The extended finite element method in thermoelastic fracture mechanics

The extended finite element method (XFEM) is applied to the simulation of thermally stressed, cracked solids. Both thermal and mechanical fields are enriched in the XFEM way in order to represent discontinuous temperature, heat flux, displacement, and traction across the crack surface, as well as singular heat flux and stress at the crack front. Consequently, the cracked thermomechanical problem may be solved on a mesh that is independent of the crack. Either adiabatic or isothermal condition is considered on the crack surface. In the second case, the temperature field is enriched such that it is continuous across the crack but with a discontinuous derivative and the temperature is enforced to the prescribed value by a penalty method. The stress intensity factors are extracted from the XFEM solution by an interaction integral in domain form with no crack face integration. The method is illustrated on several numerical examples (including a curvilinear crack, a propagating crack, and a three‐dimensional crack) and is compared with existing solutions. Copyright © 2007 John Wiley & Sons, Ltd.     

S35C型板坯连续式热处理炉炉温均匀性测试与分析

利用自研的黑匣子炉温测试系统，依据AMS270E《高温测量》设计了大型连续式热处理炉内运动板坯的均匀性测试方案，并基于设计方案对某钢厂S35C型板坯连续式热处理炉进行实际均匀性测试与分析。测试结果表明，自研的黑匣子炉温测试系统能满足高温板坯连续运动条件下的温度均匀性测试要求。板坯入炉后温度迅速上升，并逐渐达到目标温度进入均热阶段，对比均热段数据，板坯各个位置温度都达到指标要求，整体温度均匀性较好，板坯在炉内的热处理温度和时间与规定的工艺设计要求一致。为大型连续炉均匀性和板坯测试提供一种有效的方法。     

Thermal shock in an edge-cracked plate subjected to uniform surface heating

Thermal shock due to sudden surface heating of an edge-cracked plate is examined and compared with the opposite thermal shock condition that is associated with surface cooling. The plate is assumed to be insulated on one face with convective thermal boundary conditions existing on the side of the plate containing the crack. It is shown that surface heating results in compressive transient thermal stresses close to the plate surface which force the crack surfaces together over a certain contact length. The resulting nonlinear crack contact problem is formulated in terms of a singular integral equation and solved numerically. Calculated results include the transient stress intensity factors for various crack lengths at different values of the Biot number. A result of particular interest is the crack length at which the maximum stress intensity factor during heating exceeds the maximum stress intensity factor for cooling with otherwise identical heat transfer conditions.     

有挤压墙面板堆石坝的面板温度应力分析及改善措施研究

该文在综合考虑挤压式边墙、面板、坝体相互作用的基础上开发了面板堆石坝面板温度应力的数值模拟方法并验证了其合理有效性,然后重点分析了挤压式边墙这种结构对于面板堆石坝面板温度应力的影响规律.分别采用沈珠江双屈服面弹塑性模型和清华弹塑性损伤模型描述堆石料和土与结构接触面,结合三维有限元分析方法计算了设置挤压式边墙以及面板与挤...     

Three-dimensional thermal analysis of an infinite solid containing an elliptical surface crack

This paper deals with the thermal problem of an infinite solid with an elliptical insulated surface crack subjected to a uniform heat flow. Using conformal mapping technique, the elliptical crack region is first mapped conformally onto a penny-shaped crack for which the solution on the crack surface is available. The complete solution of the temperature field of the entire solid studied is then obtained by the inverse Fourier transform technique and the singularity of temperature gradient on the crack surface near the crack front can be found. To explore the temperature gradient along and around the crack front further, a three-dimensional finite element model with collapsed quarterpoint singular elements around the crack front is employed. Several examples with various crack aspect ratios are solved analytically and numerically. The influence of the elliptical insulated surface crack on the local intensification of temperature gradient and heat flow is also illustrated.     

Calculation of temperature distribution and thermo-optical effects in double-end-pumped slab laser

The temperature distribution and thermo-optical effects in a double-end-pumped slab laser are investigated analytically. The theoretical model is given by considering heat generation on both sides of an active medium due to pumping. With account for the pump beam divergence and the heat load, the heat conduction equation is solved, and the temperature distribution and thermal effects, such as thermal lensing and thermal stress, are obtained. The results are applied to a typical Nd:YVO₄ laser crystal slab and discussed.     

