Goodman relation

Within the branch of materials science known as material failure theory, the Goodman relation (also called a Goodman diagram, a Goodman-Haigh diagram, a Haigh diagram or a Haigh-Soderberg diagram) is an equation used to quantify the interaction of mean and alternating stresses on the fatigue life of a material. The equation is typically presented as a linear curve of mean stress vs. alternating stress that provides the maximum number of alternating stress cycles a material will withstand before failing from fatigue.
A scatterplot of experimental data shown on an amplitude versus mean stress plot can often be approximated by a parabola known as the Gerber line, which can in turn be (conservatively) approximated by a straight line called the Goodman line.
Mathematical description.
The relations can be represented mathematically as:
formula_1, Gerber Line(parabola)
where formula_4 is the stress amplitude, formula_5 is the mean stress, formula_6 is the fatigue limit for completely reversed loading, formula_7 is the ultimate tensile strength of the material and formula_8 is the factor of safety. 
The Gerber parabola is indication of the region just beneath the failure points during experiment.
The Goodman line connects formula_7 on the abscissa and formula_6 on the ordinate. The Goodman line is much safer consideration than the Gerber parabola because it is completely inside the Gerber parabola and excludes some of area which is nearby to failure region.
The Soderberg Line connects formula_11 on the abscissa and formula_6 on the ordinate, which is more conservative consideration and much safer.
The general trend given by the Goodman relation is one of decreasing fatigue life with increasing mean stress for a given level of alternating stress. The relation can be plotted to determine the safe cyclic loading of a part; if the coordinate given by the mean stress and the alternating stress lies under the curve given by the relation, then the part will survive. If the coordinate is above the curve, then the part will fail for the given stress parameters.