含界面裂纹圆形夹杂的十二次对称二维准晶热应力分析

针对点热源作用下,无限大十二次对称二维准晶基体和圆形弹性夹杂界面之间含多条裂纹的问题进行了研究。基于复变函数分区全纯理论、留数定理、广义 Liouville 定理、Riemann-Schwarz 解析延拓定理及复应力函数奇性主部分析方法,获得了集中热源作用于准晶基体内任意一点时,准晶基体和圆形弹性夹杂内外温度场、声子场热应力的一般复势解。由此获得了含一条界面裂纹和两条界面裂纹时温度场以及声子场热应力的封闭形式解答,将所得结果与已有结果进行了对比,验证了该方法的有效性。最后通过数值算例分析了夹杂半径、点热源强度及裂纹角度对热应力和裂纹尖端热应力强度因子的影响规律。结果表明：随着热源强度的增大,裂纹尖端的声子场热应力也逐渐增大;随着裂纹角度的增大,裂纹尖端的声子场热应力强度因子变大;随着半径的增大,热应力强度因子的变化趋势越来越明显,并且取得的峰值越高,即裂纹角度和夹杂半径的增加,促进了裂纹的扩展。这些结论为准晶材料的结构设计和使用提供了科学依据。     

Analysis of temperature distribution near the crack tip under constant amplitude loading

An analytical/numerical method has been developed to find the temperature rise near the crack tip under fatigue loading. The cyclic plastic zone ahead of the crack tip is assumed to be the shape of the source of heat generation and some fraction of plastic work done in cyclic plastic zone as heat generation. Plastic work during fatigue load was found by obtaining stress and strain distribution within the plastic zone by Hutchinson, Rice and Rosengren (HRR) crack tip singularity fields applied to small scale yielding on the cyclic stress strain curve. A two‐dimensional conduction heat transfer equation, in moving co‐ordinates, was used to obtain temperature distribution around the crack tip. Temperature rise was found to be a function of frequency of loading, applied stress intensity factor and thermal properties of the material. A power–law relation was found between the rise in temperature at a fixed point near the crack tip and range of stress intensity factor.     

Investigations on the stress intensity factor field for unstable dynamic crack growth

In this study, the unstable dynamic crack propagation due to static loading in an elastic material is analyzed for both antiplane and inplane conditions. Of particular concern is the investigation of limitations on the assumption that the stress intensity factor field is fully established over a region of given size near the tip of a growing crack. The transient analysis of the stress for a material particle at a small fixed distance from the moving crack tip is examined in detail. Some estimations are made of the time required for the stress at a point near the moving crack tip to reach the value it would have if the stress field were actually given by the near tip stress intensity factor field. In addition, a simple formulation obtained from the equivalent static problem is proposed which can be used as a good approximation to the associated complicated dynamic transient problem.     

Generalized stress intensity factors due to steady and transient thermal loads with applications to welded joints

This paper deals with the elastic and plastic stress fields induced by thermal loads in the vicinity of sharp V‐notch tips in plates. Under the hypothesis of steady‐state heat transfer and plane‐strain conditions, the thermal and mechanical problem requires the numerical solution of an ordinary differential equation (ODE) system, obtained by extending the ‘stress function approach’. The intensity of the stress distributions ahead of V‐notch tips can be expressed in terms of thermal notch stress intensity factors (thermal NSIFs), as for external loads. The problem becomes much more demanding in the presence of transient thermal loads. The residual asymptotic stress distribution arising from the solidification of a fusion zone during an arc welding process is obtained by considering different boundary conditions. An aluminium butt‐welded joint is analysed after having modelled the weld toe region as a sharp V‐notch. A finite element (FE) simulation of the welding process is carried out by means of SYSWELD code (version 2004.1) modelling the arc welding torch by means of Goldak's source. Near the weld toe, the intensity of the residual stress field is given in terms of elastic or elastic—plastic generalized NSIFs.     

