NONLINEAR ANALYSIS FOR FROST-HEAVING FORCE OF LAND BRIDGES ON QING-TIBET RAILWAY IN COLD REGIONS

ABSTRACT

A mathematical mechanical model and the governing differential equations of the coupled problem of temperature, moisture migrating, and stress fields with phase change, are first derived from the theory of heat transfer, the theory of moisture migration, and frozen soil mechanics. Then the finite element formulas of this problem are obtained by using Galerkin's method. Using the finite element formulas, a nonlinear analysis for the frost-heaving process of the land bridge in the next 20 years is made. The calculated results show that only soil at the bottom of the pile generates plastic deformation, and the deformation is quite small; therefore, the studied land bridge is safe.     

Hydrogen permeation and distribution at a high-strength X80 steel weld under stressing conditions and the implication on pipeline failure

Hydrogen permeation and distribution at pipeline welds is critical to integrity maintenance of the pipelines, especially for those made of high-strength steels. The situation becomes even more important under stressing conditions. In this work, metallographic characterization and micro-hardness measurements were conducted at an X80 steel weld. Potentiodynamic polarization and electrochemical hydrogen permeation testing were performance at various zones at the weld, along with numerical modeling of hydrogen distribution at the zones. The X80 steel contains a microstructure of bainite bundles and polygonal ferrite. There are more polygonal ferrite, fewer bainite and some segregated cementite at heat-affected zone (HAZ). The weld metal is featured with acicular ferrite and some grain boundary ferrite. HAZ softening occurs at the weld. The hardness of the weld metal, HAZ and base steel is about 290, 248 and 261 HV_0.2, respectively. There is the greatest corrosion current density, i.e., corrosion rate, at HAZ under both elastic and plastic stresses. An applied stress further increases the corrosion current density. Under the plastic stress of 1.1σ_ys (σ_ys is yield strength), the corrosion current densities of HAZ, base steel and weld metal are 41.04, 17.03 and 25.49 μA/cm², respectively. There are always the greatest hydrogen trapping density and the smallest hydrogen diffusivity at HAZ. Hydrogen, once penetrating the welded steel, tends to accumulate at the HAZ, compared with other two zones. When the welded steel is under stresses, especially a plastic stress (i.e., 1.1σ_ys), the hydrogen diffusivity and permeability decrease, while the subsurface hydrogen concentration and hydrogen trapping density increase remarkably. Plastic deformation favors the hydrogen permeation and trapping at weld, especially the HAZ, to elevate the susceptibility to hydrogen damage. The hydrogen distribution at different welding zones can be evaluated and determined by a developed modeling method.     

Thermal Stress Analysis for an Inclusion with Nonuniform Temperature Distribution in an Infinite Kirchhoff Plate

Abstract

An elliptic inclusion with prescribed polynomial eigenstrains in an infinite Kirchhoff plate is analyzed. The integral type general solutions for the in-plane and out-of-plane displacements on the mid-plane of the plate were derived. The integrals were simplified by using Green's function for the Kirchhoff plate. The integrals could be explicitly expressed by calculating two potential functions defined in this work. After some manipulation of Ferrers and Dyson's formula related to the integration of the harmonic potential for the three-dimensional ellipsoid, we evaluated the potential functions, which can be algebraically expressed by the I-integrals. The results were applied to the analysts of the thermal stress for an inclusion with non uniform temperature distribution that might be approximated by a polynomial. For mathematical convenience, we consider an inclusion with a linear temperature distribution. The expressions for the displacements were decomposed in order to separately investigate the effects of the constant and the first-order term of the temperature distribution. The elastic fields caused by an elliptic inhomogeneity with polynomial eigenstrains, which is called the inhomogeneous inclusion, were also determined by the equivalent eigenstrain method.     

A THERMOELASTOPLASTIC SOLUTION FOR A CIRCULAR SOLID CYLINDER SUBJECTED TO HEATING AND COOLING

Abstract

This paper presents a theoretical study of the stresses in an infinite circular solid cylinder subjected to rapid surface heating and cooling. A quasistatic, uncoupled, thermoelastoplastic analysis based on the incremental theory of plasticity is formulated, and a numerical procedure is developed for a method of successive elastic solutions. The material of the cylinder is assumed to have temperature-dependent properties and to be characterized by the Romberg-Osgood stress-strain relation. The transient and residual stress distributions are discussed in detail, along with variations of the equivalent stress and plastic strain with time.     

