Theoretical Study for Dynamic Strain Aging in Niobium: Effect of Temperature and Strain Rate on the Flow Stress
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Theoretical Study for Dynamic Strain Aging in Niobium: Effect of Temperature and Strain Rate on the Flow Stress Yooseob Song1 · William Peterson1 Received: 11 August 2020 / Accepted: 13 October 2020 © The Korean Institute of Metals and Materials 2020
Abstract A constitutive model for niobium with the effect of dynamic strain aging is proposed. The crystal structure of metals hugely influences the dynamic strain aging phenomenon and causes considerable alterations in the material’s macroscopic mechanical responses. Dynamic strain aging needs to be accounted for in a constitutive model to obtain accurate predictions of material’s thermo-mechanical behaviors during deformation. The proposed constitutive model attempts to describe the material’s flow stress responses during deformation by separating the flow stress contributions into the athermal component, thermal component, and dynamic strain aging component. Two different mathematical equations are proposed to model the dynamic strain aging component. The proposed model attempts to describe the mechanical response of niobium for a wide range of strain rates: from quasi-static loading ( 𝜀̇ = 0.001 s−1 ) to dynamic loading ( 𝜀̇ = 3300 s−1 ) across the temperature ranges 77 K–800 K. Keywords Constitutive model · Niobium · Dynamic strain aging · Strain rate effect · Thermal effect
1 Introduction Dynamic strain aging (DSA) is a phenomenon that induces strain hardening in metallic materials at specific temperature ranges. Strain rate and temperature are the main factors that influence flow stress during the deformation process. A rise in temperature generally causes a decline in the flow stress. However, there are temperature ranges where flow stress increases with the increase in temperature as shown in Fig. 1. As the temperature continues to rise, flow stress increases and then starts to decline. As a result, a bellshaped peak is formed. The maximum stress caused by DSA is dependent on the strain rate, total strain, and the temperature range where DSA occurs. In other words, DSA is observed at distinct combinations of temperature and strain rate ranges. From the data in Nemat-Nasser and Guo [1], DSA was observed at 400 K≲T≲800 K under 𝜀̇ = 0.001 s−1 , but it was not observed at all at this temperature range under 𝜀̇ = 3300 s−1 and 𝜀̇ = 8000 s−1 . The temperature range where DSA manifests itself is heavily affected by the crystal * Yooseob Song [email protected] 1
Department of Civil Engineering, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA
structure of metals. It is also observed that metals with identical crystal structure even may have different responses. Nemat-Nasser and coworkers have conducted extensive studies of the thermomechanical behaviors of bodycentered cubic (bcc) and face-centered cubic (fcc) metals [1–4]. This work focuses on the experimental data from the study of DSA on niobium conducted by Nemat-Nasser and Guo [1]. Samples of niobium were subjected to quasi-static and dynamic loading under a large range of tempera
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