scholarly journals Simulation of nonstationary hydrogen diffusion processes near the crack tip in a field of inhomogeneous mechanical stresses

2021 ◽  
pp. 93-98
Author(s):  
Yaroslav Pelekh ◽  
Andrii Kunynets ◽  
Serhii Mentynskyi ◽  
Bohdan Fil
Keyword(s):  
Hydrogen Diffusion ◽  
Diffusion Processes ◽  
Crack Tip ◽  
Isotropic Body ◽  
Local Error ◽  
Abscissa Axis ◽  
Third Order ◽  
Order Of Accuracy ◽  
Rectilinear Crack ◽  
Hydrostatic Stresses

An elastic-plastic isotropic body is investigated, weakened by a rectilinear crack directed along the abscissa axis, under the action of stresses symmetric with respect to its plane. The hydrogen concentration near the crack tip is calculated. An approximate solution of this problem is constructed under the condition that the distribution of hydrostatic stresses along the crack extension is approximated by a parabola. For a numerical solution, a method of the third order of accuracy with a two-sided estimate of the main term of the local error is proposed.

scholarly journals 3D Unsteady Diffusion and Reaction-Diffusion with Singularities by GFEM with 27-Node Hexahedrons

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Finite Element ◽  
Variable Temperature ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Third Order ◽  
Order Of Accuracy ◽  
Finite Element Approximations ◽  
Temperature Solution ◽  
The One ◽  
Primary Variable

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

scholarly journals Transient Hydrogen Diffusion-Elastoplastic Coupling Analysis near a Blunting Crack Tip

2008 ◽  
Vol 74 (737) ◽  
pp. 28-36 ◽  
Author(s):  
Hirokazu KOTAKE ◽  
Ryosuke MATSUMOTO ◽  
Shinya TAKETOMI ◽  
Noriyuki MIYAZAKI
Keyword(s):  
Hydrogen Diffusion ◽  
Crack Tip ◽  
Coupling Analysis

scholarly journals On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
The Difference

This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

2713 Unsteady hydrogen diffusion analysis around the crack tip on cyclic loading

2007 ◽  
Vol 2007.20 (0) ◽  
pp. 615-616
Author(s):  
Hirokazu KOTAKE ◽  
Ryosuke MATSUMOTO ◽  
Shinya TAKETOMI ◽  
Noriyuki MIYAZAKI
Keyword(s):  
Cyclic Loading ◽  
Hydrogen Diffusion ◽  
Crack Tip ◽  
Diffusion Analysis

The characteristics of hydrogen diffusion and concentration around a crack tip concerned with hydrogen embrittlement

2002 ◽  
Vol 44 (3) ◽  
pp. 407-424 ◽  
Author(s):  
A.Toshimitsu Yokobori ◽  
Yasrou Chinda ◽  
Takenao Nemoto ◽  
Koji Satoh ◽  
Tetsuya Yamada
Keyword(s):  
Hydrogen Embrittlement ◽  
Hydrogen Diffusion ◽  
Crack Tip

Numerical Effects on the Prediction of Flow Instabilities in Channels With Sudden-Expansions

2003 ◽  
Author(s):  
S. Patel ◽  
D. Drikakis
Keyword(s):  
Wave Speed ◽  
Flow Instability ◽  
Flow Instabilities ◽  
Computational Investigation ◽  
Third Order ◽  
Order Of Accuracy ◽  
First Order ◽  
Bifurcation Phenomena ◽  
Flow Through ◽  
Stable Flow

We have considered the problem of flow through a suddenly-expanded channel and performed a computational investigation to examine numerical effects on the prediction of flow instability and bifurcation phenomena. The results revealed that the solution of the flow depends on the numerical method employed. We have employed Godunov-type methods in conjunction with first-, second- and third-order accurate interpolation schemes. It is shown that the order of accuracy of the interpolation used in the discretisation of the wave-speed dependent term and averaged part of the intercell flux affects the prediction of the instability. Computations using first-order discretisation for the calculation of the flux components results in symmetric stable flow, whereas second- and third-order discretisations lead to a symmetry-breaking bifurcation.

scholarly journals Methods for solving the initial value problem with a two-sided estimate of the local error

2021 ◽  
pp. 88-92
Author(s):  
Yaroslav Pelekh ◽  
Andrii Kunynets ◽  
Halyna Beregova ◽  
Tatiana Magerovska
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problem ◽  
Local Error ◽  
Initial Value ◽  
Order Of Accuracy ◽  
Embedded Methods ◽  
The Right

Numerical methods for solving the initial value problem for ordinary differential equations are proposed. Embedded methods of order of accuracy 2(1), 3(2) and 4(3) are constructed. To estimate the local error, two-sided calculation formulas were used, which give estimates of the main terms of the error without additional calculations of the right-hand side of the differential equation, which favorably distinguishes them from traditional two-sided methods of the Runge- Kutta type.

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