Goodman and Gerber methods

To evaluate fatigue safety using Goodman or Gerber methods, the durability solver first identifies all the loading cycles, and the stress amplitude and mean stress. Using either Goodman or Gerber diagrams, it considers the most damaging cycles in the event.

To calculate FSF and FFI result sets using Goodman or Gerber methods, the durability solver needs the following material properties:

• Ultimate tensile strength, Su, for isotropic materials.

• Ultimate tensile strengths in 1–direction, 2–direction, and in-plane respectively, Xu, Yu, and Su, for orthotropic materials.

• Maximum alternating stress amplitude not causing any fatigue damage, ∆s/2

Maximum alternating stress

Maximum alternating stress is defined as the maximum value of the stress amplitude that does not cause failure in a given life cycle, using a standard 6 mm diameter polished specimen. You can define the value for maximum alternating stress in one of the following ways:

• Specify the value for maximum alternating stress.

• Use a given design life cycle, Nf, to identify a design stress amplitude with the S-N curve.

For ferrous materials, a fatigue strength factor, Kf, can also be used along with the standardized maximum alternating stress, Sf, to approximate the maximum alternating stress of a real structure, ∆s/2 :

∆s/2 = Sf/Kf

The fatigue strength factor accounts for the effect of surface finish, surface treatment, type of loading, and so on. You can evaluate the fatigue strength factor using the following equation:

				where:Cs is the component size empirical factor.Cl is the type of loading empirical factor.Cn is the notch effect empirical factor.Cf is the surface finish empirical factor.Ct is the surface treatment empirical factor.

Example of FSF and FFI calculation

An example is shown using the Goodman diagram. The X-axis is mean stress, while the Y-axis is alternating stress.

				C is the identified stress cycle on the Goodman diagram.M is the mean stress of the cycle.A is the stress amplitude of the cycle.

Depending on the option you choose, FSF and FFI are calculated from the Goodman diagram as follows:

• If both stress amplitude and mean stress are varying:FSF = 0Z/0CFFI = 0C/0Z

• If mean stress is fixed and stress amplitude is varying:FSF = MX/MCFFI = MC/MX

• If stress amplitude is fixed and mean stress is varying:FSF = AY/ACFFI = AC/AY

FSF and FFI calculation options

The following table lists the FFI equation that is used to compute the fatigue failure index, FFI, depending on the fatigue safety factor output method you specify.

	Both stress amplitude and mean stress are varying	Stress amplitude is varying and mean stress is fixed	Mean stress is varying and stress amplitude is fixed
Goodman criterion
Gerber criterion

where

• is the stress amplitude of the ith cycle.

• r is the stress biaxial ratio. r = 0 for orthotropic materials.

• (σm)i is the mean stress of the ith cycle.

For both criteria: FSF = 1/FFI

For orthotropic materials, the durability solver computes FSF and FFI for 1–direction, 2–direction, and in-plane separately. You can display only the worst case FSF and FFI results in the Post Processing Navigator.

Learn more

Static events

Transient events

Look up more details

Understanding the fatigue safety evaluation

Computation of the maximum alternating stress

Dang Van fatigue safety factor

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Goodman and Gerber methods, Simcenter 3D 2021.1 Series

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