Analysis of the impression creep test method using a rectangular indenter for determining the creep properties in welds

The results of a theoretical and finite element investigation of an impression creep test method using a long rectangular indenter under plane strain conditions, rather than the conventional cylindrical indenter, are presented. The application of the technique for determining the creep properties of the various zones within welds is considered. The finite element method is used to obtain accurate (creep) or approximate (elasto-plastic limit load) reference stress solutions for the rectangular indenters placed at several positions in the base material, heat affected zone and weld metal. The effect of varying the geometric test parameters is reported. The possible advantages of the technique for determining some of the important creep properties in welded structures are identified.     

Prediction of creep failure in aeroengine materials under multi-axial stress states

The creep and creep rupture behaviour of two, significantly different, aeroengine materials, namely a nickel-base superalloy at 700°C and a high temperature titanium alloy at 650°C, were studied. Experimental creep tests were conducted on uniaxial specimens and axisymmetric notched bars under constant tensile loads conditions. From the uniaxial creep test results, a creep continuum damage model was established for each of the materials. The skeletal point stress approach was used to obtain the approximate creep rupture stress criterion in the multi-axial generalization of the creep continuum damage models. This approximation was cross-checked using axisymmetric Finite Element (FE) analyses in a trial and error procedure. Multi-axial creep continuum damage models were then used in further FE creep analyses to predict the creep rupture times in specimens subjected to different tensile loads. The FE predictions of the rupture times in these notched specimens were found to be in good agreement with the experimental results for the nickel-base superalloy (Waspaloy) at 700°C and the titanium alloy (IMI834) at 650°C.     

High-temperature rupture of 5083-Al alloy under multiaxial stress states

High-temperature rupture behavior of 5083-A1 alloy was tested for failure at 548K under multiaxial stress conditions : uniaxial tension using smooth bar specimens, biaxial shearing using double shear bar specimens, and triaxial tension using notched bar specimens. Rupture times were compared for uniaxial, biaxial, and triaxial stress conditions with respect to the maximum principal stress, the von Mises effective stress, and the principal facet stress. The results indicate that the von Mises effective and principal facet stresses give good correlation for the material investigated, and these parameters can predict creep life data under the multiaxial stress states with the rupture data obtained from specimens under the uniaxial stress. The results suggest that the creep rupture of this alloy under the testing condition is controlled by cavitation coupled with highly localized deformation process, such as grain boundary sliding. It is also conceivable that strain softening controls the highly localized deformation modes which result in cavitation damage in controlling rupture time of this alloy.     

Modelling the effect of HAZ undermatching on the crack-tip stress distribution in idealized welds

In order to study the influence of the heat-affected zone softening on the fracture behaviour of welds with cracks in the weld metal centre line, a large variety of weld geometries and undermatch conditions of the heat affected zone mechanical properties, relative to the weld metal and base material, were addressed in this study. With this aim, the opening stress distribution in notched welded specimens was analysed using the numerical simulation of the three-point bending test. The numerical results show a reduction in the stress levels ahead of the crack tip for welded specimens with severe heat-affected zone undermatch. The stress distribution is strongly influenced by the crack position relative to the weld material/heat-affected zone interface, independently of heat-affected zone width.     

Stress analysis of a composite material with short elastic fibre in power law creep matrix

An approximate stress analysis of a composite material, power law creep material (matrix) reinforced by an elastic short fibre is performed by modifying the Cox model, elastic monofibre in a unit cell of an elastic matrix. The numerical calculation is performed by using aluminium (6061)-SiC (whisker aspect ratio of 10). The result obtained by using the analysis is compared with that obtained by experiments performed by a previous investigator. The result shows that composite stress obtained by the analysis is compatible with that obtained by the experiment in order of magnitude, while stress exponent obtained by the experiment is much higher than that obtained by the analysis. A correction factor relating analytical to experimental results is found and the physical meaning of the factor associated with the actual deformation process is discussed. In addition to this analysis, a rigid fibre in power law creep material (matrix) is analysed. The fibre stress distribution obtained by the analysis is compatible with that obtained by the previous investigator.     

