Homogeneous deformation theory for piezoelectric crystals using the Ewald transformation and relationships among electrostatic contributions to second- and third-order elastic constants

1985 ◽  
Vol 31 (12) ◽  
pp. 8275-8279 ◽  
Author(s):  
Subinay Dasgupta ◽  
S. Sengupta
Keyword(s):  
Elastic Constants ◽  
Deformation Theory ◽  
Homogeneous Deformation ◽  
Third Order ◽  
Piezoelectric Crystals ◽  
Third Order Elastic Constants

scholarly journals Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Trigonal Calcite

2005 ◽  
Vol 2 (4) ◽  
pp. 207-217
Author(s):  
Thresiamma Phlip ◽  
C. S. Menon ◽  
K. Indulekha
Keyword(s):  
Elastic Constants ◽  
Deformation Theory ◽  
Elastic Stiffness ◽  
Higher Order ◽  
Second Order ◽  
Model Approximation ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Grüneisen Parameters ◽  
Gruneisen Parameters

The second- and third-order elastic constants of trigonal calcite have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The seven second-order elastic constants and the fourteen non-vanishing third-order elastic constants of trigonal calcite are obtained. The second-order elastic constants C11, which corresponds to the elastic stiffness along the basal plane of the crystal is greater than C33, which corresponds to the elastic stiffness tensor component along the c-axis of the crystal. First order pressure derivatives of the second-order elastic constants of calcite are evaluated. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in calcite. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.

Third Order Elastic Constants and Rayleigh Wave Dispersion of Shot Peened Aero-Engine Materials

2013 ◽  
Vol 768-769 ◽  
pp. 201-208 ◽  
Author(s):  
Marek Rjelka ◽  
Martin Barth ◽  
Sven Reinert ◽  
Bernd Koehler ◽  
Joachim Bamberg ◽  
...  
Keyword(s):  
Residual Stress ◽  
Rayleigh Wave ◽  
Elastic Constants ◽  
Cold Work ◽  
High Strength ◽  
Wave Dispersion ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Aero Engine ◽  
Rayleigh Wave Dispersion

Aero-engine components exposed to high mechanical stresses are made of high-strength alloys and additionally, they are surface treated by shot peening. This process introduces compressive residual stress into the material making it less sensitive to stress corrosion cracking and fatigue and therefore benefits the components performance and lifetime. Moreover cold work is induced in an amount depending on the peening parameters. To approximate the remaining lifetime, a quantitative, non-destructive method for stress assessment is required. It was shown that surface treatment of such alloys can be characterized by broadband Rayleigh wave dispersion measurements. However, the relative contributions of residual stress and cold work, respectively, remained an open point. This paper presents the determination of third order elastic constants (TOEC) for IN718 and Ti6246, providing, together with a model for the inversion of dispersion data, a quantitative access to the acoustoelastic effect. Finally, some measurements of differently treated samples are given.

Sign in / Sign up

Export Citation Format

Share Document