Neutron diffraction and finite element analysis of quenching residual stress of GH4169 super alloy

The quenching process is indispensable for manufacturing the superalloys. However, high residual stress is inevitably induced by the large heat gradient, which influences the mechanical properties of the alloys. Therefore, it is of great significance to accurately characterize the internal residual stress of the super alloy and establish an effective finite element modeling. The quench- induced residual stresses of GH4169 super alloy were measured using neutron diffraction stress instrument. The results show that the center of the workpiece is subjected to tensile stress in three directions (hoop, radial and axial), which is about 400MPa. The rims of workpiece are subjected to compressive stress in one or two directions (hoop or axial), which is from -300MPa to -400MPa. The temperature and strain/stress fields of the GH4169 super alloy workpiece during quenching process were simulated by a 3D finite element model. The calculated residual strain/stress at the center and rim of the workpiece are compared to those by neutron diffraction, which shows good correspondence. These data provide reliable evidences to the formation of the residual stress during quenching.     

预热对铍环激光束钎焊过程的影响研究

研究预热对铍环激光束钎焊过程温度场和应力场分布的影响。采用轴对称模型和热力解耦的有限元方法，并假定沉积到钎缝表面的激光束能量为Gauss分布，预热通过在焊接加热前添加一个能量密度低、有效加热半径大的单独工况实现。结果表明，预热使镀环钎缝外表面焊接最高温度增加，温度梯度减小，但焊深明显增加；采用预热工况焊接后，钎缝附近塑性变形区焊接残余应力明显减小，而热影响区残余应力增大。从整体分布来看，预热使铍环外表面焊接残余应力分布均匀化。对铍环外表面钎缝附近焊接残余应力进行X射线应力测试，并与有限元分析结果对比，二者应力变化趋势基本一致。     

Antiplane (SH) Waves Diffraction by a Semicircular Cylindrical Hill Revisited: An Improved Analytic Wave Series Solution

An improved accurate closed-form wave function analytic solution of two-dimensional scattering and diffraction of antiplane SH waves by a semicircular cylindrical hill on an elastic half space is presented. In the previous solution, stress and displacement residual auxiliary functions were defined at the circular interface above and below the circular hill. The method of weighted residues (moment method) was used to solve for the unknown scattered and transmitted waves by requiring each term of Fourier series expansion of these auxiliary residual functions to vanish. It was found that the stress residual amplitudes on both (left and right) rims of the hill (ideally should be zero) are not numerically insignificant, irrespective of how many terms used. It was pointed out that the shear stress at the rim is infinite, and that the stress auxiliary function is discontinuous at both rims of the hill, exhibiting a problem for the numerical solution that is more complicated than Gibbs’ phenomenon. The problem with the overshoot of the stress residual amplitudes at the rim was most likely numerical. In this paper, all displacement and stress waves were expressed as cosine functions, and the solution of the circular hill problem was reformulated in this paper, and, for the solution to be correct, the computed stress and displacement residual amplitudes were shown to be numerically negligible everywhere, including those at both rims of the hill. Displacements at higher frequencies are also computed.     

常温下局部加载拉应力对柱壳应力场分布的影响

研究采用有限元模拟技术,考察常温局部加载条件下,加载宽度和试样尺寸对柱壳应力场分布的影响,揭示应力场的变化规律及机理.在常温下,柱壳结构局部受轴向外载拉伸时,随结构体长度的增加,在距加载区越远的横截面上应力分布越均匀;随加载宽度的增加,在结构体的中截面上应力最大值逐渐增加.当外加载荷大小、加载宽度及结构体长度相同时,柱壳结构中截面上拉应力最大值大于平板.因此可以预见,对于应用局部加载降低结构体焊接残余应力,柱壳结构要比平板结构效果更好.     

The effect of residual strain on the diastolic function of the left ventricle as predicted by a structural model

The unloaded heart is not stress-free. It is subjected to residual stress and strain. Their extent and influence on the global performance of the left ventricle and on local phenomena in the ventricular wall are studied by model simulation. The analysis focuses on the equatorial region of the ventricle, with an approximate thick-walled cylindrical geometry. The in vivo myocardium is considered to be incompressible, consisting of fibers embedded in a fluid matrix, with transmurally varying anisotropic microstructure in accordance with morphological characteristics. The results show that residual strain is transmurally distributed with a pattern and magnitude which agree well with measurements. The calculated residual strains are within mean +/- one standard deviation of the measured ones. Their magnitude was found to increase with increasing opening angle and with increasing wall thickness. The residual strain was found to have several effects on ventricular function: At volumes higher than the reference one it gives rise to more uniform transmural distributions of stress and intramyocardial pressure; it causes about 50% increase in the ventricular compliance at high volumes and doubles the suction of atrial blood at low volumes, thus facilitating the diastolic filling. In addition, residual strains cause bias of in vivo measured strains from their true values. This may significantly affect physiological interpretation of measured ventricular deformations. In conclusion, the present structural analysis predicts that residual strain has favorable effect on left-ventricular diastolic performance, and gives rise to more uniform ventricular stress distribution.     

