Elastic Constants Of Aluminum Research Articles

Inverse Method Based on Modal Vibration Testing for Characterizing the Elastic Properties

This paper presents a inverse method to derive the material properties from the resonance frequencies of a free-edge test specimen based on modal vibration test. A mixed numerical experimental identification procedure is used for this purpose. Finite element models of the test plate is simultaneously updating and reproduces the updating frequencies, then optimal procedure is running. The sum of the squared differences between the experimental and the finite element method numerical resonance frquencies is the objective function. To seek practical solutions, here presents a global optimization method--simulated annealing method for the determination of the elastic properties. The inverse method is applied to determine the elastic constants of aluminum , carbon/epoxy , Glass/PP composite material and double coated steel plate. The results indicate that the method can obtain very accurate elastic constants for aluminum , Glass/PP , carbon/epoxy composite material ,but for double coated steel plate , if the individual layer of the three different layers is as isotroptic material having six elastic constants , the method can obtain very accurate results , but if it is as transversely isotropic material having twelve elastic constants, the evaluating elastic constants are bad.

Determination of Elastic Constants of Aluminium Using Laser Based Ultrasonics

This paper deals with the determination of the elastic constants of aluminium from the analysis of laser generated ultrasonic bulk waves. A pulsed Nd:YAG laser (1064 nm) is used for ultrasonic generation in a thick stepped Al sample and a He-Ne laser is used for heterodyne detection of the generated signals. Ultrasonic signals obtained at epicenter and at off-epicenter position of the detection points are analyzed using wavelet transforms. Here the identification and of pressure as well as shear waves and the estimation of their velocities are done successfully. From the estimated velocities the elastic constants (Young's modulus, shear modulus, bulk modulus, Lames constant and Poisson's ratio) are calculated. The agreement of these constants with the standard values confirms the identification of shear waves at off-epicenter position. The work presented in this paper brings out the applicability of the study of laser generated bulk waves for the determination of elastic constants of any bulk material.

Thermally-induced stresses in thin aluminum layers grown on silicon

Elevated-temperature X-ray diffraction (XRD) was used to evaluate residual stresses in aluminum thin films on Si(100). The films with a thickness of 2 μm were deposited by magnetron sputtering at different temperatures, and XRD measurements were carried out with the heating stage DHS 900 mounted on a Seifert 3000 PTS diffractometer. The strains were characterized always in temperature cycles from room temperature up to 450 °C with steps of 50 °C. Stress values in weakly textured thin films were calculated using the Hill model, applying temperature-dependent X-ray elastic constants of aluminum. The thin films exhibit specific temperature hysteresis of stresses depending on the deposition temperature (being from the range of 50 °C–300 °C). The results allow us to quantify contributions of intrinsic and extrinsic stresses to the total stress in the layers as well as to evaluate phenomena related to plastic yield. The comparison of the data from thin films deposited at different temperatures indicate a dependence of intrinsic stresses on the substrate temperature during deposition as well as the presence of the plastic yield in films during the cool-down after deposition

Stresses in Passivated Films

ABSTRACTAlthough wafer curvature measurement provides a rapid and accurate determination of stress in a uniform thin film, the technique is not applicable to patterned films. To study the stress in metal lines, and the effect of passivation on that stress, it is necessary to use X-ray diffraction. To obtain the sensitivity and precision required, a generalized focusing diffractometer (GFD), that had been developed especially for work on thin films, was used in this study.The elastic strain tensors for aluminum and aluminum-silicon films and patterned lines were determined by X-ray diffraction. The corresponding stress tensors were calculated with the use of the known elastic constants of aluminum. The effect of various oxide and oxynitride passivations was investigated. Passivation over uniform metal films has very little effect, while passivation over patterned metal results in substantial triaxial tensile stress in the metal. Contrary to the conventional wisdom, high compressive stress in the passivation does not result in additional tensile stress in the metal. A possible explanation for the frequently observed deleterious effect (increased tendency for formation of cracks and voids) of highly compressive silicon nitride and silicon oxynitride passivations will be discussed.

