scholarly journals THE PROCEDURE OF THE SLIP MODELS OF POLYCRYSTALLINE PLASTICITY IN THE GENERAL CASES

1992 ◽  
Vol 14 (2) ◽  
pp. 13-16
Author(s):  
Bui Huu Dan
Keyword(s):  
Vector Space ◽  
Clifford Algebra ◽  
Strain State ◽  
Stress And Strain ◽  
Slip Model ◽  
Dimension Vector ◽  
Computation Procedure ◽  
Five Dimension ◽  
The Many

The computation procedure of the slip model of polycrystalline plasticity was extended for the most general cases, when the stress and strain state are expressed in the five-dimension vector space this extent ion is based on the know ledges of Clifford algebra in the many-dimension (more than 3) vector space. The results would be reduced into the old results given in the more simple cases.

Effect of pipe expansion on the redistribution of residual stresses after molding

2020 ◽  
Vol 10 (2) ◽  
pp. 122-126
Author(s):  
Nikolay A. Makhutov ◽  
◽  
Dmitry A. Neganov ◽  
Eugeny P. Studenov ◽  
◽  
...  
Keyword(s):  
Residual Stresses ◽  
Strain Distribution ◽  
Strain State ◽  
Stress And Strain ◽  
Cylindrical Shape ◽  
Pipe Material ◽  
Pipe Expansion ◽  
Calculation Results ◽  
Residual Deformations ◽  
Stress And Strain Distribution

In the factory, pipes for trunk oil and oil product pipelines are obtained by molding and welding. To ensure a cylindrical shape and reduce technological residual stresses, expansion technology is used. Pipe expansion causes a significant change in the values of residual deformations and stresses. The article presents both the calculation results and graphs regarding stress and strain distribution during bending of the stock and their redistribution after expansion. Based on the calculation results, the final total values of residual stresses and residual deformations caused by bending and expansion were stated to be important components of the stress-strain state observed in pipelines being operated under cyclic loading, as well as those used in assessing how degradation affects the ductility of the pipe material. These factors were concluded as being reasonably taken into account when performing verification calculations regarding long-running pipelines if, based on their diagnostics and analysis, their state does not meet modern strength requirements.

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

Strain, Stress, and Magnetic Surfaceanisotropy of Epitaxial FE(110)/MO (110) Multilayers

1993 ◽  
Vol 317 ◽  
Author(s):  
R.M. Osgood ◽  
B.M. Clemens ◽  
R.L. White ◽  
S. Brennan
Keyword(s):  
Strain State ◽  
Single Layer ◽  
Grazing Incidence ◽  
Magnetic Surface ◽  
Stress And Strain ◽  
Surface Anisotropy ◽  
X Ray Diffraction ◽  
X Ray ◽  
Plane Direction ◽  
Strain Stress

ABSTRACTGrazing incidence and asymmetric X-ray diffraction were used to measure the stress and strain state of Fe(110)/Mo(110) Multilayers. The highest stress in the Fe constituent of the multilayer was along the [110] in-plane direction and was due to interaction with the substrate. The Magnetic anisotropy of the Fe Multilayer constituent was measured and the magnetic surface anisotropy, which favored in-plane [001] magnetization, was deduced. In contrast, the magnetic surface anisotropy of a single layer of Fe on W preferred in-plane [110] magnetization, in agreement with the Néel Model.

Experimental and numerical investigation of Armox 500T armor steel perforation process

2021 ◽  
Vol 70 (1) ◽  
pp. 43-61
Author(s):  
Arkadiusz Popławski
Keyword(s):  
Plastic Deformation ◽  
Strain State ◽  
Numerical Study ◽  
Stress And Strain ◽  
Failure Model ◽  
Modes Of Failure ◽  
State Of Stress ◽  
Computational Code ◽  
Armor Steel ◽  
Plate Perforation

This paper presents the results of an experimental and numerical study of the perforation of Armox 500T armoured steel. The plate perforation was performed with a pneumatic gun using three types of penetrators. Sharp, spherical and blunt penetrators were used. The use of different geometries of penetrators causes the process of perforation and destruction of plates in a different state of stress and strain, which leads to the appearance of three basic modes of failure. Numerical analyses of the perforation process have been carried out using the Ls-Dyna computational code with an advanced constitutive model of the material and the integrated failure model. The obtained experimental and numerical results were analysed and compared. The failure shape, the level of plastic deformation and the parameters of stress and strain state were analysed.

scholarly journals Building of a space form of the flexible inextensible one-layer conic shell

2021 ◽  
Vol 34 (01) ◽  
pp. 489-503
Author(s):  
Marina V. Byrdina ◽  
Mikhail F. Mitsik ◽  
Lema A. Bekmurzaev ◽  
Svetlana V. Kurenova ◽  
Anastasiya A. Movchun
Keyword(s):  
Strain State ◽  
Space Form ◽  
Shell Structures ◽  
Stress And Strain ◽  
Thin Wall ◽  
Linear Deformation ◽  
Program Module ◽  
Gravitational Forces ◽  
Conic Shell ◽  
Elastic Forces

