Elastic Property Estimation in Polycrystalline Films with Crystallographic Texture and Grain Shape

1995 ◽  
Vol 403 ◽  
Author(s):  
B. C. Hendrix ◽  
L. G. Yu ◽  
K. W. Xu ◽  
J. W. He
Keyword(s):  
Thin Films ◽  
Elastic Constants ◽  
Crystallographic Texture ◽  
Grain Shape ◽  
Elastic Anisotropy ◽  
Polycrystalline Films ◽  
Property Estimation ◽  
Bulge Testing ◽  
Consistent Model ◽  
Self Consistent

AbstractAlthough methods of measuring the elastic properties of thin films have made great advances with the use of bulge testing of membranes, deflection of micromachined beams, and nanoindentation, most results are still being compared to either isotropic or single crystal elastic constants, neither of which are, in general, appropriate for textured polycrystalline films. This paper uses recent results of a self-consistent model (after Krbner and Kneer) which calculates the elastic anisotropy arising from crystallographic texture and which has been extended to predict the anisotropy resulting from grain shape. These results are compared to the various Voigt, Reuss, and Hill approximations that are appropriate for different crystallographic textures. The accuracies of the different models are evaluated in terms of their ability to predict the biaxial modulus and indentation compliance that are most commonly measured in thin films.

scholarly journals The Rules for the Lattice Rotation Accompanying Slip as Derived From a Self-Consistent Model

1999 ◽  
Vol 31 (4) ◽  
pp. 217-230 ◽  
Author(s):  
R. A. Lebensohn ◽  
T. Leffers
Keyword(s):  
Solid Mechanics ◽  
Grain Shape ◽  
Rolling Plane ◽  
Lattice Rotation ◽  
Consistent Model ◽  
Plane Strain Deformation ◽  
Self Consistent ◽  
The One ◽  
Equiaxed Grains ◽  
Very High

The rules for the lattice rotation during rolling (plane strain) deformation of fcc polycrystals are studied with a viscoplastic self-consistent model. Very high values of the ratesensitivity exponent are used in order to establish Sachs-type conditions with large local deviations from the macroscopic strain. The lattice rotation depends on the grain shape. For equiaxed grains the lattice rotation follows the MA rule, which is the one normally used in solid mechanics. For elongated and flat grains the lattice rotation follows a different rule, the PSA rule. In the standard version the model performs a transition from MA to PSA with increasing strain. There is avery clear difference between the textures resulting from the two different rules. MA leads to a copper-type texture, and PSA leads to a brass-type texture.

Relating mechanical testing and microstructural features of polysilicon thin films

1999 ◽  
Vol 14 (3) ◽  
pp. 688-697 ◽  
Author(s):  
S. Jayaraman ◽  
R. L. Edwards ◽  
K. J. Hemker
Keyword(s):  
Thin Films ◽  
Elastic Constants ◽  
Crystalline Silicon ◽  
Silicon Substrates ◽  
X Ray Diffraction ◽  
Silicon Thin Films ◽  
Bulge Testing ◽  
Transmission Electron ◽  
Wide Range ◽  
Out Of Plane

Polycrystalline silicon thin films (polysilicon) have been deposited on single crystalline silicon substrates, and square and rectangular windows have been etched into these substrates using standard micromachining techniques. Pressure-displacement curves of the resulting polysilicon membranes have been obtained for these geometries, and this data has been used to determine the elastic constants E and v. The microstructural features of the films have been investigated by transmission electron microscopy (TEM) and x-ray diffraction. The grains were observed to be columnar and were found to have a 〈011〉 out-of-plane texture and a random in-plane grain orientation. A probabilistic model of the texture has been used to calculate the bounds of the elastic constants in the thin films. The results obtained from bulge testing (E = 162 ± 4 GPa and v = 0.20 ± 0.03) fall in the wide range of values previously reported for polysilicon and are in good agreement with the microsample tensile measurements conducted on films deposited in the same run as the present study (168 ± 2 GPa and 0.22 ± 0.01) and the calculated values of the in-plane moduli for 〈1103〉 textured films (E = 163.0–165.5 GPa and v = 0.221–0.239).

