Modeling of hydraulic autofrettage of thick-walled cylindrical shells taking into account elastoplastic anisotropy caused by the Baushinger effect

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Abstract

The present work is aimed at developing a method for calculating residual stresses during autofrettage of cylindrical shells, allowing for elastic-plastic anisotropy caused by the Bauschinger effect. The proposed calculation method is based on the joint solution by the method of variable elasticity parameters of integral equations of equilibrium and compatibility of deformations, written in Euler coordinates for nonlinear deformation measures. The results of the work are in good agreement with the results of other authors obtained with similar initial data.

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About the authors

S. I. Feoktistov

Komsomolsk-na-Amure State University

Author for correspondence.
Email: serg_feo@mail.ru
Russian Federation, Komsomolsk-na-Amure

I. K. Andrianov

Komsomolsk-na-Amure State University

Email: ivan_andrianov_90@mail.ru
Russian Federation, Komsomolsk-na-Amure

Lin Htet

Komsomolsk-na-Amure State University

Email: linhtetnaining513028@gmail.ru
Russian Federation, Komsomolsk-na-Amure

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Supplementary files

Supplementary Files
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1. JATS XML
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2. Fig. 1. Typical deformation diagram of high-strength steels under uniaxial tension-compression.

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3. Fig. 2. Change in the Bauschinger effect coefficient (a) and elastic modulus (b) during unloading-compression depending on the magnitude of the previous deformation under loading ei′ for steel A723-1130.

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4. Fig. 3. Deformation diagrams of steel A723-1130 under uniaxial tension, subsequent unloading and compression for different levels of deformation si [MPa].

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5. Fig. 4. Deformation diagram for isotropic and kinematic hardening models: 1 – direct loading, 2 – reverse loading (isotropic hardening); 3 – reverse loading (kinematic hardening) [24]. si[MPa].

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6. Fig. 5. Comparison of the results of calculating the circumferential stresses sq′ in the loaded state (4, 5, 6) and residual circumferential stresses sq0 (1, 2, 3) for isotropic hardening at paut = 1720 MPa; Soverstr = 0.47: 1, 4 – according to the methodology of this study, 2, 5 – by the finite element method [24], 3, 6 – by the method of variable material properties [24].

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7. Fig. 6. Comparison of the results of calculating the residual radial sr0 (4, 5, 6) and axial sz0 stresses for isotropic hardening (1, 2, 3) at paut = 1720 MPa; Soverstr = 0.47: 1, 4 – according to the methodology of this study, 2, 5 – by the finite element method [24], 3, 6 – by the method of variable material properties [24].

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8. Fig. 7. Comparison of the results of calculating the circumferential stresses sq′ in the loaded state (4, 5, 6) and residual circumferential stresses sq0 (1, 2, 3) for kinematic hardening at paut = 1720 MPa; Soverstr = 0.47: 1, 4 – according to the methodology of this study, 2, 5 – by the finite element method [24], 3, 6 – by the method of variable material properties [24].

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9. Fig. 8. Comparison of the results of calculating the residual radial sr0 (4, 5, 6) and axial sz0 stresses for kinematic hardening (1, 2, 3) at paut = 1720 MPa; Soverstr = 0.47: 1, 4 – according to the methodology of this study, 2, 5 – by the finite element method [24], 3, 6 – by the method of variable material properties [24].

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10. Fig. 9. Comparison of the results of calculating the circumferential stresses sq′ in the loaded state (4, 5, 6) and residual circumferential stresses sq0 (1, 2, 3) for isotropic hardening at paut = 1679 MPa; Soverstr = 0.44: 1, 4 – according to the methodology of this study, 2, 5 – by the finite element method [24], 3, 6 – by the method of variable material properties [24].

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11. Fig. 10. Comparison of the results of calculating the residual radial sr0 (4, 5, 6) and axial sz0 stresses (1, 2, 3) for isotropic hardening at paut = 1679 MPa; Soverstr = 0.44: 1, 4 – according to the methodology of this study, 2, 5 – by the finite element method [24], 3, 6 – by the method of variable material properties [24].

