Stress-Life (S-N) Approach

The Stress-Life Approach for the Multiaxial Fatigue Analysis is similar to Uniaxial Fatigue Analysis. See the S-N Curve and Cycle Counting sections of Uniaxial Fatigue Analysis for introductory information for Stress-Life approach in Multiaxial Fatigue Analysis.

Mean Stress Correction

Depending on the material, stress state, environment, and strain amplitude, fatigue life will usually be dominated either by microcrack growth along shear planes or along tensile planes. Critical plane mean stress correction methods incorporate the dominant parameters governing either type of crack growth. Due to the different possible failure modes, shear or tensile dominant, no single mean stress correction method should be expected to correlate test data for all materials in all life regimes. There is no consensus yet as to the best method to use for multiaxial fatigue life estimates. Multiple methods are available and can be used concurrently in HyperLife Multiaxial Fatigue Analysis. For stress-based mean stress correction method, Goodman model is used for tensile crack. Findley model is used for shear crack. You can define mean stress correction methods in the Multiaxial Fatigue dialog. If multiple models are defined, HyperLife selects the model which leads to maximum damage from all the available damage values.

Goodman Model

The Goodman model in Uniaxial Fatigue Analysis is used at critical plane to assess damage caused by tensile crack growth.

Findley Model

The Findley criterion is often applied for finite long-life fatigue.(1)

\frac{Δ τ}{2} + k σ_{n} = τ_{f}^{*} {(N_{f})}^{b}

Where,

τ_{f}^{*}

is computed from the torsional fatigue strength coefficient,

τ_{f}^{'}

using:(2)

τ_{f}^{*} = \sqrt{1 + k^{2}} τ_{f}^{'}

The correction factor

\sqrt{1 + k^{2}}

typically has a value of about 1.04. Note that

τ_{f}^{*}

has to be defined based on amplitude. If

τ_{f}^{'}

is not defined by you, HyperLife automatically calculates it using the following equation.(3)

\begin{array}{l} τ_{f}^{'} = C f * 0.5 * S R I 1 \\ W h e r e, \\ C f = \frac{2}{1 + \frac{k}{\sqrt{1 + k^{2}}}} \end{array}

The constant $k$ is determined experimentally by performing fatigue tests involving two or more stress states. For ductile materials, $k$ typically varies between 0.2 and 0.3. Its default value in HyperLife is 0.3.

FKM

FKM mean stress correction is available for both Uniaxial and Multiaxial S-N Fatigue. For more information, see Mean Stress Correction under Uniaxial S-N Fatigue in the User Guide.