What is in this article?

1. Introduction

2. Fatigue Assessment

3. Mesh Refinement and Hotspots Creation

4. Stress Cycle Counting

5. Fatigue Damage Accumulation

6. Appendix

Annotations

Terminologies

1. Introduction

This document provides the deterministic fatigue calculation methodology with 3 following operations:

• Hotspots creation: refining the mesh around the weld lines and creating the hotpots (pre-processing).
• Stress cycles counting: computing the effective stress history from the simulation stress and counting stress cycles (post-processing).
• Fatigue assessment: computing the accumulated fatigue damage for hotspots (post-processing).

The assessments are applied for marine structures, based on the standards DNV-RP-C203 [1]. The input for those processes is a structural model (finite element model) using quadrilateral elements

The output of the assessment is the yearly fatigue damage D_y and minimum fatigue life F. Acceptance criteria to pass checks is F ≤ F_d for a hotspot.

Configuration of load cases and boundary conditions are not in the scope of this document. Each structural model configuration is analyzed to determine its stress response which is input for post-processing assessments discussed in this document.

2. Fatigue Assessment

2.1. Procedure Overview

Fatigue assessment is a procedure to check if cracks can appear under a given cyclic loading. Fatigue damage value is computed using explicit formulas from standards, where the inputs to the formulas are the stress history, the S-N curve, and the thickness of the shell at the hotspot location. This assessment results are the yearly accumulated fatigue damage and the minimum fatigue life values which are used for checks at each hotspot.

Figure 2. Fatigue assessment workflow

Figure 3. Core deterministic fatigue analysis workflow

Fatigue Assessment Procedure (Figure 2) has three main steps:

• Identifying critical regions with high fatigue damage based on fatigue screening analysis results.
• Refining the mesh and creating the hotspots in the critical regions.
• Run the final fatigue analysis.

Both the fatigue screening and the final fatigue analyses use the same core deterministic fatigue procedure (Figure 3) which has four main steps:

• Getting the FE solution using the RB-FEA method.
• Computing the effective stress history of hotspots.
• Counting the stress cycles in the effective stress history of hotspots.
• Calculating the yearly fatigue damage of hotpots and performing fatigue checks.

Fatigue stress is read directly from FE mesh at predefined hotspot locations. Stress Concentration Factor (SCF) is not applicable in Akselos’ Fatigue Procedure because the FE solution already takes into account the stress concentration at abrupt cross-section changes. See how stress is extracted in the Mesh Refinement and Hotspots Creation section (section 3 below).

2.2. Summary of capabilities

Fatigue deterministic fatigue analysis jobs can be submitted via Akselos Modeler and performed calculation of fatigue damage on Akselos Cloud leveraging RB-FEA fast computing technology. Results are displayed on Akselos Modeler in 3D graphical form with information of fatigue damage, effective stress history, and stress cycle counting results, Figure 4.

Figure 4. Fatigue assessment results in Akselos HUI

For each hotspot location, users can configure:

• S-N curve: select a desired S-N curve available on the software, support 1-slope, 2-slope, and user-defined S-N curves.
• Design Fatigue Factor (DFF): scale fatigue damage value.
• Stress calculation method: select the desired hotspot stress calculation method, for example:
  1. Tubular joint.
  2. Effective hotspot stress (Method B).

Thickness correction is taken into account by default based on t_ref  and k of the selected S-N curve:

3. Mesh Refinement and Hotspots Creation

Mesh refinement is required by the standard to have detailed and precise stress distribution near the weld lines where fatigue damage calculation is performed.

“Hotspots” in Akselos fatigue workflow is “edge mesh” that is perpendicular to the weld line, and the stress read-out point is in the middle of the edge. Hence, it is necessary to have appropriate meshing size near weld line regions, for example:

• For the tubular join, the meshing size is ~ 0.2×√(rt) and the stress read-out point is ~ 0.1×√(rt), see Tubular joints section
• For the plated structure, the meshing size is ~ t × t   (thickness by thickness) and the stress read-out point is ~ 0.5t, see Plated structures section

At each read-out point, the plane stress tensor is exported in the local coordinate system of the hotspot edge (Figure 5).

Figure 5. Dimensions, local coordinate system, and stress extraction at hotspot

Determine local coordinate system:

• The local x-axis is collinear to the hotspot direction.
• The local z-axis is the shell element’s normal vector.
• The local y-axis is the cross-product of z and x.

Determine extracted stress and parameter in the effective stress formula:

• Top/bottom stress xx (σ_xx) is perpendicular to the weld line, equivalent to ().
• Top/bottom stress yy (σ_yy) is parallel to the weld line, equivalent to (σ_//).
• Top/bottom shear stress xy (τ_xy) is equivalent to (τ_//).

3.1.  Tubular joints

For the tubular joint, the stress along the brace, chord, and saddle position is extrapolated at a = 0.2×√(rt), with r - the outer radius and t - the thickness of the brace, equation (4.2.1) to (4.2.3) in DNV-RP-C203. Akselos uses 0.2×√(rt) as the meshing size for the region around the tubular joint weld line.

