# Fatigue Assessment Methods

In SimSolid, uniaxial and multiaxial fatigue analysis using S-N (stress-life) and E-N (strain-life) approach is supported.

Models with uniaxial loads consist of loading in only one direction and result in one principal stress. In Uniaxial Fatigue Analysis, SimSolid converts the stress tensor to a scalar value using user-defined combined stress method (signed von Mises, maximum principal, absolute max principal, signed maximum shear stress, and critical plane).

For critical plane stress, nominal stress resolved at each plane 𝜃 is calculated by:

(1)
$\begin{array}{l}\sigma ={\sigma }_{x}\left({\mathrm{cos}}^{2}\theta \right)+{\sigma }_{y}\left({\mathrm{sin}}^{2}\theta \right)+2{\sigma }_{xy}\left(\mathrm{cos}\theta \mathrm{sin}\theta \right)\\ \theta =0,10,20,30......170\text{\hspace{0.17em}}\text{degrees},\end{array}$

SimSolid expects the number of planes as input, which are converted to equivalent 𝜃 using the following equation:

(2)
$\theta =\frac{180}{n-2}$

In Multiaxial Fatigue Analysis, SimSolid uses the stress tensor directly to calculate damage. Multiaxial Fatigue Analysis theories assume that stress is in the plane-stress state.

In multiaxial fatigue analysis, SimSolid always searches for the most damaging plane by assessing damage using tensile crack damage model and shear crack damage model. At the end of search, SimSolid reports damage at the most damaging plane which is the critical plane.

## Critical Plane Approach

Experiments show that cracks nucleate and grow on specific planes known as critical planes. The Critical Plane Approach captures the physical nature of damage in its damage assessment process.

Depending on the material and stress states, the critical planes can be either maximum shear planes or maximum tensile stress planes. Therefore, to assess damage from multiaxial loads, two separate damage models are required. One is for crack growth due to shear, and the other is for crack growth due to tension.
You can use any damage model the critical plane approach. The damage models require a search for the most damaging plane. There are two possible damaging (or failure) modes. One is tensile crack growth, which occurs on planes that are perpendicular to the free surface. The angle θ is the angle that a crack is observed on the surface relative to the σx direction. The second failure system is shear crack growth, which occurs on planes oriented 45 degrees to the surface. Both in-plane and out-of-plane shear stresses are considered on this plane. θ can take on any value on the surface. The shear stress τA is an in-plane shear stress and causes microcracks to grow along the surface. The maximum out-of-plane shear, τB occurs on a plane that is oriented at 45 degrees from the free surface and causes microcracks to grow into the surface.