On accounting for preferred crystallite orientations in determination of average elastic strain by diffraction

2018 ◽  
Vol 51 (1) ◽  
pp. 148-156
Author(s):  
A. Morawiec
Keyword(s):  
Strain Tensor ◽  
Simulated Data ◽  
Average Stress ◽  
Closed Form Expression ◽  
Polycrystalline Materials ◽  
Spatial Correlations ◽  
Polycrystalline Specimen ◽  
Pole Figures ◽  
Measurement Results ◽  
Strain Tensors

Standard diffraction-based measurements of elastic strains in polycrystalline materials rely on shifts of Bragg peaks. Measurement results are usually given in the form of a single tensor assumed to represent the average stress in the material, but the question about the true relationship between the tensor and the average stress generally goes without notice. This paper describes a novel procedure for analysis of data obtained from such measurements. It is applicable in cases when spatial correlations in the material are ignored and statistical information about the polycrystalline specimen is limited to texture-related intensity pole figures and strain pole figures. A tensor closest to auxiliary strain tensors linked to the results of measurements in particular specimen directions is considered to represent the strain state. This tensor is shown to be a good approximation of the average strain tensor. A closed-form expression allowing for its direct computation from experimental pole figures is given. The performance of the procedure is illustrated using simulated data.

Description of Large Deformation Problem Using Means of Visual Strain

2013 ◽  
Vol 275-277 ◽  
pp. 16-22
Author(s):  
You Liang Xu
Keyword(s):  
Constitutive Equation ◽  
Large Deformation ◽  
Strain Tensor ◽  
Visual Image ◽  
Linear Strain ◽  
Deformation Problem ◽  
Practical Engineering ◽  
Large Deformation Problem ◽  
Strain Tensors ◽  
Linear Strain Tensor

The constitutive equation of large deformation problem is closely related to geometric description. Nowadays, linear strain tensor is no longer unsuitable to describe large deformation. However, the existing non-linear strain tensors have complicated forms as well as no apparent geometric or physical meaning. While, the increment method is used to solve, however, convergence and efficiency are low sometimes. Thus the idea of visual strain tensor is proposed, with distinct meaning and visual image. Beside, it is likely to be used in engineering measurement, and it can be connected with measured constitutive equation directly. Thus this research provides a new idea and method for solving large-deformation problems in practical engineering.

Modelling of biofilters for ammonium reduction in combined sewer overflow

2009 ◽  
Vol 60 (3) ◽  
pp. 825-831 ◽  
Author(s):  
M. Henrichs ◽  
A. Welker ◽  
M. Uhl
Keyword(s):  
Reactive Transport ◽  
Simulated Data ◽  
Filter Material ◽  
Degradation Process ◽  
Operating Conditions ◽  
Combined Sewer Overflow ◽  
Measurement Results ◽  
Combined Sewer ◽  
Outflow Rate ◽  
Sewer Overflow

Biofiltration has proved to be a useful system to treat combined sewer overflow (CSO). The study presented uses numerical simulation to detect the critical operating conditions of the filter. The multi-component reactive transport module CW2D was used for the simulation study. Single-event simulations of lab-scale-column experiments with varying boundary conditions regarding the throttle outflow rate were carried out. For the calibration of the CW2D model measurement results of four experiments in two lab-scale columns were used. The model was validated by simulating four events of two further columns filled with the same filter material. These columns were operating with higher throttle outflow rates than the columns used for calibration. For ammonium (NH4-N) a good fit between measured and simulated data could be achieved. However, the comparison of simulated and measured effluent concentrations of nitrate (NO3-N) showed that there is a need for further investigations mainly due to the uncertainties in the degradation process during dry periods between the loadings.

scholarly journals ON DIFFERENT DEFINITIONS OF STRAIN TENSORS IN GENERAL SHELL THEORIES OF VEKUA-AMOSOV TYPE

2021 ◽  
Vol 17 (1) ◽  
pp. 117-126
Author(s):  
Sergey Zhavoronok
Keyword(s):  
Shell Theory ◽  
Strain Tensor ◽  
Translation Vector ◽  
Dimensional Manifold ◽  
Vector Systems ◽  
Base Vector ◽  
Main Basis ◽  
Definition Of ◽  
Strain Tensors ◽  
Main Definition

