Bracket — Fatigue Evaluation

The S-N curve, also called the Wöhler curve, is one of the most popular methods for fatigue evaluation. The curve relates the stress amplitude to the limiting fatigue life and can be obtained directly from a set of standard fatigue test. Often, a structure is however subjected to conditions different from the experimental conditions of the fatigue tests. The fatigue data must then be appropriately modified in order to take the actual operating conditions into account.

In this example it is shown how to perform a fatigue evaluation when the material data needs to account for harsh environmental conditions and poor manufacturing process.

Model Definition

The bracket geometry can be seen in Figure 1. The component is subjected to external loads that lift one arm up and pull the other arm down. The load magnitude is cycled between a zero load, a peak load and back to zero load. Additional information regarding the model set up can be found in the documentation of the application Bracket-Spring Foundation Analysis, found in the Structural Mechanics Module.

Figure 1: Bracket geometry.

The structural steel in the bracket has poor cleanliness and contains fairly large inclusions. It is well known that with decreasing purity the endurance limit decreases and thus large inclusions shorten the lifetime. The fatigue properties of the material have been tested in a material laboratory and are summarized in Table 1. The material has a distinct endurance limit at 110 MPa. Tests were performed in nominal testing conditions and on specimens with a very good surface finish.

Table 1: S-n curve Data.
Fatigue lifetime (cycles)	Stress amplitude (MPa)
1.10e3	360
2.17e3	320
3.82e3	290
7.15e3	260
1.45e4	230
3.23e4	200
5.92e4	180
1.16e5	160
2.51e5	140
6.09e5	120
1.00e6	110

As opposite to the testing conditions, the bracket was machined and has a rough surface as the result. Moreover the bracket operates in salt water that has a strong influence on the fatigue resistance. Since there is lack of test data for the operating conditions, the S-N curve data must be modified. One approach is to use

(1)

where σa is the stress amplitude, k is the modification factor, N is the fatigue lifetime, and fSN is the S-N curve. Based on the experience, the modification factor for the corrosion in salt water can be set to 0.4. The modification factor for the surface finish, due to machining manufacturing technique, can be set to 0.7. The modification factor in Equation 1 for the combined effect is simply the product of the modification factors for all operating conditions and thus 0.28.

In the fatigue analysis the modification due to machining, k = 0.7, and due to the combined effect is evaluated, k = 0.28.

Results and Discussion

The stress distribution in the bracket a the peak load is shown in Figure 2.

Figure 2: Stress in the bracket at the peak operating load.

A close-up of the part with stress concentrations reveals that also on the inner side of the bracket there are significant stresses, see Figure 3.

Figure 3: A close-up of the part of the bracket that experiences highest stresses.

The fatigue analysis of the bracket material modified for the manufacturing conditions predicts infinite life. When submerged in saltwater, the stresses in most of the bracket are not high enough to cause fatigue. Only in a few local points is there is a risk of fatigue, see Figure 4. The bracket most probably fails in the connection between the two flat parts since the stresses on both the upper and the lower sides are high enough to initiate fatigue.

Figure 4: Fatigue lifetime when bracket is submerged in salt water.

In Figure 4 a finite life is predicted close to the holes that fasten the bracket. Those results are highly dependent on the boundary conditions that were applied there. In this model a spring foundations was used to fasten the bracket, but the constraint could have also been applied using a fixed connection of with a full contact analysis. This would change the stress field in the vicinity of the holes and result in a different fatigue lifetime.

Notes About the COMSOL Implementation

The S-N curve can be defined using different function types in COMSOL Multiphysics. When using an interpolation function it is important to use many points to specify the relation between fatigue life and stress amplitude, since the range of the fatigue life is very large and a small change in the stress amplitude results in a large change in the fatigue life. The function value between two data points can be evaluated in different ways but linear interpolation is the most common one. In Figure 5 the S-N curve is specified with eleven and with four measurement points respectively. Note that the fatigue life is displayed in a logarithmic scale and therefore the interpolation is not a straight line. The two curves display large differences. At 200 MPa one curve predicts 3.23·104 cycles while the other one predicts 5.80·104 cycles; a difference by almost a factor two.