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Description of Residual Stress Distribution in the Surface Layer After Heat Treatment and Shot Peening

Konstanty Skalski
Konstanty Skalski
, 
Grzegorz Mońka
Grzegorz Mońka
 e 
Ryszard Filipowski
Ryszard Filipowski
   | 13 set 2023
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Article Category: Research Article
Pubblicato online: 13 set 2023
Pagine: 28 - 39
Ricevuto: 13 mar 2023
Accettato: 12 giu 2023
DOI: https://doi.org/10.2478/tar-2023-0015
Parole chiave
© 2023 Konstanty Skalski et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Profiles of diffraction lines obtained at different angles of incidence ψ of the beam of X-ray waves: (A) horizontal axis – angle 2Θ; and (b) vertical axis – intensity of X-ray diffraction.
Profiles of diffraction lines obtained at different angles of incidence ψ of the beam of X-ray waves: (A) horizontal axis – angle 2Θ; and (b) vertical axis – intensity of X-ray diffraction.

Figure 2.

Report on the measurement of residual stresses using the X-ray method, using the PSWF-3M device from the Rigaku Company: Young’s modulus E = 210,000.0 MPa and Poisson’s ratio ν = 0.280.
Report on the measurement of residual stresses using the X-ray method, using the PSWF-3M device from the Rigaku Company: Young’s modulus E = 210,000.0 MPa and Poisson’s ratio ν = 0.280.

Figure 3.

PEEN-IMP device for pneumatic peening (patent PL204718).
PEEN-IMP device for pneumatic peening (patent PL204718).

Figure 4:

Graph of residual stress distribution in the sample after shot peening: sample NR50 (HRC, 35 MPa), shot N = 1, curve 1 – measured distribution of residual stresses, to a depth of 0.5 mm, curve 2 – distribution of residual stresses created by REGSTEP.EXE, represented by the equation: y = 493,96x2 + 426,43x_501,59.
Graph of residual stress distribution in the sample after shot peening: sample NR50 (HRC, 35 MPa), shot N = 1, curve 1 – measured distribution of residual stresses, to a depth of 0.5 mm, curve 2 – distribution of residual stresses created by REGSTEP.EXE, represented by the equation: y = 493,96x2 + 426,43x_501,59.

Statistical evaluation of the obtained regression function using the statistical parameters R2 (the square of the multiple correlation coefficient) and F (Snedecor’s test).

STEP 9
VARIABLE ENTERED..... 8
(FORCED VARIABLE)
SUM OF SQUARES REDUCED IN THIS STEP.... 18743.844
PROPORTION REDUCED IN THIS STEP........ 0.006
CUMULATIVE SUM OF SQUARES REDUCED...... 2162765.250
CUMULATIVE PROPORTION REDUCED.......... 0.741 OF 2919265.000
FOR 9 VARIABLES ENTERED
MULTIPLE CORRELATION COEFFICIENT... 0.861
(ADJUSTED FOR D.F.)........... 0.851
SQUARE MULTIPLE CORRELATION COEFFICIENT ⊠ 0.741
F-VALUE FOR ANALYSIS OF VARIANCE... 37.483
STANDARD ERROR OF ESTIMATE......... 80.069
(ADJUSTED FOR D.F.)........... 82.716

Coefficients of the regression function calculated by the program for the results of measurements.

Variable number Regression coefficient Std. Error of reg. coeff. Computed T-value
(c1) 1 −0.845537E+02 303.47275 −0.279
(c7) 7 −0.865059E+01 1.82461 −4.741
(c6) 6 0.259431E+02 52.86755 0.491
(c2) 2 −0.109254E+03 26.07856 −4.189
(c10) 10 0.798438E+02 14.47331 5.517
(c9) 9 0.160997E+01 0.35632 4.518
(c3) 3 −0.114981E+03 60.96822 −1.886
(c5) 5 0.138582e+02 7.15698 1.936
(c8) 8 0.493962E+03 288.88644 1.710
(c0) 0.168799E+04

Values of residual stresses σ as a function of changing the X1 depth extending into the surface layer calculated by the FUNVAL3.EXE program.

Type of function - NATURAL -N-
Values of Bi coefficients in the calculated function
B0= 0.1688E+04, B1= −0.8455E+02, B2= −0.1093E+03,
B3= −0.1150E+03
B12= 0.1386E+02, B13= 0.2594E+02, B23= −0.8651E+01,
B11= 0.4940E+03, B22= 0.1610E+01, B33= 0.7984E+02
NUMBER OF POINTS N = 8
Values of X1, X2, X3 variables at set points
X1 X2 X3
0.000 35.0000 1.0000
0.1000 35.0000 1.0000
0.2000 35.0000 1.0000
0.3000 35.0000 1.0000
0.4000 35.0000 1.0000
0.5000 35.0000 1.0000
0.6000 35.0000 1.0000
0.7000 35.0000 1.0000
0.8000 35.0000 1.0000
Xi depth and Yi function values at set points
No. Xi Yi
1 0.000 −501.1677
2 0.1000 −454.0123
3 0.2000 −396.5508
4 0.3000 −329.2101
5 0.4000 −251.9901
6 0.5000 −164.8909
7 0.6000 −67.9124
8 0.7000 38.9453
9 0.8000 155.6822

Measurements of stresses σ MPa as a function of distance d mm from the surface.

LP Distance from the surface d mm Hardness HRC Steel shotN 1,2,3,4 Stresses σ MPa
1 0.000 35 1 −506.37
2 0.079 35 1 −465.59
3 0.127 35 1 −390.06
4 0.194 35 1 −397.08
5 0.241 35 1 −244.17
6 0.299 35 1 −209.32
7 0.399 35 1 −232.61
8 0.456 35 1 −172.24
…
25 0.000 30 2 −448.40
26 0.046 30 2 −540.25
27 0.106 30 2 −571.50
28 0.150 30 2 −547.69
29 0.210 30 2 −527.38
30 0.258 30 2 −514.13
31 0.315 30 2 −427.26
32 0.340 30 2 −354.94
33 0.396 30 2 −305.50
…
70 0.000 45 3 −682.34
71 0.051 45 3 −602.13
72 0.111 45 3 −615.84
73 0.191 45 3 −552.10
74 0.206 45 3 −395.75
75 0.227 45 3 −259.79
76 0.340 45 3 −249.39
77 0.393 45 3 −293.09
78 0.419 45 3 −195.22
…
120 0.000 50 4 −643.16
121 0.116 50 4 −737.91
122 0.166 50 4 −745.57
123 0.220 50 4 −509.45
124 0.284 50 4 −394.01
125 0.347 50 4 −432.17
126 0.401 50 4 −321.01
127 0.462 50 4 −254.92
128 0.565 50 4 −261.30
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