Fig. 3. True Stress-True strain curves from SHTB experiments compared to the quasi-static one at room temperature (left) and dynamic effective diameter-based true strain rate vs. true strain curves (right)
In the first part of the dynamic tests, the temperature is very close to the room one and it is possible to see a clear strain rate effect, with both dynamic curves higher than the static ones and, among the dynamics, the 26 kN curves higher than the 15 kN ones. Then, the temperature rises with the strain and, at the end of all the dynamic tests, it is so high that the corresponding thermal softening has a greater effect than the strain rate amplification; in fact, at late strains the dynamic true curves become lower than the quasi-static ones at room temperature.
To complete the description of the dynamic tests, in the right part of Fig. 3 also the strain rate vs strain curves are shown for all the dynamic tests.
Classical strain rate histories from SHTB tests are supposed to remain constant from the end of the rise time up to failure. Instead optical measurements of the current specimen diameter show that the necking induces an intense spontaneous increase of the effective strain rate, so that the strain rate histories in Figure 3 exhibit a plateau just limited to the necking onset, followed by a steep increasing ramp extending up to failure.
Such intense spontaneous increase of the strain rate after necking onset was firstly evidenced by Mirone20, confirmed by Mirone et al.21 and recently acknowledged by Zhang et al.22.
In order to calculate the temperature increase due to plastic work conversion during dynamic tests, it is necessary to evaluate the equivalent stress-strain curves; these are obtained here by correcting the experimental true curves all over their postnecking range, through the MLR function15. The plastic work is then converted into heat via the Taylor-Quinney Coefficient (TQC) assumed to be equal to 1, according to the findings of Kapoor & Nemat-Nasser10 and Walley et al.11. The calculated temperature histories for all the dynamic tests are shown in Fig. 4. The necking strains identified from experiments are then reported in Table 3 together with the corresponding temperature at that instant.
Fig. 5 shows the necking strains against the temperature from quasi-static and dynamic tests. The dynamic necking strains (around 0.2 at nearly 70 °C) lie below the fitting curve of the quasi-static necking strains, delivering a value of about 0.35 at 70 °C.
This means that the anticipation effect induced by\(\frac{\partial S}{\partial T}\ \bullet\ \frac{\partial T}{\partial\varepsilon_{\text{True}}}\)in eq.(8) is greater than the delaying effect of the strain rate, resulting in lower dynamic necking strains with respect to the quasi-static counterparts at the same temperature.
It is important to underline that, without the coupling between strain and temperature within the thermal softening function, no explanation could have been provided for the dynamic necking strains being lower than their quasi-static counterparts at the same temperature.