Elastic Anisotropy in Deformed (Textured) and Directionally Grown Crystalline and Polycrystalline Materials

Author(s):  
Lawrence E. Murr
2002 ◽  
Vol 17 (2) ◽  
pp. 104-111 ◽  
Author(s):  
I. C. Dragomir ◽  
T. Ungár

Diffraction peak profiles broaden due to the smallness of crystallites and the presence of lattice defects. Strain broadening of powders of polycrystalline materials is often anisotropic in terms of the hkl indices. This kind of strain anisotropy has been shown to be well interpreted assuming dislocations as one of the major sources of lattice distortions. The knowledge of the dislocation contrast factors are inevitable for this interoperation. In a previous work the theoretical contrast factors were evaluated for cubic crystals for elastic constants in the Zener constant range 0.5≤Az≤8. A large number of ionic crystals and many refractory metals have elastic anisotropy, Az, well below 0.5. In the present work the contrast factors for this lower anisotropy-constant range are investigated. The calculations and the corresponding peak profile analysis are tested on ball milled PbS and Nb and nanocrystalline CeO2.


2015 ◽  
Vol 30 (2) ◽  
pp. 99-103 ◽  
Author(s):  
Conal E. Murray ◽  
Jean L. Jordan-Sweet ◽  
Stephen W. Bedell ◽  
E. Todd Ryan

The quantification of stress in polycrystalline materials by diffraction-based methods relies on the proper choice of grain interaction model that links the observed strain to the elastic stress state in the aggregate. X-ray elastic constants (XEC) relate the strain as measured using X-rays to the state of stress in a quasi-isotropic ensemble of grains. However, the corresponding interaction models (e.g., Voigt and Reuss limits) often possess unlikely assumptions as to mechanical response of the individual grains. The Kröner limit, which employs a self-consistent scheme based on the Eshelby inclusion method, is based on a more physical representation of isotropic grain interaction. For polycrystalline aggregates composed of crystals with cubic symmetry, Kröner limit XEC are equal to those calculated from a linear combination of Reuss and Voigt XEC, where the weighting fraction, xKr, is solely a function of the single-crystal elastic constants and scales with the material's elastic anisotropy. This weighting fraction can also be experimentally determined using a linear, least-squares regression of diffraction data from multiple reflections. Data on metallic thin films reveals that this optimal experimental weighting fraction, x*, can vary significantly from xKr, as well as that of the Neerfeld limit (x = 0.5).


2021 ◽  
Vol 56 (16) ◽  
pp. 10053-10073
Author(s):  
Jordan A. Evans ◽  
Blake T. Sturtevant ◽  
Bjørn Clausen ◽  
Sven C. Vogel ◽  
Fedor F. Balakirev ◽  
...  

AbstractPolycrystalline materials can have complex anisotropic properties depending on their crystallographic texture and crystal structure. In this study, we use resonant ultrasound spectroscopy (RUS) to nondestructively quantify the elastic anisotropy in extruded aluminum alloy 1100-O, an inherently low-anisotropy material. Further, we show that RUS can be used to indirectly provide a description of the material’s texture, which in the present case is found to be transversely isotropic. By determining the entire elastic tensor, we can identify the level and orientation of the anisotropy originated during extrusion. The relative anisotropy of the compressive (c11/c33) and shear (c44/c66) elastic constants is 1.5% ± 0.5% and 5.7% ± 0.5%, respectively, where the elastic constants (five independent elastic constants for transversely isotropic) are those associated with the extrusion axis that defines the symmetry of the texture. These results indicate that the texture is expected to have transversely isotropic symmetry. This finding is confirmed by two additional approaches. First, we confirm elastic constants and the degree of elastic anisotropy by direct sound velocity measurements using ultrasonic pulse echo. Second, neutron diffraction (ND) data confirm the symmetry of the bulk texture consistent with extrusion-induced anisotropy, and polycrystal elasticity simulations using the elastic self-consistent model with input from ND textures and aluminum single-crystal elastic constants render similar levels of polycrystal elastic anisotropy to those measured by RUS. We demonstrate the ability of RUS to detect texture-induced anisotropy in inherently low-anisotropy materials. Therefore, as many other common materials have intrinsically higher elastic anisotropy, this technique should be applicable for similar levels of texture, providing an efficient general diagnostic and characterization tool.


