Third-order elastic constants of aluminium

Abstract

The six independent third‐order elastic constants of aluminium single‐crystal were determined at 298°K by measuring the uniaxial stress derivatives of the effective second‐order elastic constants of the crystal in 〈110〉 direction. A pulse interference technique at 10 MHz was used, capable of measuring natural velocities to a few parts in 106. The specimen was irradiated with a neutron beam to pin down dislocation network under uniaxial stresses.

Modeling ramp compression experiments using large-scale molecular dynamics simulation.

“…Measured values for the second-and thirdorder constants for aluminum were taken from Refs. [94] and [95], respectively. For the elastic loading calculations considered here, the entropy dependence of the elastic coefficients can be neglected.…”

“…Because of the limited data available, the Cauchy relations [98] were invoked to reduce the number of independent fourth-order elastic constants from 11 to four. The fitting was performed using a previously developed anisotropic approach for wave propagation simulations in single crystals, [99] along with the known second-order [94] and third-order [95] elastic constants. The resulting fourth-order elastic constants are: C 1111 = 25000 GPa, C 1112 = 3000 GPa, C 1122 = 3000 GPa and C 1123 = 500 GPa.…”

Explicit Formulae Showing the Effects of Texture on Acoustoelastic Coefficients

“…We adopt the following values for the second-order [10] and third-order stiffnesses [11] of single-crystal aluminum: c11 = 106.75, c12 = 60.41, c44 = 28.34, c111 = -1224, cu2 = -373, c123 = 25, Ct44 = -64, Ctss = -368, and C4ss = -27, all of which are in units of GPa. Equations (9) and (13) respectively, where the stresses are in units of GPa.…”

On the separation of stress-induced and texture-induced birefringence in acoustoelasticity

“…If we replace the values of the third-order stiffnesses of the crystallites by those reported by Sarma and Reddy [34] (for single-crystal aluminum of 99.999% purity, at 25°C; they did not report the second-order elastic constants of their samples), we obtain Ciso = -4.32 x 10 .5 MPa -1.…”

“…Using the data ofThomas [33] on the second-and third-order elastic constants of single-crystal aluminum at 25°C, we obtain from our computations the following formula for the acoustoelastic birefringence:where the stresses are in units of GPa. If we use the third-order stiffnesses of aluminum reported by Sarma and Reddy[34] (but keepingThomas' values of the second-order elastic constants), then the birefringence formula becomes Remark 5.4, Whether the ad hoe formula (5) would furnish an acceptable approximation to Equation (72) for a polycrystalline aggregate depends on the texture of the aggregate and on the values of Giso,/31,/32,..., 75 for the material in question. Equation (73) or (74), for instance, shows that for aluminum the coefficients W6z0 and W640 dominate the influence of texture on the acoustoelastic coefficients in the birefringence formula.…”