Elastic Constants Of Hcp
The elastic behavior of a hexagonal close-packed (HCP) single crystal for a metal is anisotropic, meaning that the stiffness of the material depends on the direction of loading. This Demonstration illustrates the elastic anisotropy of 24 HCP metals when undergoing uniaxial stress, as shown in the 3D plot (left). This shows the variation of the elastic modulus (in GPa) as a function of direction. For reference, the axis of the plot is parallel to the axis of the HCP unit cell, and the axis is parallel to the direction of the HCP unit cell. The 2D plot (right) shows the elastic modulus on the plane.
Elastic Constant Units
Elastic Constants Of Hcp Research
The anisotropy factor is determined by, where and are compliance constants of the selected material. DetailsThe general relationship between stresses and strains in crystals can be represented using the fourth-rank tensors for stiffness and for compliance:.
Each involves 81 coefficients, but the number is drastically reduced for crystals of high symmetry, such as HCP.The five independent elastic constants (, and ) for the 24 HCP metals were taken from 1.Reference1 D. Tromans, 'Elastic Anisotropy of HCP Metal Crystals and Polycrystals,' International Journal of Research and Reviews in Applied Science, 6(4), 2011 pp.
AbstractThe elastic constant tensors for the hcp phases of three transition metals (Co, Re, and Fe) are computed as functions of pressure using the Linearized Augmented Plane Wave method with both the local density and generalized gradient approximations. Spin-polarized states are found to be stable for Co (ferromagnetic) and Fe (antiferromagnetic at low pressure). The elastic constants of Co and Re are compared to experimental measurements near ambient conditions and excellent agreement is found. Recent measurements of the lattice strain in high pressure experiments when interpreted in terms of elastic constants for Re and Fe are inconsistent with the calculated moduli.