Residual stress analysis in surface-hardened rotating prismatic elements with semicircular notches under high-temperature creep

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Abstract

A numerical method is developed to calculate the relaxation of residual stresses in a rotating surface-hardened prismatic sample with a semicircular notch under high-temperature creep conditions. The problem models the stressed-deformed state of a sample fixed on a disk rotating at a constant speed.
The methodology includes the following steps:
– reconstruction of residual stress and plastic deformation fields after preliminary surface plastic deformation;
– calculation of residual stress relaxation during creep in a rotating prismatic rod.
A detailed analysis is performed on a prismatic sample measuring 150 $\times$ 10 $\times$10 mm made of EP742 alloy. One face of this sample is hardened using mechanical ultrasonic treatment. The problem is analyzed for samples with semicircular notches of 0.1 mm and 0.3 mm radii, located 2 mm and 75 mm from the fixed edge.
For the notched regions after preliminary surface plastic deformation, the problems are solved in both elastic and elastoplastic formulations. The obtained initial fields of residual stresses and plastic deformations are used as input data for the creep problem.
The analysis of the influence of notch radius, location, angular velocity, and initial residual stress fields on the relaxation of residual stresses is conducted at a temperature of 650 °C based on phenomenological flow theory established from known experimental data for this alloy.
Results show that to determine the initial stressed-deformed state after preliminary plastic deformation for a notch radius of 0.1 mm, an elastoplastic solution is necessary, while for a radius of 0.3 mm, the differences between elastic and elastoplastic solutions are minimal.
The study of residual stress relaxation is conducted at angular velocities of 1500 and 2000 RPM over a period of 100 hours. Despite significant relaxation of residual stresses for samples with notches of radii 0.1 mm and 0.3 mm, a substantial level of residual compressive stresses remains in the notch regions after complete thermal-mechanical unloading. This indicates the high effectiveness of surface hardening under high-temperature creep conditions.

About the authors

Vladimir P. Radchenko

Samara State Technical University

Author for correspondence.
Email: radchenko.vp@samgtu.ru
ORCID iD: 0000-0003-4168-9660
SPIN-code: 1823-0796
Scopus Author ID: 7004402189
ResearcherId: J-5229-2013
http://www.mathnet.ru/person38375

Dr. Phys. & Math. Sci., Professor; Head of Department; Dept. of Applied Mathematics & Computer Science

Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244

Mikhail N. Saushkin

Samara State Technical University

Email: saushkin.mn@samgtu.ru
ORCID iD: 0000-0002-8260-2069
SPIN-code: 9740-1416
Scopus Author ID: 35318659800
ResearcherId: A-8120-2015
https://www.mathnet.ru/person38368

Cand. Phys. & Math. Sci.; Associate Professor; Dept. of Applied Mathematics & Computer Science

Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244

Dmitry M. Shishkin

Syzran’ Branch of Samara State Technical University

Email: shishkin.dim@yandex.ru
ORCID iD: 0000-0003-3205-2262
https://www.mathnet.ru/person164459

Cand. Techn. Sci.; Associate Professor; Dept. of General Theoretical Disciplines

Russian Federation, 446001, Samara region, Syzran, Sovetskaya str., 45

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Supplementary files

Supplementary Files
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1. JATS XML
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2. Figure 1. The loading scheme for a surface-hardened sample with semicircular notches

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3. Figure 2. Data for the component ${\sigma_x=\sigma_x(y)}$ after ultrasonic surface hardening of a prismatic sample measuring $150{\times}10{\times}10$ mm made of EP742 alloy: experimental data (markers) [28, 32], calculated data from approximation (6) (solid line), and for the thermoelastic problem (dashed line)

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4. Figure 3. The stress-strain curves of the EP742 alloy under elastic-plastic deformation at a temperature of 20 °C: 1 — experimental data [23], 2 — calculation in coordinates $\sigma _{0}$ – $\varepsilon$, 3 — calculation in coordinates $\sigma$ – $\varepsilon$

