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The Effect of Mean Stress on Endurance Strength

In general, the stresses acting on any component may be fluctuating i.e., The stress variation is such that it can have a mean-stress component and alternating stress component, as discussed before and shown below.

The presence of a mean-stress component has a significant effect on failure of the component. When a tensile mean stress is added to the alternating component, the material fail at lower alternating stress than it does under a fully reversed stress.

The figures shown below are the results of tests made on steels and aluminium alloys for various levels of mean and alternating stress combinations. The plots are normalised by dividing the alternating stress by fatigue endurance strength for fully reversed condition. The mean stress is divided by ultimate strength Su. There is a large scatter in the data.

A parabola drawn between the data points that intercept vertical axis and horizontal axis at unity fits the data with reasonable accuracy and this line is called Gerber line.

A straight line connecting the points on both axes whose values are unity is called Goodman line. Goodman line is a reasonable fit to the lower envelope of data.

The Gerber line is a measure of the average behaviour of these parameters for ductile materials and Goodman line is a measure of their minimum behaviour. The Goodman line is often used as a design criterion since it is safer than Gerber line.

Figure (c) shows the effect of mean stress (both compressive and tensile) on failure when combined with alternating tensile stress. One can see that compressive mean stress is beneficial in that a larger alternating stress can be applied. This fact provides an opportunity to mitigate the effect of alternate tensile stress by deliberate introduction of mean compressive stress.

The figure shown below depicts all the failure criteria for fatigue along with yield line plotted on sm - sa axes. Gerber parabola best fits the experimental failure data. Goodman line fits beneath the scatter in the data. A yield line connecting Sy on both axes serve as a limit on the first cycle stress (If the part yields, it has failed, regardless of its safety in the fatigue). Another line is shown connecting Sn on vertical axes to Sy on horizontal axis and is thus a more conservative which is called Soderberg line. Whichever line (failure criterion) is chosen to represent failure, safe combinations of sm and sa lie to the left and below the envelope. These failures are defined by

Gerber Parabola

Goodman line

Soderberg line

Goodman line is commonly used failure criterion when designed parts subjected to mean plus alternating stresses.

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