PSI - Issue 24

Giuseppe Mirone et al. / Procedia Structural Integrity 24 (2019) 259–266 Mirone & Barbagallo / Structural Integrity Procedia 00 (2019) 000 – 000

261

( , ̇ , ) = − ( ) ∙ ( ̇ ) ∙ ( )

3

(2)

Therefore, it is possible to firstly neglect the thermal softening (i.e. assuming isothermal dynamic straining) and secondly turning off the dynamic amplification (i.e. considering quasistatic tests at different controlled temperatures) in order to separately analyze the two effects. In the first case, the general instability condition of eq. (1) with − in the form of a Hollomon hardening − = ∙ delivers the necking strain of eq. (3). − = 1− 1 ∙ ̇ ∙ ̇ (3) The static necking strain − , due to the abovementioned Hollomon-like static hardening, is equal to , therefore to understand whether the strain rate history anticipates or postpones the necking strain onset means to assess whether the denominator of the fraction of eq. (3) is greater or less than one. In an SHTB test, ̇ usually grows with respect to ; moreover, in all materials, the function ( ̇ ) is usually positive and increasing. Therefore, the product at the denominator is always positive, meaning that the denominator is always less than one and, consequently, that − > − . Neglecting the dynamic amplification, i.e. following the same reasoning in the case that is the product of the same Hollomon-like static hardening − = ∙ times the thermal softening ( ) , it is possible to obtain the necking strain in eq. (4). − = 1− 1 ∙ ∙ (4) In an SHTB test, always grows in respect to ; moreover, in all materials, the function ( ) is always positive and decreasing with the temperature. Therefore, the product at the denominator is always negative, meaning that the denominator is always greater than one and, consequently, that − ℎ < − . It is worth noting that, according to eq. (3) and (4), the necking initiations is not affected by constant strain rates nor constant temperature histories. Such simple qualitative analysis highlights that in a standard SHTB test the combined increase of the strain rate and of the temperature leads to a competition between two opposite mechanisms, respectively of delay and anticipation of the necking onset. 3. Experimental Campaign 3.1. Overview In order to analyze experimentally the necking phenomenon and the effects on it of temperature and strain rate, a complete experimental campaign on A2-70 steel specimens, summarized in Table 1, including static and dynamic tensile tests has been carried out. In such table, the shown reference true strain rate is, for each tests, the true strain rate reached just before the necking inception. All the tests have been performed on nominally identical specimens, with 3 mm diameter and 9 mm length of the constant cross section segment. Static tensile tests are carried out at 20, 80, 140, 200 and 300 °C by motor driven machines. Dynamic tests are carried out by the direct-tension split Hopkinson tension bar (SHTB) developed at the University of Catania, with an incident wave of 15 and 26 kN (preload of the input bar equal to 30 and 52 kN). From the static and dynamic tests, it was possible to obtain the true stress-true strain curves and the strain rate histories, according to eqs. (5), (6) and (7): = /4 ∙ 2 (5) = 2 ∙ ( 0 ) (6)