Several possible definiions of strains in a general shell theory of I.N. Vekua – A.A. Amosov type are considered. The higher-order shell model is definedon a two-dimensional manifold within a set of fieldvariables of the firstkind determined by the expansion factors of the spatial vector fieldof the translation. Two base vector systems are introduced, the firs one so-called concomitant corresponds to the cotangent fibrtion of the modelling surface while the other is defind on a surface equidistant to the modelling one. The distortion appears as a two-point tensor referred to both base systems after covariant differentiationof the translation vector feld. Thus, two main definition of the strain tensor become possible, the firstone referred to the main basis whereas the second to the concomitant one. Some possible simplificationsof these tensors are considered, and the interrelation between the general theory of A.A. Amosov type and the classical ones is shown.

Study of the anisotropy of the polycrystal properties based on texture data

2019 ◽  
Vol 85 (9) ◽  
pp. 46-51
Author(s):  
A. V. Stepanenko
Keyword(s):  
Experimental Data ◽  
Physical Properties ◽  
Thermomechanical Processing ◽  
Physical And Mechanical Properties ◽  
Polycrystalline Materials ◽  
X Ray ◽  
Anisotropic Properties ◽  
Pole Figures ◽  
Quantitative Changes ◽  
Crystallographic Orientations

The results of studying correlation between the crystallographic texture of polycrystalline materials and anisotropy of their physical and mechanical properties are considered. The methods for calculating the anisotropic properties of polycrystals based on the data obtained by X-ray methods of direct and inverse pole figures are reviewed. Calculation methods based on the use of the distribution function of crystallite orientations require the use of a large amount of experimental data and, hence, they are not suitable for express estimation of the anisotropy level of the physical properties of samples upon their thermomechanical processing. A method for rapid estimation of the anisotropic properties of the sample based on the use of Д; ("orientation factors") in the calculations, is proposed. Experimental data of X-ray analysis (method of inverse pole figures) are used to calculate the absolute and relative deviations of the physical parameter of textured polycrystal from the same value in the isotropic sample. The contributions of individual crystallographic orientations to the formation of the anisotropy of the properties of the sample are estimated. The dynamics of quantitative changes in the anisotropic properties of a polycrystal in the process of texture formation is studied. To analyze the source of the most rapid changes in the anisotropy of properties, we used the coefficients of the "response" matrix, the calculation of which does not depend on the results of specific diffractometric measurements, but is common for all metals with a hexagonal close-packed (hep) lattice. The anisotropy of the coefficient of thermal conductivity, electrical conductivity, and thermal diffusivity was calculated for the samples of deformed yttrium which underwent cold rolling with a reduction ratio of e = 25%. It is shown that the final physical properties_of the hep polycrystal are largely determined by the pyramidal crystallographic orientations {1015}, {1124}. The results of the study form a basis for analysis of the anisotropy of the physical properties of hep-metal samples upon thermomechanical processing.

Mapping of Strain Tensor Components in Polycrystalline Samples using EBSD.

2014 ◽  
Vol 1664 ◽  
Author(s):  
David J Dingley ◽  
Graham Meaden ◽  
Seiichi Suzuki ◽  
Tatsuya Fukino
Keyword(s):  
Hot Spots ◽  
Electron Backscatter Diffraction ◽  
Strain Tensor ◽  
Polycrystalline Materials ◽  
Static Tests ◽  
Stress Relieving ◽  
Elastic Loading ◽  
Residual Strains ◽  
Backscatter Diffraction ◽  
Better Than

ABSTRACTThe advance in Electron Backscatter Diffraction known as High Resolution EBSD has permitted the strain tensor components and neighbour disorientation measurements to be mapped at resolutions better than 2 parts in 10000. Following earlier research into this technique which was focused on verifying the sensitivity and accuracy of the measurements, recent studies have involved investigations on semiconductor and metallic polycrystalline materials. In particular observations of localized regions where residual strains exceeded the macroscopic yield stress have been thoroughly investigated to eliminate experimental error as a possible explanation. No such cause was found. Strain measurements on polycrystalline steels in uniaxial tension and during thermal stress relieving thermal treatment have also been carried out. Maps of the strain distribution during elastic loading and early stages of plastic flow showed hot spots of high strain as in the static tests but overall the measured elastic strain was equal to the applied strain.