Theoretical Consideration on Elastic Deformations of Aluminum by Pseudopotential Method

To discuss the elastic properties of aluminum, the variations of the crystal energy at OK with the (100) lattice deformations are evaluated by means of the pseudopotential methods based on the model potential proposed by the authors previously. A distinction is made between the mechanical behavior of a face centered cubic (fcc) lattice in (100) loading (i.e. transverse stresses are zero) and in (100) deformation (i.e. transverse strains are zero). The fcc-bcc transitions and the elastic instabilities associated with the deformations are briefly discussed. Some elastic constants of aluminum at OK are calculated. The stress-strain relations for large elastic strains up to the theoretical tensile strength are presented.

Theoretical Discussions on Elastic Deformations of Aluminum by Pseudo-Potential Method

To discuss the elastic properties of aluminum, the variations of the crystal energy at 0 K with the (1 0 0) lattice deformations are evaluated by means of the pseudopotential methods, using the model potential proposed by the authors previously. A distinction is made between the mechanical behaviour of a face centered cubic (fcc) lattice in (1 0 0) loading (i.e. transverse stresses are zero) and in (1 0 0) deformation (i.e. transverse strains are zero). The fcc-bcc transitions and the elastic instabilities associated with the deformations are briefly discussed. Some elastic constants of aluminum at 0 K have been calculated. The stress-starin relations in so large elastic strains up to the theoretical tensile strength are presented.

Effect of pressure on the elastic constants of aluminium from -196° to +25°C

The effect of pressure on the elastic shear constants C = c 44 and C' = 1 2 (c 11 − c 12) of Al has been measured from -196° to +25°C and up to 2500 atm using the recently developed torsional-bar resonance technique. The pressure derivatives of both shear constants are found to decrease at lowering temperatures. The experimental results are compared with existing theories based on lattice anharmonicity. At lower temperatures, the Grüneisen parameter γ calculated from the results is in good agreement with the value obtained from thermal data.

Lattice Theory of Second- and Third-Order Elastic Constants of Aluminum, Copper, and Nickel

Lattice theory has been used to obtain the expressions for the second- and third-order elastic constants for face-centered-cubic lattices in terms of the second- and third-order coupling parameters, considering the general interaction between the nearest-neighbor atoms. The number of constants have been reduced by expressing the third-order coupling parameters in terms of the coupling parameters of second order and second-order elastic constants. The general expressions of the elastic constants have been evaluated for Al, Cu, and Ni in a special case of central forces. The force constants involved in the expressions have been determined by representing the central interaction between the pair of atoms by the Morse potential function. It is found that the Cauchy relations for second-order elastic contants C12=C44 and for third-order elastic constants C112=C166 and C123=C456=C144 are satisfied in the case of central forces. It is also seen that the values of C111 for all the three metals are the largest and C112 is approximately half as that of C111 and almost all the values of C123 are negative and small compared with the other third-order elastic constants. The pressure derivatives of second-order elastic constants, the anisotropy factor, and the Debye temperatures have also been calculated for these metals. The values obtained are in good agreement with the experimental values available in the literature.

A Calculation of the Second‐ and Third‐Order Elastic Constants of Aluminium

AbstractA calculation of the second‐ and third‐order elastic constants of aluminium has been made by the method of homogeneous deformation. The electronic contributions to the elastic constants are calculated using second‐order perturbation theory, Ashcroft's model potential, and a dielectric function with corrections for exchange and correlation effects, as suggested by Singwi et al. Within this model we have also estimated the difference between the calculated static and dynamic bulk modulus. This difference results from neglecting certain higher order model potential terms in the dynamic approach.

Third-Order Elastic Constants of Aluminum,

The complete set of six third-order elastic constants of single-crystal Al has been experimentally determined by measuring both hydrostatic-pressure and uniaxial-stress derivatives of the natural sound velocities using a two-specimen interferometric technique. The specimens were neutron-irradiated to eliminate dislocation effects from the uniaxial experiments. A self-consistent set of hydrostatic-pressure derivatives of the second-order elastic constants has been calculated from the measured third-order constants. The third-order elastic constants have also been used to calculate the thermal expansion in the anisotropic-continuum model at both high and low temperatures, and a comparison has been made with the directly measured expansion coefficients.

Elastic Constants of Aluminum from 20°C to 400°C

The use of the ultrasonic pulse technique as a means of determining the elastic constants of polycrystalline aluminum at high temperatures has been considered in some detail. The C11 and C44 elastic constants, Debye temperature, and Young's modulus were computed from the longitudinal and transverse velocity measurements. The variations of these constants with temperature showed the predicted linear decrease expected from solid state theory.