Estimation of Single-Crystal Elastic Constants of Polycrystalline Materials from Back-Scattered Grain Noise

2006 ◽  
Author(s):  
P. Haldipur
Keyword(s):  
Single Crystal ◽  
Elastic Constants ◽  
Polycrystalline Materials

Residual Stress Measurement of Silicon Nitride and Silicon Carbide by X-Ray Diffraction Using Gaussian Curve Method

1988 ◽  
Vol 32 ◽  
pp. 459-469 ◽  
Author(s):  
Masanori Kurita ◽  
Ikuo Ihara ◽  
Nobuyuki Ono
Keyword(s):  
Residual Stress ◽  
Single Crystal ◽  
Elastic Constants ◽  
Stress Measurement ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
X Ray ◽  
Small Areas ◽  
Curve Method ◽  
The Continuum

The residual stress induced by grinding or some thermal treatment has a large effect on the strength of ceramics. The X-ray technique can be used to nondestructively measure the residual stress in small areas on the surface of polycrystalline materials. The X-ray stress measurement is based on. the continuum mechanics for macroscopically isotropic polycrystalline materials. In this method, the stress value is calculated selectively from strains of a particular diffraction plane in the grains which are favorably oriented for the diffraction. In general, however, the elastic constants of a single crystal depend on the plane of the lattice, since a single crystal is anisotropic, The behavior of the deformation of individual crystals in the aggregate of polycrystalline materials under applied stress has not yet been solved successfully. Therefore, the stress constant and elastic constants for a particular diffracting plane should be determined experimentally in order to determine the residual stress accurately by X-ray diffraction.

scholarly journals Elastic Properties of Polycrystals: A Review

1990 ◽  
Vol 12 (1-3) ◽  
pp. 1-14 ◽  
Author(s):  
S. Hirsekorn
Keyword(s):  
Single Crystal ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Polycrystalline Materials ◽  
Effective Elastic Constants ◽  
Structure Properties

The elastic properties of polycrystals depend on the single-crystal elastic constants of the crystallites which build up the polycrystal and on the manner in which the crystallites are connected. Because of the technical importance of polycrystalline materials a lot of papers deal with the problem to calculate effective elastic constants of polycrystals from single-crystal and structure properties. This paper gives a review concerning the most important theories and methods respecting this matter.

Measurement of single-crystal elastic constants by neutron diffraction from polycrystals

1999 ◽  
Vol 32 (4) ◽  
pp. 624-633 ◽  
Author(s):  
C. J. Howard ◽  
E. H. Kisi
Keyword(s):  
Neutron Diffraction ◽  
Single Crystal ◽  
Elastic Constants ◽  
Tetragonal Zirconia ◽  
Uniaxial Stress ◽  
Polycrystalline Materials ◽  
Transformation Toughening ◽  
Reflection Index ◽  
Higher Symmetry ◽  
The Given

The relationships of diffraction averaged elastic compliances for an ideally random polycrystal to the single-crystal elastic compliances are given, within the Reuss approximation, for crystal systems with orthorhombic and higher symmetry. For anisotropic materials, these diffraction elastic compliances are dependent on the reflection indexhkl. Expressions for the conventional elastic constants (Young's modulus, Poisson's ratio) are also given. A connection is made to the `X-ray elastic constants' used for diffraction-based measurements of residual stress. The relationships are used to calculate diffraction averaged constants for comparison with neutron diffraction data recorded from samples under applied uniaxial stress. The Reuss approximation works well for materials with the capacity for plastic deformation, such as metals and transformation toughening ceramics, whereas for other materials the Voigt–Reuss–Hill approximation gives better results. Based on the given relationships and experimental determinations of the diffraction elastic compliances for polycrystalline materials, a method is developed for determining the single-crystal elastic constants. The method for estimating single-crystal compliances is demonstrated here by application to extant data on Ni–Cr–Fe and Ti–6 wt% Al–4 wt% V alloys, and new measurements on cubic zirconia. It has been applied very recently [Kisi & Howard (1998).J. Am. Ceram. Soc.81, 1682–1684] to determine the previously unknown elastic constants for a tetragonal zirconia.

