# Failure Modelling of CP800 Using Acoustic Emission Analysis
## 3 Results and Discussion
### Failure Behaviour
The curves of the loading angles from \(-3^{\circ}\) to 28\({}^{\circ}\)  
Figure 8: Comparison of the experimental and numerical force—displacement curves for the three evaluation methods. Figure 9: Comparison of the optically measured and numerically calculated equivalent plastic strain distributions of the butterfly tests for the optical evaluation method. proceed similarly for the three evaluation methods. For the other loading angles, there is a high difference for the acoustical evaluation method compared to the other two methods. The equivalent plastic strain-triaxiality curves of the acoustical evaluation method are shifted to higher triaxialities. This difference can be explained by the area, where material failure was assumed in the experiment and, therefore, evaluated in the simulations. For the mechanical and the optical evaluation methods the specimen data are analysed on the surface, while for the acoustical evaluation method the specimen data are analysed inside the specimen. A similar difference can be seen at the equivalent plastic strain-normalised Lode angle curves in Figure 10B. Here all curves for all loading angles show a similar behaviour except for a loading angle of \(59^{\circ}\) and \(74.5^{\circ}\), where a higher difference is visible for the acoustical evaluation method. Based on the equivalent plastic strain-triaxiality and the equivalent plastic strain-normalised Lode angle curves, the characteristic stress states were estimated. To obtain the characteristic values, the area-weighted centroid was calculated from the equivalent plastic strain--triaxiality and the equivalent plastic strain-normalised Lode angle curves. The area-weighted stress state is plotted in Figure 11A for all loading angles and the three evaluation methods. Likewise to the curves in Figure 10, the area-weighted stress state is similar for the three evaluation methods for the loading angles from \(-3^{\circ}\) to \(28^{\circ}\). For the other loading angles, the stress state of the acoustical method shows a difference to the stress state of the other two methods located at higher triaxialities. Exemplarily for the loading angle \(90^{\circ}\), the characteristic value of the normalised Lode angle is about 0.1 for all three methods. The characteristic value of the triaxiality is about 0.61 for the mechanical and optical evaluation methods, but about 0.79 for the acoustical evaluation method. In Figure 11B, the maximum equivalent plastic strain is shown for all loading angles and evaluation methods. The maximum equivalent plastic strain is the highest at a loading angle of \(-3^{\circ}\) with about 0.85 and reduces up to \(28^{\circ}\) with about 0.53. It then rises again to about 0.61 for a loading angle of \(59^{\circ}\), reduces to about 0.47 for a loading angle of \(74.5^{\circ}\) and rises again to about 0.54 for a loading angle of \(90^{\circ}\). Comparing the three evaluation methods, the highest equivalent plastic strain is always present for the mechanical evaluation method due to the highest failure displacement and therefore the highest deformation. This shows the low sensitivity of the mechanical evaluation method to material failure. For the loading angles from \(-3^{\circ}\) to \(59^{\circ}\), the optical evaluation method shows higher maximum equivalent plastic strains than the acoustical evaluation method. However, for the loading angles \(74.5^{\circ}\) and \(90^{\circ}\) the acoustical evaluation method estimates higher maximum equivalent plastic strain than the optical evaluation method. The higher maximum equivalent plastic strains for the acoustical evaluation method at the loading angles \(74.5^{\circ}\) and \(90^{\circ}\) can be explained  
Figure 10: Equivalent plastic strain–triaxiality curves (**A**) and equivalent plastic-strain-normalised Lode angle curves (**B**) of the butterfly specimens for the three evaluation methods. by the failure area of the material.