Goodman fatigue relation

σa is half the difference between maximum and minimum stress in a cycle; σm is their mean. Se is the fatigue limit used at zero mean stress, and Sut is ultimate tensile strength. The dimensionless sum measures linear utilization of these limits. Use consistent definitions and units for every stress. Goodman is a simplified linear mean-stress model. Material data, load history and safety factors must be established separately for any real design. Application: Screen alternating loading at a stated mean stress in a first fatigue assessment. The numerical example Take Se=200 MPa, Sut=600 MPa, σm=150 MPa and σa=100 MPa. Utilization is 100/200+150/600=0.75≤1. The ideal amplitude boundary at this mean stress is 150 MPa. This is a model calculation, not component approval anchors the idea in a concrete measurement case.

The alternating component uses σa/Se=100/200=0.50 of the normalized limit. Tensile mean stress contributes σm/Sut=150/600=0.25. Their sum is 0.75, below one in this idealized model. Without corrections and a safety factor, that does not establish that a real component is safe. Goodman is a simplified linear mean-stress model. Material data, load history and safety factors must be established separately for any real design. The corresponding units are σa, σm, Se and Sut in the same stress unit; utilization dimensionless. Take Se=200 MPa, Sut=600 MPa, σm=150 MPa and σa=100 MPa. Utilization is 100/200+150/600=0.75≤1. The ideal amplitude boundary at this mean stress is 150 MPa. This is a model calculation, not component approval. This checks that the reference quantities are compatible.

A common teaching form requires σa/Se+σm/Sut≤1/n. Larger n shrinks the permitted region. Document which factors are already included in strengths or loads to avoid double counting. Binding component checks must follow the applicable standard and its material and load definitions. Goodman is a simplified linear mean-stress model. Material data, load history and safety factors must be established separately for any real design. Scope: The line joins (σm=0, σa=Se) and (σm=Sut, σa=0). Its left side is a teaching utilization; design also needs material, surface, size, notch, reliability and loading corrections plus a safety factor. It is commonly applied to tensile mean stress. It is neither a universal life prediction nor code approval; compressive mean stress and real histories need suitable models. A practical application is Screen alternating loading at a stated mean stress in a first fatigue assessment.

A value below one lies inside the idealized line connecting fatigue strength and ultimate tensile strength; it screens the selected stress cycle. It proves neither a service life nor safety of the real component. Surface, notches, size, reliability, load spectrum and safety factor affect assessment. Record material properties and corrections, and do not treat the value as blanket approval. Goodman is a simplified linear mean-stress model. Material data, load history and safety factors must be established separately for any real design.

Mean stress shifts the whole cycle, whereas amplitude describes its cyclic variation. A tensile mean stress consumes more of the strength margin than an equal alternating component centered at zero. Goodman models that effect linearly toward ultimate strength. Compressive mean stress or complex histories may require another diagram and cycle-counting method; define each cycle’s maximum and minimum first. Goodman is a simplified linear mean-stress model. Material data, load history and safety factors must be established separately for any real design.