Performance enhancement of a household refrigerator by addition of latent heat storage

This paper studies the effect of adding a phase change material (PCM) slab on the outside face of a refrigerator evaporator. A dynamic model of the vapour compression cycle including the presence of the phase change material and its experimental validation is presented. The simulation results of the system with PCM show that the addition of thermal inertia globally enhances heat transfer from the evaporator and allows a higher evaporating temperature, which increases the energy efficiency of the system. The energy stored in the PCM is yielded to the refrigerator cell during the off cycle and allows for several hours of continuous operation without power supply.     

The response of a confined gas to a thermal disturbance: rapid boundary heating

Summary An inert compressible gas confined between infinite parallel planar walls is subjected to significant heat addition at the boundaries. The wall temperature is increased during an interval which is scaled by the acoustic time of the container, defined as the passage time of an acoustic wave across the slab. On this time scale heat transfer to the gas occurs in thin conductive boundary layers adjacent to the walls. Temperature increases in these layers cause the gas to expand such that a finite velocity exists at the boundary-layer edge. This mechanical effect, which is like a time-varying piston motion, induces a planar linear acoustic field in the basically adiabatic core of the slab. A spatially homogeneous pressure rise and a bulk velocity field evolve in the core as the result of repeated passage of weak compression waves through the gas. Eventually the thickness of the conduction boundary layers is a significant fraction of the slab width. This occurs on the condition time scale of the slab which is typically a factor of 10⁶ larger than the acoustic time. The further evolution of the thermomechanical response of the gas is dominated by a conductive-convective balance throughout the slab. The evolving spatially-dependent temperature distribution is affected by the homogeneous pressure rise (compressive heating) and by the deformation process occurring in the confined gas. Superimposed on this relatively slowly-varying conduction-dominated field is an acoustic field which is the descendent of that generated on the shorter time scale. The short-time-scale acoustic waves are distorted as they propagate through a slowly-varying inhomogeneous gas in a finite space. Solutions are developed in terms of asymptotic expansions valid when the ratio of the acoustic to conduction time scales is small. The results provide an explicit expression for the piston analogy of boundary heat addition.     

Wave propagation in cracked elastic slabs and half-space domains—TBEM and MFS approaches

In this paper, the traction boundary element method (TBEM) and the method of fundamental solutions (MFS), formulated in the frequency domain, are used to evaluate the 3D scattered wave field generated by 2D empty cracks embedded in an elastic slab and a half-space. Both models overcome the thin-body difficulty posed when the classical BEM is applied.The crack exhibits arbitrary cross section geometry and null thickness. In neither model are the horizontal formation surfaces discretized, since appropriate fundamental solutions are used to take them into consideration.The TBEM models the crack as a single line. The singular and hypersingular integrals that arise during the TBEM model's implementation are computed analytically, which overcomes one of the drawbacks of this formulation. The results provided by the proposed TBEM model are verified against responses provided by the classical BEM models derived for the case of an empty cylindrical circular cavity.The MFS solution is approximated in terms of a linear combination of fundamental solutions, generated by a set of virtual sources simulating the scattered field produced by the crack, using a domain decomposition technique. To avoid singularities, these fictitious sources are not placed close to the crack, and the use of an enriched function to model the displacement jumps across the crack is unnecessary.The performances of the proposed models are compared and their limitations are shown by solving the case of a C-shaped crack embedded in an elastic slab and a half-space domain.The applicability of these formulations is illustrated by presenting snapshots from computer animations in the time domain for an elastic slab containing an S-shaped crack, after applying an inverse Fourier transformation to the frequency domain computations.     

On the singularity of temperature gradient near an inclined crack terminating at bimaterial interface

This paper deals with the singularity of temperature gradient near an inclined crack terminating at a bimaterial interface. The temperature field is solved by considering the continuity of temperature and heat flux at the interface and appropriate thermal boundary conditions on crack surfaces. The singularity of temperature gradient around the crack tip is then studied for the cases for which the temperature on crack surfaces is prescribed or crack surfaces are insulated. It is found that, unlike the oscillatory singularity of the stress field, no oscillatory character near the crack tip is observed for these problems. The dependence of the singularity of temperature gradient on the inclined angle of crack and thermal conductivity ratio of two dissimilar media is also shown.     

Temperature fields near a running crack tip

Near a running crack tip, the plastic work rate is high. According to the theory of irreversible thermodynamics, the plastic work will be almost completely converted into heat which may lead to high temperature rise at the running crack tip. The plastic zone is regarded as the zone of the heat source, and the plastic work rate as the strength of the heat source. In this paper, the plastic work rate is derived from the solution of stress and strain fields obtained by Chitaley and McClintock[1] for a steady state crack growth under anti-plane shear in an elastic perfectly-plastic material. The dependence of the thermal conductivity on temperature has been considered and a non-linear model for temperature fields has been proposed. The numerical results for glass have been given and compared with other papers.     

