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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1. Introduction

The sensitivity of structural metals to strain rate and temperature is known to affect the necking onset. Ghosh (1977) and Hart (1967) obtained different evaluations of the necking strain under dynamic loading, based on slightly different hypotheses about the elongation modes. Lin (1977) derived plastic instability criteria for rate-sensitive materials in bars under uniaxial tension and ballooning in thin-walled tubes under internal pressure mixed to axial loading. Guan (2014) proposed an upgrade of the Hart criterion for identifying the dynamic necking onset. In these formulations, the temperature is not taken into account, but high strain rates are known to induce significant temperature rises, so that the accompanying thermal softening of the material can really affect the necking onset. Also the ductility of the material is greatly influenced by strain rate and temperature as was proven by Ruggiero et Al. (2018) and Scapin et Al. (2014), respectively for ADI JS/1050-6 iron and pure copper. Regarding the strain rate effect during dynamic tests, Mirone et Al. (2016) and Mirone et Al. (2019a) analyzed the interactions between the effective true strain rate and the dynamic amplification of the flow stress. In order to estimate the temperature evolution in the material during a test, Kapoor & Nemat-Nasser (1998) and Walley et al. (2000) proved that for several metals the dissipative plastic work occurring during a high strain rate test is almost completely converted into heat. Other researchers such as Jovic et al. (2006) and Rittel et al. (2017) arrived at a different conclusion calculating different fractions of plastic work converted to heat depending on the stress conditions. The plastic work is directly related to the area underlying the equivalent stress-strain curve of the material via the Taylor-Quinney parameter therefore, to estimate the temperature evolution during a test, it is necessary to correctly evaluate the above curve. Regarding this topic, the well-known method proposed by Bridgman (1952) allows to calculate the equivalent curve from the true curve. More recently, Mirone (2004) proposed a simpler and more effective method to achieve the same goal. The experimental true curve for implementing such methods is simple to be obtained via optical measurements from cylindrical specimens, but is much less simple to be derived from thick flat tensile specimens. For such cases, Mirone et al. (2019b) developed a material independent method able to obtain the true curve from the engineering one for smooth specimens with arbitrary solid cross sections. On the other hand, the difficulties regarding the transformation of the true curve into the equivalent curve are related to the necking phenomenon which was accurately analysed by Rusinek et al. (2005) and Osovski et al. (2013) who investigated in particular the multiple necking phenomenon, while Besnard et al. (2012) used stereocorrelation to have a better understanding of such phenomenon. There are also different methods to obtain the equivalent material curve without passing through the true curve. Peroni et al. (2015) developed an inverse iterative method in which the equivalent curve is obtained by aiming at the necking profile for each strain level as the objective function of finite element simulations. Sasso et al. (2016) proposed a new procedure for the calibration of the material curve by means of FEM simulations targeting the experimental load-displacement response. In this work, the way how strain rate, softening and their variability in time, typical of SHTB tests, may affect the onset of tensile instability is firstly theoretically analyzed and, then, experimentally investigated by means of the analysis of static/dynamic/temperature tensile tests on A270 stainless steel. 2. Instability criteria and necking onset under static and dynamic conditions The tensile instability is addressed here by focusing on the influences of both the strain rate and the temperature, together with their variations in time. Starting from the general Considère conditions and implementing the role of temperature and true strain rate ̇ , it is possible to obtain the general instability condition under dynamic straining and variable temperature shown in eq. (1), where is the equivalent stress, is the true strain, is the material temperature and − is the necking inception strain in dynamic conditions. − ( , ̇ , ) = − − ̇ ∙ ̇ − ∙ = 0 → − (1) Now, considering an SHTB test, it is useful to analyze mathematically how the strain rate and temperature, both increasing during the test, can affect the necking inception strain. To do that, it is considered here a general material model according to the uncoupled formulation shown in eq. (2) where the static hardening − , the dynamic amplification and the thermal softening S are independent from each other.