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.     

Estimates of the creep rupture lives of structures subjected to cyclic loading

Constitutive relationships are discussed for materials which undergo creep rupture due to cyclic loading. Relationships are proposed which describe the strain rates in terms of the current stress and a single state variable. An approximate method is derived which enables a lower bound on the rupture life to be obtained for kinematically determinate structures subjected to cyclic load and isothermal conditions. The bound on the rupture life is expressed in terms of the energy dissipation rates within the structure corresponding to stationary-state creep. The effect of multi-axial stress creep-rupture upon the structural performance is examined and bounds are derived for materials which obey maximum tension and octahedral shear stress criteria. For both multi-axial stress rupture laws and structures subjected to cyclic and reverse load conditions formulae are derived which express the lower bound rupture life in terms of the behaviour of a steady-load uni-axial creep rupture test. Results of experiments which have been carried out on copper and aluminium beams are presented for cyclic and reverse load conditions. For both rupture laws the experimental rupture times are closely predicted by the representative rupture stresses and uni-axial data.     

An approximate method for computing structural creep deformation due to non-proportional cyclic loading

A method is proposed for estimating structural creep deformation due to histories of non-proportional cyclic loading. The method applies to structures composed of materials whose creep strain is given by an equation of the form: . Knowledge of the form of the creep law for time varying stress is not required, as use is made of data obtained from a single cyclic creep test.     

The influence of stress concentration on creep rupture at non-stationary loading

A method is given for the calculation of creep rupture strength of parts containing stress concentrations. The creep theory takes account of the damage and anisotropy of materials. which arise during deformation. For the example of a plane specimen with a notch, results of calculations are compared with experimental data. The results of an investigation into the creep strength of the fir-tree root of a turbine blade at non-stationary loading is given.     

A lower bound to the creep rupture time of pressurised thick cylinders

A lower bound to the creep rupture time of internally pressurised thick cylinders is derived. Material behaviour is described by a phenomenological creep rupture theory that accounts for all phases of creep, and for the full coupling between the deformation and damage processes. To obtain the desirable lower bound, the effective stress and the equivalent rupture stress, which represent the effects of multiaxial stress states on the creep strain and damage rates, respectively, were approximated by the maximum shear stress in the constitutive equations. By comparing the lower bound estimations for a wide range of cylinder dimensions and different engineering materials with the rupture times determined from accurate finite element calculations, it is shown that the lower bound estimations provide quite conservative lifetime predictions.     

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.     

考虑应力松弛的涡轮盘蠕变持久寿命可靠性分析方法

提出考虑应力松弛的轮盘蠕变持久寿命可靠性分析方法。该方法基于概率Miner累积损伤理论,考虑载荷和材料参数的分散性以及应力松弛效应,通过对若干计算点有限元蠕变分析结果响应面回归,获得损伤临界函数的近似表达式。进而采用Monte-Carlo法获得轮盘蠕变持久寿命可靠度或给定可靠度的蠕变持久寿命。并分析了应力松弛和各随机变量对蠕变持久寿命的影响。     

考虑载荷交互作用的蠕变损伤累积和剩余寿命估算

提出两级加载条件下考虑加载历史影响的蠕变损伤演变方程和剩余寿命估算方法,分析结果表明,高一低加载时,由于硬化严重,损伤演变速率减缓,使寿命分数之和大于1;而在低一高加载时,由于硬化较弱,引起损伤演变速率加速,使寿命分数之和小于1。受损材料的硬化状态对后续载荷下的损伤演变过程具有明显的影响,本文方法反映的加载顺序效应与试验观察一致。     

镍基单晶高温合金蠕变-疲劳寿命评估方法进展

论述镍基单晶合金的滑移变形机制和疲劳裂纹萌生机理，分别介绍镍基单晶合金蠕变寿命和低循环疲劳寿命分析评估模型；镍基单晶合金蠕变、疲劳寿命的研究方法可分为应用各向异性张量描述非弹性各向异性变形的宏观力学(唯象)模型和基于晶体学滑移变形理论的微观力学模型；晶体取向、平均应力、环境温度、循环频率、循环应力比是影响单晶合金蠕变-疲劳寿命的主要因素。复杂应力状态下的单晶合金多轴低循环疲劳损伤，单晶合金在疲劳-蠕变交互作用下的疲劳损伤和单晶合金的接触疲劳损伤等问题是需要研究的重要课题。     

Multi-axial creep rupture of a model structure using a two parameter material model

A simplified, two parameter creep curve model is developed, which represents primary-secondary-tertiary creep behaviour. The two parameters are related via the secondary strain respectively to: the sum of secondary and primary strains; and, the sum of secondary and tertiary strains. Techniques are described for fitting the model to laboratory data; and, for the determination of the parameters which characterize primary-secondary and secondary-tertiary creep. The single state variable theory used to describe tertiary creep is compared with mechanisms based models and shown to closely predict the effect of stress-state on rupture strain. A two bar plane strain model component subjected to steady load is studied and used to determine the effect on the component lifetime of primary creep; and, of the multi-axial creep rupture criterion. The representative rupture stress is found to be weakly dependent on primary creep and strongly dependent on the multi-axial rupture criterion of the material.     

