The applicability of analytical elasto-plastic solutions and issues of the formation of shear bands zones

2020 ◽  
Author(s):  
Elena Grishko ◽  
Artyom Myasnikov ◽  
Denis Sabitov ◽  
Yuri Podladchikov ◽  
Aboozar Garavand
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Analytical Solutions ◽  
Applied Mathematics ◽  
Shear Bands ◽  
Wellbore Stability ◽  
Plastic Behavior ◽  
Frictional Material ◽  
Support Of Research ◽  
Element Technique

<p><strong>Key Words:</strong> numerical modelling, elasto-plastic analytical solutions, shear bands, geomechanics.</p><p>The correct analysis of wellbore stability in unconventional reservoirs receives much interest from the industry as shale rock and tar sands demonstrate perceptible plastic behavior which influences the estimation of rock failure. To tackle this problem the 3D finite element code has been developed for computing the stress-strain state in the elastoplastic medium near a borehole. The accuracy of the results, obtained due to the application of the finite element technique, can be affected by various numerical effects. Since the theory of plasticity assumes infinitesimal load increments, errors associated with finite increments are almost inevitable. The accuracy of the numerical solution can be verified by comparing the numerical results with the analytical solutions. Elasto-plastic analytical solutions [1], [2] stand out among others because they are the only ones among many others, mentioned in the cited monographs, that consider analytical solutions under conditions of non-hydrostatic loading.</p><p>In this study, the numerical and analytical solutions were verified and relative errors were calculated for different loading paths. It turned out, for example, that Galin’s analytical solution works well not only in the field of its applicability, but also outside of it, despite different errors. This work discusses questions related to the influence of the increment of the applied load on the structure of a stationary elasto-plastic solution, including in the case of the formation of zones of localized plastic deformation. The issue of the appearance of shear bands zones is also considered: these bands develop directly around the hole under certain boundary conditions or gradually grow out of the zones of elliptical plastic deformation.</p><p>The first, third and fifth authors acknowledge support of research by Geosteering technologies company within the scope of Geonaft project sponsored by Skolkovo foundation, Russia.</p><p>The second and fourth authors acknowledge support of research by Government of Russian Federation under grant 2019-220-07-9139.</p><p><strong>REFERENCES</strong></p><p>[1] Detournay, E. (1986). An approximate statical solution of the elastoplastic interface for the problem of Galin with a cohesive-frictional material. International Journal of Solids and Structures, 22(12), 1435–1454.</p><p>[2] Galin, L.A. (1946). Plane elastoplastic problem. Applied Mathematics and Mechanics, 10 (3), 365–386.</p>

Elastoplastic Analysis of a Miniature Circular Disk Bending Specimen

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Vishnu Verma ◽  
A. K. Ghosh ◽  
G. Behera ◽  
Kamal Sharma ◽  
R. K. Singh
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Material Properties ◽  
Finite Element Solution ◽  
Bending Test ◽  
Experimental Result ◽  
Strain Hardening Exponent ◽  
Plastic Behavior ◽  
Element Solution ◽  
Element Analysis

The miniature disk bending test is used to evaluate the mechanical behavior of irradiated materials and their properties (e.g., yield stress and strain hardening exponent) to determine mainly ductility loss in steel due to irradiation from the load-deflection behavior of the disk specimen. In the miniature disk bending machine the specimen is firmly held between the two horizontal jaws of punch, and an indentor with a spherical ball travels vertically. Analytical solutions for large amplitude plastic deformation become rather unwieldy. Hence, a finite element analysis has been carried out. The finite element model considers contact between the indentor and test specimen, friction between various pairs of surfaces, and elastic plastic behavior. This paper presents the load versus deflection results of a parametric study where the values of various parameters defining the material properties have been varied by ±10% around the base values. Some well-known analytical solutions to this problem have also been considered. It is seen that the deflection obtained by analytical elastic bending theory is significantly lower than that obtained by the elastoplastic finite element solution at relatively small values of load. The finite element solution has been compared with one experimental result and values are in reasonably good agreement. With these results it will be possible to determine the material properties from the experimentally obtained values of load and deflection.