Application of the 3D X-Ray Crystal Microscope to Study Mesoscale Structure of Materials

2003 ◽  
Vol 779 ◽  
Author(s):  
Gene E. Ice ◽  
Wenjun Liu ◽  
Bennett C. Larson ◽  
Fredrick J. Walker
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Three Dimensions ◽  
Polycrystalline Materials ◽  
Crystalline Orientation ◽  
Materials Properties ◽  
X Ray ◽  
Mesoscale Structure ◽  
Elastic And Plastic Deformation ◽  
Strain Tensors

AbstractThe 3D x-ray crystal microscope is an emerging tool for the study of mesoscale structure in polycrystalline materials. With this nondestructive device, local crystalline orientation, phase, elastic and plastic strain tensors can be measured with submicron spatial resolution in three dimensions. A key step in analyzing the Laue patterns from the 3D microscope is indexing the reflections, which determines the orientation of the sub-grain. With current algorithms, the angles between pairs, triplets and quadruplets of reflections are compared to theoretical angles to make guesses as to the reflection indices. The ability to index a pattern can however be compromised by both elastic and plastic deformation of a grain; elastic deformation changes the angles between reflections and plastic deformation increases the uncertainty in the centroid of each reflection. Here we report on the use of an indexing algorithm that simultaneously fits all peaks from a subgrain. This algorithm is more robust than previous methods and allows for indexing of deformed or strained grains. Some applications to studies of mesoscale materials properties are described.

Testing and Evaluation of Infrared Radiation Property of Cordierite Based Glass-Ceramic Materials

2010 ◽  
Vol 177 ◽  
pp. 455-458 ◽  
Author(s):  
Shu Ming Wang ◽  
Ying Chun Zhang ◽  
Feng Hua Kuang ◽  
Qing Zhi Yan ◽  
Chang Chun Ge ◽  
...  
Keyword(s):  
Infrared Radiation ◽  
Glass Ceramics ◽  
Ceramic Materials ◽  
Test Methods ◽  
Polycrystalline Materials ◽  
Radiation Property ◽  
Radiation Heating ◽  
Radiation Properties ◽  
Measurement Results ◽  
Systematic Exposition

In this article we present the testing, evaluation of infrared radiation properties of polycrystalline materials especially as cordierite-based glass-ceramics. Researches aim to make a comprehensive and systematic exposition of emissivity definition, test principles and test methods. And on the basis of measurement results of the infrared emissivity of cordierite-based glass-ceramics, the Infrared radiation property of this polycrystalline material was discussed. Research has a positive significance on the development of the infrared radiation heating and drying materials.

scholarly journals Residual lattice strain in quartzites as a potential palaeo-piezometer

2020 ◽  
Vol 222 (2) ◽  
pp. 1363-1378 ◽  
Author(s):  
Hans-Rudolf Wenk ◽  
Brian Chase Chandler ◽  
Kai Chen ◽  
Yao Li ◽  
Nobumichi Tamura ◽  
...  
Keyword(s):  
Lattice Distortion ◽  
Lattice Strain ◽  
Strain Tensor ◽  
Tectonic Deformation ◽  
Laue Diffraction ◽  
X Ray ◽  
Pole Figures ◽  
Strain Axis ◽  
Greenschist Facies Metamorphism ◽  
The Ideal

SUMMARY If a crystal lattice is subjected to a stress, it becomes distorted and no longer represents the ideal crystal symmetry, and if the stress introduces defects such as dislocations, some of this distortion is preserved after the applied stress is removed. In this study, we investigate lattice distortion in quartz at the micron scale with synchrotron X-ray Laue diffraction. From Laue images the local deviatoric strain tensor is derived and corresponding stresses are calculated based on elastic properties. The method is applied to metasedimentary quartzites from the Bergell Alps that were deformed at conditions of greenschist facies metamorphism. The residual palaeostrain is represented in maps of the deviatoric strain tensor components and with deviatoric strain axis pole figures. Data suggest overall shortening perpendicular to the schistosity plane but with considerable asymmetry relative to foliation and lineation, probably attributed to simple shear. Crystallographic pole figures from Laue diffraction agree with neutron diffraction and EBSD measurements and display quartz c-axes girdle distributions with maxima also perpendicular to schistosity. The method shows promise to be used as a palaeo-piezometer to unravel the stress field during tectonic deformation.

Sign in / Sign up

Export Citation Format

Share Document