PSI - Issue 76

Christina Mamagkinidou et al. / Procedia Structural Integrity 76 (2026) 82–88

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3. Results and discussion 3.1. Residual stress profiles and correction

The as-measured residual stress profiles in rolling direction and perpendicular to the rolling direction are presented in Fig. 3(a) and (b), respectively, with black, solid lines. A total of 17 points were measured, with an estimated error ranging from 7 to 24 MPa. The profile in rolling direction reveals a complex through-thickness stress distribution, with both tensile and compressive regions across different depths. A maximum tensile residual stress of +152 MPa was determined at the centre of the sheet thickness, transitioning to compressive stress of approximately − 150 MPa towards both surfaces of the sheet. At the surface, pronounced compressive residual stresses of around − 400 MPa were detected, which are typically attributed to surface finishing operations. It is, therefore, assumed that they resulted from surface grinding. Residual stress measurements performed perpendicular to the rolling direction show highly compressive values at the surface of around − 500 MPa, followed by nearly uniform compressive stresses between − 14 MPa and − 52 MPa in the interior. Due to the relaxation and redistribution of residual stresses that occurs with incremental material removal, subsequent correction of the measured values is required. This is particularly evident for the residual stress profile measured perpendicular to the rolling direction, as shown in Fig. 3(b), which exhibits exclusively compressive values throughout the thickness – an outcome that is physically unrealistic. For comparative evaluation, two different numerical approaches were applied for the residual stress correction calculations. Both approaches are based on the solution proposed by Moore and Evans (1958), which consists of an analytical solution accounting for the stress and bending moment redistribution occurring during surface layer removal for a flat plate of uniform thickness: σ ሺ z 1 ሻ = σ m ሺ z 1 ሻ + 2 න σ m ( z )d z z െ 6z 1 න σ m ( z )d z z 2 H z 1 H z 1 , (1) with H referring to the original thickness of the plate and z 1 describing the thickness of the plate after material is removed between each measurement step. σ m ( z 1 ) denotes the measured residual stress after removal of a layer with thickness H − z 1. A relatively simple computational formulation of Eq. (1) was proposed by Sikarskie (1967), which consists of Taylor series expansions of the original solution by Moore & Evans: σ ሺ z 1 ሻ = σ m ሺ z 1 ሻെ 4 σ m ሺ H ሻ൬ H - z 1 H ൰ + ቆ σ m ሺ H ሻ +2 H ∂ σ m ሺ H ሻ ∂ z ቇ൬ H - z 1 H ൰ 2 +… (2) In case of incremental electrolytic polishing with shallow depth of material removed (e.g., a few micrometres) corresponding to each measurement step, only the first term of the series can be used for the correction of the measured values: σ ሺ z 1 ሻ = σ m ሺ z 1 ሻ െ 4 σ m ሺ H ሻ൬ H െ z 1 H ൰ . (3) The simplified Taylor series given in Eq. (3) was employed by incrementally calculating the corresponding corrected value for each measurement step, and the results are plotted with orange triangles in Fig. 3. The residual stresses computed with this method mainly shift the profile towards higher values, compared to the uncorrected measurement data. However, the correction for the residual stress profile perpendicular to the rolling direction, as shown in Fig. 3(b), still does not compensate for the predominantly compressive stresses. As a second approach, the corrected values of the residual stresses measured were incrementally calculated by