A method for estimating the stress distributions on the centre line of an axisymmetric, two-material, cross-weld, creep test specimen

Finite element analyses have been performed for an axisymmetric, two-material, cross-weld, creep test specimen. Stationary-state stress (and strain-rate) results were obtained for various geometries and relative material properties. Using these results, it has been shown that a simple interpolation technique can be used to obtain the stress distributions for any geometry and relative creep properties.     

异种耐热钢焊接接头低塑性蠕变失效力学因素的研究

用有限元法计算了异种耐热钢接头邻近焊缝界面低强度材料区的蠕变应变分布,建立了蠕变拘束区（CRZ）应力三轴度（σ(av)/σ）与蠕变应变速率的比值（εw/εb）之间的数学关系模型,并通过蠕变断裂试验证明了数学模型的正确性。理论分析和试验结果表明,焊缝界面低强度材料蠕变拘束区的应力三轴度是接头发生低塑性蠕变失效的主要力学因素。     

Novel mathematical approaches for analyzing time dependent creep deformations in reinforced metals

The objective of this paper is to present some novel insights for solving a second stage creep problem in metal matrix composites. First, a new analytical approach is developed for obtaining some unknowns in second stage creep of short fiber composites under an applied axial load. The unknowns are the radial, circumferential, axial, shear and equivalent stresses, which are determined by approximation of creep constitutive equations and using proper assumed displacement rates. A nonlinear differential equation is solved employing suitable and correct approximate assumptions. Then, the difference of the stress components utilizing creep constitutive equations and assumed displacement rates is determined. Finally, the axial stress behavior in matrix is predicted by linear and nonlinear boundary value approaches, as well as displacement rates in matrix. For the purpose of the analysis, the steady state creep behavior of matrix material is described by an exponential law. As an important application, factor of safety n will be determined for fibers in order to have a good composite design. Based on the results, the aforementioned methods such as general boundary value approaches can be used to simply determine the approximate behavior of unknowns. These analytical results are then verified by the results of FEM simulation and other available research works. Interestingly, good compatibilities are found among the original mathematical approaches, numerical modeling and also previous available results.     

Finite element study for determination of material’s creep parameters from small punch test

Compared with the conventional tensile creep test, it is much more difficult to obtain the creep properties of a material by the small punch creep test due to the complex deformation response and stress distribution in the miniature specimen of the material. Although creep behavior has been investigated by the small punch test, most studies have been limited to a specimen geometry and therefore, cannot be extended to other conditions conveniently. In this study, a new developed analysis routine is presented to derive the creep parameters of a material using data obtained from the small punch creep test. With the aid of the finite element method, the displacement and the displacement rate of the small punch are obtained for different load levels. The relationship between the stress and creep strain of the specimen and the applied load and the punch displacement is obtained by a dimensional analysis and the membrane stretching model. The creep properties obtained from small punch tests and the conventional creep tests are also compared. The values of the creep properties between the two types of tests agree well with each other within an acceptable accuracy range. This indicates that it is possible to obtain the creep parameters of a material from the small punch creep test instead of the conventional creep test by the analysis routines proposed in this study. Some suggestions for data reduction of the small punch creep tests are also presented to obtain more accurate material creep parameters.     

基于最弱环理论的缺口件概率疲劳寿命预测方法

基于最弱环理论和光滑试样疲劳寿命的Weibull分布,建立了一种缺口件概率疲劳寿命预测方法。该方法首先基于最弱环理论和光滑试样的疲劳强度分布,通过定义缺口件的Weibull有效应力,建立了缺口件在给定循环载荷下的疲劳失效概率计算公式。基于Weibull有效应力和光滑试样的疲劳应力-特征寿命方程,可计算得到给定循环载荷时缺口件的特征疲劳寿命,进一步根据光滑试样的Weibull疲劳寿命分布可最终获得缺口件在给定循环载荷下的疲劳寿命分布。采用上述方法对TC4缺口试样进行了概率疲劳寿命预测,并与局部应力应变法预测结果进行了对比。结果表明:局部应力应变法预测结果过于保守,本文方法预测精度较高,50%失效概率时的疲劳寿命预测结果与缺口试样试验均值寿命吻合很好,10%和90%失效概率时的疲劳寿命预测结果基本分布在试验均值寿命的两倍分散带之内。     

