Applying the Walker mean-stress correction to AM fatigue data

Wrought coupons feeding MMPDS are typically tested at R = -1 (fully reversed) or R = 0.1, and the resulting S-N curves are used directly across a narrow band of service R-ratios. Additively manufactured parts rarely live there. Residual stress from un-stress-relieved L-PBF builds can sit at 60–80% of yield, biasing the local R-ratio toward 1 even when the applied loading is fully reversed.

Goodman and Soderberg corrections collapse under that bias because they assume the mean-stress sensitivity is linear up to UTS or yield. AM data sets, particularly Ti-6Al-4V and Inconel 718 in the as-built and HIP+aged conditions, fit the Walker model materially better (Dowling, 2009; Sangid et al., 2020).

We express the Walker-equivalent fully reversed stress amplitude as σ_ar = σ_max · (1 − R)^γ. The exponent γ is the Walker fitting parameter, bounded 0 < γ ≤ 1. γ = 0.5 reproduces the SWT (Smith-Watson-Topper) parameter; γ = 1 collapses to a pure σ_max (no mean-stress dependence); γ → 0 collapses to σ_a (no max-stress dependence).

For each material × condition we fit γ from at least three R-ratios (typically R = -1, 0.1, 0.5) and the lowest-scatter dataset available. The fitted γ is stored alongside the S-N curve and re-applied at design time to translate the user's service R-ratio back to the fully reversed allowable.

• L-PBF Inconel 718 (HIP + sol + aged): γ ≈ 0.45–0.50
• L-PBF Ti-6Al-4V (HIP + α/β anneal): γ ≈ 0.40–0.48
• L-PBF AlSi10Mg (T6): γ ≈ 0.55–0.65
• Wrought 4340 baseline (reference): γ ≈ 0.65 (Dowling, 2009)

Assume an MMPDS-style S-N curve at R = -1 gives σ_ar,allow = 410 MPa at 10⁷ cycles for HIP'd L-PBF Ti-6Al-4V. The service loading is σ_max = 520 MPa, σ_min = 156 MPa, so R = 0.3 and σ_a = 182 MPa.

Using γ = 0.44 (project default for this material × condition), σ_ar = 520 · (1 − 0.3)^0.44 = 520 · 0.857 = 446 MPa. Because σ_ar > σ_ar,allow, the design fails the 10⁷-cycle check by ~9% and must be reworked, even though the raw σ_a (182 MPa) sits well below the curve.

Goodman with σ_u = 950 MPa would have given σ_ar ≈ 220 MPa and passed comfortably. Walker is the more honest answer here.

First, applying a wrought γ to an as-built AM coupon. As-built surface roughness and sub-surface lack-of-fusion shift γ closer to 0.3, not 0.5. If your dataset is as-built, fit γ on as-built coupons.

Second, ignoring residual stress when computing R. A part that sees applied R = -1 but carries +400 MPa of tensile residual stress is effectively at a much higher local R. Either stress-relieve before allowables analysis or include residual stress in σ_max explicitly.

Third, extrapolating γ outside the R-ratio range it was fit on. γ fit on R = {-1, 0.1, 0.5} should not be applied at R = 0.8 without re-fitting; the assumption of a single exponent breaks down as R → 1.