Simulation-Based Fatigue Assessment of Welded Joints: What the New 4R Method Study Reveals

Fatigue failure in welded joints remains one of the most persistent engineering challenges—especially when high-strength steels and complex load histories are involved. While traditional fatigue methods rely on simplified assumptions about residual stresses and material response, modern welded structures demand simulation-based approaches that can capture real material behavior.

A new 2025 study published in the European Journal of Mechanics / A Solids takes a major step forward by combining:

• Computational Weld Mechanics (CWM)
• Finite Element Analysis (FEA)
• Local fatigue assessment using the 4R method
• Global sensitivity analysis with SimDec

This combination offers one of the most comprehensive fatigue assessments of welded gusset joints to date.

Why this research matters

Traditional fatigue evaluation often assumes:

• high tensile residual stresses in as-welded joints
• simplified material properties in the heat-affected zone (HAZ)
• constant-amplitude loading
• limited understanding of residual stress relaxation under overloads or variable-amplitude loads

But real welded structures experience:

• overload peaks (e.g., proof tests)
• variable-amplitude loading
• temperature-dependent material softening
• complex stress redistribution in the HAZ

This study directly addresses these realities by numerically simulating not only welding mechanics but also the full cyclic response under CA, quasistatic overloads, and VA loading (see load diagrams on page 5, Fig. 6).

What the study did

1. Simulating welding + HAZ material changes

The authors run a sequentially coupled thermal–mechanical simulation (Fig. 2, p. 3).
Key elements:

• double conical–ellipsoidal heat source
• temperature-dependent material properties
• mapping of hardness-based HAZ material groups (Fig. 11b, p. 8)
• prediction of residual stresses (Fig. 12, p. 9)

2. Cyclic simulation under realistic load histories

Four load types were simulated (Fig. 6):

• constant amplitude (CA)
• overload + CA
• variable amplitude with high mean stress (VA-max)
• variable amplitude with low mean stress (VA-min)

3. Fatigue assessment using the 4R method

The 4R method uses:

• notch stress range
• residual stress
• applied stress ratio
• material tensile strength

to compute a local fatigue-effective stress.

4. Global sensitivity analysis (SimDec)

The study generated 315 simulation cases, analyzing material uncertainty and load conditions.

The sensitivity analysis (Table 13, p. 12) found:

• Nominal stress range Δσnom is the dominant driver of fatigue life (SI = 0.81)
• Cyclic strength coefficient H′ strongly affects local stress response
• A clear multi-scenario decomposition emerges (Fig. 20), showing interactions between Δσnom and H′

Key findings

1. Simulated fatigue capacity aligns well with experiments

The simulation-based S–N curve shows a very low scatter index of Tσ = 1.25 (Fig. 17), compared to typical welded-joint scatter of ~1.5.

This indicates excellent predictive capability.

2. Overloads significantly relieve residual stresses

Residual stress profiles in as-welded, OL06, and OL08 cases (Fig. 12) match experiments, confirming:

• high residual stresses in AW
• strong relaxation in OL conditions
• major impact on mean stress and fatigue life

3. Variable-amplitude loads produce stress relaxation that improves fatigue life

Figures 15 (p. 11) show stress relaxation phenomena during long VA sequences—an effect analytical fatigue models cannot capture.

4. Cyclic strength coefficient H′ is the most influential material parameter

From global sensitivity analysis (Table 13), the cyclic strength factor H′ strongly shapes:

• maximum/mean/minimum stress
• simulated life
• notch stress range

5. Fatigue-critical region consistently located at CGHAZ

The local fatigue hotspot was found near the coarse-grained HAZ close to the weld toe (Fig. 13).

Why this matters for engineers & researchers

This study demonstrates that combining:

• high-fidelity welding simulation
• material updating in the HAZ
• nonlinear cyclic simulation
• local 4R fatigue assessment
• SimDec global sensitivity analysis

produces fatigue predictions that align closely with experimental behavior under multiple load types.

This is essential if we want to move toward simulation-driven certification of welded structures and reduce the reliance on costly large-scale fatigue testing.

Reference

Pesonen, T., Kozlova, M., Ahola, A., Björk, T., & Moshtaghi, M. (2025). Simulation-based fatigue assessment using the 4R method in different load conditions. European Journal of Mechanics / A Solids, 111, 105600. https://doi.org/10.1016/j.euromechsol.2025.105600

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