# Fracture Prediction in Weldox 700E Steel Subjected to High Velocity Impact Using LS-DYNA
## 2 Materials and Methods
### Material and Fracture Model Constants  
The material constants for the material and fracture model are calibrated using experimental data available in the literature [5]. The relevant relationships for the material constants for the material model and fracture model are given in Figures 1 and 2, respectively. The normalized stress to the normalized material parameters is given in Figure 1 and normalized fracture strain to the normalized fracture parameters is presented in Figure 2. Normalized value is the ratio of actual value to the maximum value. The maximum values are given as 1217.3 MPa for yield stress, 1.136 for equivalent strain, 2.1296 for fracture strain, 1.90 for triaxiality, 500 \({}^{\circ}\)C for temperature, and 922.5 for strain rate, respectively. The values of material constants for fracture strain are calibrated using a non-linear fitting method using MATLAB R2023b (_nlinfit_ function) by maximizing the R-squared value between the experimental data and the model results. The value of R-squared during non-linear fit in MATLAB for data calibration was 99.9% for equivalent stress vs. equivalent strain curve, 82.5% for equivalent stress vs. strain rate curve, and 97.6% for equivalent stress vs. temperature curve which is shown in Figure 1 in the form of normalized value. In the calibration of fracture parameter during the non-linear fit, the R-squared value for fracture strain vs. triaxiality curve was 98.3%, for fracture strain vs. strain rate was 63%, and for fracture strain vs. temperature was 68% which is shown in Figure 2 in the normalized form. The respective values of material constants for the material model and fracture model are listed in Table 1. Further, the projectile is assumed to be rigid, and the in-built bi-linear hardening material model is used to model the projectile (\(\sigma_{y}=A+B\varepsilon_{eq}^{p}\)). The relevant properties of the projectile material are given in Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material Constants** & **Notation** & **Value** \\ \hline Young’s modulus (GPa) & E & 210 \\ Poisson’s ratio & v & 0.33 \\ Density (kg/m\({}^{3}\)) & \(\rho\) & 7850 \\ Initial Yield Stress (MPa) & A & 913 \\ Hardening Coefficient (MPa) & B & 275 \\ Hardening exponent & r & 0.8215 \\ Strain rate hardening & N & 0.0161 \\ Thermal softening constant & q & 1.0875 \\ Reference strain rate (s\({}^{-1}\)) & \(\varepsilon_{0}\) & \(5\times 10^{-4}\) \\ Reference temperature (K) & T\({}_{0}\) & 298 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties for Weldox 700E steel.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material Constants** & **Notation** & **Value** \\ \hline Melting temperature (K) & T\({}_{\text{m}}\) & 1800 \\ Specific heat (J/kg-K) & c\({}_{\text{p}}\) & 452 \\ Fracture strain & \(D_{1}\) & 0.365 \\ & \(D_{2}\) & 4.5296 \\ & \(D_{3}\) & \(-5.0397\) \\ & \(D_{4}\) & \(-0.0033\) \\ & \(D_{5}\) & 1.3864 \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._  
Figure 1: Normalized stress with respect to normalized material parameters.  
Figure 2: Normalized fracture strain with respect to normalized fracture parameters.