# Modelling of High-Velocity Impact on Woven Carbon Fibre-Reinforced Plastic Laminate
## 5 Conclusions  
The modelling of progressive damage in composite materials is still a challenging task, particularly when the material undergoes extreme loading, including shock. This paper presents a new constitutive model for orthotropic materials, developed in the framework of thermodynamics, where the damage evolution equations are based on a modified Tuler-Bucher criterion. Numerical results demonstrated the model capabilities to capture different damage modes developed in the material at different impact velocities above the plate ballistic limit. The prediction of the model with damage agreed well with experimental measurements, for both the size of the hole generated during the penetration and the size of the delamination zone. The simulation results were within 8% of the experimental measurements for all measurements, except the size of the delamination zone in the minor material direction. This may be due to delamination development within the material, which was not visible on the surface ply; see, for instance, Figure 11. This discrepancy may also be due to a number of uncertainties, including material properties and quality of manufacturing of the samples, and should be investigated further in future work.  
Conceptualization, N.D. and R.V.; methodology, N.D. and R.V.; software, N.D. and T.D.V.; validation, N.D. and K.H.; formal analysis, N.D., R.V., K.H. and T.D.V.; investigation, N.D. and R.V.; resources, R.V.; writing--original draft preparation, N.D. and R.V.; writing--review and editing, N.D., R.V., K.H. and T.D.V.; visualization, N.D., R.V. and K.H. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data presented in this study are available on request from the corresponding author.  
The authors would like to thank COST Action CA21155--Advanced Composites under HIgh STRAin RaTEs Loading: A route to certification-by-analysis HISTRATE.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.  
The simulation results for the damage distribution in a 12 mm thick CFRP composite target plate obtained in the impact of a sphere projectile at 1219 m/s at response time t = 35 \(\mu\)s are given in Figures 13-13. The simulation results clearly suggest that the damage area is significantly larger than the impactor size on the top and rear surface, whilst it is almost minimum in the midsection of the target plate.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & & & \multicolumn{2}{c}{**Impact Face**} & \multicolumn{2}{c}{**Rear Face**} \\  & **Velocity,** & \(x_{1}\) & \(x_{2}\) & \(y_{1}\) & \(y_{2}\) & \(y_{1}\) & \(y_{2}\) \\  & \(v\) **(m/s)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** \\ \hline Measurement & 1219 & 11.6 & 12.8 & 42.8 & 35.1 & 44.6 & 40.7 \\ Simulation C3 & 1219 & 12.0 & 13.0 & 41.9 & 40.7 & 42.0 & 39.6 \\ Error C3 & n/a & 3.4 & 1.6 & 2.1 & 16.0 & 5.8 & 2.7 \\ \hline \end{tabular}
\end{table}
Table 7: Experimental C-scan measurements and simulation results for composite plate C3—12 mm.  
Figure A1: Damage distribution in 12 mm thick CFRP target plate C3 at response time t = 35 \(\upmu\)s; 3 solid elements per layer.  
Figure A2: Damage distribution in 12 mm thick CFRP target plate C3 at response time t = 35 \(\upmu\)s; (**a**) impact side and (**b**) rear side.