## 2 Finite Element Model of the Taylor Impact Test  
Finite element modelling of the direct Taylor impact test was performed using ABAQUS/Explicit. The developed model consisted of a deformable three-dimensional (3D) cylinder impacting on a rigid surface at an initial prescribed velocity. The diameter and length of the cylindrical model used in this study were 5 mm and 15 mm, respectively. Furthermore, due to the axisymmetric nature of the cylindrical model, a quarter-symmetric model of the cylinder shown in Figure 1 was used in all analyses to reduce the total number of mesh elements used and therefore, the computation resources. A hard contact with separation after contact was used as the normal interaction property between the rigid surface and the deformable symmetrical model of the cylinder. The tangential behaviour between the symmetrical model of the cylinder and the rigid surface was modelled as frictionless. An initial prescribed velocity was assigned to the deformable quarter cylindrical model in the negative \(z\)-direction as shown in Figure 1. The prescribed impact velocities used for this study were 130 m/s, 200 m/s, and 250 m/s. The Taylor impact test specimens were modelled as elastic-plastic. The elastic properties of the Ti6 Al4V (ELI) model were assigned as: elastic modulus, 113 GPa and Poisson's ratio, 0.34 [20]. The plastic material model was defined by the microstructural-based constitutive model presented in Equation (1) that was developed and validated for LPBF Ti6 Al4V (ELI) in [3]. The definitions of the parameters of this constitutive model are summarised in Table 1.  
\[ \begin{split}\sigma&=\left(\frac{\mu(T)}{\mu_{0}} \right)\sigma^{o}\bigg{(}1-\left(\left(\frac{k_{B}T}{g_{0}\mu(T)^{b}}\right)ln \frac{\dot{e}_{e}}{\dot{e}}\right)^{\frac{1}{b}}\bigg{)}^{\frac{1}{b}}+\zeta.\big{(}1-exp\big{(}-X\cdot\dot{e}_{p}\big{)}\big{)}\\ &+\frac{k_{B}-p}{\sqrt{d}}+\alpha\mu(T)bM\left(\frac{h}{k_{2}} \left(1-exp\big{(}-k_{2}\epsilon_{p}\ \big{)}\right)+\rho_{o}exp\big{(}-k_{2}\epsilon_{p}\big{)}\right)^{\frac{1}{ 2}}\end{split}  \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Parameters Description** & **Value and Units** & **Ref** \\ \hline \(k_{b}\) & Boltzmann constant & \(1.38\times 10^{-23}\) m\({}^{2}\cdot\)kg s\({}^{-2}\cdot\) K\({}^{-1}\) & - \\ \(\mu_{0}\) & Shear modulus at absolute zero temperature & K & \\ \(\mu\) & Shear modulus & \(49.02-5.821\big{/}\left(\frac{k_{B}T}{g_{0}\mu(T)^{b}}-1\right)\) GPa & [21] \\ \(b\) & Burgers vector & \(2.95\times 10^{-10}\) m & [22] \\ \(\dot{e}_{e}\) & Reference strain rate & \(10^{7}\) s\({}^{-1}\) & [21] \\ \(\dot{e}\) & Test strain rate & \(s^{-1}\) & \\ \(\sigma^{o}\) & Threshold stress & \(1063.2\) MPa & Calibrated \\ \(g_{0}\) & Normalised activation energy & 0.25 & Calibrated \\ \(h\) & Dislocation accumulation coefficient & \(8.3\times 10^{5}\) m\({}^{-2}\) & Calibrated \\ \(k_{2}\) & Dislocation annihilation coefficient & 10 & Calibrated \\ \(p\) & Fitting constant & 1 & [21] \\ \(q\) & Fitting constant & 2 & [21] \\ \(M\) & Taylor factor & 3 & [23] \\ \(\kappa\) & Geometrical factor & 0.2 & [24] \\ \(K_{H-P}\) & Hall–Petch constant & 0.328 MPa.m\({}^{1/2}\) & [25] \\ T & Temperature & K & \\ \(\zeta\) & Material constant & Calibrated for different microstructures \\ \(\chi\) & Effective damping coefficient & Calibrated for different microstructures \\ \(\rho_{o}\) & Initial dislocation density & Measured in different microstructures \\ \(d\) & Average grain size & Measured in different microstructures \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definitions and values of the constant parameters of the analytical model obtained from the literature, and those calibrated, as well as those determined from the microstructure of Ti6 Al4V (ELI) samples. Figure 1: A quarter-symmetrical model of the Taylor impact test in (**a**) isometric view and (**b**) front view. The arrows show the direction of prescribed velocity.