# Failure Modelling of CP800 Using Acoustic Emission Analysis
## 2 Materials and Methods  
### Flow Behaviour  
The investigated steel is the complex phase steel CP800, also known as HCT780C, in 1.6 mm sheet thickness from voestalpine Stahl GmbH (Linz, Austria). The microstructure of the steel consists of different amounts of ferrite, bainite, and martensite. Table 1 displays the chemical composition [14]. Metallographic examinations of the delivered material were carried out to analyse the microstructure. To prepare cross sections, specimens were cut from the sheet metal using water jet cutting. The specimens were then embedded in epoxy resin and ground using 2000 mm, 1200 mm, and 500 mm grit SiC paper. Afterwards, the specimens were polished with diamond paste of grit size 0.003 mm and 0.001 mm. A 4 wt% alcoholic nitric acid was used at room temperature for 20 s to enable light microscopic images of the microstructure. For imaging, the light microscope Polyvar Met 66 from Reichert-Jung (Depew, NY, USA) was used. To characterise the flow behaviour of the CP800, tensile tests in rolling direction (RD), in 45\({}^{\circ}\), and in transverse direction (TD) were performed according to DIN 10275 [15]. The tests were conducted with the tensile testing machine S100/ZD from DYNA-MESS Prufsysteme GmbH (Aachen, Germany) at room temperature for the quasistatic forming speed of 0.02 mm/s. The forming force was measured using the tensile testing machine and the displacements using the optical measuring system Aramis from Carl Zeiss GOM Metrology GmbH (Braunschweig, Germany). For the optical measurement, a stochastic pattern was applied to the surface of the specimen. It consisted of a white primer with black speckles created with a spray can, as suggested by DIN 12004 for the optical determination of forming limit in sheet metals [16]. Each test was repeated five times to identify outliers and achieve statistical validation. Based on the experimental results, a uniaxial flow curve was calculated using the conventional methods for determining the true stress and the true strain from the forming force and the displacement [17]. The begin of plastic deformation was calculated using the 0.2% offset method for determining the yield strength [17]. To extend the flow curve from the tensile test for higher equivalent plastic strains, hydraulic bulge tests were executed in accordance to DIN 16808 [18]. For the bulge tests, the hydraulic press Dunkes HD 250 from S. DunkES GmbH Maschinenfabrik (Kirchheim, Germany) and the optical measuring system Aramis were used. As for the tensile tests, a stochastic pattern was applied on the surface of the bulge test's specimen. Based on the experimental results, the biaxial flow curves were calculated according to DIN 16808 and transformed to the uniaxial stress state using the common approach to equivalent plastic work [19]. By using the extended flow curves, enough experimental data were available to parametrise the commonly used Swift extrapolation approach [20]. The Swift extrapolation approach  
\[k_{\text{f,Swift}}=A\times\left(B+\epsilon_{\text{pl}}\right)^{C} \tag{1}\]  
describes the flow stress \(k_{\text{f,Swift}}\) as a function of the equivalent plastic strain \(\epsilon_{\text{pl}}\), whereas \(A\), \(B\), and \(C\) are material parameters [21]. Using a solver, the material parameters can be determined by the data sets. To model the anisotropic material behaviour of the CP800, the tensile tests in RD, 45\({}^{\circ}\), and TD were analysed further according to DIN 10113 to determine the anisotropy coefficients [22]. Using the anisotropy coefficients \(r_{0}\), \(r_{45}\), as well as \(r_{90}\), the Hill48 parameters  
\[F=\frac{r_{0}}{r_{90}\times(1+r_{0})};G=0.5\times\left(1+\frac{1-r_{0}}{1+r_{ 0}}\right);H=0.5\times\left(1+\frac{r_{0}-1}{1+r_{0}}\right);N=1.5\times\frac {(1+2r_{45})\times(r_{0}+r_{90})}{3r_{90}\times(1+r_{0})} \tag{2}\]  
were calculated. The Hill48 parameters \(L\) and \(M\) were set to 1.5.