## 5 Optimisation of Material Parameters
### Indentification Process  
The identification is based on the so-called FEMU approach, which was briefly described in the introduction chapter. In this paper, we use a combination of three material models (Chaboche model, Perzyna model and Norton model) and two types of tests (tensile test, creep test) with several experiments. Usually, all parameters are optimised, see [38; 39], or parameters are selected with regard to the sensitivity to a given set of specimens, see [40; 41]). The following applies to the set of experiments and material models used:  
* The parameters for the Chaboche model can be estimated from one tensile test.
* One tensile test is not enough to estimate the parameters of the Perzyna model.
* The parameters of the Perzyna model can be estimated from two tensile tests at different strain rates.
* The parameters of the Norton model can be estimated from one creep test carried out on the shape of an hourglass specimen.
* Two tensile tests at different strain rates and one creep test are the minimum for tuning all parameters for the given material models.  
These considerations led to a remediation of the procedure based on the gradual addition of experiments to the identification process and the gradual tuning of all material models. The identification process took place in several steps, with the gradual addition of experiments and tuning of selected parameters:  
1. Optimisation for the Chaboche model (always \(\gamma_{3}=0\)) and elastic parameter (Young modulus, yield stress): In total, seven parameters were tuned. Other parameters were fixed on their initial values. To estimate the parameters, the first tensile experiment of 1 mm/min was used.
2. Optimisation for the Perzyna model: two parameters were tuned. All other parameters are fixed at their initial values or values from the previous step. Two tensile experiments with different position rates (1 and 5 mm/min) were used for tuning.
3. Optimisation for the Chaboche model and the Perzyna model: seven parameters were tuned. All other parameters are fixed at their initial values or values from the previous step. Two tensile experiments with different strain rates (1 and 5 mm/min) were used for tuning.
4. Optimisation for the Norton model: two parameters were tuned. All other parameters were fixed at their values from previous steps. One creep test for the smallest cross-section (stress 28.03 MPa) was used for tuning.
5. Optimisation for the Norton model and the Perzyna model: in total, four parameters were tuned. All other parameters were fixed at their values from previous steps. The two creep tests for the two cross-sections (stress 28.03 and 27.22 MPa) were used for the tuning.
6. Optimisation for all material models: in total, nine parameters were tuned. All other parameters (\(E\), \(\sigma_{y}\), \(\gamma_{3}=0\)) were fixed at their values from the previous steps.
7. Adding the last tensile test at speed 10 mm/min. Optimisation for the Chaboche model (always \(\gamma_{3}=0\)) and elastic parameter (Young modulus, yield stress): in total, seven parameters were tuned. All other parameters were fixed at their values from the previous steps.
8. Adding the last creep test at stress 25.05 MPa. Two parameters were tuned for the Norton model. All other parameters were fixed at their values from the previous steps.
9. Optimisation for the Norton model and the Perzyna model: in total, four parameters were tuned. All other parameters were fixed at their values from the previous steps.
10. Optimisation for all material models: in total, nine parameters were tuned. All other parameters (\(E\), \(\sigma_{y}\), \(\gamma_{3}=0\)) were fixed at their values from the previous steps.  
During the identification process, the weight values for individual experiments were changed so that both types of tests (tensile tests and creep tests) had the same importance.