# Failure Modelling of CP800 Using Acoustic Emission Analysis
## 2 Materials and Methods
### Failure Behaviour  
For the characterisation of the failure behaviour of the CP800, experimental investigations with butterfly specimens were performed. The butterfly specimen and a close-up of the investigation area with its unique shape are shown in Figure 1A. The RD and TD of the specimen are indicated in the figure. The test setup shown in Figure 1B is installed in the tensile testing machine S100/ZD; the specimen can be tested under different loading angles at 15.5\({}^{\circ}\) intervals, varying the stress state in the investigation area. Loading angles from \(-3^{\circ}\) to 90\({}^{\circ}\) can be induced to create stress states from shear stress to uniaxial tension. Seven loading angles were tested with a quasistatic forming speed of 0.02 mm/s at room temperature. For statistical validity, each test was performed five times. While testing, the forming force was measured by the tensile testing machine S100/ZD. The displacements in x- and y-direction of the butterfly specimens were tracked with the optical measuring system Aramis. Therefore, a stochastic pattern was applied on the investigation area of the butterfly specimens, as also shown in Figure 1A. Further, the acoustic emissions of the butterfly specimens during the tests were recorded using the acoustical measuring system AMSY-6 from Vallen Systeme GmbH (Wolfrathaushen, Germany). A more detailed description of the test setup is presented by [PERSON] et al. in [24]. The specimen failures are evaluated and compared with three evaluation methods: a mechanical, an optical, and an acoustical evaluation method. For an overview, a measured forming force and amplitude-over-time curve is shown in Figure 2A. The mechanical method determined the failure of the specimen by a sudden drop in the forming force over a short time period, as shown in Figure 2B. According to the optical method displayed in Figure 2C, the failure initiation time is derived from the images of the investigation area of the butterfly specimens from the optical measuring system. Using the acoustical method, the material failure is obtained by clearly recognisable burst signals, as demonstrated in Figure 2D. Based on the three evaluation methods, three different failure initiation times and, hence, three sets of failure displacements in x- and y-direction were generated for each butterfly specimen. Figure 1: Butterfly specimen with close-up of the investigation area as well as stochastic pattern (**A**), and schematic representation of the test setup for butterfly specimen with optical as well as acoustical measuring system (**B**). In order to determine the triaxiality, normalised Lode angle, and equivalent plastic strain for the parametrisation of a failure model, the butterfly tests were numerically mapped. The average failure displacements in x-direction \(\widetilde{u}_{\mathrm{x}}\) and in y-direction \(\widetilde{u}_{y}\) from the five experiments were used as boundary conditions in the numerical models, as shown in Figure 3. The models were created in LS-PrePost for each evaluation method and each loading angle. Only the investigation area of the butterfly specimen was modelled as a half using the symmetry axis in z-direction. For each loading angle, one side of the specimen was fixed by a set of nodes and the other side was moved in x- as well as y-direction by a set of nodes. The forming speed was set to 0.02 mm/s, as in the experiments. Using hexahedron elements (constant stress solid elements) with an element edge length of 0.1 mm, the geometries were discretised. To model the material behaviour of the CP800, the material card \"Mat_103_Anisotropic_Viscoplastic\" was used. Density, young's modulus and Poisson's ratio were set according to the standard data to 7.85 \(\times\) 10\({}^{-9}\) ton/mm\({}^{3}\), 2.1 \(\times\) 10\({}^{5}\) MPa and 0.3. For the flow behaviour, the extrapolated flow curve from the Swift approach and the parametrised Hill48 yield criterion were used. According to the loading angle, the RD of the butterfly specimen was adjusted in the material card.