Goodman Diagram Fatigue Spreadsheet

The attached spread sheet presents a graphical representation of the Goodman Diagram.  Material yield and ultimate strength are entered along with known maximum and minumum stresses for a given loading cycle.  Endurance limit can be entered although spread sheet defaults to 1/2 of ultimate strength.  Endurance limit modification factors as well as stress concentration factors can be entered as well.  Spread sheet resolves non-zero mean stress to zero mean for comparison to zero mean cyclic stress state.  Graphical representation clearly indicates whether or not cyclic stress state is acceptable or not.

Note:  This spreadsheet has been protected to prevent inadvertant modification of critical cell formulas.  Password is "brab"

Many ductile materials exhibit a well defined stress/cycle survival limit.  These survival  limits have been calculated for many materials utilizing a round, polished specimen, placed in bending and rotated until fracture occurs.  Different levels of bending stress are applied and a log/log curve arises which plots loading cycles versus applied stress.  As the applied stress diminshes, the number of cycles increases until a level is reached for which the specimen survives indefinitely; this stress level is known as the endurance limit.

The type of loading to which the test specimen is subjected is known as "Complete Reversal Loading" where through one stress cycle, a stress element experiences equal values of tension and compression, with a mean stress of zero.

But most loading situations involve non-zero mean stress and most materials are not polished but have surface finishes which vary greatly in texture.

The Goodman Linear relationship is a method of resolving a non-zero mean stress situation to an "Equivalent Zero Mean  Stress" situation so that a comparison can be made to the testing data.

The user data entered above for applied stress is data obtained either empircally or via calculation.  Maximum stress and minumum stress should be known for the load cycle.  The yield and ultimate strength of the material can be obtained from the manufacturer or from the literature.  The endurance limit of the material can be found in the literature or nominally computed as 1/2 of the ultimate strength.  Various surface finish, load factors and stress concentration factors are also available in the literature.   Upon entering that data, if the applied stress line falls within the envelope then "Infinite Life", usually taken to be surviavbility in excess of 1E7 loading cycles, is predicted.

For stress cycles that are wholly or largely compressive, fatigue is sometimes discounted as nonexistent or the compressive stress magnitude is derated. 

Calculation Reference

Fatigue

Goodman Diagram

Jouvinall Machine Design