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12. Fig. 11. Comparison of the results of calculating the circumferential stresses sq′ in the loaded state (4, 5, 6) and residual circumferential stresses sq0 (1, 2, 3) for kinematic hardening at paut = 1679 MPa; Soverstr = 0.44: 1, 4 – according to the methodology of this study, 2, 5 – by the finite element method [24], 3, 6 – by the method of variable material properties [24].

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13. Fig. 12. Comparison of the results of calculating the residual radial sr0 (4, 5, 6) and axial stresses sz0 (1, 2, 3) for kinematic hardening at paut = 1679 MPa; Soverstr = 0.44: 1, 4 – according to the methodology of this study, 2, 5 – by the finite element method [24], 3, 6 – by the method of variable material properties [24].

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14. Fig. 13. Circumferential residual stresses sq0 obtained by different calculation methods at R0 /r0 = 2; Soverstr = 0.7: 1 – according to the methodology of this study, 2 – by the method of variable material properties [39], 3 – by the finite element method in the case of plane deformation [39], 4 – by the finite element method in the case of plane stress state [39]. sq0[MPa], r[mm].

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15. Fig. 14. Circumferential residual stresses sq0 obtained by different calculation methods at R0 /r0 = 2.25; Soverstr = 0.7: 1 – according to the methodology of this study, 2 – by the method of variable material properties [39], 3 – by the finite element method in the case of plane deformation [39], 4 – by the finite element method in the case of plane stress state [39]. sq0[MPa], r[mm].

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16. Fig. 15. Relative change in the elastic modulus –E during unloading-compression across the shell thickness for different values ​​of the plastic region during autofrettage for R0 /r0 = 2: 1 – Soverstr = 0.1; 2 – Soverstr = 0.3; 3 – Soverstr = 0.5; 4 – Soverstr = 0.7; 5 – Soverstr = 0.9; 6 – Soverstr = 1.0.

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17. Fig. 16. Relative change in the elastic modulus –E during unloading-compression across the shell thickness for different values ​​of the plastic region during autofrettage for R0 /r0 = 3: 1 – Soverstr = 0.1; 2 – Soverstr = 0.3; 3 – Soverstr = 0.5; 4 – Soverstr = 0.7; 5 – Soverstr = 0.9; 6 – Soverstr = 1.0.

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18. Fig. 17. Relative change in the yield strength siY = aY siY during unloading-compression across the shell thickness for different values ​​of the plastic region during autofrettage for R0 /r0 = 2: 1 – Soverstr = 0.1; 2 – Soverstr = 0.3; 3 – Soverstr = 0.5; 4 – Soverstr = 0.7; 5 – Soverstr = 0.9; 6 – Soverstr = 1.0.

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19. Fig. 18. Relative change in the yield strength siY = aY siY during unloading-compression across the shell thickness for different values ​​of the plastic region during autofrettage for R0 /r0 = 3: 1 – Soverstr = 0.1; 2 – Soverstr = 0.3; 3 – Soverstr = 0.5; 4 – Soverstr = 0.7; 5 – Soverstr = 0.9; 6 – Soverstr = 1.0.

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20. Fig. 19. Distribution of residual circumferential stresses sq0 across the shell thickness for different values ​​of the plastic region during autofrettage for R0 /r0 = 2: 1 – Soverstr = 0.1; 2 – Soverstr = 0.3; 3 – Soverstr = 0.5; 4 – Soverstr = 0.7; 5 – Soverstr = 0.9; 6 – Soverstr = 1.0. sq0 [MPa].

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21. Fig. 20. Distribution of residual circumferential stresses sq0 across the shell thickness for different values ​​of the plastic region during autofrettage for R0 /r0 = 3: 1 – Soverstr = 0.1; 2 – Soverstr = 0.3; 3 – Soverstr = 0.5; 4 – Soverstr = 0.7; 5 – Soverstr = 0.9; 6 – Soverstr = 1.0. sq0 [MPa].

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22. Fig. 21. Change in compressive residual circumferential stresses sq0|r = r on the inner surface of the shell with a change in the size of the plastic region during autofrettage for R0 /r0 = 2. sq0|r = r [MPa].

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23. Fig. 22. Change in compressive residual circumferential stresses sq0|r = r on the inner surface of the shell with a change in the size of the plastic region during autofrettage for R0 /r0 = 3. sq0|r = r [MPa].

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