5. Optimization of laser shock peening process using design of experiments
5.5 DOE based on corrected residual stress profiles
91 Figure 5.19 Residual stress profiles of the verification observations. LSP parameters: 1mm
optics, 4.0 J energy, 2 overlap.
Furthermore, prediction accuracy was calculated as a ratio of the predicted value to an averaged experimental value and was compared with the R2 factor. In terms of all responses, the prediction accuracy of the model is lower than its ability for data fitting. The observed differences are 7%, 5%, and 5% for the stress area, stress at 0.01 mm, and stress at 0.5 mm, respectively. The deterioration in prediction accuracy is caused by the measurement error of new observations, which is not included in the regression model.
The widely accepted level of the model prediction accuracy is 80%. Within the current experimental runs, only the stress at 0.01 demonstrates a slightly lower prediction accuracy of 77%, which is still acceptable within the framework. The prediction accuracy can be improved by performing additional observations at different factor levels or by performing extra replicates aimed to stress at 0.01 mm. The hole drilling measures the subsurface residual stresses at 0.01 mm depth less precisely due to the roughness of material surface and inaccurate definition of the position at which the driller touches the surface (null position). Therefore, the stress at 0.01 mm reflects the higher systematic measurement error.
5.5 DOE based on corrected residual stress profiles
5.5.1 Correction of measured residual stresses through the established methodology
At the DOE optimization stage, various shapes and magnitudes of the residual stress profiles are examined. For the correction of the plasticity effect, which occurs when measuring LSP-shaped residual stresses approaching 80% of material yield strength, the established methodology using ANN is applied to all stress profiles. After the correction trained ANN returns the actual stress
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profile regardless of the presence of plastic deformations, the stress profiles affected by nonlinearity are corrected, and no affected profiles are left unchanged.
Out of 50 experimental observations, 10 (20%) were corrected by ANN, while other observations remained unchanged. The required correction in the measured stress profiles (stress responses) and the corresponding LSP parameters are listed in Table A2. After correction, the stress area and stress at 0.5 mm are decreased up to 15%. Stress at 0.01 mm remains the same as prior to correction analogously with the profiles’ correction discussed in Chapter 4.3.3, which is an artifact of the stress profile shapes used in the generation of ANN training patterns. Moreover, 15% of stress correction is comparable with 10–20% measurement error of the hole drilling equipped with ESPI and can be considered to be not significant when carrying out a single measurement. However, in the current work, the DOE is performed where a relationship between factor and response variables is obtained from the carefully planned experiments using statistical methods. Thus, the measurement error is considered by the regression model when predicting new observations. Therefore, the performed DOE is enhanced by including the correction of the measured stress profiles obtained through the ANN methodology.
5.5.2 Correction of the DOE regression model
The regression models of stress at 0.5 mm and stress area responses have been improved by taking into the account the stress correction of 10 observations. The response stress at 0.5 mm, as a function of overlap and energy factors for the corrected regression model, is presented in Figure 5.20. The stress area response as a function of overlap and energy factors for the corrected regression model is presented in Figure 5.21. Both surface functions in Figure 5.20 and Figure 5.21 show a similar pattern as Figure 5.13 and Figure 5.9, respectively: the overlap and energy have an almost equal influence on the stress at 0.5 mm and stress area, the responses decrease by increasing either factor. The surfaces are horizontally inclined at an angle of approximately 45 degrees. However, the corrected surface functions demonstrate higher curvature at higher negative values due to the reduction (correction) of the stress values approaching the yield strength of the material. Therefore, in the range of surface curvature, higher overlap and energy values have to be used in order to achieve the desired stress value.
The minimum compressive stress at 0.5 mm increases from -359 MPa to -332 MPa and the minimum stress area increases from -298 MPa mm to -265 MPa mm.
5.5 DOE based on corrected residual stress profiles
93 Figure 5.20 Stress at 0.5 mm response as a function of overlap and energy factors for the
corrected data.
Figure 5.21 Stress area response as a function of overlap and energy factors for the corrected data
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The stress area, stress at 0.01 mm and stress at 0.5 mm are plotted over the overlap and energy for the corrected regression model in Figure 5.22. As demonstrated in Figure 5.20 and Figure 5.21, the corrected models show the curvature of stress area and stress at 0.5 mm functions, shifting the region of the minimum stress values towards the higher values. This makes the stress at 0.01 mm and stress area acceptable regions are almost identical after correction; they build up a feasible region of all responses. This means that after correction of stress profiles, stress at 0.01 mm and stress area — which directly influence the fatigue and fatigue crack propagation, respectively — require comparable effort for achieving desired values.
In conclusion, within the range of factor variations defined in the framework of DOE of LSP, the application of the correction by ANN methodology has slightly changed the regression model, because 80% of all observations did not reveal nonlinear deformations during the hole drilling measurements. However, there is a change in the minimum stress values and minimum integral stress area that can be achieved to lower values by 9% and 11%, respectively.
Figure 5.22 Residual stress responses optimization: the feasible range of the energy and overlap variation, 1mm optics for the corrected data.