The paper covers the visualization of a volume-space form of the flexible inextensible one-layer shell that is represented in the stress and strain state appearing during fastening the shell on the upper edge and its free location below the fastening border in the field of gravitational and elastic forces of the material. With no account taken of the gravitational forces, the shell is a right circular flattened cone. A developed program module can be used in designing and calculating the thin-wall shell structures during their non-linear deformation and their visualization. Visualization of the space form of the shell structure can be used for simulating various products, for instance, the cone antennae or the textile products, flexible elastic shells in the hydraulic engineering, etc.

scholarly journals Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host

Solid Earth ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 817-833
Author(s):  
Xin Zhong ◽  
Marcin Dabrowski ◽  
Bjørn Jamtveit
Keyword(s):  
Residual Stress ◽  
Aspect Ratio ◽  
Analytical Solution ◽  
Strain State ◽  
Spherical Inclusion ◽  
Raman Shift ◽  
Stress And Strain ◽  
Wide Range ◽  
Inclusion Shape ◽  
Diamond Inclusions

Abstract. Raman elastic thermobarometry has recently been applied in many petrological studies to recover the pressure and temperature (P–T) conditions of mineral inclusion entrapment. Existing modelling methods in petrology either adopt an assumption of a spherical, isotropic inclusion embedded in an isotropic, infinite host or use numerical techniques such as the finite-element method to simulate the residual stress and strain state preserved in the non-spherical anisotropic inclusions. Here, we use the Eshelby solution to develop an analytical framework for calculating the residual stress and strain state of an elastically anisotropic, ellipsoidal inclusion in an infinite, isotropic host. The analytical solution is applicable to any class of inclusion symmetry and an arbitrary inclusion aspect ratio. Explicit expressions are derived for some symmetry classes, including tetragonal, hexagonal, and trigonal. The effect of changing the aspect ratio on residual stress is investigated, including quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Quartz is demonstrated to be the least affected, while rutile is the most affected. For prolate quartz inclusion (c axis longer than a axis), the effect of varying the aspect ratio on Raman shift is demonstrated to be insignificant. When c/a=5, only ca. 0.3 cm−1 wavenumber variation is induced as compared to the spherical inclusion shape. For oblate quartz inclusions, the effect is more significant, when c/a=0.5, ca. 0.8 cm−1 wavenumber variation for the 464 cm−1 band is induced compared to the reference spherical inclusion case. We also show that it is possible to fit an effective ellipsoid to obtain a proxy for the averaged residual stress or strain within a faceted inclusion. The difference between the volumetrically averaged stress of a faceted inclusion and the analytically calculated stress from the best-fitted effective ellipsoid is calculated to obtain the root-mean-square deviation (RMSD) for quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Based on the results of 500 randomly generated (a wide range of aspect ratio and random crystallographic orientation) faceted inclusions, we show that the volumetrically averaged stress serves as an excellent stress measure and the associated RMSD is less than 2 %, except for diamond, which has a systematically higher RMSD (ca. 8 %). This expands the applicability of the analytical solution for any arbitrary inclusion shape in practical Raman measurements.

Application of Numerical and Block Geomechanical Modelling to Determine Parameters of Large-Section Chambers

2021 ◽  
pp. 127-131
Author(s):  
M.A. Sonnov ◽  
A.V. Trofimov ◽  
A.E. Rumyantsev ◽  
S.V. Shpilev
Keyword(s):  
Rock Mass ◽  
Strain State ◽  
Stress And Strain ◽  
Underground Structures ◽  
Geomechanical Model ◽  
Principal Stresses ◽  
Mine Support ◽  
History Of ◽  
Crushing Plant ◽  
Ore Pass

The study is exemplified by complex workings of a main ore pass that include a variety of underground structures, usually with unique dimensions which depend on the function and size of the equipment placed. The technical solutions for the underground crushing plant and associated structures envisage construction of chambers with the height of up to 35 m and the width of up to 20 m at the depths exceeding 800-1000 m. Such conditions call for a closer attention to be paid to the mine support parameters, especially the bolting depth. A block geomechanical model was designed in the Micromine Mining Software for the rock mass of the new main ore pass. Geotechnical boreholes logs and results of physical and mechanical rock tests were used as the input data for the model. Four domains were identified in the block geomechanical model for subsequent numerical modelling. A 3D model of the stress-and-strain state of the rock mass was made using the CAE Fidesys software based on the Micromine wire-frame model of the main ore pass. The history of the rock mass incremental loading was reconstructed for correct simulation of its stress-and-strain state. Prior to the excavation, the rock mass is pre-stressed by the weight of the rock strata. The excavation phase was then simulated in the stepwise manner. An array of points with the values of maximum principal stresses was downloaded from the numerical model post-processing program and interpolated into the block geomechanical model to refine the SRF parameter of the Barton's Q rating. Based on the obtained Q values, the mine support parameters for chambers were determined using the Barton, Hutchinson and Potvin empirical methods.

scholarly journals Determining intrinsic stress and strain state of fibre-textured thin films by X-ray diffraction measurements using combined asymmetrical and Bragg-Brentano configurations

2019 ◽  
Vol 181 ◽  
pp. 108063 ◽  
Author(s):  
Fakhrodin Motazedian ◽  
Zhigang Wu ◽  
Junsong Zhang ◽  
Bashir Samsam Shariat ◽  
Daqiang Jiang ◽  
...  
Keyword(s):  
Thin Films ◽  
Strain State ◽  
Intrinsic Stress ◽  
Stress And Strain ◽  
X Ray Diffraction ◽  
X Ray
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