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.