1970 ◽  
Vol 27 (297) ◽  
pp. 21-32
Author(s):  
Sadao Hibi ◽  
Matsuo Maeda ◽  
Fumihiro Ito

2003 ◽  
Vol 36 (5) ◽  
pp. 1159-1168 ◽  
Author(s):  
Axel Steuwer ◽  
Javier Roberto Santisteban ◽  
Philip J. Withers ◽  
Lyndon Edwards ◽  
Mike E. Fitzpatrick

The pulsed neutron transmission diffraction technique exploits the sharp steps in intensity (Bragg edges) appearing in the transmitted spectra of thermal neutrons through polycrystalline materials. In this paper the positions of these edges acquired by the time-of-flight (TOF) technique are used to measure accurately the interplanar lattice distances to a resolution of Δd/d≃ 10−4of specimens subjected toin situuniaxial tensile loading. The sensitivity of the method is assessed for elastically isotropic (b.c.c. ferritic) and anisotropic (f.c.c. austenitic) polycrystalline specimens of negligible and moderately textured steels. For the more anisotropic austenitic steel, the elastic anisotropy is studied with regard to a Pawley refinement, and compared with previous results from conventional neutron diffraction experiments on the same material. It is shown that the method can be used to determine anisotropic strains, diffraction elastic constants, the residual and applied stress state as well as the unstrained lattice parameter by recording transmission spectra at different specimen inclinations, by complete analogy with the sin2ψ technique frequently used in X-ray diffraction. The technique is shown to deliver reliable measures of strain even in the case of moderate texture and elastic anisotropy.


1989 ◽  
Vol 11 (1) ◽  
pp. 41-56 ◽  
Author(s):  
Kei Sakata ◽  
Dominique Daniel ◽  
John J. Jonas

Generally only the 4th order ODF coefficients are deduced from the observed elastic anisotropy of textured polycrystalline materials with cubic/orthorhombic symmetry. In this study, a method is described for the prediction of the 4th and 6th order ODF coefficients from the elastic properties of cold rolled and annealed steel sheets of 5 different types. In order to link these properties with the texture, the elastic energy method of Bunge (1974) is employed. By estimating the volume fractions of the principal preferred orientations and their gaussian spreads, ODF coefficients of the 4th (C411, C412 and C413) and 6th (C611, C612 and C614) orders can be successfully obtained. As a result, the planar r-value distribution can be predicted more accurately than when only the 4th order coefficients are employed.


2013 ◽  
Vol 768-769 ◽  
pp. 26-30
Author(s):  
Marianna Marciszko ◽  
Andrzej Baczmański ◽  
Mirosław Wróbel ◽  
Wilfrid Seiler ◽  
Chedly Braham ◽  
...  

Multireflection grazing incidence X-ray diffraction (MGIXD) was applied to measure residual stresses in thin surface layers and the problem of X-ray elastic constants (XEC) used for the interpretation of results was studied. To show the influence of the X-ray elastic constants on the interpretation of MGIDX results, polycrystalline materials having low (Ti alloy) and high elastic anisotropy of crystallites (Ni alloy) were investigated.


1982 ◽  
Vol 26 ◽  
pp. 225-231
Author(s):  
Rolf A. Prümmer ◽  
H. W. Pfeiffer-Vollmar

X-ray stress analysis is a nondestructive method enabling one to measure residual and loading stresses in polycrystalline materials. Known as a difficult method for several decades, the introduction of microprocessors allowed the automation of the measuring procedure and the subsequent storage and computation of diffraction data. Also the availability of position sensitive counters increased the efficiency of the method. Nowadays a residual stress or loading stress determination can be a problem of a few minutes if the time required for installation and alignment of the equipment is neglected. As the penetration of the X-ray beam into the investigated surface of polycrystalline materials is low and only a few micrometers the obtained information is that of a surface stress state. A further specialty of the method is the selective nature of X-ray stress analysis: lattice strains are measured in certain crystallographic directions. Therefore the elastic anisotropy of the single crystal has to be taken into account. If second phases are present in the investigated sample, also the effect of heterogeneity contributes to the stress analysis. Therefore, the “X-ray elastic constants” had to be introduced.


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