# Strain Rate Dependencies and Competitive Effects of Dynamic Strength of Some Engineering Materials
## 4 Discussion
### A Possible Way to Predict the Competition of Strength Characteristics  
According to the considered examples, the competitive effect of strength characteristics can be observed for various materials. Even the same material but with a different organization of the microstructure can have different sensitivity of critical stresses to loading rate. In the case of assessing the strength or comparing materials according to the classical principle of comparing values of ultimate strength (or yield strength), calculation of a structure or a detail intended for operation in dynamic modes can prove to be unreliable and lead to damage of the structure or the equipment.  
It becomes necessary to determine the possibility of the competitive effect of strength characteristics at the design stage. As shown above, this can be achieved based on a comparison of the critical stresses (ultimate strength or yield strength) under a quasi-static load and the incubation times (failure or plastic yield). For example, if one material has an ultimate strength and incubation time of failure that are greater than those of another material, then the competitive effect of critical stresses will not be realized. If one material has a greater ultimate strength and a shorter incubation time of fracture than those of another material, then, in the case of close modules of elasticity, the effect of critical stress competition may occur. In this case, the intersection point (\(\varepsilon^{cc}\), \(\sigma^{cc}\)) of the strain/stress rate dependences  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & **Condition** & **E (GPa)** & \(\sigma^{comp}_{FS}\) (MPa) & \(\sigma^{sp}_{FS}\)(MPa) & \(\tau^{comp}_{F}\)(\(\mu\)s) & \(\tau^{sp}_{F}\)(\(\mu\)s) \\ \hline PBB & C, R & 0.76 (0.07) & 2.6 * & - & 38 (0.9) & - \\ RBB & C, R & 0.70 (0.06) & 1.4 * & - & 29 (1.4) & - \\ BND & C, R & 0.65 (0.08) & 6 * & - & 28 (0.8) & - \\ PBB & S, M & - & - & 1.1 * & - & 75 (0.4) \\ RBB & S, M & - & - & 0.5 * & - & 102 (24.2) \\ BND & S, M & - & - & 0.8 * & - & 62 (5.1) \\ \hline \hline \end{tabular}  
* The conditional value determined by the extrapolation of dynamic data to the quasi-static regime.  
\end{table}
Table 3: Parameters of bitumen binders: \(\sigma^{comp}_{FS}\) is the quasi-static compression strength; \(\sigma^{sp}_{FS}\) is the quasi-static splitting strength; \(\tau^{comp}_{F}\) is the incubation time of failure under compression; \(\tau^{sp}_{F}\) is the incubation time of failure under splitting; C—compression; S—splitting; R—room temperature; M—temperature of \(-10\) \({}^{\circ}\)C. Mean (standard deviation).  
Figure 9: Calculated dependences of critical stress in bitumen binders on strain rate at compression (room temperature) (**a**) and stress rate at splitting ( \(-10\) \({}^{\circ}\)C) (**b**). Curves are calculated by Equation (3). \(R^{2}\) is the coefficients of determination.  
of the critical stresses can be easily determined by the calculation of strain \(\varepsilon^{\alpha}\) or stress \(\sigma^{\alpha}\) rate and the corresponding stress \(\sigma^{\alpha\alpha}\) using Equation (3).  
\[\begin{split}\varepsilon^{\alpha}&=\frac{2\left( \sigma_{st}^{I}-\sigma_{st}^{II}\right)}{E_{II}\tau_{II}-E_{I}\tau_{I}},\quad \sigma^{\alpha\alpha}=\sigma_{\alpha r}(\varepsilon^{\alpha})\;or\\ \sigma^{\alpha c}&=\frac{2\left(\sigma_{st}^{I}- \sigma_{st}^{II}\right)}{\tau_{II}-\tau_{I}},\quad\sigma^{c\alpha}=\sigma_{ \alpha r}(\sigma^{\alpha}).\end{split} \tag{4}\]  
Superscript I and II denote the compared materials I and II, respectively.  
Thus, the competition of critical stresses can be estimated by introducing only one additional material parameter with the dimension of time. The incubation time approach allows one to estimate critical stresses at high loading rates based on simple calculations suitable for use in engineering applications. It opens up great opportunities for using the incubation time concept in analytical or computer modelling of dynamic processes of failure or plastic flow.