# Failure Modelling of CP800 Using Acoustic Emission Analysis
## 3 Results and Discussion
### Failure Behaviour  
The average failure displacements in x- and y-direction \(\overline{u}_{\mathrm{x}}\) and \(\overline{u}_{\mathrm{y}}\) from the butterfly tests are shown in Figure 7. Obviously, the displacement in the y-direction is larger than in the x-direction for all methods due to the test setup. The maximum displacement in x-direction is about 0.52 mm and in y-direction is 2.82 mm. In general, it can be stated that the failure displacement in y-direction is reduced from about 2.82 mm to 0.46 mm by increasing the loading angle from \(-3^{\circ}\) to \(90^{\circ}\). However, the failure displacement in x-direction increases from about 0.09 mm to 0.52 mm with a loading angle of \(-3^{\circ}\) to \(43.5^{\circ}\) and decreases again at \(90^{\circ}\) to 0.03 mm, which can be explained by the rotation of the test setup. Comparing the three evaluation methods, it can be seen that for most of the specimens the average failure displacement in x- and y-direction is the highest for the mechanical evaluation method, gets lower for the optical evaluation method, and is lowest for the acoustical evaluation method, as assumed. However, the acoustical evaluation method estimates mostly marginally lower displacements than the optical evaluation method. For example, at a loading angle of \(90^{\circ}\) the displacement in y-direction is 0.464 mm, 0.366 mm, and 0.357 mm for the mechanical, optical, and acoustical evaluation methods. The failure displacements were used as boundary conditions in the numerical models of the butterfly tests. To validate the simulation models, the force-displacement curves are compared to the experimental values from the butterfly tests in Figure 8. For both the numerical and the experimental force-displacement curves, the maximum force reduces from a loading angle of \(90^{\circ}\) to \(12.5^{\circ}\) from about 10.5 kN to 7 kN, while the maximum displacement increases from about 0.46 mm to 1.96 mm. The maximum force of about 7.3 kN for the loading angle \(-3^{\circ}\) is at the same level as \(12.5^{\circ}\), but the maximum displacement is higher for \(-3^{\circ}\) with about 2.77 mm. Comparing the experimental and the numerical results, it can be seen that the numerical results fit well to the experimental. Within increasing deformation, the numerically calculated force slightly overestimates the experimental force. It can be seen well for the loading angle \(43.5^{\circ}\). The numerical curves fit well to the experimental curve until a displacement of about 0.9 mm and proceeds above the experimental curve until 1.01 mm at the end of forming. This is because no damage model was used for the numerical models and the damage accumulation reduces the force during forming. Therefore, it is assumed that the modelling of the material and of the tests represents the flow behaviour of the material well. Figure 7: Average failure displacement in x-direction \(\overline{u}_{\mathrm{x}}\) and in y-direction \(\overline{u}_{\mathrm{y}}\) of the butterfly tests for CP800. In Figure 9, the distribution of the numerically calculated equivalent plastic strain is compared to the distribution measured in the experiments by the optical evaluation method. The overall distribution of the equivalent plastic strain in the investigation area of the butterfly specimen is represented well by the numerical model. In the specimen centre, the maximum equivalent plastic strain is slightly underestimated by the numerical models compared to the measured values for the loading angle of 12.5\({}^{\circ}\) to 90\({}^{\circ}\). At the loading angle 90\({}^{\circ}\) for example, the optically measured maximum equivalent plastic strain is about 0.505 and the numerically calculated is 0.458. Overall, it can be stated that the numerical modelling represents the butterfly tests in an adequate way with enough precision. In Figure 10A, the equivalent plastic strain-triaxiality curves of all loading angles for the three evaluation methods are shown.