Summary
To study how the rate of deformation effects forming rate sensitive materials, the Bodner-Partom elastic-viscoplastic constitutive law is incorporated into a finite element program. This law postulates both elastic and plastic components of deformation at any stress level. The stress is a Hookean function of the elastic strain, while the plastic deformation rate is a function of the deviatoric stress and an internal state variable defining the load history. The finite element derivation adopts the small strain assumption with updated coordinates. The equilibrium rate equation is formulated using total velocities with the nonlinearities incorporated into an equivalent plastic load vector depending upon the current stress. The resulting equation explicitly includes time and is a true rate equation. The program calculates the current stress field using the incremental equilibrium equation. An iterative technique is used to ensure that the assumed current load rate used to calculate the current stress field is correct. Convergence of the iteration procedure needs only be monitored at the velocity specified nodes. To demonstrate the applicability of this method, two plane strain problems, a tensile bar and strip rolling, with rate sensitive materials are investigated.
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Frick, R.N., Chen, Y. Analysis of forming rate sensitive materials. Acta Mechanica 74, 171–184 (1988). https://doi.org/10.1007/BF01194349
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DOI: https://doi.org/10.1007/BF01194349