Von Mises effective amplitude approach

With the Von Mises effective amplitude approach, the durability solver selects one of the two effective principal axes as the primary loading direction, and designates the other as the secondary loading direction.

It processes the stress or strain data in the primary loading direction, and uses the stress biaxial ratio to include the effect from the secondary loading direction. Therefore, the durability solver only performs one rainflow cycle counting for the stress or strain history in the primary loading direction. NOTE

When the stress or strain amplitude and mean stress of each cycle is obtained, the durability solver then uses the stress biaxial ratio to update the stress-based and strain-based life equations, and the Smith-Watson-Topper equation.

Updating stress-based life equations

For the stress life and user-defined S-N curve, the fatigue life equations are updated using the effective stress amplitude of the biaxial cycle instead of the stress amplitude and the effective mean stress of the biaxial cycle instead of the mean stress in the life equation.

where

• is the effective stress amplitude in the primary loading direction of the biaxial cycle.

• is the stress amplitude in the primary loading direction without accounting for the biaxial effect.

• is the effective mean stress of the biaxial cycle.

• σm is the mean stress without accounting for the biaxial effect.

• r is the stress biaxial ratio.

Updating strain life (maximum principal) equations

By including the stress effect from the secondary loading direction, the life equation can be derived as:

where:

• is the maximum principal strain amplitude.

• 2Nf is the number of reversals to failure.

• E is the modulus of elasticity.

• σ'f is the fatigue strength coefficient material property.

• b is the fatigue strength exponent material property.

• ε'f is the fatigue ductility coefficient material property.

• c is the fatigue ductility exponent material property.

• νe is the Poisson's ratio.

Updating Smith-Watson-Topper equations

By including the stress effect from the secondary loading direction, the life equation can be derived as:

For more information see:

• Principal axes approach

• Maximum damage approach

• Stress biaxial ratio

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Von Mises effective amplitude approach, Simcenter 3D 2021.1 Series

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Matsuishi, M., and Endo, T., “Fatigue of Metals Subjected to Varying Stress”, Japan Society of Mechanical Engineers, March, 1968.

Endo, T., et. al., “Damage Evaluation of Metals for Random or Varying Loading”, Proceedings of the 1974 Symposium on Mechanical Behavior of Materials, Volume 1, Society of Materials Science, Japan, 1974. pp. 371-380.

Tipton, S.M., and Fash, J.W., “Multiaxial Fatigue Life Predictions for the SAE Specimen Using Strain-based Approach”, in Multiaxial Fatigue: Analysis & Experiments, SAE AE-14, 1989, pp. 67-80.

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