On the Taylor–Quinney coefficient in dynamically phase transforming materials. Application to 304 stainless steel

Abstract

a b s t r a c tWe present a thermodynamic scheme to capture the variability of the Taylor-Quinney coefficient in austenitic steels showing strain induced martensitic transformation at high strain rates. For that task, the constitutive description due to Zaera et al. (2012) has been extended to account for the heat sources involved in the temperature increase of the material. These are the latent heat released due to the exothermic character of the transformation and the heat dissipated due to austenite and martensite straining. Through a differential treatment of these dissipative terms, the Taylor-Quinney coefficient develops a direct connection with the martensitic transformation becoming stress, strain and strain rate dependent. The improved constitutive description sheds light on experimental results available in the literature reporting unusual ð> 1Þ values for the Taylor-Quinney coefficient.

Dynamic necking in materials with strain induced martensitic transformation

“…l h is the latent heat per unit volume of transformed austenite, therefore the last term in the above equation accounts for the heat released due to the exothermic character of the phase transformation. This has been reported by different authors for dynamically phase transforming materials (Rittel et al, 2006;Jovic et al, 2006;Rusinek and Klepaczko, 2009) and rationalized in Zaera et al (2013). By virtue of its contribution, the heat power may strongly increase upon a certain range of strain, thus enhancing the coupling between temperature and transformation: SIMT contributes to heat through a latent heat term and heat, in turn, hinders SIMT.…”

“…The constitutive model for the metastable austenitic stainless steel uses Huber-Mises plasticity and the features related to martensitic transformation are based on the previous works of Olson and Cohen (1975), Stringfellow et al (1992) and Zaera et al (2012Zaera et al ( , 2013. Since inception and development of necks in a slender bar will be analyzed using linear stabilityderived within a 1D framework -and finite element simulations -developed within a 3D framework -, both onedimensional and three-dimensional approaches will be presented, on the understanding that both coincide in their essential features and that, for a uniaxial state of stress, the 3D model provides the same results as its 1D counterpart.…”

“…Table 1 shows the values of the model parameters for the AISI 304 grade, as taken from Zaera et al (2012Zaera et al ( , 2013. s Y a and s Y m were adopted as representative of the plastic flow stress in austenite and martensite, respectively .…”

“…(17) and (18) and (20)- (22) Table 1 Parameters related to transformation kinetics and yield stresses, elastic moduli, and conventional physical constants for AISI 304 steel (Zaera et al, , 2013 …”

“…2. Adiabatic loading process: both the stability analysis and the finite element modeling take into account the thermomechanical coupling in the phase transformation kinetics according to the experimental observations reported elsewhere (Olson and Cohen, 1975;Tomita and Iwamoto, 1995;Rodríguez-Martínez et al, 2011;Zaera et al, 2012Zaera et al, , 2013. Thus, this section examines the effect of temperature on the transformation rate which, in turn, affects the transformation hardening and consequently the processes of necking inception and energy absorption.…”