Spectral factors in the perception of vowel quantity in Icelandic

The aim of this study was to clarify the effect of heating rate on the development of both transient and residual stresses in investment molds. Solid, cylindrical, gypsum-based molds were modeled and theoretical calculations made of temperature distributions with a constant heating rate. These calculations used experimental thermal diffusivity data obtained with a laser flash method. The simulations calculated transient thermal stresses during heating and at the end of heating for two surface conditions: an unrestricted surface, and a surface restricted by a casting ring. The simulation model developed nonuniform strains and stresses at casting temperature; tangential stress was compressive at the surface and tensile at the mid-point for the unrestricted surface model. The surface restricted model developed compressive tangential stresses throughout the mold at the casting temperature. This resulted in significant thermal strain differences compared to the magnitudes of expansion of the mold due to heating.     

数值模拟在镁合金焊接接头深冷处理中的应用

利用所建立的有限元模型,对焊接接头进行深冷处理前后的温度场分析,再把模型转化成结构单元进行应力应变场分析。计算结果表明:深冷处理后,受焊接热源影响的焊缝及附近区域横向残余应力和纵向残余应力均增大,距焊缝较远的母材区产生了预压应力;深冷处理后,横向和纵向残余变形均减小。     

Effect of thermal residual stresses on fatigue crack opening and propagation behavior in an Al/SiC p metal matrix composite

The effects of a thermal residual stress field on fatigue crack growth in a silicon carbide particle-reinforced aluminum alloy have been measured. Stress fields were introduced into plates of material by means of a quench from a solution heat-treatment temperature. Measurements using neutron diffraction have shown that this introduces an approximately parabolic stress field into the plates, varying from compressive at the surfaces to tensile in the center. Long fatigue cracks were grown in specimens cut from as-quenched plates and in specimens which were given a stress-relieving overaging heat treatment prior to testing. Crack closure levels for these cracks were determined as a function of the position of the crack tip in the residual stress field, and these are shown to differ between as-quenched and stress-relieved samples. By monitoring the compliance of the specimens during fatigue cycling, the degree to which the residual stresses close the crack has been evaluated. formerly Research Student, Department of Materials Science and Metallurgy, University of Cambridge formerly Lecturer, Department of Materials Science and Metallurgy, University of Cambridge This article is based on a presentation made in the symposium entitled “Creep and Fatigue in Metal Matrix Composites” at the 1994 TMS/ASM Spring meeting, held February 28–March 3, 1994, in San Francisco, California, under the auspices of the Joint TMS-SMD/ASM-MSD Composite Materials Committee.     

Residual stresses in a welded superalloy disc: Characterization using synchrotron diffraction and numerical process modeling

The residual stress state in an electron-beam welded assembly of IN718 nickel-based superalloy has been studied both experimentally and using computer modeling. Diffraction measurements were made at the European Synchrotron Radiation Facility (ESRF), using the ID11 beamline. The assembly consisted of a 1.75-mm-thick web of rolled IN718 sheet, welded between two 14-mm-thick circular forgings. Four radial scans each of 400 measuring points were made across the web at 90-deg intervals. Diffraction patterns were recorded using a charge-coupled device (CCD) detector, which enabled the collection of information from several diffraction peaks and, thus, the determination of in-plane lattice strains; the macroscopic residual strain and stress fields were then estimated using appropriate values of the diffraction elastic constants. The experimental results were compared with the predictions from a sequentially coupled thermal-mechanical model based upon the finite-element (FE) method. The agreement between the experimental data and the results from the model is reasonable. It is shown that the residual strain/stress field is strongly influenced by the constraint imposed by the geometry of the assembly, i.e., by the inner and outer forgings, and that, as a result, the web is in a state of biaxial tension. The FE model predicts that a steady state is reached during welding and, thus, that there are systematic errors associated with the strain scanning measurements. These are considered to arise from the uncertainty associated with the positioning of the assembly and a sensitivity analysis for this effect is presented.     

