First-Principles Calculations to Investigate the Third-Order Elastic Constants and Mechanical Properties of Mg, Be, Ti, Zn, Zr, and Cd

We present theoretical studies for the third-order elastic constants of Mg, Be, Ti, Zn, Zr, and Cd with a hexagonal-close-packed (HCP) structure. The method of homogeneous deformation combined with first-principles total-energy calculations is employed. The deformation gradient F i j is applied to the crystal lattice vectors r i , and the elastic strain energy can be obtained from the first-principles calculation. The second- and third-order elastic constants are extracted by a polynomial fit to the calculated energy-strain results. In order to assure the accuracy of our method, we calculated the complete set of the equilibrium lattice parameters and second-order elastic constants for Mg, Be, Ti, Zn, Zr, and Cd, and our results provide better agreement with the previous calculated and experimental values. Besides, we have calculated the pressure derivatives of SOECs related to third-order elastic constants, and high-pressure effects on elastic anisotropy, ductile-to-brittle criterion, and Vickers hardness are also investigated. The results show that the hardness model H v = 1.877 k 2 G 0.585 is more appropriate than H v = 2 k 2 G 0.585 − 3 for HCP metals under high pressure.

Determination of third order elastic constants from Morse potential for a Nitinol shape memory alloy

The current paper determines the third order elastic constants of the Ni-Ti based shape memory alloy from Morse potential using second nearest neighbour embedded atomic model (2NNEAM) in LAMMPS Molecular Dynamics (MD) simulation package. The complexities involved in the current work are lack of experimental data, such as amount of stress induced for the first order martensitic phase transition and plane about which the phase transformation takes place, which in our current work is considered as the amount of vibrations that the inherent anharmonicity possessed by the Shape memory alloy (SMA) for the first order phase transition. It is further attempted to justify the third elastic constants that are evaluated using VRH approximation, but however VRH approximation lacked stability and hence it is concluded that Morse potential is suitable.

Nonlinear Guided Wave Tomography for Detection and Evaluation of Early-Life Material Degradation in Plates

In this paper, the possibility of using nonlinear ultrasonic guided waves for early-life material degradation in metal plates is investigated through both computational modeling and study. The analysis of the second harmonics of Lamb waves in a free boundary aluminum plate, and the internal resonance conditions between the Lamb wave primary modes and the second harmonics are investigated. Subsequently, Murnaghan’s hyperelastic model is implemented in a finite element (FE) analysis to study the response of aluminum plates subjected to a 60 kHz Hanning-windowed tone burst. Different stages of material degradation are reflected as the changes in the third order elastic constants (TOECs) of the Murnaghan’s model. The reconstructed degradations match the actual ones well across various degrees of degradation. The effects of several relevant factors on the accuracy of reconstructions are also discussed.

Early Fatigue Damage Evaluation of Nonlinear Guided Wave Imaging in Hyperelastic Materials

Nonlinear ultrasonic guided waves have superior sensitivity of the early fatigue damage. This paper investigates the analysis of the second harmonics of Lamb waves in a free boundary aluminum plate, and the internal resonance conditions between the Lamb wave primary modes and the second harmonics. The Murnaghan’s model is implemented in a finite element (FE) analysis to describe the hyperelastic constitutive relation for nonlinear acoustic modeling. The second harmonics of s0 mode are actuated by a 60kHz Hanning-windowed tone burst. A guided wave signal processing platform is developed for tomographic imaging. The different stages of fatigue are reflected by the changes of third-order elastic constants (TOECs) in Murnaghan’s model. The reconstructed damage locations match well with the actual ones cross different degrees and depths of fatigue.

Pressure dependent ultrasonic properties of hcp hafnium metal

The elastic and ultrasonic properties have been evaluated at room temperature between the pressure 0.6 and 10.4 GPa for hexagonal closed packed (hcp) hafnium (Hf) metal. The Lennard-Jones potential model has been used to compute the second and third order elastic constants for Hf. The elastic constants have been utilized to calculate the mechanical constants such as Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, and Zener anisotropy factor for finding the stability and durability of hcp hafnium metal within the chosen pressure range. The second order elastic constants were also used to compute the ultrasonic velocities along unique axis at different angles for the given pressure range. Further thermophysical properties such as specific heat per unit volume and energy density have been estimated at different pressures. Additionally, ultrasonic Grüneisen parameters and acoustic coupling constants have been found out at room temperature. Finally, the ultrasonic attenuation due to phonon–phonon interaction and thermoelastic mechanisms has been investigated for the chosen hafnium metal. The obtained results have been discussed in correlation with available findings for similar types of hcp metals.