A thermal-medium crack model

In analyzing the fracture behavior of a cracked thermoelastic material, of much importance are the effects of thermal loadings on the crack growth. Under the consideration of a medium in an opening crack, a thermal-medium crack model is proposed in this paper. The heat flux at the crack surfaces is assumed to depend on the jumps of the temperature and the elastic displacement across the crack. The thermally permeable and impermeable crack models are the limiting cases of a thermal-medium one. The proposed crack model is applied to solve the problem of a Griffith crack in a transversely isotropic material under thermal and mechanical loadings. Using two introduced displacement functions and the Fourier transform technique, the thermoelastic field and the elastic T-stress are determined in explicit forms by using elementary functions. Numerical results are presented to show the effects of the thermal conductivity inside a crack and applied mechanical loadings on the heat flux at the crack faces, the jumps of temperature across the crack and mode-II stress intensity factor in graphics respectively. The obtained results reveal that the mode-II stress intensity factor for a thermal-medium crack in a thermoelastic material depends not only on applied thermal loadings but also on applied mechanical ones.     

Mixed boundary value problem of an infinite thick elastic slab containing a flat annular crack under torsion

In the present paper we consider the problem of determining the stress distribution in an infinitely long isotropic, compressible, homogeneous elastic slab containing a flat annular crack which is opened by internal shear stress. The faces of the slab are assumed to be stress free and the crack is located in the middle plane of the slab. The problem is formulated in triple integral equations which reduce to an infinite system of simultaneous equations, which are solved numerically.     

含中心裂纹正交各向异性板均匀热流作用下的温度场解析解

研究了含中心裂纹的正交各向异性板,在远场均匀热流作用下温度场的分布。考虑了两种温度边界条件,即裂纹表面分别维持恒定的温度与恒定的温度梯度,包括了绝热裂纹与导热裂纹等情况。采用各向异性热弹性理论与复变函数理论,得出了精确满足给定边界条件的温度场的全场解析解。算例中的温度场分布数值结果,出现了一些新的现象,值得进一步进行深入理论探讨与实验观测的证实。     

Stress intensity factors evaluation for through-transverse crack in slab track system under vehicle dynamic load

The stress intensity factors (SIFs) for through-transverse crack in the China Railway Track System (CRTS II) slab track system under vehicle dynamic load are evaluated in this paper. A coupled dynamic model of a half-vehicle and the slab track is presented in which the half-vehicle is treated as a 18-degree-of-freedom multi-body system. The slab track is modeled as two continuous Bernoulli–Euler beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The model is applied to calculate the vertical and lateral dynamic wheel–rail forces. A three-dimensional finite element model of the slab track system is then established in which the through-transverse crack at the bottom of concrete base is created by using extended finite element method (XFEM). The wheel–rail forces obtained by the vehicle-track dynamics calculation are utilized as the inputs to finite element model, and then the values of dynamic SIFs at the crack-tip are extracted from the XFEM solution by domain based interaction integral approach. The influences of subgrade modulus, crack length, crack angle, friction coefficient between cracked surfaces, and friction coefficient between faces of concrete base and subgrade on dynamic SIFs are investigated in detail. The analysis indicates that the subgrade modulus, crack length and crack angle have great effects on dynamic SIFs at the crack-tip, while both of the friction coefficients have negligible influences on variations of dynamic SIFs. Also the statistical characteristics of varying SIFs due to random wheel–rail forces are studied and results reveal that the distributions of dynamic SIFs follow an approximately Gaussian distribution with different mean values and standard deviations. The numerical results obtained are very useful in the maintenance of the slab track system.     

General solution for arc crack problem in thermoelastic medium

A problem of a circular arc-shaped crack in an infinite plate under the thermal loading is solved by using the complex variable function and the integral equation method. General solution for arbitrary heat flux along the crack face is obtained. For some particular cases, for example, the constant heat flux case and remote heat flux case, a closed form solution is obtained. The solution technique is effective in derivation and compact in form.     

