Mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systems
We propose a method for modeling stress-strain state in surface-hardened elements of statically indefinable rod systems under creep. A method we propose is considered for a three-element asymmetric rod system. The solution consists of two steps: reconstruction of the stress-strain state after the pr...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2018-12-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20604/16851 |
| _version_ | 1811330151568375808 |
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| author | Vladimir P Radchenko Ekaterina E Derevyanka |
| author_facet | Vladimir P Radchenko Ekaterina E Derevyanka |
| author_sort | Vladimir P Radchenko |
| collection | DOAJ |
| description | We propose a method for modeling stress-strain state in surface-hardened elements of statically indefinable rod systems under creep. A method we propose is considered for a three-element asymmetric rod system. The solution consists of two steps: reconstruction of the stress-strain state after the procedure of surface plastic hardening of the cylindrical elements of the system (pneumatic blasting with micro balls) and the method for calculating the relaxation of residual stresses in the hardened elements amidst the creep state of rod system (as a whole structure). Rheological relations are determined on the basis of a model describing the first and second phases of creep. The solution of both stages and special aspects of the problem is illustrated on a model example of creep of systems with hardened elements made of ZhS6U alloy at the temperature of 650 °C. For hardening the rods of this alloy, real experimental data were used for axial and circumferential residual stresses. The technique of reconstruction of the stress-strain state after pneumatic blasting treatment is illustrated in detail. To build a rheological model, experimental data were used for the uniaxial creep curves of the ZhS6U alloy under various constant stresses at the temperature of 650 °C. The numerical values of the model parameters are given in the article. The uniaxial model is generalized to a complex stress state. The main problem is solved numerically using discretization by spatial and temporal coordinates. The stationary asymptotic stress-strain state of the rod system is investigated, which corresponds to the steady-state creep stage, which was used to estimate the convergence of the numerical method. The dependencies of the kinetics of all components of the residual stress tensor in all three strengthened elements of the system due to creep under a given external load are obtained. A comparative analysis of the residual stress relaxation rate in different rods is performed. The algorithm and software for solving the problem is developed. The main results of the work are illustrated by the residual stresses graphs over the depth of the hardened layer. Issues of applying the results obtained in the work to practical problems of assessing the reliability of hardened rod systems are discussed. |
| first_indexed | 2024-04-13T15:56:16Z |
| format | Article |
| id | doaj.art-680ab66d65a34ebc8c9549d7147fc31e |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T15:56:16Z |
| publishDate | 2018-12-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-680ab66d65a34ebc8c9549d7147fc31e2022-12-22T02:40:40ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812018-12-0122464766810.14498/vsgtu163118024Mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systemsVladimir P Radchenko0Ekaterina E Derevyanka1Samara State Technical UniversitySamara State Technical UniversityWe propose a method for modeling stress-strain state in surface-hardened elements of statically indefinable rod systems under creep. A method we propose is considered for a three-element asymmetric rod system. The solution consists of two steps: reconstruction of the stress-strain state after the procedure of surface plastic hardening of the cylindrical elements of the system (pneumatic blasting with micro balls) and the method for calculating the relaxation of residual stresses in the hardened elements amidst the creep state of rod system (as a whole structure). Rheological relations are determined on the basis of a model describing the first and second phases of creep. The solution of both stages and special aspects of the problem is illustrated on a model example of creep of systems with hardened elements made of ZhS6U alloy at the temperature of 650 °C. For hardening the rods of this alloy, real experimental data were used for axial and circumferential residual stresses. The technique of reconstruction of the stress-strain state after pneumatic blasting treatment is illustrated in detail. To build a rheological model, experimental data were used for the uniaxial creep curves of the ZhS6U alloy under various constant stresses at the temperature of 650 °C. The numerical values of the model parameters are given in the article. The uniaxial model is generalized to a complex stress state. The main problem is solved numerically using discretization by spatial and temporal coordinates. The stationary asymptotic stress-strain state of the rod system is investigated, which corresponds to the steady-state creep stage, which was used to estimate the convergence of the numerical method. The dependencies of the kinetics of all components of the residual stress tensor in all three strengthened elements of the system due to creep under a given external load are obtained. A comparative analysis of the residual stress relaxation rate in different rods is performed. The algorithm and software for solving the problem is developed. The main results of the work are illustrated by the residual stresses graphs over the depth of the hardened layer. Issues of applying the results obtained in the work to practical problems of assessing the reliability of hardened rod systems are discussed.https://journals.eco-vector.com/1991-8615/article/viewFile/20604/16851three-element statically indefinable systemsurface-hardeningresidual stressescreepstress relaxation |
| spellingShingle | Vladimir P Radchenko Ekaterina E Derevyanka Mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systems Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki three-element statically indefinable system surface-hardening residual stresses creep stress relaxation |
| title | Mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systems |
| title_full | Mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systems |
| title_fullStr | Mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systems |
| title_full_unstemmed | Mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systems |
| title_short | Mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systems |
| title_sort | mathematical modeling of creep and residual stresses relaxation in surface hardened elements of statically indefinable rod systems |
| topic | three-element statically indefinable system surface-hardening residual stresses creep stress relaxation |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20604/16851 |
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