Investigations on welding residual stresses in penetration nozzles by means of 3D thermal elastic plastic FEM and experiment

Recent discoveries of stress corrosion cracking (SCC) in weldments including penetration nozzles at pressurized water reactors (PWRs) and boiling water reactors (BWRs) have raised concerns about safety and integrity of plant components. It is well known that welding residual stress is an important factor resulting in SCC in weldments. In the present work, both experimental method and numerical simulation technology are used to investigate the characteristics of welding residual stress distribution in penetration nozzles welded by multi-pass J-groove joint. An experimental mock-up is fabricated to measure welding residual stress at first. In the experiment, each weld pass is performed using a semi-circle balanced welding procedure. Then, a corresponding finite element models with considering moving heat source, deposition sequence, inter-pass temperature, temperature-dependent thermal and mechanical properties, strain hardening and annealing effect is developed to simulate welding temperature and residual stress fields. The simulation results predicted by the 3D model are generally in good agreement with the measurements. Meanwhile, to clarify the influence of deposition sequence on the welding residual stress, the welding residual stress field in the same geometrical model induced by a continuous welding procedure is also calculated. Finally, the influence of a joint oblique angle on welding residual stress is investigated numerically. The numerical results suggest that both deposition sequence and oblique angles have effect on welding residual stress distribution.     

On a thermo-mechanical effect and criterion of crack propagation

A thermo-mechanical effect from partial conversion of fracture work into heat energy during crack propagation is considered with a simple mathematical model. It is assumed that the heat production zone in the vicinity of the crack tip is very small. Thus, the crack propagation process can be viewed as propagation of the crack in elastic material with a point thermal heat source fixed at the tip of the crack. This thermal heat source generates its own temperature and stress fields around the crack tip. As shown in this paper it also generates a negative stress intensity factor that specifies fracture mode I and has to be accounted for in the energetic fracture criterion. The model developed may help to explain many experimental observations such as the increase in the specific surface energy that accompanies an increase in the crack speed and why fracture mode I has a special role in crack propagation phenomena.     

Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Plastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.     

Particle-size dependence of thermoelastic stress intensity factor in two-phase materials

The stress intensity factor is estimated for an annular crack originating from the particle-matrix interface in residual stress fields associated with a spherical particle of lower thermal expansion than that of the matrix. It is shown that the stress intensity factor is a function of particle size and pre-existing crack length. Spontaneous matrix cracking will occur when the particle size exceeds a critical value,R _c. Close agreement between the calculated and experimental values forR _c is obtained. The analysis is applicable to all particulate composites where there is volume increase of a particle induced either by phase transformation or thermal expansion mismatch.     

On singular stress at the crack tip of a thick plate under in-plane loading

By superposition of three asymptotic solutions, which collectively satisfy all the equilibrium and compatibility equations as well as boundary conditions, the three-dimensional crack tip stresses of a thick plate with a through-the-thickness cut are shown to be of square root singularity throughout the thickness. The near tip deformation is shown to be plane strain with stress intensity factor changing in the thickness direction. All components of the singular stresses vanish on plate surfaces. The profile of the stress intensity factor in the thickness direction cannot be determined by the asymptotic analysis alone.     

Crack redirection with thermal secondary loading

In the current paper crack redirection due to a strategic placing of a heat source in the vicinity of a crack tip is studied. Analysis suggests that for PMMA and considered temperature range the only factor responsible for the deviation of crack trajectory is thermal stress. The simulation of crack growth in PMMA under external tension and secondary heat loading shows that a moving heat source in the vicinity of a crack tip can serve as a pointer for the crack trajectory. In highly conductive materials, redirection can be possibly effected with low-power thermal dipoles.     

Prediction of welding distortion in butt joint of thin plates

This paper investigates distortions and residual stresses induced in butt joint of thin plates using Metal Inert Gas welding. A moving distributed heat source model based on Goldak’s double-ellipsoid heat flux distribution is implemented in Finite Element (FE) simulation of the welding process. Thermo-elastic–plastic FE methods are applied to modelling thermal and mechanical behaviour of the welded plate during the welding process. Prediction of temperature variations, fusion zone and heat affected zone as well as longitudinal and transverse shrinkage, angular distortion, and residual stress is obtained. FE analysis results of welding distortions are compared with existing experimental and empirical predictions. The welding speed and plate thickness are shown to have considerable effects on welding distortions and residual stresses.     