Kinetics of static strain aging after temper rolling of low carbon steel

Abstract

In this study, static strain aging behaviour of cold rolled steel strips was considered with emphasis on the distribution of residual hydrostatic stress developed during temper rolling. In order to assess residual stress distribution produced by the temper rolling, a three-dimensional model was first employed. Then, samples were rolled at a reduction of 4% under single and double pass rolling programmes and the kinetics of static strain aging phenomenon as well as the required activation energies were then evaluated using hardness and tensile tests on the deformed samples. Considering the predicted residual hydrostatic stress distribution, it was found that tensile hydrostatic stresses promote the kinetics of the static strain aging process and alter the activation energy required for the phenomenon. In addition, it was revealed that different positions of the rolled steel show different aging behaviour owing to non-uniform distribution of residual stresses after temper rolling.     

As-Cast Residual Stresses in an Aluminum Alloy AA6063 Billet: Neutron Diffraction Measurements and Finite Element Modeling

The presence of thermally induced residual stresses, created during the industrial direct chill (DC) casting process of aluminum alloys, can cause both significant safety concerns and the formation of defects during downstream processing. Although numerical models have been previously developed to compute these residual stresses, most of the computations have been validated only against measured surface distortions. Recently, the variation in residual elastic strains in the steady-state regime of casting has been measured as a function of radial position using neutron diffraction (ND) in an AA6063 grain-refined cylindrical billet. In the present study, these measurements are used to show that a well-designed thermomechanical finite element (FE) process model can reproduce relatively well the experimental results. A sensitivity analysis is then carried out to determine the relative effect of the various mechanical parameters when computing the as-cast residual stresses in a cylindrical billet. Two model parameters have been investigated: the temperature when the alloy starts to thermally contract and the plasticity behavior. It is shown that the mechanical properties at low temperatures have a much larger influence on the residual stresses than those at high temperatures.     

基于平面弹性复变方法的冷轧带钢分布位错-残余应力模型

为揭示冷轧带钢可见浪形的形成机理,通过实测残余应力值计算分布位错,提出分布位错-残余应力模型.利用平面弹性复变方法计算弹性平板中一条带有典型分布位错的直线粘接边界所产生的应力场,分析该应力场的特点及多条互相平行的带有分布位错的直线粘接边界所产生应力场间的相互影响.同时结合实测数据,给出实际分布位错的计算结果,其对应的残余应力近似值与残余应力实测值误差较小,且这一方法具有一般性.进一步分析分布位错,给出带钢屈曲挠度函数的形式,与现场实际起浪形式相吻合.     

Influence of the stress state on the structure and properties of welded steel and alloy structures

The residual stress due to welding in steel and alloy structures is analyzed. The greatest residual stress is produced by cooling of the welded structure. The results of calculations are in satisfactory agreement with the experimental deformation of the structure in welding on a test bench. The tests reveal the direction of the internal stress and permit assessment of the geometry of parts on the basis of a model of the temperature fields in the butt welding of steel and titanium-alloy workpieces. A coercimeter may be used to assess the stress state of the material and its defect content. By that means, it is possible to predict the structural state and properties of weld joints. The dynamics of welding deformation may be understood on the basis of the internal residual stress and the structural transformations produced by the welding process.     

Pretension-Dependent Residual Stress of Alumina Fiber-Reinforced Composite Wire

The relationship between pretension and residual stress of an aluminum wire reinforced with 45 vol pct continuous Nextel? 610 alumina fibers is investigated. It is shown that as pretension stress increases, the matrix residual stress decreases. A transition in matrix residual stress from tension to compression occurs at a pretension stress of about 80 MPa. The initial rapidly decreased residual stress caused by pretension at relatively low pretension stresses is a result of matrix elastic compressive deformation; while the later gradually decreased residual stress at higher pretension stresses comes from matrix plastic compressive deformation. As the matrix yield stress and hardening exponent increase, the decrease in matrix residual stress with pretension stress is more rapid and the absolute value of matrix residual stress increases. An analytical model suitable for fiber-reinforced metal matrix composites (MMCs) with strong interfacial bonding is developed to describe the relationship between pretension and matrix residual stress and is shown to be in good agreement with the experimental and finite-element calculated results. The pretension-dependent matrix residual stress phenomenon suggests that the mechanical properties of fiber-reinforced MMCs associated with matrix residual stress may be effectively improved by applying tensile loads.     