An investigation on strain and temperature rate-dependent thermoelasticity and its infinite speed behavior

Abstract

The present work is aimed at a mathematical analysis of the newly proposed strain and temperature rate-dependent thermoelasticity theory, also called a modified Green–Lindsay model (MGL) theory, given by Yu et al. (2018). This model is also an attempt to remove the discontinuity in the displacement field observed under temperature rate-dependent thermoelasticity theory proposed by Green and Lindsay. We study thermoelastic interactions in an infinite homogeneous, isotropic elastic medium with a cylindrical cavity based on this model when the surface of the cavity is subjected to thermal shock. The solutions for the distribution of displacement, temperature, and stress components are obtained by using the Laplace transform technique. The inversion of the Laplace transform is carried out by short-time approximation. A detailed comparison of the analytical results predicted by the MGL model with the corresponding predictions by the Lord–Shulman model and the Green–Lindsay model is performed. It is observed that strain rate terms in the constitutive equation avoid the prediction of discontinuity in the displacement field and other significant effects are noted. However, the new theory predicts the infinite speed of disturbance like the classical theory. Variations of field variables at different time are graphically displayed for different models and compared by using a numerical method.     

The numerical study of the thermal performance of a condensing gas-water heater

Abstract

Cast silicon-aluminum alloys exhibit corrosion resistance and heat transfer characteristics, and can be used as new materials in a condensing gas-water heater. A 3D mathematical model is established, and verified by the experiment, and then the flow and heat transfer characteristics are studied. It is observed the temperature misdistribution of the flue gas resulted from the condensation of water vapor. The temperature drop occurring in the high temperature zone exceeds 80%. Nusselt (Nu) empirical formulas for flue gas and water are obtained for two conditions. When inlet water gauge pressure reaches 0.02?MPa, heat transfer efficiency is the highest.     

The effect of fractional thermoelasticity on two-dimensional problems in spherical regions under axisymmetric distributions

Abstract

Two-dimensional axisymmetric problems are considered within the context of the fractional order thermoelasticity theory. The general solution is obtained in the Laplace transform domain by using a direct approach without the use of potential functions. The resulting formulation is used to solve two problems of a solid sphere and of an infinite space with a spherical cavity. The surface in each case is taken to be traction free and subjected to a given axisymmetric temperature distribution. The inversion of the Laplace transforms is carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series to obtain the temperature, displacement, and stress distributions in the physical domain. Numerical results are represented graphically and discussed. Some comparisons are shown in figures to estimate the effect of the fractional order parameter on all studied fields.     

Flow and heat transfer during a single drop impact on a liquid film

ABSTRACT

A two-dimensional incompressible laminar computational model was established to analyze flow and heat transfer characteristics during a single liquid drop impinging onto a liquid film, with an underneath surface of relatively low temperature. Using the coupled level set and volume of fluid method, the gas–liquid interface at different time sequences can be obtained clearly. Concerning the heat transfer process, three different factors including impact velocity, film thickness, and drop diameter were discussed. Results indicate that liquid inside the film can be classified as three zones: the impact zone, the transition zone, and the static zone, specifically according to different heat flux. Average surface heat flux can be increased by increasing impact velocity, while effects of film thickness and drop diameter are minor. Corresponding mechanisms were interpreted as well. For heat flux distribution in the impact and transition zones, both film thickness and drop diameter influence the distribution greatly. With an increment in film thickness and drop diameter, heat flux in the impact zone decreases, while heat flux in the transition zone appears to be an opposite trend. Also in the transition zone, the fluctuation amplitude of the heat flux rises as the two factors are reduced.     

