Modifying Factors, Size Effects


The fatigue failure of a material is dependent on the interaction of a large stress with a critical flaw. In essence, fatigue is controlled by the weakest link of the material, with the probability of a weak link increasing with material volume. This differs from bulk material properties such as yield strength and modulus of elasticity. This phenomenon is evident in the fatigue test results of a material using specimens of varying diameters. The size effect has been correlated with the thin layer of surface material subjected to 95% or more of the maximum surface stress. A large component will have a less steep stress gradient and hence a larger volume of material subjected to this high stress. Consequently, there will be a greater probability of initiating a fatigue crrack in large components. This concept is backed up by test results which show a less pronounced size effect for axial loading, where there is no gradient, than for bending or torsion. The idea of a highly stressed volume is important when considering stress gradients due to notches.

There are many empirical fits to the size effect data. A fairly conservative on is, in English units:

Csize = 1.0      if d ≤ 0.3 in.
Csize = 0.869d −0.097      if 0.3 in. ≤ d ≤ 10 in.

Csize = 1.0      if d ≤ 8 mm
Csize = 0.869d −0.097      if 8 mm ≤ d ≤ 250 mm

where d is the diameter of the component. Some other points to consider when dealing with the size effect are:

1. The effect is seen mainly at very long lives.
2. The effect is small in diameters up to 2.0 in. even in bending or torsion.
3. Due to the processing problems inherent in large components, there is a greater chance of having residual stresses and various metallurgical variables, which may adversely affect fatigue strength.

The idea of critical volume can also be used to find a size modification factor for noncircular sections.


Related
▪ L - Power Equation for Stress-Life
▪ L - Endurance Limit and Ultimate Strength