The application of an approximate analysis of the diffusion process for a description of creep and creep rupture

An analysis of the environmental effect on creep and creep rupture of metals is presented. It is pointed that the investigation of the diffusion processes leads to significant computational difficulties. These difficulties arise on representing the solution of the diffusion equation with variable boundaries in the form convenient for analysis.The process of damage accumulation is modelled for a material, which is subjected to the combined action of mechanical loads and the aggressive environment. The Rabotnov kinetic theory is applied in which two parameters are taken into account: the damage of the material and the concentration of chemical elements reducing the resistance of the material to mechanical loads. An approximate solution of the diffusion equation is suggested for rod or shell subjected to axial tension. This solution is based on dividing the cross-section of rod or shell into the disturbed and undisturbed parts and determining the motion of the boundary between these parts. The system of constitutive equations which describe the interaction between the diffusion and rupture fronts during the creep process until failure is obtained. A good quantitative agreement between experimental and theoretical results has been received.     

马氏体/贝氏体异种耐热钢焊接接头的力学性能及界面失效

采用脉冲氩弧焊接工艺、高温加速模拟工况、高温持久、常温力学性能试验研究了不同焊缝强度匹配条件下,马氏体耐热钢9Cr1MoVNbN与贝氏体耐热钢12Cr2MoWVTiB异种钢焊接接头的力学性能、高温强度、蠕变损伤及界面破坏特征。研究结果表明,焊前预热250℃,焊后回火750℃×1 h条件下,加速模拟运行500h、1 000 h、1 500 h后低匹配焊接接头的界面蠕变损伤较严重,力学性能下降明显,失效倾向较大;而中匹配接头的蠕变损伤及失效倾向较小,中匹配与低匹配接头的持久强度比较接近:而高匹配接头的持久强度最低。因此,对于9Cr1MoVNbN/12Cr2MoWVTiB异种钢焊接接头采用中匹配比较合适。     

Derivation of creep long-term fracture criteria under plane state of stress

A new approach has been suggested for the construction of long-term fracture criteria under creep conditions and multi-axial loading. The method developed overcomes former problems with a view to identifying stresses responsible for failure and material constants, and is based on the equivalent long-term strength diagrams. The criteria are chosen in the form of a mixed invariant relating two stress components, which give rise to brittle and viscous fracture. The values of stress characteristics combined in a mixed invariant take signs of principal stresses into account. The fracture criteria derived have been approved on unified long-term strength diagrams of thin-walled tubular specimens under internal pressure, internal pressure with tension, pure torsion and tension with torsion.     

Creep damage evaluation of thick-walled spheres using a long-term creep constitutive model

This paper describes a numerical model developed for the computation of creep damages in a thick-walled sphere subjected to an internal pressure and a thermal gradient. The model predicts the creep damage histories during the life of the sphere, owing to variations in stresses with time and through-thickness variations. The creep damage fraction is based on the Robinson’s linear life fraction damage rule, which has been incorporated in a nonlinear time-dependent stress analysis. Following the stress histories, the effective stress histories are obtained and the creep damages are calculated and summed during the life of the sphere. The material long-term creep properties up to the rupture and creep rupture data are defined by the Θ projection concept [1]. The damage histories up to 38 years are calculated and the results show that the maximum damages are always located at the inner surface of the sphere, while the outer surface of the vessel sustains minimum damages.     

A theory of anisotropic creep after plastic pre-straining

Plastic pre-strain induces directional material response. It has been observed that uni-directional pre-strain results in anisotropic creep. Creep tests in various directions with respect to the direction of pre-strain have shown different steady creep rates and times to rupture.A theory of anisotropic creep is proposed employing the properties of tensor functions. The creep rate in the steady creep range is expressed as a tensor valued tensor function of the stress and pre-strain. In comparison with the Odqvist theory additional material constants appear in the law proposed. The constants are established and predictions from the theory advanced are compared with the results of experiments concerning two pre-strain magnitudes and seven inclinations of the uniaxial creep tests with respect to the pre-strain direction.     