Determination of the Mechanical Properties of Polysilicon Thin Films Using Bulge Testing

1997 ◽  
Vol 505 ◽  
Author(s):  
S. Jayaraman ◽  
R. L. Edwards ◽  
K. J. Hemker
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Elastic Constants ◽  
Polycrystalline Silicon ◽  
Silicon Substrates ◽  
Bulge Testing ◽  
Good Agreement

ABSTRACTUsing standard deposition and micromachining techniques, silicon substrates with square and rectangular windows covered with membranes of polycrystalline silicon (polysilicon) have been fabricated. Pressure-displacement curves obtained during the bulge testing of membranes with the above geometries have been used to determine the elastic constants E and v of the polysilicon. The results obtained (E = 162± 4 GPa and v = 0.19±0.03) are in good agreement with literature values for bulk polycrystalline silicon.

In situdiffraction strain analysis of elastically deformed polycrystalline thin films, and micromechanical interpretation

2009 ◽  
Vol 42 (6) ◽  
pp. 1073-1084 ◽  
Author(s):  
D. Faurie ◽  
O. Castelnau ◽  
R. Brenner ◽  
P.-O. Renault ◽  
E. Le Bourhis ◽  
...  
Keyword(s):  
Thin Films ◽  
Crystallographic Texture ◽  
Elastic Anisotropy ◽  
Large Strain ◽  
Strain Analysis ◽  
Tensile Tests ◽  
Theoretical Background ◽  
Polycrystalline Thin Films ◽  
Au Thin Films ◽  
Supported Gold

In situtensile tests have been carried out under synchrotron radiation on supported gold (Au) thin films exhibiting a pronounced crystallographic texture. The 2θ shift of X-ray diffraction lines has been recorded for different specimen orientations and several loading levels in the elastic domain. The data obtained demonstrate the large strain heterogeneities generated within the specimen because of the intergranular interactions associated with the large elastic anisotropy of Au grains. To interpret these results, the use of a multi-scale micromechanical approach is unavoidable. The theoretical background of such methods is described, and the points where exact results can be obtained and where approximations have to be introduced are highlighted. It is shown that the Vook–Witt model, for which a general formulation is provided, is the exact solution for polycrystals exhibiting a laminate microstructure, which is a significant departure from the standard thin-film microstructures. Among several standard models used in the field, the self-consistent model is the only one that reproduces the experimental data correctly. This is achieved by accounting for the actual crystallographic texture of the specimen, and assuming pancake-shaped two-point statistics for the morphological texture. A discussion of the limitations of this approach, originally developed for bulk materials, is given for the specific case of thin films.

Numerical Simulation of the Crystallographic Texture Evolution during Hot Extrusion of Oxides Dispersed Strengthened Steels

2014 ◽  
Vol 622-623 ◽  
pp. 136-147
Author(s):  
Denis Sornin ◽  
Abdellatif Karch ◽  
Françoise Barcelo ◽  
Roland E. Logé
Keyword(s):  
Stainless Steels ◽  
Crystallographic Texture ◽  
Texture Evolution ◽  
Hot Extrusion ◽  
Finite Element Method Simulation ◽  
Deformation Texture ◽  
Consistent Model ◽  
Self Consistent ◽  
Service Conditions ◽  
Thermal Histories

Oxides Dispersed Strengthened (ODS) stainless steels are foreseen for fuel cladding tubes in the coming generation of fission nuclear reactors. In spite of a bcc matrix, those steels present a convenient creep behavior thanks to very fine oxides dispersion. Those grades are currently obtained by Powder Metallurgy (PM). After mechanical alloying with the oxide, the powder is commonly consolidated as seamless tube. On CEA facilities, new ferritic ODS stainless steels are produced by Hot Extrusion (HE). The control of the microstructure after extrusion is a key issue for this grade regarding service conditions. In order to explain the microstructure induced by hot processing, the thermo-mechanical history applied to the material must be taken into account. In this study, the strain and thermal histories are obtained from Finite Element Method simulation. Thus, crystallographic texture development during hot extrusion of ODS ferritic steels is simulated using a Visco-Plastic Self-Consistent (VPSC) model. By comparing the texture predictions with the experimental observations, it is shown that self-consistent model reproduces the extrusion texture, α-fiber, very well in the case of monotonic loading. However, for complexes strain path observed during HE, VPSC results differ from the experimental deformation texture.

