Glossary term
Goodman Criterion
An empirical fatigue design criterion that combines alternating stress and mean stress in a linear failure boundary.
Definition
methodThe Goodman criterion is a fatigue design rule that estimates whether a component is safe under combined alternating stress and tensile mean stress.
The criterion assumes a linear interaction between alternating stress amplitude and mean stress. In its modified form, the safe boundary connects the endurance limit at zero mean stress to the ultimate tensile strength at zero alternating stress. It is widely used in machine design because it gives a conservative, simple, and transparent way to account for the damaging effect of tensile mean stress on fatigue life.
The Goodman criterion is used when cyclic stress is not purely reversed about zero. Many components carry a steady load and a fluctuating load at the same time. A bolt may be preloaded in tension and then experience cyclic service load. A rotating shaft may carry steady bending plus alternating torsion. A pressure vessel may see a static membrane stress with pressure pulsation superimposed. In these cases, fatigue resistance depends on both the alternating stress amplitude and the mean stress.
The modified Goodman relation is commonly written as:
where S_a is alternating stress amplitude, S_m is mean stress, S_e is the endurance limit or fatigue strength for the target life, and \sigma_{UTS} is ultimate tensile strength. Points below the line are treated as safe under the criterion. Points on the line are at the predicted fatigue boundary. Points above the line are not acceptable without redesign, lower load, better material data, reduced stress concentration, or a more detailed fatigue assessment.
Goodman diagram
The Goodman diagram plots mean stress on the horizontal axis and alternating stress on the vertical axis. The line connecting (0, S_e) and (\sigma_{UTS}, 0) defines the fatigue boundary. Tensile mean stress reduces the allowable alternating stress because cracks open more easily during the tensile part of the load cycle. Compressive mean stress is usually beneficial, but the Goodman relation is often applied conservatively rather than taking full credit for compression.
Yielding must be checked separately. A design can satisfy the Goodman fatigue line and still yield under peak stress if the combined mean and alternating stresses exceed yield strength. In practical design, engineers check both fatigue and static limits, then apply appropriate safety factors or design factors.
Engineering use
Goodman analysis is useful during preliminary design because it converts complex cyclic loading into a clear screening calculation. It helps compare materials, adjust section sizes, evaluate fillets and notches, choose surface treatments, and decide whether a component needs more detailed analysis. Stress concentration factors and notch sensitivity are often applied before placing the operating point on the diagram.
For finite-life design, S_e may be replaced by fatigue strength at the required number of cycles from the S-N curve. For variable-amplitude loading, the Goodman correction may be combined with cumulative damage methods such as the Miner rule, although the assumptions must be stated clearly.
Limitations
The Goodman criterion is empirical. It is most appropriate for ductile metals under uniaxial or equivalent stress states where fatigue data support the method. It does not directly handle multiaxial fatigue, welded details, corrosive environments, fretting, residual stress relaxation, plastic strain fatigue, or crack-growth analysis. For critical parts, Goodman screening should be followed by validated material data, representative load spectra, fracture mechanics where cracks may exist, and inspection planning.