API 579-1 (2021) Annex 9D — Welding residual stress profile through thickness
Estimates the welding residual stress profile through the wall, \sigma^r(x), for a range of weld joints, per API 579-1/ASME FFS-1 (2021) Annex 9D. The result feeds the secondary-stress term of a fracture assessment, so this calculator gives the profile and its membrane/bending split rather than a final K_I. It covers ten joint families:
Tee main plates and repair welds use piecewise profiles.
You pick the joint type, the stress direction (perpendicular or parallel to the weld), the material (ferritic or austenitic), and the post-weld condition (as-welded or PWHT). All profile amplitudes are scaled by the effective yield \sigma_{ys}^r = \sigma_{ys} + 69 MPa (Eq. 9D.1), which raises the specified yield to bound the as-welded residual field. For an as-welded girth weld with stress perpendicular to the weld, the heat-input ratio \dot{q}/t selects a low (\le 50), medium (\le 120) or high band. PWHT replaces the profile with a uniform reduced value — 0.2\,\sigma_{ys}^r perpendicular (Eq. 9D.3) or 0.3\,\sigma_{ys}^r parallel (Eq. 9D.4).
Outputs are the through-wall profile, the inner- and outer-surface stresses, and the equivalent membrane \sigma_m and bending \sigma_b from linearizing that profile. The through-wall coordinate x runs from the reference (bore) surface, with x/t in [0,1]. Profiles apply at the weld centre-line; the along-surface decay away from the weld is not modelled. The cylinder girth profiles match the BS 7910 Annex Q transverse solutions, giving an independent cross-check.
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