Elasto-Plastic Analysis of a Miniature Circular Disk Bending Specimen

2006 ◽  
Author(s):  
Vishnu Verma ◽  
A. K. Ghosh ◽  
G. Behera ◽  
Kamal Sharma ◽  
R. K. Singh
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Yield Stress ◽  
Material Properties ◽  
Stable Solution ◽  
Bending Test ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Plastic Behavior ◽  
Element Analysis

Miniature disk bending test is used to evaluate the mechanical behavior of irradiated materials and its properties — mainly ductility loss due to irradiation in steel. In Miniature Disk Bending Machine the specimen is firmly held between the two horizontal jaws of punch, and an indentor with spherical ball travels vertically. Researchers have observed reasonable correlations between values of the yield stress, strain hardening and ultimate tensile strength estimated from this test and mechanical properties determined from the uniaxial tensile test. Some methods for the analysis of miniature disk bending, proposed by various authors have been discussed in the paper. It is difficult to distinguish between the regimes of elastic and plastic deformation since local plastic deformation occurs for very small values of load when the magnitude of spatially averaged stress will be well below the yield stress. Also, the analytical solution for large amplitude, plastic deformation becomes rather unwieldy. Hence a finite element analysis has been carried out. The finite element model, considers contact between the indentor and test specimen, friction between various pairs of surfaces and elastic plastic behavior. The load is increased in steps and converged solution has been obtained and analysis terminated at a load beyond which a stable solution cannot be obtained. A sensitivity study has been carried out by varying the various parameters defining the material properties by ±10% around the base values. This study has been carried out to generate a data base for the load-deflection characteristics of similar materials from which the material properties can be evaluated by an inverse calculation. It is seen that the deflection obtained by analytical elastic bending theory is significantly lower than that obtained by the elasto-plastic finite element solution at relatively small values of load. The FE solution and experimental results are in reasonably good agreement.

Finite Element Analysis of Elastic and Plastic Deformation during Growth of Si1−xGex/Si Heterostructures

2004 ◽  
Vol 824 ◽  
Author(s):  
F. Sahtout Karoui ◽  
A. Karoui ◽  
G. Rozgonyi
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Stress Distribution ◽  
Von Mises Stress ◽  
Plastic Behavior ◽  
Element Analysis ◽  
Strained Si ◽  
Von Mises ◽  
Elastic And Plastic Deformation ◽  
Plastic Stress

AbstractThe elastic and plastic stress distribution in strained Si1−xGex heterostructure (x=0.2 and x=0.5), was investigated during the growth process using a nonlinear transient finite element modeling. The material plastic behavior is described by the von Mises yield criteria coupled with isotropic work hardening conditions. The calculated stress distribution during growth of the SiGe cap layer shows that the von Mises stress fluctuates strongly within the layers and at the interfaces. The surface of constant composition Si1−xGex layer is found under compressive stress in both cases. Within that layer the normal stress in the growth direction remains compressive for x=0.2, while it changes from compressive to tensile for x=0.5. In the graded layer the stress goes from tensile to compressive for x=0.5 and in the opposite way for x=0.2. High plastic deformation is observed in the layers, with the maximum von Mises plastic stress being higher for x=0.5 and localized in the SiGe graded region. The plastic strain vanishes monotonically up to 8 μ deep into the Si bulk substrate, in agreement with TEM images that revealed dislocation loops penetrating into the substrate. The time dependent analysis shows that elastic and plastic deformation appear almost instantaneously in the sublayers, while in the Si substrate it is delayed up to 300 s.

