Modeling of Delayed Hydride Crack Initiation

1991 ◽  
Vol 113 (4) ◽  
pp. 443-448 ◽  
Author(s):  
A. F. Shalabi ◽  
D. A. Meneley
Keyword(s):  
Crack Initiation ◽  
Plastic Zone ◽  
Stress Level ◽  
Diffusion Problem ◽  
Transient Condition ◽  
Temperature Dependent ◽  
Mathematical Solution ◽  
One Dimensional ◽  
Percent Niobium ◽  
The One

This paper presents a solution to the one-dimensional time (transient condition) and temperature dependent diffusion problem adjacent to a crack-tip/flaw within the plastic zone region. The solution is used in addressing the problem of delayed hydride crack initiation in zirconium-2.5 wt. percent niobium. The mathematical solution predicts the critical hydride length at a given stress level and temperature for crack initiation.

Analysis of thick beams with temperature-dependent material properties under thermomechanical loads

2020 ◽  
Vol 23 (9) ◽  
pp. 1838-1850 ◽  
Author(s):  
Zhong Zhang ◽  
Ding Zhou ◽  
Xiuli Xu ◽  
Xuehong Li
Keyword(s):  
Material Properties ◽  
Mechanical Load ◽  
Stress Fields ◽  
Steel Beam ◽  
State Space Method ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Simply Supported ◽  
The One ◽  
Space Method

This study focuses on the thermoelastic behavior of simply supported thick beams with temperature-dependent material properties under thermomechanical loads. The heat conduction analysis is based on the one-dimensional Fourier’s law, and the displacement and stress analysis is based on the two-dimensional thermoelasticity theory. The solution of temperature field across the thickness is obtained. By dividing the beam into a series of thin slices, the temperature and the material properties in each slice are considered to be uniform. The state space method is used to give the displacements and stresses for every slice. The transfer-matrix method is used to give the displacements and stresses for the beam. Finally, an example is conducted to analyze the temperature, displacement, and stress fields in a carbon steel beam. The example reveals that the temperature not only produces displacements and stresses itself but also affects the displacements and stresses induced by the mechanical load.

Mesoscopic free energy as a framework for modeling shape memory alloys

2019 ◽  
Vol 30 (13) ◽  
pp. 1969-2012
Author(s):  
Wesley Ballew ◽  
Stefan Seelecke
Keyword(s):  
Free Energy ◽  
Shape Memory ◽  
Latent Heat ◽  
Compressive Behavior ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Dimensional Shape ◽  
The Difference ◽  
The One

This article presents a reinterpretation of the one-dimensional shape memory alloy model by Müller, Achenbach, and Seelecke (M-A-S) that offers extended capabilities and a simpler formulation. The cornerstone of this model is a continuous, multi-well free energy that governs phase change at a mesoscopic material scale. The free energy has been reformulated to allow asymmetric tensile and compressive behavior as well as temperature-dependent hysteresis while maintaining the necessary smoothness conditions. The free energy is then used to derive expressions for latent heat coefficients that include the influence of stress, the difference in stiffness between the phases, and irreversibility. Special attention is devoted to the role of irreversibility and latent heat predictions, which are compared to experimental measurements. The new model also includes an updated set of kinetics equations that operate on the convexity of the energy wells instead of the height of the energy barriers. This modification eliminates several sets of equations from the overall formulation without any compromises in performance and also bypasses limitations of the barrier-based equations.

scholarly journals One-dimensional compressible heat-conducting gas with temperature-dependent viscosity

2016 ◽  
Vol 26 (12) ◽  
pp. 2237-2275 ◽  
Author(s):  
Tao Wang ◽  
Huijiang Zhao
Keyword(s):  
Initial Data ◽  
Vacuum Solution ◽  
Viscosity Coefficient ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
One Dimensional ◽  
The One ◽  
Dependent Viscosity

We consider the one-dimensional compressible Navier–Stokes system for a viscous and heat-conducting ideal polytropic gas when the viscosity [Formula: see text] and the heat conductivity [Formula: see text] depend on the specific volume [Formula: see text] and the temperature [Formula: see text] and are both proportional to [Formula: see text] for certain non-degenerate smooth function [Formula: see text]. We prove the existence and uniqueness of a global-in-time non-vacuum solution to its Cauchy problem under certain assumptions on the parameter [Formula: see text] and initial data, which imply that the initial data can be large if [Formula: see text] is sufficiently small. Such a result appears to be the first global existence result for general adiabatic exponent and large initial data when the viscosity coefficient depends on both the density and the temperature.

scholarly journals A Study on the Creep Characteristics of Airport Viscous Subsoil Based on Unsaturated Stress Level

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jun Feng ◽  
Yue Ma ◽  
Zaobao Liu
Keyword(s):  
Stress Level ◽  
Unsaturated Soil ◽  
Three Dimensional ◽  
Matric Suction ◽  
Creep Model ◽  
Creep Stage ◽  
One Dimensional ◽  
Creep Characteristics ◽  
Stress Levels ◽  
The One

The present study takes the ratio of the matric suction to the net vertical stress and the ratio of the matric suction to the net mean stress as new unsaturated stress levels f and F , respectively. Based on the laboratory tests and theoretical derivation, the modified one-dimensional Mesri creep model and three-dimensional creep model were established, which takes the unsaturated stress level into account. Then, the one-dimensional and three-dimensional creep characteristics of the unsaturated viscous subsoil of an airport under different unsaturated stress levels were analyzed. The following conclusions could be drawn: (1) under different stress levels, the one-dimensional creep deformation of unsaturated soil has a power function relationship with time, and the change rate exponentially decreases with the stress level, which can be well-expressed by the proposed modified one-dimensional Mesri creep model; (2) under different stress levels, the three-dimensional creep strain of the unsaturated soil shows a hyperbolic curve with time and a near-linear relationship at the semilogarithmic coordinate, which can be well-expressed by the proposed modified three-dimensional creep model; (3) under different stress levels, both the one-dimensional creep and three-dimensional creep of the unsaturated soil can be divided into two stages, which are the accelerated creep stage and stable creep stage.

