## 7 Transferring Materials Data onto Notched Components  
### Simulation Results for Unnotched Specimens--The Three-Component Chaboche Plasticity Model  
Appropriate understanding of a material's behavior, specifically also at a microscopic level is a major prerequisite to allow components in service to be assessed appropriately. The more and adequate information that can be obtained, the better an assessment can become. The way to get materials data with an enhanced usage of NDT technology, as  
Figure 6: Change in temperature \(\Delta T\) results of one SIT at RT. presented and discussed above, is therefore an essential element, which even becomes more essential once an aging component has to be assessed. Assessment of components, pristine as well as aged, is initially to be performed on a numerical basis. For this, an adequate material database is required such that an appropriate description of a material's behavior can be made based on the mechanical models available. An example in that regard is the three-component Chaboche model [19; 20], which claims to describe the nonlinear kinematic hardening of a material. In this model, the displacement of the yield surface of the stress states is described by the back stress tensor \(\alpha\). The temporal changes of the three back stress components \(\alpha_{i}\) are linked to the change in plastic strain via model parameters as follows:  
\[\dot{\alpha_{i}}=\frac{2}{3}C_{i}\dot{e}^{pl}-\gamma_{i}\Big{|}\dot{e}^{pl} \Big{|}\alpha \tag{4}\]  
The parameters \(C_{i}\), \(\gamma_{i}\), \(i=1,\,2,\,3\) are constants in the Chaboche kinematic hardening model, generated from the uniaxial strain controlled stable hysteresis loop. The uniaxial yield stress \(\sigma_{x}\) is the sum of the offset yield stress \(\sigma_{0}\) and the back stress component in the uniaxial direction, expressed as:  
\[\sigma_{x}=\sigma_{0}+\sum_{i=1}^{n}\alpha_{i} \tag{5}\]  
These descriptive quantities were determined separately for two selected test temperatures (RT and 240 \({}^{\circ}\)C in the present case). To get the parameters determined, stress-strain hystereses of total strain-controlled tests on unnotched specimens are required, preferably performed at different strain amplitudes. The parameters of the material studied were determined on an SIT with an initial \(\varepsilon_{a,t}\) of 0.05% and a step increase of 0.05% performed at RT and 240 \({}^{\circ}\)C respectively. Figure 7a shows the results of the SIT conducted at RT (Specimen NA01). The red line represents the controlled total strain amplitude \(\varepsilon_{a,t}\) and the blue the resulting stress amplitude \(\sigma_{a}\). The green line represents the mean stress \(\sigma_{M}\), which is a consequence of the strain-controlled mode and the brown the plastic strain amplitude \(\varepsilon_{a,p}\). It can be seen that at lower total strain amplitudes (0.05% to 0.3%), no material hardening or softening does occur, while from 0.35% onwards cyclic hardening is to be seen. Moreover, mean stresses mainly vanish from a total strain amplitude of 0.4% and above. Figure 7b shows the stress-strain hysteresis in the middle of each step. From these hystereses, it was concluded that from \(\varepsilon_{a,t}=0.4\%\) onwards plastic effects are clearly present. Based on this, the step at \(\varepsilon_{a,t}=0.45\%\) (shown in red) was chosen to represent the material under plastic strain and hence for the determination of the parameters in the three-component Chaboche model to be then used in the FE simulations to follow, the cycle used was cycle 9941. Figure 8 presents the results of a SIT run at 240 \({}^{\circ}\)C with the same test parameters as at RT. The respective material responses are presented with the same colors as in Figure 7a. It can be seen, that at the beginning of the test there is a lower mean stress than at RT, which becomes 0 at \(\varepsilon_{a,t}=0.3\%\).