ASME PVP Code stress linearization is needed for assessment of primary and primary-plus-secondary stresses. The linearization process is not precisely defined by the Code; as a result, it may be interpreted differently by analysts. The most comprehensive research on stress linearization is documented in the work of Hechmer and Hollinger . Recent non-mandatory recommendations on stress linearization are provided in Annex 5A of Section VIII, Division 2 of ASME PVP Code . In the work of Kalnins  some linearization questions are discussed in two examples; the first is a plane-strain problem and the second is an axisymmetric analysis of primary plus secondary stress at a cylindrical-shell/flat-head juncture. Paper  concludes that for the second example the linearized stresses produced by Abaqus  diverge, therefore they should not be used for stress evaluation for this specific case.
This paper revisits the axisymmetric analysis discussed in  and attempts to show that the linearization difficulties can be avoided. The paper explains in details the reason for the divergence; the Abaqus program does not linearize all stress components in axisymmetric elements; two stress components are calculated from assumed formulas and all others are linearized. It is shown that when the axisymmetric structure from  is modeled with 3D elements, the linearization results are convergent. Further, it is demonstrated that both axisymmetric and 3D modeling produce the same and correct stress Tresca stress, if the stress is evaluated from all stress components linearized, without any further modification.
The stress evaluation of the axisymmetric model of  is the primary-plus-secondary-stresses evaluation for which the limit analysis described in  cannot be used. The paper shows how the original primary-plus-secondary-stresses problem can be converted into the equivalent primary-stress problem, that is for a problem for which limit analysis can be used; it is further shown how the limit analysis had been used for verification of the linearization results.