scholarly journals Accounting for a Distribution of Morphologies and Orientations on Stresses Analysis by X-Ray and Neutron Diffraction: Normalized Self-Consistent Modeling

2014 ◽  
Vol 996 ◽  
pp. 82-87
Author(s):  
Viwanou Hounkpati ◽  
Sylvain Fréour ◽  
David Gloaguen ◽  
Vincent Legrand
Keyword(s):  
Neutron Diffraction ◽  
Crystallographic Texture ◽  
X Ray ◽  
Consistent Model ◽  
Self Consistent

The historical Eshelby-Kröner self-consistent model is only valid in the case when grains can be assumed similar to ellipsoids aligned preferentially along a same direction into the polycrystal. In this work, distributions of crystallites morphologies and geometrical orientations were accounted for, owing to the so-called generalized self-consistent model, in order to satisfy Hills averages principles. Different nonlinear εφψ-vs.-sin2ψ distributions were predicted in elasticity, even in the absence of crystallographic texture, in the case when several morphologies and geometrical orientations coexist within the same polycrystal.

X-Ray Residual Stress Measurement in Films with Crystallographic Texture and Grain Shape

1995 ◽  
Vol 403 ◽  
Author(s):  
L. G. Yu ◽  
B. C. Hendrix ◽  
K. W. Xu ◽  
J. W. He ◽  
H. C. Gu
Keyword(s):  
Thin Films ◽  
Residual Stress ◽  
Crystallographic Texture ◽  
Grain Shape ◽  
Stress Measurement ◽  
Residual Stress Measurement ◽  
Powerful Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Ψ Angle

AbstractX-ray diffraction provides an easy and powerful method for measuring residual stress in thin films. However, nonlinearity of the d vs. sin2ψ relation can lead to the misinterpretation of results, especially when one of the measurements is made at low values of ψ relation for different combinations of ideal crystallographic textures and grain shapes are given. In all cases, a high ψ angle range exists where the d vs. sin2ψ relation in the low ψ angle range.

Advanced Resonant-Ultrasound Spectroscopy for Studying Anisotropic Elastic Constants of Thin Films

2005 ◽  
Vol 875 ◽  
Author(s):  
Hirotsugu Ogi ◽  
Nobutomo Nakamura ◽  
Hiroshi Tanei ◽  
Masahiko Hirao
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Film Thickness ◽  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Thickness Direction ◽  
Resonant Ultrasound Spectroscopy ◽  
Out Of Plane ◽  
Resonant Ultrasound ◽  
Anisotropic Elastic

AbstractThis paper presents two advanced acoustic methods for the determination of anisotropic elastic constants of deposited thin films. They are resonant-ultrasound spectroscopy with laser-Doppler interferometry (RUS/Laser method) and picosecond-laser ultrasound method. Deposited thin films usually exhibit elastic anisotropy between the film-growth direction and an in-plane direction, and they show five independent elastic constants denoted by C11,C33,C44,C66 and C13 when the x3 axis is set along the film-thickness direction. The former method determines four moduli except C44, the out-of-plane shear modulus, through free-vibration resonance frequencies of the film/substrate specimen. This method is applicable to thin films thicker than about 200 nm. The latter determines C33, the out-of-plane modulus, accurately bymeasuring the round-trip time of the longitudinal wave traveling along the film-thickness direction. This method is applicable to thin films thicker than about 20 nm. Thus, combination of these two methods allows us to discuss the elastic anisotropy of thin films. The results for Co/Pt superlattice thin film and copper thin film are presented.

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