Ideal flow theory for the double _ shearing model as a basis for metal forming design

2017 International Conference on Sensors, Materials and Manufacturing

工业技术;材料科学;机械制造

Alexandrov, S.^1,2 ; Trung, N.T.^2,3

Division of Computational Mathematics and Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam^1

Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam^2

Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam^3

关键词: Associated flow rule;    Cartesian coordinate;    Double-shearing models;    Elementary function;    Linear ordinary differential equations;    Metal-forming process;    System of equations;    Tresca yield criterion;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/311/1/012013/pdf
DOI  :  10.1088/1757-899X/311/1/012013

来源: IOP

【 摘 要 】

In the case of Tresca' solids (i.e. solids obeying the Tresca yield criterion and its associated flow rule) ideal flows have been defined elsewhere as solenoidal smooth deformations in which an eigenvector field associated everywhere with the greatest principal stress (and strain rate) is fixed in the material. Under such conditions all material elements undergo paths of minimum plastic work, a condition which is often advantageous for metal forming processes. Therefore, the ideal flow theory is used as the basis of a procedure for the preliminary design of such processes. The present paper extends the theory of stationary planar ideal flow to pressure dependent materials obeying the double shearing model and the double slip and rotation model. It is shown that the original problem of plasticity reduces to a purely geometric problem. The corresponding system of equations is hyperbolic. The characteristic relations are integrated in elementary functions. In regions where one family of characteristics is straight, mapping between the principal lines and Cartesian coordinates is determined by linear ordinary differential equations. An illustrative example is provided.