PSI - Issue 24

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

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Fig. 4. Evolution of the material temperature during each dynamic test Fig. 5. Comparison regarding necking strain between static and dynamic tests All necking strains from dynamic tests are close to 0.2 (temperatures around 70 °C), quite lower than their static counterparts at the same temperature, close to 0.35. The reason is that for the static necking at constant 70 °C eq. (8) applies with = 0 , so only the term anticipates the necking; instead, the dynamic necking is also affected by variable temperature histories, so eq. (8) applies with both the above terms leading to more remarkable anticipation of the necking onset. Fig. 5 shows that the contribution of ∙ in further anticipating the necking during dynamic tests prevails over the necking delay induced by the strain rate. It is worth noting that, without the coupling of strain and temperature in the softening function, no explanation can be found for the experimental evidence that necking strain decreases as higher constant temperatures are imposed during a tension test. In this work, the instability criteria and the necking onset under static and dynamic conditions are analyzed from a theoretical viewpoint and by means of a comprehensive experimental campaign on an A2-70 steel. Firstly, the instability strains are derived for a general material model, including the effects of variable temperature and strain rate histories, finding that in standard SHTB tests the strain rate and the temperature variabilities respectively cause delay and anticipation of the necking onset. Then, the effects of temperature and strain rate on the behavior of an A2-70 steel are investigated by experiments. Static tests at different temperatures evidenced that the thermal softening of the material is function of both temperature and strain. Also, the necking strain was significantly reduced when passing from tests at room temperature to tests at constant 300 °C (from 0.44 to 0.18): this can only be explained by the coupling of temperature and plastic strain variables within the thermal softening function. Then, such coupling is included in the general material model and an enhanced expression of the necking strain under static loading under variable temperature is determined, including a new term which expresses the sensitivity of the softening function to the plastic strain. The experimental true curves from Hopkinson bar tests are then transformed into Mises stress-strain curves and the temperature histories due to adiabatic dissipation of plastic work are calculated, in order to relate the necking strains to the corresponding temperatures reached at necking onset. The comparison of dynamic necking strains, all occurring at about 70 °C, with the static necking strains at the same temperature, evidenced that the anticipation due to the temperature variability prevails over the delay of the necking onset promoted by the strain rate. 4. Conclusions