Forgeabilité des aciers inoxydables austéno-ferritiques

tel-00672279, version 1 - 21 Feb 2012
Chapter IV. STRAIN PARTITIONING 157
� Step5.
Starting with the optimal starting point found above, a line search procedure is then carried. It involves
iterative minimisation of the Residual by tuning one flow parameter at a time with a predefined step in
the direction of descent. When Residual is no longer decreasing further for that parameter, the direc-
tion of descent for the next flow parameter is found and the tuning of it is continued. The procedure is
terminated when all parameters are considered for the optimization. The iteration at which Residual is
the least is considered as the optimal solution for the final step.
� Step6.
To ensure the stability of the solution, the line search procedure is repeated one more time starting
with the optimal solution found in Step 5 but with a different ordering of the optimization of the flow
parameters. The evolution of Residual during line search procedure is shown in Figure IV.50.b. It is
clear that the Residual does not decrease significantly further assuring the uniqueness of the solution.
The iteration that yields the least Residual by the end of this last run is taken as the best solution.
a) b)
Figure IV.50. Evolution of the residual as a function of simulation number a) during the set of 64
simulations and b) during the line search procedure. The last run assures that the residual does not
decrease further. It is observed in general that the best solution is achieved within 100 simulations.
The simulated strain distribution for the best solution is shown in Figure IV.49.b. The displacement
profile on the edges of the micrograph is very well reproduced. Like in experiments, the simulation also
shows that the strain localization is predominant in ferrite, see Figure IV.49 and Figure IV.51.