Influences of heat source model on welding residual stress and distortion in a multi-pass J-groove joint

Welding mechanical behaviors including residual stress and distortion are highly non-linear phenomena in nature. When numerical simulation methods such as thermal elastic plastic finite element method (FEM) are used to quantitatively predict welding residual stress and distortion, a long computational time is required especially for multi-pass joints. In real engineering structures, many weldments have large dimensions and complex shapes, and they are usually assembled by a multi-pass welding process. Therefore, it is necessary to develop time-effective computational approaches for practice engineering analysis. In this study, a method based on variable length heat sources was proposed for the analysis of thermo-mechanical behaviors for multi-pass joints. The welding residual stress field in a dissimilar metal J-groove joint with axis-symmetric geometrical shape, which was performed by a semi-circle balanced welding process, was investigated using the proposed method. The simulation results were compared with the measured data as well as the simulation results computed by a moving heat source. Meanwhile, the instantaneous line heat source was also employed to estimate the welding residual stresses in the same joint in an extreme case. The influences of heat source model (type) on welding residual stress and distortion were discussed.     

Temperature, stress and microstructure in 10Ni5CrMoV steel plate during air–arc cutting process

Although the air–arc cutting process has been widely used in the material processing engineering, little information about temperature, stress and microstructure in the plate air–arc cut is known. A three-dimensional finite element model including the material removal and the thermal effect of the arc is developed to study the temperature and stress fields of 10Ni5CrMoV steel plate during air–arc cutting process in this paper. The microstructures and micro-mechanical properties of the parts near the groove especially in heat affected zone (HAZ) are studied by experimental methods, and they also can be used as a method to verify the numerical results. Effects of stresses induced by air–arc cutting process on the initial residual stress fields of base materials are also researched. The results show that the cooling velocity in HAZ is higher than the one of the welding process for the same base material, and the zone with high temperature is very narrow, which means that the temperature gradients near the groove are very steep during the air–arc cutting process; this special temperature field depresses multiphase transformations and coarse microstructures. The evolution of the stress during the air–arc cutting is described, and the numerical results indicate that the characteristics of the evolution of stresses and the residual stresses distribution in the plate in air–arc cutting process seem to be similar to the ones of the butt welding for flat plates. The influences of air–arc cutting process on initial stress fields present two aspects: thermal effect and material removal effect, and the former plays a primary role. Both numerical temperature and stress fields are compared with the experimental ones. It is very important for researchers to clarify the temperatures, stresses and microstructures in the plate during air–arc cutting process, and understand fully the mechanism of influences of air–arc cutting on the plate; it is also very valuable for engineering application of the air–arc cutting process.     

CORRELATION BETWEEN HYDROGEN INDUCED CRACKING INITIATION SITES AND CRITICAL STRESS INTENSITY FACTORS

Hydrogen induced cracking (HIC) initiation sites and their correlation with the critical stress intensity factors of hydrogen charged specimens were studied under combined I/II mode loading. Two series of tests, is. constant load (CL) tests and slow strain rate (SSR) tests, were carried out. Experimental results showed that in CL tests, irrespective of the ratio KIJKl, the HIC initiation sites always correspond to the point of maximum hydrostatic stress; which is located some distance ahead of the notch tip. However, for SSRT tests, when K₁₁/K₁> 1, HIC started at the notch tip which corresponds to the point of maximum equivalent plastic strain. When K₁₁/K₁<1 in SSR tests, HIC occurred initially some distance ahead of the notch tip. The relationship between the critical stress intensity factor for HIC and K₁₁/K₁ was shown to be different for the two types of test. Multiple effects of stress and strain on hydrogen redistribution and hence on HIC initiation sites, as well as critical stress intensity factors, are discussed.     

