What kind of tube forming?
In any case, you need the material parameters i.e. yield, hardening etc.
To find it analytically: First of all, the deformation must be uniform. You must determine the uniform major strain at the end of the process. You must also assume a srress state for e.g uniaxial, plane strain or biaxial etc. You also need the hardening curve (or true stress strain curve). If you know all these then you can analytically (or with a small iterative loop) determine the stress (yield stress) at end of the process.
If you are usin FEM then the equivalent stress at end of process (before unloading) gives the new yield stress.
Sharing the point of view of Muhammad Niazi, I could also offer to analyze the change in the thermodynamic potentials of a deformable volume.
According to the first law of thermodynamics, energy that is absorbed by the crystalline solid body at rendering of deforming influence on it,
dEab = dH = d(TS) + dG - fijdeijdVdisp,
where H - is the enthalpy (heat content) of the deformable volume; TS - the bound energy of its substance; G - its Gibbs thermodynamic potential; fij and eij - are components of stress and strain tensors accordingly; Vdisp - is the displaced volume.
The Gibbs thermodynamic potential characterizes the natural deformability of your material, and the latest product in the right-hand side of equation expresses its resistance to deformation.
Changing of these two values allows to judge on the hardening.
Dear Eugene,
Your approach seems interesting to me. I am trying to figure out how the unknowns in the equation could be measured with related to physical process.
Would you guide me on that too.
Thanks
Pranav
Dear Pranav,
This is only an example of the application of fundamental representations to solve of practical problem.
The quantities that included in the proposed equation are calculated on the basis of the deformation parameters.
You know, of course, the work that is committed by deforming device, the value of the stress that is generated in the deformable volume, the temperature, to which the metal is heated during of cold deformation.
Knowing the specific heat and the mechanical properties of the metal, you can to calculate its thermodynamic potentials in the initial state and to analyze the nature of their change in the deformation process.
Practically, this analysis resembles the problem of the propagation of combustion in a tube having a heaves.
It can be done, for example, using the finite element method, basing on the law of energy conservation and thermodynamic laws.
You can to renew necessary theoretical information using the original work of one of the founders of the theory of thermodynamic equilibrium and disturbances J. W. Gibbs (pages 108 - 248 and 343 et seq.) that I've added.
There is one feature. In the classical thermodynamics there are considered only equilibrium processes.
Plastically deformed metal is strongly nonequilibrium self-organizing multi-level system, capable to natural self-organization at the expense of adaptive development of the internal interaction.
On behavior of such systems you can to read, for example, in the book: Haken H. Advanced Synergetics. Instabilities of Self-Organizing Systems and Devices. - Berlin: Springer-Verlag; Springer series in Synergetics, 1983. - Vol. 20. - 356 p.
Unfortunately, I have only its Russian translation.
This is a relatively new domain of natural science and by this reason the thermodynamic theory of nonequilibrium processes haven't been worked out to the end yet.
Currently, this disadvantage is compensated by the adoption of a law of change of thermodynamic deformation parameters in time.
In practice, you can to obtain such law, approximated the calculation results for some number of deformation stages.
Regards.
E. V. Kuznetsow
Thank you very much Eugene for comprehensive discussion. It is really helping.
Regards
Pranav
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