scholarly journals Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Kolade M. Owolabi ◽  
Kailash C. Patidar
Keyword(s):  
Patch Size ◽  
Reaction Diffusion ◽  
Mathematical Community ◽  
Diffusion Problem ◽  
One Dimensional ◽  
Critical Patch Size ◽  
The One ◽  
Exponential Time Differencing Method ◽  
Theoretical Results

We have given an extension to the study of Kierstead, Slobodkin, and Skellam (KiSS) model. We present the theoretical results based on the survival and permanence of the species. To guarantee the long-term existence and permanence, the patch size denoted asLmust be greater than the critical patch sizeLc. It was also observed that the reaction-diffusion problem can be split into two parts: the linear and nonlinear terms. Hence, the use of two classical methods in space and time is permitted. We use spectral method in the area of mathematical community to remove the stiffness associated with the linear or diffusive terms. The resulting system is advanced with a modified exponential time-differencing method whose formulation was based on the fourth-order Runge-Kutta scheme. With high-order method, this extends the one-dimensional work and presents experiments for two-dimensional problem. The complexity of the dynamical model is discussed theoretically and graphically simulated to demonstrate and compare the behavior of the time-dependent density function.

Climate: A Chain of Identical Reservoirs

1991 ◽  
Author(s):  
James C. G. Walker
Keyword(s):  
Differential Equation ◽  
Energy Balance ◽  
Differential Equations ◽  
Climate Model ◽  
Diffusion Problem ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
The Difference ◽  
A Chain ◽  
The One

One class of important problems involves diffusion in a single spatial dimension, for example, height profiles of reactive constituents in a turbulently mixing atmosphere, profiles of concentration as a function of depth in the ocean or other body of water, diffusion and diagenesis within sediments, and calculation of temperatures as a function of depth or position in a variety of media. The one-dimensional diffusion problem typically yields a chain of interacting reservoirs that exchange the species of interest only with the immediately adjacent reservoirs. In the mathematical formulation of the problem, each differential equation is coupled only to adjacent differential equations and not to more distant ones. Substantial economies of computation can therefore be achieved, making it possible to deal with a larger number of reservoirs and corresponding differential equations. In this chapter I shall explain how to solve a one-dimensional diffusion problem efficiently, performing only the necessary calculations. The example I shall use is the calculation of the zonally averaged temperature of the surface of the Earth (that is, the temperature averaged over all longitudes as a function of latitude). I first present an energy balance climate model that calculates zonally averaged temperatures as a function of latitude in terms of the absorption of solar energy, which is a function of latitude, the emission of long-wave planetary radiation to space, which is a function of temperature, and the transport of heat from one latitude to another. This heat transport is represented as a diffusive process, dependent on the temperature gradient or the difference between temperatures in adjacent latitude bands. I use the energy balance climate model first to calculate annual average temperature as a function of latitude, comparing the calculated results with observed values and tuning the simulation by adjusting the diffusion parameter that describes the transport of energy between latitudes. I then show that most of the elements of the sleq array for this problem are zero. Nonzero elements are present only on the diagonal and immediately adjacent to the diagonal. The array has this property because each differential equation for temperature in a latitude band is coupled only to temperatures in the adjacent latitude bands.

Arsenic Redistribution and Outdiffusion in Implanted Czochralski-Grown P-Type Silicon During Rapid Thermal Annealing

1988 ◽  
Vol 100 ◽  
Author(s):  
G. Chaussemy ◽  
B. Canut ◽  
S. N. Kumar ◽  
D. Barbier ◽  
A. Laugier
Keyword(s):  
Thermal Annealing ◽  
Rapid Thermal Annealing ◽  
Diffusion Coefficients ◽  
Good Description ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Type Silicon ◽  
The One ◽  
P Type ◽  
Diffusion Profiles

ABSTRACTThe effects of the implantation parameters (dose and energy) on the Arsenic redistribution and outdiffusion rate in (100) p-type silicon, after 7–12 s Rapid Thermal Annealing in the 1100–1200°C temperature range have been investigated. Four doses ranging from 2×1014 to l×1016 cm−2, and As+ energies between 70 and 170 keV, have been studied. The experimental diffusion profiles obtained from the SIMS measurements, in complement with the RBS results, were modelled using the one dimensional Fick's equation with semi-infinite boundary conditions, using a concentration and temperature dependent diffusion coefficient D(C, T). The As diffusivity was classically attributed to As+V0, As+V−, and As+V − pairs with the related diffusion coefficients taken from the literature. A relatively good description of the As redistribution was obtained without introducing any transient or SPE effects.

scholarly journals Transient Heat Diffusion with Temperature-Dependent Conductivity and Time-Dependent Heat Transfer Coefficient

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Raseelo J. Moitsheki
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Lie Algebras ◽  
Diffusion Problem ◽  
Heat Diffusion ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Surrounding Environment ◽  
Transient Heat Diffusion

Lie point symmetry analysis is performed for an unsteady nonlinear heat diffusion problem modeling thermal energy storage in a medium with a temperature-dependent power law thermal conductivity and subjected to a convective heat transfer to the surrounding environment at the boundary through a variable heat transfer coefficient. Large symmetry groups are admitted even for special choices of the constants appearing in the governing equation. We construct one-dimensional optimal systems for the admitted Lie algebras. Following symmetry reductions, we construct invariant solutions.

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