PSI - Issue 79

Oleg Plekhov et al. / Procedia Structural Integrity 79 (2026) 168–175

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Fig. 4. (a) The free surface velocity; pressure (b) of titanium specimens with a thickness of 0.8 mm (averaging over 6-8 profiles)

CRS in flat specimens were measured using the hole-drilling method [20]. The measurements were performed with the MTS3000-Restan residual stress analysis system. This system implements the strain-gauge hole-drilling technique via a high-speed pneumatic turbine (400,000 rpm). A three-element strain gauge rosette was mounted on the specimen surface. A 2 mm diameter hole was drilled at the rosette's geometric center using incremental step drilling. After each drilling step, strain relief deformations caused by residual stress relaxation were recorded. The measurement error did not exceed 1 μ m/m. The residual stress profile was determined by solving the inverse problem using the acquired strain data. In cases of non-uniformly distributed residual stresses through the depth, the strain measured after completing drilling j- step depends on the residual stresses originally present at all prior depth intervals 1 ≤ k ≤ j: = 1+ ∑ =1 ((( х ) +( ) )/2) + 1 ∑ =1 ((( х ) −( ) )/2 ) 2 + 1 ∑ =1 ( ) 2 (2) where (σ x ) k – nornal stress in x direction , (σ y ) k – nornal stress in y direction , (τ xy ) k – shear stress in the plane xy, E – Young's modulus , ν – the Poisson's ratio, a jk and b jk – the calibration coefficients, θ – the orientation angle of each strain gauge. In this study, Type A strain gauge rosettes (manufactured by TML) were used to measure residual stresses at depths up to 1 mm. Characteristic measurement results for a 1x1 mm square laser spot, 1 J pulse energy, and 0% overlap are presented in figure 5.

Fig. 5. Characteristic CRS distribution caused by LSP treatment.

For residual stress measurement on surfaces with non-zero curvature, X-ray diffraction can be employed. The standard stress calculation method is the sin²ψ technique. This method relies on precision measurements of changes