Estimation of the risk for early thermal cracking for SCC containing fly ash

Cracking of concrete must be avoided during the hardening phase in order to minimize the risk of durability problems in the future, such as corrosion of the reinforcement, water tightness and damages due to frost. Estimation of the risk of early age cracking requires knowledge of the combined effects from temperature development and mechanical behaviour during the hydration. In the present paper, the influence of fly ash on the young concrete behaviour has been investigated. The concrete is based on a Swedish cement aimed for civil engineering structures, and the fly ash is of class F. A comparison of crack risks between concrete containing fly ash in different amounts with concrete without fly ash is presented. Also a previously tested concrete containing limestone filler is considered. The fly ash was added to replace a part of the aggregate, which gives a higher heat evolution. However, a numerical stress analysis showed that the risk for early age through cracking for a typical civil engineering structure is significantly decreased in the mixes containing fly ash. The denotation typical civil engineering structure is used here for concrete structures such as tunnels, bridges, and ramps of common cross-section dimensions. In the case of fly ash added to concrete by a partial replacement of cement, the crack risk will probably be further decreased. For a self-balancing structure of young concrete there is no restraint from adjacent structures, and the temperature and moisture gradients within the young concrete cause self-stresses governed by equilibrium with zero external forces for any cut. The estimated risk for surface cracking on a self-balancing wall or slab was not improved by an addition of fly ash. It is probably an effect of the increased heat development, which most likely counteracts the positive effect of the increased early age creep for concrete containing fly ash. If the heat evolution decreases when cement is partly replaced with fly ash, the use of fly ash might reduce the risk of surface cracks.     

Temperature distribution and heat flow around a crack of arbitrary orientation in a functionally graded medium

This paper investigates the heat transfer problem of an infinite functionally graded medium containing an arbitrarily oriented crack under uniform remote heat flux. In the mathematical treatment the crack is approximated as a perfectly insulating cut. By using Fourier transformation, the mixed boundary value problem is reduced to a Cauchy-type singular integral equation for an unknown density function. The singular integral equation is then solved by representing the density function with a Chebyshev polynomial-based series and solving the resulting linear equation using a collocation technique. The temperature field in the vicinity of the crack and the crack-tip heat flux intensity factor are presented to quantify the effect of crack orientation and grading inhomogeneity on the heat flow around the crack.     

Microwave heating of materials with impurities

The microwave heating of materials is important in many industrial processes. For example, it is used for the smelting of metals and the sintering of ceramics. Hot-spots (localised areas of high temperature) can develop in the material being heated or in the microwave oven itself, with disastrous consequences. Impurities in the material or in a component of the microwave oven can have different electromagnetic and thermal properties to the surrounding material. Different rates of heating occur at these sites, which gives rise to differential heating, which can lead to the generation of hot-spots. The generation of hot-spots by this mechanism is considered for a finite one-dimensional slab with a single impurity at its centre. A fixed-temperature boundary condition is applied at both ends of the slab and one end of the slab is irradiated by microwaves of constant amplitude. The heat absorption at the impurity is assumed to have a power-law dependence on temperature (hence hot-spot generation can occur via thermal runaway). Depending on the electrical and thermal properties of the material there are two possibilities; either a hot-spot occurs or a steady-state solution occurs due to a balance between heat absorption in the material and heat loss through the boundaries. These steady-state solutions are found for both linear and non-linear thermal absorptivity and constant and decaying electric-field amplitude. If possible the region of parameter space in which they occur (in the rest of the parameter space hot-spots occur) is also found. In addition, numerical solutions are developed to verify the steady-state solutions and to investigate cases where analytical solutions are difficult to derive, such as for materials with multiple impurities.     

Evaluating the heat energy dissipated in a small volume surrounding the tip of a fatigue crack

Fatigue crack initiation and propagation involve plastic strains that require some work to be done on the material. Most part of this irreversible energy is dissipated as heat and consequently the material temperature increases. The heat being an indicator of the intense plastic strains occurring at the tip of a propagating fatigue crack, the hypothesis is formed that it can be used to assess the fatigue damage accumulation rate of cracked components. Moreover, the heat energy at the crack tip is averaged according to Neuber’s finite particle concept. The aim of the present paper is to present the theoretical framework and the corresponding experimental technique to evaluate the heat energy dissipated in a structural volume surrounding the crack tip. The shape and size of the structural volume have been assumed according to the literature, even though the definition of the structural volume size of the analysed material in a fatigue sense is not the scope of the present paper. The proposed experimental technique to evaluate the averaged heat energy is based on the radial temperature profiles measured around the crack tip by means of an infrared camera. The temperature fields measured within few millimetres from the crack tip have been compared successfully with existing analytical solutions.