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

scholarly journals Finite element modelling of microstructural changes during equal channel angular drawing of pure aluminium

2021 ◽  
Author(s):  
Serafino Caruso ◽  
Stano Imbrogno
Keyword(s):  
Plastic Deformation ◽  
Grain Size ◽  
Finite Element ◽  
Size Variation ◽  
Fe Model ◽  
Pure Aluminium ◽  
Continuous Dynamic Recrystallization ◽  
Research Activities ◽  
Hardness Change ◽  
Continuous Dynamic

AbstractGrain refinement by severe plastic deformation (SPD) techniques, as a mechanism to control microstructure (recrystallization, grain size changes,…) and mechanical properties (yield strength, ultimate tensile strength, strain, hardness variation…) of pure aluminium conductor wires, is a topic of great interest for both academic and industrial research activities. This paper presents an innovative finite element (FE) model able to describe the microstructural evolution and the continuous dynamic recrystallization (CDRX) that occur during equal channel angular drawing (ECAD) of commercial 1370 pure aluminium (99.7% Al). A user subroutine has been developed based on the continuum mechanical model and the Hall-Petch (H-P) equations to predict grain size variation and hardness change. The model is validated by comparison with the experimental results and a predictive analysis is conducted varying the channel die angles. The study provides an accurate prediction of both the thermo-mechanical and the microstructural phenomena that occur during the process characterized by large plastic deformation.

Tissue necrosis and passage of fluid due to cold stress from the thermally damaged human body peripherals: A mathematical model

2015 ◽  
Vol 04 (02) ◽  
pp. 1550012
Author(s):  
M. A. Khanday ◽  
Fida Hussain ◽  
Khalid Nazir
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Heat Equation ◽  
Cold Stress ◽  
Human Body ◽  
Human Subjects ◽  
Diffusion Equations ◽  
Tissue Necrosis ◽  
Cold Temperatures ◽  
Element Technique

The development of cold injury takes place in the human subjects by means of crystallization of tissues in the exposed regions at severe cold temperatures. The process together with the evaluation of the passage of fluid discharge from the necrotic regions with respect to various degrees of frostbites has been carried out by using variational finite element technique. The model is based on the Pennes' bio-heat equation and mass diffusion equations together with suitable initial and boundary conditions. The results are analyzed in relation with atmospheric temperatures and other parameters of the tissue medium.

Computation on continuous grain refinement in AA1050 aluminum during repetitive tube expansion and shrinking technique

2015 ◽  
Vol 232 (4) ◽  
pp. 307-318
Author(s):  
H Jafarzadeh ◽  
K Abrinia
Keyword(s):  
Finite Element Method ◽  
Plastic Deformation ◽  
Grain Size ◽  
Finite Element ◽  
Dislocation Density ◽  
Severe Plastic Deformation ◽  
Grain Refinement ◽  
Half Cycle ◽  
Tube Expansion ◽  
Element Method

The microstructure evolution during recently developed severe plastic deformation method named repetitive tube expansion and shrinking of commercially pure AA1050 aluminum tubes has been studied in this paper. The behavior of the material under repetitive tube expansion and shrinking including grain size and dislocation density was simulated using the finite element method. The continuous dynamic recrystallization of AA1050 during severe plastic deformation was considered as the main grain refinement mechanism in micromechanical constitutive model. Also, the flow stress of material in macroscopic scale is related to microstructure quantities. This is in contrast to the previous approaches in finite element method simulations of severe plastic deformation methods where the microstructure parameters such as grain size were not considered at all. The grain size and dislocation density data were obtained during the simulation of the first and second half-cycles of repetitive tube expansion and shrinking, and good agreement with experimental data was observed. The finite element method simulated grain refinement behavior is consistent with the experimentally obtained results, where the rapid decrease of the grain size occurred during the first half-cycle and slowed down from the second half-cycle onwards. Calculations indicated a uniform distribution of grain size and dislocation density along the tube length but a non-uniform distribution along the tube thickness. The distribution characteristics of grain size, dislocation density, hardness, and effective plastic strain were consistent with each other.

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