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5. Figure 4. Experimental (points) and theoretical (solid lines) creep curves of the EP742 alloy at a temperature of 650 °C: 1 — $\sigma=588.6$ MPa, 2 — $\sigma=637.6$ MPa, 3 — $\sigma=686$ MPa

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6. Figure 5. The kinetic data for the components $\sigma _{x}$ under creep conditions at an angular rotation speed of 1500 RPM in the section $x = 75$ mm, obtained for a smooth sample using FEM (a) and the mesh method (b) [32]. Calculated values: 1 — after the hardening procedure at 20 $^\circ$C at time $t = 0 - 0$; 2 — after temperature loading up to 650 $^\circ$C at time $t = 0 + 0$; 3 — after force loading from rotation at 650 $^\circ$C at time $t = 0 + 0$; 4 — after creep under temperature-force loading at 650 $^\circ$C at time $t = 100 - 0$ h; 5 — after force unloading at 650 $^\circ$C at time $t = 100 + 0$ h; 6 — after temperature unloading to 20 $^\circ$C at time $t = 100 + 0$ h

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7. Figure 6. The kinetic data for the components $\sigma _{x}$ under creep conditions at an angular rotation speed of 1500 RPM in the section $x = 75$ mm, obtained for a smooth sample using FEM (a) and the mesh method (b) [32]. The markers mean the same thing as in Figure 5

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8. Figure 7. The kinetic data for the components $\sigma _{x}$ under creep conditions at an angular velocity of 1500 RPM in the section $x = 2$ mm for $\rho = 0.1$ mm, obtained from the elastic solution (a) and the elastoplastic solution (b). The markers mean the same thing as in Figure 5

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9. Figure 8. The kinetic data for the components $\sigma _{x}$ under creep conditions at an angular velocity of 1500 RPM in the section $x = 75$ mm for $\rho = 0.1$ mm, obtained from the elastic solution (a) and the elastoplastic solution (b). The markers mean the same thing as in Figure 5

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10. Figure 9. The kinetic data for the components $\sigma _{x}$ under creep conditions at an angular velocity of 2000 RPM in the section $x = 2$ mm for $\rho = 0.1$ mm, obtained from the elastic solution (a) and the elastoplastic solution (b). The markers mean the same thing as in Figure 5

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11. Figure 10. The kinetic data for the components $\sigma _{x}$ under creep conditions at an angular velocity of 2000 RPM in the section $x = 75$ mm for $\rho = 0.1$ mm, obtained from the elastic solution (a) and the elastoplastic solution (b). The markers mean the same thing as in Figure 5

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12. Figure 11. The kinetic data for the components $\sigma _{x}$ under creep conditions at an angular velocity of 1500 RPM in the section $x = 2$ mm for $\rho = 0.3$ mm, obtained from the elastic solution (a) and the elastoplastic solution (b). The markers mean the same thing as in Figure 5

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13. Figure 12. The kinetic data for the components $\sigma _{x}$ under creep conditions at an angular velocity of 1500 RPM in the section $x = 75$ mm for $\rho = 0.3$ mm, obtained from the elastic solution (a) and the elastoplastic solution (b). The markers mean the same thing as in Figure 5

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14. Figure 13. The kinetic data for the components $\sigma _{x}$ under creep conditions at an angular velocity of 2000 RPM in the section $x = 2$ mm for $\rho = 0.3$ mm, obtained from the elastic solution (a) and the elastoplastic solution (b). The markers mean the same thing as in Figure 5

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15. Figure 14. The kinetic data for the components $\sigma _{x}$ under creep conditions at an angular velocity of 2000 RPM in the section $x = 75$ mm for $\rho = 0.3$ mm, obtained from the elastic solution (a) and the elastoplastic solution (b). The markers mean the same thing as in Figure 5

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