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General Planar Ideal Flow Solutions with No Symmetry Axis
Sergei Alexandrov1,2, Vyacheslav Mokryakov1
1Ishlinsky Institute for Problems in Mechanics RAS, 101-1 Prospect Vernadskogo, Moscow 119526, Russia.
Materials (Basel, Switzerland)
|December 9, 2023
Summary
This study presents general solutions for bulk ideal flows in plasticity, enabling the design of tools for specific material flows without a symmetry axis. These analytical solutions also predict tool wear by calculating pressure distribution.
Area of Science:
- Continuum Mechanics
- Plasticity Theory
- Material Science
Background:
- Bulk ideal flows are crucial in plasticity, often involving inverse problems where solutions define boundaries.
- Existing solutions typically assume a symmetry axis, limiting their applicability.
- Ideal flow models include isotropic rigid/plastic materials and the double sliding and rotation model.
Purpose of the Study:
- To develop general solutions for bulk ideal flows that do not require a symmetry axis.
- To provide a framework for determining tool shapes that generate specific ideal flow patterns.
- To enable the calculation of pressure distribution on tool surfaces for wear prediction.
Main Methods:
- Characterizing the general structure of solutions as two rigid regions connected by a plastic region.
- Utilizing straight characteristic lines between plastic and rigid zones.
- Employing Riemann's method for regions with curvilinear characteristics.
Main Results:
- Development of practically analytical general solutions for non-axisymmetric ideal flows.
- Identification of specific tool shapes required to produce these flows.
- Calculation of pressure distribution on tool surfaces.
Conclusions:
- The developed solutions extend the applicability of ideal flow analysis to more complex scenarios.
- The findings facilitate the design of forming tools and aid in predicting tool wear.
- The analytical nature of the solutions minimizes the need for complex numerical simulations.
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