Measurement of Residual Stress Field of Hardfacing Metal with RE Oxide and Its Numerical Simulation

The temperature and residual stress fields of a medium-high carbon steel, welded by a cracking resistance electrode with rare earth (RE) oxide, were measured by thermo-vision analyzer and X-ray stress analyzer respectively. Meanwhile, the martensitic transformation temperatures of matrix, hard-face welding (hardfacing) metal welded by conventional hardfacing electrode and that welded by cracking resistance electrode with RE oxide were determined. According to the experimental data and the thermo-physical, mechanical parameters of materials, finite element method (FEM) of temperature and stress fields was established. In this FEM, the effect of martensitic transformation on residual stress of hardfacing metal of medium-high carbon steel was taken into account. The results show that, by adding RE oxide in the coat of hardfacing electrode, the martensitic transformation temperature can be decreased, so that the residual tensile stress on the dangerous position can be decreased. Therefore, the cracking resistance of hardfacing metal can be improved.     

The relaxation of residual stresses with postweld heat treatment in a high-performance weld measured with neutron diffraction

The residual stresses in a cylindrical weldment of HP-9-4-30 steel were measured with neutron diffraction in the as-welded (AW) state and after postweld heat treatment (PWHT). Large residual stresses are present in the interior of the material in the as-welded condition. The maximum principal stresses measured were found around the edges of the cap-pass heat-affected zone and reached up to 1045 MPa (76 pct of the base metal yield strength) in the as-welded condition. The principal stress directions for the residual stress tensors do not in general follow the hoop, axial, and radial axes of the weld and change from position to position within the weld, although the highest values are generally in the hoop direction. The postweld heat treatment relaxed the largest residual stresses, with the maximum value being 30 pct of the base metal yield stress. The need for position-dependent stress-free standards and the implications of stress gradients over the measurement volumes are discussed.     

Thermal Relaxation of Residual Stresses in Nickel-Based Superalloy Inertia Friction Welds

This article describes an experimental study aimed at characterizing the extent of residual stress relaxation during thermal treatment of inertia friction-welded alloy 720Li nickel-based superalloy welded tubular rings. In the as-welded condition, yield level tensile hoop stresses were found by neutron diffraction in the weld region along with axial bending stresses (tensile toward the inner diameter (ID)/compressive toward the outer). The evolution of these residual stress levels during postweld heat treatment (PWHT) was mapped experimentally over the weld cross section. After 8 hours of PWHT, the axial stresses relaxed by 70 pct, whereas the hoop stresses reduced by only 50 pct. Some scatter of residual stress evolution was found between samples, particularly for the axial stress direction. This was attributed to substandard tooling to grip the rings. The results on subscale samples were transferred to a full-scale aeroengine (650-mm diameter) compressor drum assembly that was postweld heat treated for 8 hours. It was found that the residual stresses, particularly in the axial direction, were noticeably lower in this full-scale weld component compared to the subscale weld heat treated for the same time. The differences seem to be best rationalized by the different standards of jigging used during joining these two types of welds.     

Thermal transient stresses due to rapid cooling in a thermally and elastically orthotropic medium

This paper reports the residual thermal transient stresses that develop within a thermally and elastically orthotropic medium with a rectangular boundary. The material is rapidly cooled from the steady-state thermal environment under prescribed surface temperatures down to room temperature. Based upon the solution of transient temperature field, the thermal stress analysis is performed by using an elastic displacement potential approach. The two-dimensional temperature and stress fields have been obtained in series expansion forms. Numerical calculations are performed for a typical unidirectional fiber composite. The results demonstrate that the residual thermal stresses exhaust a significant portion of the tensile strength of the composite material. Formerly Visiting Scholar at the Center for Composite Materials, University of Delaware     

基于H型钢残余应力主动控制的矫直工艺设计

针对H型钢辊式矫直过程残余应力的主动控制,基于工程弹塑性理论建立一种矫直过程应力演变的分析模型;采用离散解析实现对模型的快速数值求解;继而基于该分析模型建立一套能够实现残余应力主动控制的工艺参数主动设计方法;运用该方法对典型规格H型钢矫直工艺参数进行工艺设计.建立的分析模型运算结果与有限元结果吻合且计算成本得到有效控制,模型能够实现有限时间内整个矫直工艺参数域内残余应力演变结果的分析;工艺设计方法能够得到一定目标参数和约束条件下的残余应力主动控制工艺参数.