# Fracture Prediction in Weldox 700E Steel Subjected to High Velocity Impact Using LS-DYNA
## 3 Results and Discussion
### Investigation of Fracture Behaviour
#### 3.3.2 Fracture Behaviour with Varying Fracture Strain Criteria  
Now, the study is performed with varying fracture strain criteria for the analysis of fracture behaviour. These include the Johnson-Cook (JC) fracture strain criteria termed \"ef-JC\" (Equation (3)) [27]. [PERSON] et al. [6] replaced the logarithmic strain rate function in the JC criteria with a power-law function. This modified fracture criterion overcomes the infinite value in the logarithmic function. This modification is termed \"ef-DJC\", and the equation for fracture strain criterion reads as follows:  
\[\varepsilon_{t}=(D_{1}+D_{2}\exp(D_{3}\eta))\Big{(}1+\dot{\varepsilon}_{p}^{*} \Big{)}^{D_{4}}(1+D_{5}T^{*}) \tag{4}\]  
[PERSON] et al. [26] used the modified JC fracture strain criteria, which alter the thermal softening function by introducing a multiplication factor involving two constants, with one raised to power-law exponent during high-velocity impact. This modified fracture criterion is termed \"ef-XJC\", and the equation for fracture strain criterion reads as follows:  
\[\varepsilon_{t}=(D_{1}+D_{2}\exp(D_{3}\eta))\Big{(}1+D_{4}\ln\dot{\varepsilon}_ {p}^{*}\Big{)}\Big{(}1+D_{5}T^{*D_{6}}\Big{)} \tag{5}\]  
The value of material constants for different fracture strain criteria are determined using the methodology discussed in Section 2.3 and are presented in Table 5. Other process and material parameters are kept the same with target thickness at 4 mm, projectile velocity of 400 m/s, and a mass of 6.4 g, while different fracture strain models are considered. Figure 15 shows the plug formation using different fracture strain criteria. The ef-JC fracture criteria exhibit a smoother cracked surface compared to the other fracture criteria. A slightly rough cracked surface at the mid-plane is observed in the ef-DJC criteria due to \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Fracture Strain Criterion** & **D1** & **D2** & **D3** & **D4** & **D5** & **D6** \\ \hline ef-JC & 0.365 & 4.5296 & \(-\)5.0397 & \(-\)0.0033 & 1.3864 & — \\ ef-DJC & 0.365 & 4.5296 & \(-\)5.0397 & \(-\)0.0022 & 1.3864 & — \\ ef-XJC & 0.365 & 4.5296 & \(-\)5.0397 & \(-\)0.0033 & 7.5177 & 2.1484 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Material constants for varying fracture strain criteria. For the \"mid\" element, plastic strain rate (Figure 17) and temperature (Figure 20) play a significant role, leading to greater elongation with higher values of von Mises stress (Figure 18) before fracture occurs. Due to thermal softening, the mid element carries a lower load using ef-XJC criteria. In contrast, higher strain hardening allows it to sustain a higher load with ef-DJC criteria, while the material using ef-JC criteria carries less load compared to both ef-XJC and ef-DJC fracture criteria. Figure 20 shows that the increase in  
Figure 19: Trend for von Mises stress with varying fracture strain criteria. Figure 20: Trend for temperature with varying fracture strain criteria. Figure 18: Trend for triaxiality with varying fracture strain criteria. temperature using ef-DJC fracture criteria is greater than with ef-XJC and ef-JC criteria. As a result, the effect of triaxiality is not prominent during this period with its value fluctuating around zero (Figure 19). The increase in temperature leads to an increase in equivalent plastic strain, allowing the element to experience a higher load before failure due to strain hardening. The triaxiality value increases more rapidly using ef-JC fracture criteria than with ef-XJC and ef-DJC criteria after 6 \(\upmu\)s (Figure 20). Consequently, failure occurs first with the ef-JC criteria, followed by ef-XJC, and ef-DJC fracture strain criteria, respectively.