## 7 Transferring Materials Data onto Notched Components
### Simulation of Material's Behavior in Notched Components  
A question arises when a notch is fairly small and sharp and when the local stresses and strains in the notch root cannot be determined experimentally: Can the stresses and strains in the notch root be appropriately determined through numerical simulation? The type of notched specimen shown in Figure 1, being a round bar specimen with a circumferential grooved notch of \(R_{N}=0.35\) and \(0.5\) mm in notch radius respectively, loaded under axial loading, has been analyzed experimentally as well as numerically. Results obtained from the respective fatigue tests conducted as a LIT at RT (Specimen 14.7) are presented in Figure 11a and an SIT at RT (Specimen 14.3) in Figure 11b. Since neither stresses nor strains could be measured locally, the stresses and strains are considered as nominal stress \(S\) (load divided by minimum cross-section) and nominal strain \(e\) (deflection divided by an \(8\) mm gauge length) respectively. It can be seen that significant plastic deformation occurs in the minimum cross-section of the specimen and that the notch is shortly facing a full plastic environment. The results shown in Figure 11 have been used to validate the numerical approach based on the Chaboche model, as described before. The comparison was done on the basis of nominal strains (hence the measured deflections). In general, there are differences between calculations with different Chaboche parameter sets. Therefore, a statement on  
Figure 10: Results of a simulation of a hysteresis loop using the Chaboche parameters compared to measured data for 240 \({}^{\circ}\)C.  
Figure 9: Results of a simulation of a hysteresis loop using the Chaboche parameters compared to measured data for RT (Specimen NA01). the validity of the notch-based predictions is necessary. The results obtained are shown in Figure 12. A difficulty arises in a way that the material used has shown strong softening and possibly also hardening effects. Those effects are to be seen as a variation in mean strain in load-controlled tests such as the LIT considered here. These changes do also have an influence on the parameters for the Chaboche model considered in the numerical simulation. However, in the numerical simulation presented here, only some average parameters for the Chaboche model could be considered. To avoid those changes and allow for adequate comparability, those softening and hardening effects have been removed in the first instance and have been indicated as 'centered' in Figure 12 respectively. This correlation is valid up to the validity of the plasticity model, which is considered to be the level at which the Chaboche parametrization was done, in this case at 0.45% maximum strain. Principally this approach could be extended in a way that the parameters for the Chaboche model could be determined for the different softening and hardening conditions. Even the creep-like mean stress effects could be described more appropriately. Figure 11: (**a**) Results of a nominal LIT at RT with \(\Delta S_{a}=20\) MPa and \(S_{a,start}=100\) MPa and (**b**) Results of a nominal total strain increase test at RT with \(\Delta\varepsilon_{a,t}=0.05\%\) and \(\varepsilon_{a,start}=0.05\%\). Figure 12: Comparison of simulated load increase test of a specimen with \(R_{N}=0.35\) mm using Chaboche parameter set for tests conducted at RT, with measured data of a nominal LIT (Specimen 14.7) and a nominal SIT (Specimen 14.3). With the numerical simulation being available, strains in the notch root can be determined.