scholarly journals Generalization of intrinsic ductile-to-brittle criteria by Pugh and Pettifor for materials with a cubic crystal structure

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
O. N. Senkov ◽  
D. B. Miracle
Keyword(s):  
Crystal Structure ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Single Crystal ◽  
Elastic Constants ◽  
Mechanical Analysis ◽  
Quantum Mechanical ◽  
Modulus Ratio ◽  
Cubic Crystal ◽  
The Difference

AbstractTwo classical criteria, by Pugh and Pettifor, have been widely used by metallurgists to predict whether a material will be brittle or ductile. A phenomenological correlation by Pugh between metal brittleness and its shear modulus to bulk modulus ratio was established more than 60 years ago. Nearly four decades later Pettifor conducted a quantum mechanical analysis of bond hybridization in a series of intermetallics and derived a separate ductility criterion based on the difference between two single-crystal elastic constants, C12–C44. In this paper, we discover the link between these two criteria and show that they are identical for materials with cubic crystal structures.

The dislocations contrast factors of cubic crystals in the Zener constant range between zero and unity

2002 ◽  
Vol 17 (2) ◽  
pp. 104-111 ◽  
Author(s):  
I. C. Dragomir ◽  
T. Ungár
Keyword(s):  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Profile Analysis ◽  
Anisotropy Constant ◽  
Diffraction Peak ◽  
Polycrystalline Materials ◽  
Ionic Crystals ◽  
Strain Anisotropy ◽  
Cubic Crystals ◽  
Lattice Distortions

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.

DECcalc - A Program for the Calculation of Diffraction Elastic Constants from Single Crystal Coefficients

2011 ◽  
Vol 681 ◽  
pp. 417-419 ◽  
Author(s):  
Thorsten Manns ◽  
Berthold Scholtes
Keyword(s):  
Computer Program ◽  
Single Crystal ◽  
Elastic Constants ◽  
Single Phase ◽  
Proper Function ◽  
Almost All

A Matlab based computer program was developed which gives the possibility to calculate the diffraction elastic constants (DEC) of macroscopically isotropic, single phase materials from their single crystal elastic constants. The proper function of the program was confirmed by means of results from literature. In almost all cases the results from the program DECcalc could reproduce the values and diagrams given in the appropriate publications. Discrepancies could always be assigned to the use of different single crystal coefficients.

scholarly journals Estimation of 8th, 10th and 12th Order ODF Coefficients From Elastic Properties in Cold Rolled Steel Sheets by Adjustment of Single Crystal Elastic Constants

1990 ◽  
Vol 12 (1-3) ◽  
pp. 175-185 ◽  
Author(s):  
Kei Sakata ◽  
Dominique Daniel ◽  
John J. Jonas
Keyword(s):  
Single Crystal ◽  
Elastic Constants ◽  
Elastic Energy ◽  
X Rays ◽  
Rolled Steel ◽  
Steel Sheets ◽  
Fitting Procedure ◽  
Pole Figures ◽  
Cold Rolled ◽  
Fiber Components

In an earlier paper (Sakata et al., 1989), it was shown that the 4th and 6th order ODF coefficients could be successfully derived from Young's modulus measurements using the elastic energy method. However, the values of some of the coefficients fell beyond the expected error ranges. In this study, more appropriate single crystal elastic constants are selected by means of a fitting procedure. Then the ODF coefficients are again estimated in the manner described previously. As a result, the values of the C411, C611, C612 and C614 coeffioents, which were somewhat inaccurate in the previous calculation, are improved considerably. The volume fractions of the principal preferred orientations are then employed to predict the 8th order coefficients and the fiber components of the l = 10 and l = 12 (C1011, C1211 and C1221) coefficients. With the aid of the coefficients obtained in this way, both pole and inverse pole figures are drawn, which are in better agreement with those based on X-rays than when only the 4th order coefficients are employed.

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