Principal axes approach

When you use the principal axes approach, the durability solver follows these steps:

1. It identifies and processes only the element faces on the surface of the structure or on the displayed group of elements.

2. It generates a coordinate system located at the centroid of the element face. Its Z-axis points outward and normal to the face. The other two axes are on the element face, and tangent to the face at the element centroid.

3. It calculates the stress time history at the centroid of each element free face with respect to the element coordinate system. For static durability analysis, the stress time history is calculated by superposition of static solution results and the load patterns. For transient durability analysis, the stress time history is taken from the transient solution.

4. It calculates the time history of the orientation of the two principal axes on the plane of the element face. The orientation of the principal axes is represented by the rotation angle, φ(t), from the X-axis of the face reference frame to the maximum principal axis on the plane.

5. It calculates the principal stresses at every time step.

6. It sets up a given number of bins for the angular range between 0 to 180 degrees, deposits the orientation angles from the time history φ(t) into the bins, and identifies the high-density bins. It then finds the bin containing the most data points (denoted by N), and uses all the bins with more than N/10 data points as the high-density bins.

7. It identifies the damage bin using a weighted average. It calculates the mean stress in each identified high-density bin, and uses the bin with the highest value of mean stress times the number of data points as the damage bin.

8. It determines the directions of the two effective principal axes on element face, i and j as follows:It averages the orientation angles in the damage bin. The averaged angle is denoted by θ.The effective principal axis i is located at an angle of θ from the X-axis of the element coordinate system.The effective principal axis, j is perpendicular to the effective principal axis i.

9. It performs a 2D tensor transformation to calculate the stress histories σi(t) and σj(t) along the two effective principal axes and the normal stress σk(t).For strain-based fatigue life criteria, the durability solver also calculates the strain histories in the three principal directions, εi, εj, and εk.

10. It chooses the primary loading axis as follows:For all fatigue life criteria except maximum shear strain life, the primary loading axis is chosen between i and j as follows:The solver calculates the two stress biaxial ratios:r1 = σi/σj**r2 = σj/σiThe solver compares r1 and r2.If r1 is smaller, the direction j is the primary loading direction, and σ1 = σj, σ2 = σi, ε1 = εj, and ε2 = εi.If r2 is smaller, the direction i is the primary loading direction, and σ1 = σi, σ2 = σj, ε1 = εi, and ε2 = εj.The stress biaxial ratio used later in the calculations is r = min(r1,r2).For maximum shear strain life, the durability solver uses the principal strains to calculate the shear strain history γm(t) in the maximum shearing direction (γm = max(γij,γik,γjk)). The corresponding normal strain history εn(t) and the strain biaxial ratio rε = εn(t)/γm(t) are calculated for biaxial analysis.

11. It uses the stress ,σ1, or strain, ε1, in the primary loading direction or in the case of maximum shear strain life, the shear strain γm to calculate the stress or strain amplitudes and mean values using rainflow counting. See Rainflow counting and Fatigue life criteria for more information.

12. It calculates damage and life:For uniaxial loading fatigue, it uses the stress or strain amplitudes and means in the S-N curve of the selected life criterion for damage calculation. See Fatigue life criteria for more information.For biaxial loading fatigue, it uses the biaxial ratio r or rε to update the S-N curve of the life criterion for damage calculation. See Biaxial fatigue evaluation on element free faces for more information.

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Static events

Transient events

Analyzing strain gage rosette data

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Fatigue evaluation on element free faces

Maximum damage approach

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Principal axes approach, Simcenter 3D 2021.1 Series

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