The Proceedings of the Materials and Mechanics Conference
Online ISSN : 2424-2845
2019
Session ID : OS0407
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Stress Function Determined by 3D Biharmonic Equation And Quantification of Plastic Forming
Shoji KUWAHARA
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Abstract

●The biharmonic equation is applicable to not only an elastic body but also a plasticity body indicating an n-th power hardening formula. Distribution of the stress is the same for both the elastic and the plastic bodies if same stress boundary condition is satisfied,

●When the ratio of distance between the loaded area and each stress distribution area is same,we can easily determine the stess distributed.

●There is a difference in 2-dimensional and 3-dimensional cases of stress strengths calculated using the biharmonic equation. Because the comdition of volume changing in each area influences stress distribution over the whole area..

●The transformation increases the boundary condition changes and influences stress distributionin. The Direction is constant there is little ifluence on the deformation in many cases.We can ignore this kind of transformation when the stress direction changes not so much.

●To caluculate the deformation, the mechanical properties of the workpiece are adopted. I chose tensile strength σB and Briinel hardness HB because they are easily obtained.. Also the transformation of a gas such as air driven by the pressure and thermal expansion can be caluculated.

●Necessary rupture energy of a material can be caluculated by multipling tensile strength σB.and glowth rate n indicate n-th power hardning. These rupture energy of stress fanction shows for its distribution. These rupture energy are caluculated using von-Mises stress.

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© 2019 The Japan Society of Mechanical Engineers
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