Description of the Expansion of a Two-Layer Tube: An Analytic Plane-Strain Solution for Arbitrary Pressure-Independent Yield Criterion and Hardening Law
The main objective of the present paper is to provide a simple analytical solution for describing the expansion of a two-layer tube under plane-strain conditions for its subsequent use in the preliminary design of hydroforming processes. Each layer’s constitutive equations are an arbitrary pressure-...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-05-01
|
| Series: | Metals |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-4701/11/5/793 |
| _version_ | 1797534159369928704 |
|---|---|
| author | Sergei Alexandrov Elena Lyamina Lihui Lang |
| author_facet | Sergei Alexandrov Elena Lyamina Lihui Lang |
| author_sort | Sergei Alexandrov |
| collection | DOAJ |
| description | The main objective of the present paper is to provide a simple analytical solution for describing the expansion of a two-layer tube under plane-strain conditions for its subsequent use in the preliminary design of hydroforming processes. Each layer’s constitutive equations are an arbitrary pressure-independent yield criterion, its associated plastic flow rule, and an arbitrary hardening law. The elastic portion of strain is neglected. The method of solution is based on two transformations of space variables. Firstly, a Lagrangian coordinate is introduced instead of the Eulerian radial coordinate. Then, the Lagrangian coordinate is replaced with the equivalent strain. The solution reduces to ordinary integrals that, in general, should be evaluated numerically. However, for two hardening laws of practical importance, these integrals are expressed in terms of special functions. Three geometric parameters for the initial configuration, a constitutive parameter, and two arbitrary functions classify the boundary value problem. Therefore, a detailed parametric analysis of the solution is not feasible. The illustrative example demonstrates the effect of the outer layer’s thickness on the pressure applied to the inner radius of the tube. |
| first_indexed | 2024-03-10T11:25:39Z |
| format | Article |
| id | doaj.art-3b99d2e4fddc4468b262e8984178ebfc |
| institution | Directory Open Access Journal |
| issn | 2075-4701 |
| language | English |
| last_indexed | 2024-03-10T11:25:39Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Metals |
| spelling | doaj.art-3b99d2e4fddc4468b262e8984178ebfc2023-11-21T19:41:20ZengMDPI AGMetals2075-47012021-05-0111579310.3390/met11050793Description of the Expansion of a Two-Layer Tube: An Analytic Plane-Strain Solution for Arbitrary Pressure-Independent Yield Criterion and Hardening LawSergei Alexandrov0Elena Lyamina1Lihui Lang2School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, ChinaIshlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, RussiaSchool of Mechanical Engineering and Automation, Beihang University, Beijing 100191, ChinaThe main objective of the present paper is to provide a simple analytical solution for describing the expansion of a two-layer tube under plane-strain conditions for its subsequent use in the preliminary design of hydroforming processes. Each layer’s constitutive equations are an arbitrary pressure-independent yield criterion, its associated plastic flow rule, and an arbitrary hardening law. The elastic portion of strain is neglected. The method of solution is based on two transformations of space variables. Firstly, a Lagrangian coordinate is introduced instead of the Eulerian radial coordinate. Then, the Lagrangian coordinate is replaced with the equivalent strain. The solution reduces to ordinary integrals that, in general, should be evaluated numerically. However, for two hardening laws of practical importance, these integrals are expressed in terms of special functions. Three geometric parameters for the initial configuration, a constitutive parameter, and two arbitrary functions classify the boundary value problem. Therefore, a detailed parametric analysis of the solution is not feasible. The illustrative example demonstrates the effect of the outer layer’s thickness on the pressure applied to the inner radius of the tube.https://www.mdpi.com/2075-4701/11/5/793tube hydroformingtwo-layer tuberigid plasticityarbitrary yield criterionarbitrary hardening lawanalytic solution |
| spellingShingle | Sergei Alexandrov Elena Lyamina Lihui Lang Description of the Expansion of a Two-Layer Tube: An Analytic Plane-Strain Solution for Arbitrary Pressure-Independent Yield Criterion and Hardening Law Metals tube hydroforming two-layer tube rigid plasticity arbitrary yield criterion arbitrary hardening law analytic solution |
| title | Description of the Expansion of a Two-Layer Tube: An Analytic Plane-Strain Solution for Arbitrary Pressure-Independent Yield Criterion and Hardening Law |
| title_full | Description of the Expansion of a Two-Layer Tube: An Analytic Plane-Strain Solution for Arbitrary Pressure-Independent Yield Criterion and Hardening Law |
| title_fullStr | Description of the Expansion of a Two-Layer Tube: An Analytic Plane-Strain Solution for Arbitrary Pressure-Independent Yield Criterion and Hardening Law |
| title_full_unstemmed | Description of the Expansion of a Two-Layer Tube: An Analytic Plane-Strain Solution for Arbitrary Pressure-Independent Yield Criterion and Hardening Law |
| title_short | Description of the Expansion of a Two-Layer Tube: An Analytic Plane-Strain Solution for Arbitrary Pressure-Independent Yield Criterion and Hardening Law |
| title_sort | description of the expansion of a two layer tube an analytic plane strain solution for arbitrary pressure independent yield criterion and hardening law |
| topic | tube hydroforming two-layer tube rigid plasticity arbitrary yield criterion arbitrary hardening law analytic solution |
| url | https://www.mdpi.com/2075-4701/11/5/793 |
| work_keys_str_mv | AT sergeialexandrov descriptionoftheexpansionofatwolayertubeananalyticplanestrainsolutionforarbitrarypressureindependentyieldcriterionandhardeninglaw AT elenalyamina descriptionoftheexpansionofatwolayertubeananalyticplanestrainsolutionforarbitrarypressureindependentyieldcriterionandhardeninglaw AT lihuilang descriptionoftheexpansionofatwolayertubeananalyticplanestrainsolutionforarbitrarypressureindependentyieldcriterionandhardeninglaw |