# Measurement of Strain and Strain Rate during the Impact of Tennis Ball Cores
## 4 Discussion  
The results of this investigation highlight that both compressive and tensile strains were experienced during impact with a rigid plate. Regarding maximum strain values, tensile strains above 0.4 were uncommon, with frequency distributions highlighting that no frequency bin above a 0.4 strain contained more than 1% of the distribution. Consequently, material characterisation of ball core rubber in tension should test at a 0.4 strain to encapsulate the range seen during impact. Experimental impacts of the pressurised ball core at 40\({}^{\circ}\) and 90\({}^{\circ}\) with an impact ball speed of 52.5 m\(\cdot\)s\({}^{-1}\) had approximately 5% of strain distributed between 0.3 and 0.4, further evidence that 0.4 strain is the minimum desirable tensile strain for testing tennis ball rubber. These findings are slightly lower than the findings of [PERSON] [3], who suggested that strains in the region of 0.5 can be observed during impact, which is more in keeping with the results of [PERSON] [6]. Assessing the observed tensile strain rate measured by GOM highlighted that all impact conditions other than the mean surface impact condition (18\({}^{\circ}\), 22.1 m\(\cdot\)s\({}^{-1}\)) had around 1% of the distribution between 500 and 600 s\({}^{-1}\), no frequency bin above 300 s\({}^{-1}\) accounted for more than 3.5%. [PERSON] [3,4] reported maximum strain rates during ball core impacts of approximately 300 s\({}^{-1}\). The results presented in this investigation indicated that tensile strain rates in the region of 600 s\({}^{-1}\) were apparent, but to a limited degree (<1%). The ability to characterise the material at this rate would be optimal, but capturing material behaviour with a strain rate up to and including rates in the region of 500 s\({}^{-1}\) would capture the vast majority of tensile strain rates experienced during impact. Maximum observed compressive strains from GOM analysis suggested that strains up to \(-\)0.4 were present for impacts at 90\({}^{\circ}\) and 52.5 m\(\cdot\)s\({}^{-1}\), accounting for around 1% of the distribution. Negligible amounts of strain (<0.2%) were measured for compressive strains greater in magnitude than \(-\)0.4. The results suggest that material characterisation in compression would encapsulate the vast majority (>95%) of observed compressive strain during impact if tested to strains of \(-\)0.4, whilst testing to strains of \(-\)0.3 may be sufficient depending on the severity of the impact conditions. Only impacts at 90\({}^{\circ}\) and 52.5 m\(\cdot\)s\({}^{-1}\) had more than 1% of the distribution greater in magnitude than \(-\)800 s\({}^{-1}\). The remaining impact conditions highlighted a maximum compressive strain rate closer to \(-\)700 s\({}^{-1}\). Frequency bins between \(-\)400 and \(-\)800 s\({}^{-1}\) for the 90\({}^{\circ}\), 52.5 m\(\cdot\)s\({}^{-1}\) impact condition account for more than double the percentage of the other impact conditions. Missing frames or obstructed surface coverage likely resulted in an overrepresentation of results between \(-\)400 and \(-\)800 s\({}^{-1}\). These results appear to be consistent with results in the literature. [PERSON] [6] highlighted a maximum strain for simulation at 30 m\(\cdot\)s\({}^{-1}\) of 0.3, consistent with GOM results for 90\({}^{\circ}\) and 30.5 m\(\cdot\)s\({}^{-1}\), whereby all frequency bins above a 0.3 strain contained less than 1% of the distribution. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Strain Rate Distribution** & \multicolumn{4}{c}{**Pressurised**} & \multicolumn{4}{c}{**Pressurised**} \\ \hline \multirow{2}{*}{**Bin Edges**} & **18\({}^{\circ}\), 22.1** & **40\({}^{\circ}\), 52.5** & **90\({}^{\circ}\), 30.5** & **90\({}^{\circ}\), 52.5** & **18\({}^{\circ}\), 22.1** & **40\({}^{\circ}\), 52.5** & **90\({}^{\circ}\), 30.5** & **90\({}^{\circ}\), 52.5** \\  & **m-s\({}^{-1}\)**GOM distributions for the mean surface impact test case (18\({}^{\circ}\), 22.1 m\(\cdot\)s\({}^{-1}\)) appear to follow a normal distribution, but the remaining cases do not.