Micro-mechanical analysis and TEM study of crack initiation in dislocation free zone

Dislocation emission, dislocation-free zone (DFZ) formation and crack initiation in the DFZ and/or at the crack tip were analyzed by micromechanics. The results show that a DFZ is formed after dislocation emission under constant load. The DFZ size decreases with increase in the applied stress intensity factor K _Ia or lattice friction stress _f. There are two stress peaks ahead of the crack tip. The first one is located at the blunt crack tip and the second one in the DFZ. With increasing in the applied stress intensity factor K _Ia, the peak stress at the crack tip may decrease while the peak stress in the DFZ increases monotonically. Microcrack will initiate when the peak stress is equal to the cohesive strength. In situ tensile tests in a transmission electron microscope (TEM) show that microcrack initiates in DFZ or/and at a blunt crack tip after dislocation emitting and DFZ formation.     

Transient thermal contact problem for axial crack in a hollow circular cylinder

The transient behavior of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated. It is shown that surface heating may induce compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, this problem can be divided into two parts and solved by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without a crack are obtained by finite element/implicit time integration method. The calculated temperature and thermal stress distributions are in good agreement with the values predicted by the analytical method. Secondly, the opposite senses of the stress distributions along the cracked surfaces, which are obtained previously, are treated as the traction boundary conditions, and the contact length and contact pressure of the real cracked cylinder are obtained by a modified elimination finite element scheme. In this scheme, the concepts of contact-node-pairs' penetration, contact-double-forces and compliance matrix are introduced. The calculated results indicate that the contact length ratio becomes smaller when the crack length ratio increases, and becomes larger as the radius ratio increases. Finally, the normalized stress intensity factor for the crack tip of the cylinder is obtained. It is shown that the larger the crack length ratio the higher the stress intensity factor.     

Estimating the importance of cyclic thermal loads in thermo-mechanical fatigue

A method for evaluating the effect of cyclic thermal loading on crack tip stress fields is developed. In its development, advantage is taken of the periodic nature of fatigue loading and only harmonic loadings are evaluated. Formulating the problem in this way permits the extraction of time as an explicit variable and replaces its role with a dependence on the frequency of the thermal loading. The means for evaluating the effect of periodic loadings on crack tip stress fields is the stress intensity factor which is calculated from numerically defined stress and displacement fields using a path independent integral. Results obtained indicate that stress intensity factors of cracked components exposed to thermal fatigue conditions have a significant dependence on the frequency of the thermal cycle and the crack geometry. Numerical estimates for mode I thermal stress intensity have been obtained using thermal fatigue test data for a titanium alloy and can be as high as 25 percent of the critical mode I mechanical stress intensity.     

初始应力对三维光学轮廓法测试焊接接头残余应力的影响

目的研究不同初始应力状态下,三维光学轮廓法测试焊接接头残余应力的变化规律。方法采用MIG焊分别对供货态与去应力退火态试板进行多层多道焊,焊后试板经慢走丝切割,经三维光学测量技术扫描切割面轮廓,将所得轮廓数据经所建立的数据处理平台处理,将其结果作为有限元计算的边界条件,经应力反算得到残余应力分布。最后再进行有限元模拟,计算焊接接头残余应力。结果含初始应力、去应力退火和数值模拟的焊缝中心均为拉应力区,最大拉应力分别为480, 450, 523 MPa,且都位于焊缝根部区域。三者试板两侧为压应力区域,最大压应力分别为380, 280, 157 MPa,三者数值相差较大。结论将含有初始残余应力试板、退火处理试板与数值模拟结果的残余应力分布进行对比,可以发现三者在焊缝中心处的残余应力分布较为一致,但沿着焊缝向两侧的区域内,应力差别逐渐变大。主要原因为焊接热循环温度高于金属再结晶温度时可以消除部分残余应力,而温度循环较低时对应力消除不明显,导致实验结果相差较大。