Simple Formulas for Thermophysical Properties of Liquid Water for Heat Transfer Calculations (from 0°C to 150°C)

Abstract

In this communication, simple formulas (based on the latest experimental tabulated data) for 11 physical properties of liquid ordinary water substance at saturation state—saturation pressure, density, volumetric thermal expansion coefficient, specific volume of saturated vapor, specific enthalpy, specific heal, latent heal of vaporization, thermal conductivity, dynamic viscosity, Prandtl number, and surface tension as a function of temperature (from 0 to 150°C)—which are used in heat transfer calculations for heat exchangers in heating systems and also for many other technological applications, are presented. Also, the uncertainties of these formulas are given. In most practical cases the pressure of liquid water is within the range from 1 to 10 absolute bar, which makes it possible to neglect the effect of pressure. All properties of saturated liquid water calculated with the recommended formulas are tabulated with a temperature increment of 5°.     

STRESS INTENSITY FACTOR FOR TRANSIENT THERMAL STRESSES IN AN INFINITE ELASTIC BODY WITH AN EXTERNAL CRACK

Abstract

This paper deals with a transient thermal stress problem in an infinite body with an external crack. The elastic medium is cooled by time- and position-dependent temperature on the external crack. It is very difficult to obtain the analytical expression for the temperature, so the finite-difference method is used with respect to a time variable. Thus, the analytical expression for the temperature with respect to the spatial variables may be obtained. The temperature solution reduces to a dual-integral equation for spatial variables by use of the finite-difference method for a time variable. The numerical results for stress intensity factor are obtained.     

INFLUENCE OF THE TEMPERATURE DEPENDENCE OF THE YIELD STRESS ON THE STRESS DISTRIBUTION IN A HEAT-GENERATING TUBE WITH FREE ENDS

Based on Tresca's yield condition and its associated flow rule, the elastic-plastic deformation of a heat-generating tube with free ends is investigated by taking into consideration the influence of the temperature dependence of the yield stress. It is found that the expansion of the inner plastic zones as well as the stress state are affected markedly owing to the reduction in the yield stress at elevated temperatures. The stress distribution and the expansion of different plastic regions are displayed graphically and discussed.     

A generalized thermoelastic problem due to nonlocal effect in presence of mode I crack

Abstract

This article constructs a new model of nonlocal thermoelasticity which resolves a dynamical problem of a homogeneous, isotropic infinite space weakened by a finite linear mode I crack. The boundary of the crack is being subjected to a prescribed temperature distribution and stress. In the context of three-phase lag model of generalized thermoelasticity, the governing equations have been solved employing the Laplace and the Fourier transforms, which reduces to four dual integral equations, the solution of which is equivalent to solving the Fredholm’s integral equation of the first kind. These integral equations have been solved employing the Maple software package, while the numerical inversion of the Laplace transform is carried out with the help of Bellman method. Numerical computations for a copper material are performed and demonstrated graphically. The results provide a motivation to further investigate the problem and draw concluding remarks due to the influence of nonlocality also.     

Generalized thermo-electro-elasticity of a piezoelectric disk using Lord-Shulman theory

Abstract

Current investigation deals with the generalized thermoelastic response of a finite hollow disk made of a piezoelectric material. The constitutive equations of the piezoelectric media are reduced to a two dimensional plane-stress state. To capture the finite speed of temperature wave, the single relaxation time theory of Lord and Shulman is used. Three coupled differential equations in terms of radial displacement, electric potential, and temperature change are obtained. These equations are written in a dimensionless presentation. With the aid of the differential quadrature method (DQM) a time-dependent algebraic system of equations is extracted. The Newmark time marching scheme is applied to trace the temporal evolution of temperature change, electric potential, radial displacement, stresses, and electric displacement. Numerical results demonstrate that radial displacement and temperature waves propagate with finite speed while the electric potential propagates with infinite speed.     

GENERALIZED THERMOELASTICITY OF AN INFINITE BODY WITH A CYLINDRICAL CAVITY AND VARIABLE MATERIAL PROPERTIES

ABSTRACT

The equations of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with temperature-dependent mechanical and thermal properties are established. The modulus of elasticity and the thermal conductivity are taken as linear function of temperature. A problem of an infinite body with a cylindrical cavity has been solved by using Laplace transform techniques. The interior surface of the cavity is subjected to thermal and mechanical shocks. The inverse of the Laplace transform is done numerically using a method based on Fourier expansion techniques. The temperature, the displacement, and the stress distributions are represented graphically. A comparison was made with the results obtained in the case of temperature-independent mechanical and thermal properties.     

