usually 5 x 108 cycles.
Fatigue can be broken down into the stages of crack initiation, crack growth and final failure. The propagation of a fatigue crack, or the fatigue crack growth rate, is expressed as da/dn, or the change of the crack length a per cycle n. When the crack growth reaches a critical point, in which the remaining cross-section can no longer carry the load, failure occurs.
Fatigue normally starts at a surface-related stress concentration, such as a fastener hole or in radii, although internal stress concentrations can also initiate cracks. Therefore, any method which removes stress concentrations, such as smoother surfaces or blended radii, will delay, or prevent, the initiation of fatigue cracking. Surface treatments that introduce compressive stresses on the surface, such as shot peening of part surfaces or cold working of fastener holes, also reduces fatigue. The applied tensile stress must first overcome the residual compressive stress on the surface before the surface actually sees any applied tensile stress.
Fig. C-11. Comparison of Steel and Aluminum Fatigue Behavior
Fatigue tests can be characterized as being high cycle fatigue tests (>105 cycles) or low cycle fatigue tests. In high cycle fatigue tests, the stresses are low enough that the strains are in the elastic region. In contrast, in low cycle fatigue tests, the stresses are high enough to cause some plastic deformation. This plastic deformation results in a hysteresis loop during the unloading portion of the cycle, where there is recovery of both the elastic and plastic deformation, as shown in Fig. C.12. Due to strain hardening of the specimen, the hysteresis loop usually stabilizes after a few hundred cycles. The area of the hysteresis loop is equal to the work done or energy loss per cycle. The total strain Ae consists of both the elastic and the plastic components.
Aee = elastic strain Aep = plastic strain
Fracture mechanics has also been applied to fatigue. In the fracture mechanics approach to fatigue crack growth, the crack growth rate, or the amount of crack extension per loading cycle, is correlated with the stress intensity parameter K. This approach makes it possible to estimate the useful safe life and inspection intervals. An idealized da/dn versus AK curve is shown in Fig. C.13. In region I, AKth is the fatigue crack growth threshold, which is at the lower end of the AK range, where crack growth rates approach zero. In region II, the crack growth rate is stable and essentially linear, and can be modeled by the power law equations, such as the Paris equation.
m where a = flaw or crack size in inches n = number of cycles C and m are material parameters
AK = AKmax — AKmin is the stress intensity parameter range max
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