The hotspots can be defined on the brace and on the chord. They are equally spaced along the weld line. The angular spacing is equal to 2π divided by the number of hotspots. The direction of the hotspots is perpendicular to the weld line, Figure 6.

Figure 6. Meshing size and hotspots configuration for tubular joints

The Stress read-out point is 0.1×√(rt) from the weld toe. The stress tensor is rotated to the local coordinate system of the hotspot.  From this stress tensor, the principal stress in the hotspot direction is used as the effective hotspot stress for the fatigue analysis. Only the top stress tensor is considered.

3.2. Plated structures

For plated structures, the meshing size is t × t, where t is the thickness of the plate. For the weld lines that join several plates with different thicknesses, the meshing interval of the weld line is the average thickness of all plates. The hotspots can be created at the following position on the weld lines:

• At the weld toe on the plate surface (Figure 7.A) or plate edge (Figure 7.B) at an ending attachment
• Along the weld of an attached plate, Figure 7.C.
• At the corner of three plates, Figure 7.D.

Figure 7. Meshing size and hotspots configuration for plated structures

Following Method B in DNV-RP-C203 section (4.3.4), both top/bottom stress tensor are extracted at 0.5t from the weld toe, where t is equivalent to the length of the hotspot due to the meshing size requirement. The top and bottom effective hotspot stresses are calculated for fatigue damage calculation. Fatigue damage is computed for both top/bottom layers but only the layer with maximum fatigue damage is reported.

Table 1. Effective hotspot stress (Method B)

α is equal to 0.9 (The construction and welding detail is classified as C2 with the stress parallel to the weld at the hotspot).

4. Stress Cycle Counting

The Rainflow counting approach is used to identify the stress cycles following the Standard Practices for Cycles Counting in Fatigue Analysis, ASTM E1049-85 [2]. The input to the Rainflow method is the principal stress history (for tubular joints) or top/bottom effective stress history (for plated structure) of a hotspot. The output is the rainflow matrix which contains the identified stress ranges and the number of cycles for each stress range, Figure 8.

Figure 8. Rainflow counting workflow

The Rainflow counting method has four main steps:

• Hysteresis filter: reducing the time series data by removing very small cycles from the effective stress history that contribute a negligible amount of damage. A stress interval, called gate, is used to filter out the small cycles. Akselos uses a gate size equal to 95% of the bin size (see binning).
• Peak-valley filter: safely removing the intermediate data between the maximum and minimum value of a given cycle. The goal of peak-valley filtering is to only keep data points necessary for the cycles counting.
• Stress range discretization or binning: dividing the effective stress range into 128 intervals (default). Each interval is called a bin. The effective stress data points are mapped to the bins. The amplitude of the data samples is slightly altered by centering them in their respective bins. According to most standards, the minimum number of bins is 64.
• Four point counting: identifying the stress ranges and counting the number of cycles using four consecutive points. The counting output data is stored in the Rainflow matrix.

Figure 9, on the left, illustrates the stress history data before and after applying the hysteresis and peak-valley filters. On the right side, an example Rainflow matrix is present. The stress ranges can be read from the x-axis (to) and y-axis (from). The number of cycles can be read from the data points.

Figure 9. Filtered effective hotspot stress data and Rainflow matrix

5. Fatigue Damage Accumulation

At each hotspot, a sum of fatigue damage for a given stress history is calculated based on the S-N fatigue approach under the assumption of linear cumulative fatigue damage (Palmgren-Miner rule) using stress ranges and counted cycles from Rainflow counting methodology.

For example, for a given stress history of a hotspot, the Rainflow counting output is:

Fatigue damage at hotspot:

N_i is computed with the selected S-N curve using the stress range. The DFF coefficient is directly multiplied by the accumulated fatigue damage of each hotspot.

Finally, the fatigue damage per year is deduced from the simulation time t_sim of the given load history (in hour) and D using the formula:

The minimum fatigue life (in year) is therefore:

6. Appendix

6.1. S-N curves for tubular joints & plated structures

Figure 10. Parameters for S-N curves in air

Figure 11. S-N curves in air

Figure 12. Parameters for S-N curves in seawater with cathodic protection

Figure 13. S-N curves in seawater with cathodic protection

Figure 14. Parameters for T curve in air & in seawater with cathodic protection

Figure 15. T curve in air & in seawater with cathodic protection

6.2. Unsupported checks

Table 2. Unsupported checks

Disclaimer

The Software and System are provided “as is” and “as available”. By using the Software and System, users acknowledge that they are only meant to be tools used to assist in operational decisions which shall be made by professional engineers skilled and trained in the use and interpretation of such results.

References

[1] “DNV-RP-C203: Fatigue design of offshore steel structures.” 2016.

[2] “ASTM E1049-85: Standard Practices for Cycles Counting in Fatigue Analysis” 2017