ELASTIC–PLASTIC STRESS ANALYSIS OF LAMINATED COMPOSITE BEAMS UNDER LINEAR TEMPERATURE DISTRIBUTION

This study deals with elastic–plastic stress analysis of symmetric laminated composite beams with perfectly clamped ends under linear temperature distribution. The Bernoulli–Euler theory is used during the solution considering infinitesimal small deformations. The composite beam is assumed to be linear strain hardening. The Tsai–Hill theory is used as a yield criterion in the solution. The stacking sequences of the composite beam are chosen as (90°/0°)_s, (30°/?30°)_s, (45°/?45°)_s, (60°/?60°)_s and also (0°)₄ and (90°)₄ in comparison with the composite beam of a single layer in the literature. The results obtained are in good agreement with the literature. The temperature that causes plastic yielding is found to be highest for the (30°/?30°)_s stacking sequence, in order to compare with the others, except for the (0°)₄ orientation. Residual thermal stresses are particularly important because they can increase the strength of the composite or may lead to premature failure. The residual stress components (σ _x ) _r are found to be highest at the upper and lower surfaces. When the plastic region expands further with increased temperature, the residual stress components become highest at the elastic–plastic interface.     

Modelling of creep in friction stir welded copper

Abstract

Copper canisters for storage of nuclear waste will be exposed to creep. The canisters will be closed with friction stir welding (FSW). To describe the creep behaviour of the welds, uniaxial creep tests have been performed. A previously developed fundamental creep model for parent metal is applied to the different weld zones. The differences in microstructure and yield strength between the weld zones are taken into account. Creep strain versus time curves for the weld zones have successfully been predicted without the use of any adjustable parameters. It should be noted that the temperature range of interest of 50–100°C is deep down in the power law break down regime with Norton exponents between 25 and 100. The constitutive equations are used in FEM computations of creep in the canister weldments.     

A MODE-I CRACK PROBLEM FOR AN INFINITE SPACE IN GENERALIZED THERMOELASTICITY

ABSTRACT

In this work, we solve a dynamical problem of an infinite space with a finite linear crack inside the medium. The Fourier and Laplace transform techniques are used. The problem is reduced to the solution of a system of four dual integral equations. The solution of these equations is shown to be equivalent to the solution of a Fredholm integral equation of the first kind. This integral equation is solved numerically using the method of regularization. The inverse Laplace transforms are obtained numerically using a method based on Fourier expansion techniques. Numerical values for the temperature, stress, displacement, and the stress intensity factor are obtained and represented graphically.     

Sensitivity Analysis of Classical Heat Conduction Solutions Applied to Materials Characterization

This paper presents the analysis of classical heat conduction solutions applied to materials characterization. The formulas for parametric derivatives are obtained and illustrated to demonstrate the evolution of the relative sensitivity functions in time. The potential of using both front-surface and rear-surface solutions for determining material thermal properties, sample thickness, and surface heat exchange parameters is discussed. The roots of the well-known transcendent equation for a non-adiabatic plate are approximated in a polynomial form. Some practical applications of the proposed formulas are reported.     

Numerical simulation of the resistance braze welded assembly of a copper Inconel 601 ground electrode and a steel shell

Abstract

The ground electrode of spark plugs are assembled to a steel shell through a resistance braze-welding technique. Two types of currents can be used in that aim: AC or DC. Based on the current type, two different kinds of models were built. The first one is a 3-D magnetodynamic-thermal model, specially suited for AC current. The magnetodynamic and thermal FE analyses are weakly coupled to calculate the temperature distribution during the process. For the second model dedicated to DC currents, the temperature distribution during the process is obtained through a fully coupled 3-D electrokinetic-thermal modeling. The temperature distributions are then used to simulate the mechanical phenomena. The results of the different models are compared. The effects on the welded zone of the frequency (50 Hz and 5000 Hz), the regulation mode (current or voltage), and the spacing between copper and Inconel 601 coating are discussed.