切口试样破坏过程试验与细观数值分析

对切口圆棒试样与切口板试样进行单向拉伸试验和有限元数值分析，以试样最小横截面上各点变化的应力应变场为体胞演化的载荷控制条件，采用三维含球形微孔洞体胞模型分别对各点微孔洞长大规律进行数值模拟。结果表明，在试样得到的断口韧性区域内，微孔洞的生长速度较快；试样失稳前微孔洞相对体积百分数最大的区域与试验时试样的起裂位置一致，因而证实微孔洞的演化是导致试样材料在拉伸条件下破坏的主要原因，同时也证实体胞模型用于局部破坏分析的有效性。     

铸铁黏聚裂纹的张开位移与应力分布

对于含缺陷材料结构的强度,以裂纹为主要特征的断裂力学是其力学行为分析的有效途径,裂纹扩展过程区能被简化成具有黏聚力的裂纹段。为探讨带切口的铸铁裂纹发展规律及黏聚裂纹张开位移与黏聚应力的本构关系,对8种不同切口尺寸的铸铁梁进行三点弯曲加载实验,通过应变计电测跟踪测试,得到预制裂纹端部的张开位移随载荷变化曲线。由确定黏聚裂纹张开位移与黏聚应力分布的解析方法,计算得到该材料黏聚裂纹张开位移及与应力的本构关系。计算预制裂纹尖端张开位移与应变计测试结果基本符合。     

B4C颗粒对AZ61蠕变及磨损性能影响的研究

采用机械搅拌法制备B4C/AZ61镁基复合材料,并通过对比AZ61镁合金和B4C/AZ61镁基复合材料的蠕变和磨损试验,分析B4C颗粒对AZ61镁合金蠕变及磨损性能的影响.结果表明:在蠕变性能上,与AZ61镁合金相比,B4C/AZ61镁基复合材料具有较小的初始蠕变量和较小的总蠕变量,进入稳态蠕变阶段的时间和进入稳态蠕变状态时的蠕变速率与AZ61镁合金基本相同;在磨损性能上,B4C颗粒的添加使得AZ61镁合金的抗磨损性能得到明显提升.     

基于试验数据的焊缝试样C*参量估算

针对焊缝和母材蠕变性能不相同的带焊缝CT试样,提出了一个等效均质材料模型,建立了焊缝中心裂纹、焊缝界面裂纹和非对称焊缝裂纹情况下由试验数据确定C*参量的修正式。采用ABAQUS软件进行了带焊缝CT试样C*参量的有限元分析。有限元数值解与修正式的预测值比较表明：与均质材料CT试样相比,低匹配焊缝会导致CT试样的hw因子增大,高匹配焊缝会导致hw因子值降低,采用ASTM E1457提供的公式在低匹配情况下会过低估算C*参量,在高匹配情况下会过高估算C*参量。无论是低匹配(M<1)焊缝还是高匹配(M >1)焊缝,修正后CT试样的C*参量计算式都可给出与有限元解非常接近的估算结果,可用于焊缝蠕变裂纹行为预测。     

An alternative definition of the reference temperature to estimate the creep deformation of a thermally loaded tube

The reference concept is applied to the creep deformation of an axially loaded tube subjected to a two-dimensional temperature distribution. First the analytical method given in the literature for the determination of the reference stress is extended, resulting directly in expressions for both the reference stress and the reference temperature. Since these expressions can be solved only with a considerable amount of computation, an alternative definition of the reference values is suggested, which is rather simple in application. A further advantage of the new method is that the creep rate resulting from a uniaxial, isothermal creep test at its reference values can be transfered directly to the structure. The prediction of creep rate is in a good agreement with the steady state solution which is shown for various types of temperature fields. The absolute magnitude of error may be somewhat larger for the new method compared to the old one. But even if an unfavourable combination of material constants is used, this disadvantage is not serious since the errors do not surpass the scatter of experimental data usually obtained in creep tests. Regarding the tendency to overestimate or underestimate the creep rate, it cannot be decided in general whether the new or the old definition provides the better prediction, since the error is a complex function of the temperature field applied.