High Temperature Elastic Properties of Reduced Activation Ferritic-Martensitic (RAFM) Steel Using Impulse Excitation Tec
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T is well known that elastic properties serve as window to understand the fundamental nature of cohesive forces and bonding in materials.[1–10] At the atomic level, the elastic tensor coefficient cijkl, connecting stress σij, and strain εkl through the relation HARAPRASANNA TRIPATHY and RAJ NARAYAN HAJRA are with the Physical Metallurgy Division of Indira Gandhi Centre For Atomic Research (IGCAR), Kalpakkam, 603102, India. SUBRAMANIAN RAJU is with the Physical Metallurgy Division, Physical Metallurgy Division of Indira Gandhi Centre For Atomic Research (IGCAR), and also with the Materials Characterization Group, Metallurgy Materials Group of Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam, 603102, India. Contact e-mail: [email protected] SAROJA SAIBABA is with the Materials Characterization Group, Metallurgy & Materials Group of Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam, 603102 and also with the Homi Bhabha National Institute (HBNI), Mumbai, India. Manuscript submitted August 14, 2017. METALLURGICAL AND MATERIALS TRANSACTIONS A
σij = cijkl9εkl, is reflective of the intrinsic stiffness of atomic spring(s).[1,2,6–10] In this sense, the elastic properties are directly traceable to the intricacies of effective interatomic interaction ϕ(r), which governs both crystal binding and stiffness of atomic bonds.[8] An appropriate quantum mechanical description of ϕ(r) in terms of attractive and repulsive contributions to bonding forces, can in principle enable the rigorous determination of elastic moduli, on an ab initio basis.[5,8,9] Further, on purely thermodynamical grounds, it may be shown that second-order elastic constants cij are connected with (∂2E/∂ε2ij)T,V;[6] the second derivative of total (internal) binding energy E with respect to strain εij at fixed temperature T and volume, V. Thus, elastic properties are also bona fide thermodynamic equation of state (EoS) parameters,[6,10] which should therefore share well established phenomenological interrelationship with other thermodynamic properties as well.[1,6,10–14] Therefore, viewed in such wholesome perspective, the availability of reliable data on elastic properties and their
frequencies of a mechanically excited sample.[38–42] In the present study, measurements have been made using a commercial IET equipment, supplied by IMCE® Belgium, together with suitable high temperature furnace and proprietary resonant frequency damping analyzer (RFDA) data analysis software.[38] It is well known that the resonance frequency of a sample that is set into a state of mechanical vibration by suitable impulse, is dependent on its mass (m), dimensions (l 9 b 9 t), and more importantly, the bulk elastic constants, E and G. For a sample of simple geometry, like that of a rectangular bar, well-defined analytical relations (approximations) connecting bulk elastic moduli with appropriate resonance frequencies exist.[38,41,43,46,47] These relations can be employed to obtain an accurate estimate of Young’s modulus (E), shear modulus (G), and Poisson ratio (μ), includ
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