Mean stress correction for normal loads

Correction of Goodman type

The Goodman correction that is used in Specialist Durability is plotted in the figure Mean Stress Influence According to Goodman below. The corresponding value in the Mean Stress Correction durability simulation object is NS / Goodman.

The slope of the line used in the Goodman correction is given by the relation

Note:

Some textbooks refer to as the Goodman equation, where the equivalent stress amplitude (with zero mean stress) is solved by using the amplitude and the mean stress of the cycle and the maximum (ultimate) stress of the material. The method used here serves the same purpose but is conceptually different to this approach. It assumes that the mean stress dependency is read from tests at different mean stress relations. In the Goodman durability simulation object provided by Specialist Durability, the M value is set to 0.3, which is good for mild to medium steel.

Mean Stress Influence According to Goodman

In the fraction in the expression, the endurance limit of a fully reversed fatigue test is divided by the endurance limit of a tensile only fatigue test with the same amplitude.

When entering the slope of the line into the Specialist Durability stress-life approach solution parameters, the value M as specified in the equation above is given (that is, the slope of the line without the negative sign).

For calculation with the Goodman correction, the mean stress and amplitude are plotted on the correction diagram, and the point is resolved back to the vertical axis to determine the equivalent stress amplitude, as illustrated in the figure below. In this figure are examples with positive and negative mean stresses, and the resulting equivalent stress amplitude.

Examples for the Goodman Correction

A straight line with the given correction factor M is assumed for

− ∞ ≤ R ≤ 1

For all cycles that are completely in compression, the same mean stress correction (namely the correction for R = −∞) is used.

Three-segment mean stress correction

The three-segment mean stress correction procedure is similar to the Goodman correction. In this case the mean stress correction diagram consists of three distinct segments, as shown in the figure Mean Stress Influence for Three Segments below. The corresponding value in the Solution parameter data set is NS/3 Segments.

In this method, the first segment consists of a line with the Goodman slope, described by M defined in the equation above; see The stress-life approach. The line is used for tensile mean stresses up to R=0 loading. (The R=0 loading line is where the stress amplitude and mean stress are equal, indicated by the 45-degree line in the first quadrant of the plot.)

The second segment consists of a line from the R = −∞ loading line to the R = −1 loading line (that is, for compressive mean stresses). You may use in this case another slope in this segment, if experiments indicate to do so. In Specialist Durability, the absolute value of the slope of this line is denoted M1 on the stress- life solution parameter data set.

The third segment is for cycles showing high mean stresses (Sm > Sa or 0 < R < 1). Using only one slope it may happen that this slope is steeper than the slope given by Goodman:

In this case very small loops having high mean stresses show high damaging effects, and even if the amplitude of those loops tend to zero their equivalent amplitude lies above the endurance limit. Specialist Durability is aware of this and gives a warning if this case may occur.

In those cases the correction according to Schütz, by setting M3 to M/3 may help out.

Mean Stress Influence for Three Segments

Four-segment mean stress correction

The four-segment mean stress correction is an extension of the three segment mean stress correction with the extra parameter Limit R. For R ratios above this value no further mean stress correction is applied. See the figure Mean Stress Influence for Four Segments below.

Mean Stress Influence for Four Segments

Five-segment mean stress correction

The five-segment mean stress correction is a further extension of the four segment mean stress correction with the extra parameter Limit R2. Here the R-Ratio Limit R is used to switch between the mean correction slopes M3 and M4. For R ratios above Limit R2 the slope M5 is used. See the figure Mean Stress Influence for Five Segments below.

Mean Stress Influence for Five Segments

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