Creep fracture modeling by use of continuum damage variable based on Voronoi simulation of grain boundary cavity

A new approach to creep cavitation damage is developed by combining the basic features of continuum damage mechanics and mechanism-based cavitation models. Based on a polycrystal microstructures simulated by Voronoi tessellation, an anisotropic continuum damage variable is defined, and its evolution is given by applying the mechanism-based equations of cavity nucleation and growth to each grain boundary. Macroscopic creep deformation coupled with the damage variable is calculated by damage mechanics equations. The proposed method has been applied to investigate the damage evolution under uniaxial tension and reversed shear loading conditions.     

Estimation of kachanov parameters and extrapolation from isothermal creep rupture data

A simple method for extrapolation of isothermal constant load creep rupture test data is presented and discussed. It is shown that the method has support from the Kachanov theory of brittle creep rupture. As a consequence, the material parameters of the Kachanov creep damage rate law can be quickly estimated from short time tests. Five sets of experimental data are used to illustrate the method and its limitations.     

汽轮机转子钢蠕变损伤的非线性超声评价

超超临界汽轮机高温部件长期服役会产生蠕变损伤,威胁设备的强度安全,快速、有效地检出高温构件蠕变损伤状况对保证设备服役安全意义重大。采用中断蠕变试验,在实验室模拟获得了汽轮机转子钢FB2不同程度的蠕变损伤,进行损伤后试样的非线性超声纵波表征试验。结果表明:非线性超声参量随转子钢FB2蠕变损伤程度的增加而增大;透射电镜微观分析表明,超声非线性参量增大与位错密度增加有关;非线性超声纵波参量与高应力水平下的位错攀移和低应力水平下的位错滑移存在较好的函数关系。进一步以位错密度为中间量,建立非线性参量22 1A A和稳态蠕变变形速率ε?的关联式。     

The sensitivity of the creep rupture of a pressurized cylinder to variations in the multiaxial rupture surface

The sensitivity of creep rupture life to variations in the multiaxial creep rupture surface is investigated for a long, thick-walled, internally pressurized circular cylinder. The cylinder is initially undamaged and accumulates damage at a rate dependent on both maximum principal stress and equivalent stress. It is shown that failure can initiate at the inner or outer radius, or at an intermediate radius, depending on the parameters in the creep and damage laws, and that the ratio of rupture time to initial failure time depends strongly on these parameters. The results are compared with estimates based on the mean diameter formula and in almost all cases a longer rupture life is predicted.     

利用蠕变等损伤曲线研究蠕变累积损伤

利用蠕变损伤的剩余寿命定义，构造了蠕变等损伤曲线，并给出蠕变等损伤曲线的近似数学描述。通过蠕变等损伤曲线研究了蠕变累积损伤规律，建立蠕变累积损伤公式。利用该公式估算变载蠕变剩余寿命，仅需要材料的蠕变断裂曲线，十分便利。     

高温时间相关单多轴疲劳损伤模型

针对高温疲劳中蠕变和氧化因素的影响,提出高温循环加载下时间相关疲劳损伤模型.根据材料高温疲劳微观观察和疲劳过程,充分考虑拉压应变率和循环周期不同而造成的不同损伤,提出高温影响折算时间的计算方法.结合损伤理论和高温对疲劳损伤的影响,把无保载时间的高温疲劳损伤分为纯疲劳损伤、时间相关损伤和交互损伤,损伤模型经高温2.25Cr-1Mo钢单多轴疲劳试验验证,结果表明,误差在两个因子之内.     

Experimental investigations into the influence of cyclic phenomena of metals on structural ratchetting behaviour

The results of experiments on 2-bar structures of 99.9% copper are compared with the prediction of classical plasticity models for loading histories which simulate the effects of thermal cycling in the presence of constant primary loading. Two material phenomena, cyclic hardening and material ratchetting, are shown to have important effects upon cyclic strain growth. Neither of these effects are contained in classical plasticity models. The steady state growth of strain due to material ratchetting is modelled in a simple way. An approximate solution method, based on the “rapid cycle” method for creep analysis, is shown to give a good prediction of the experimental data.     

The use of a constant load to generate equivalent viscoelastic strain in finite element analysis of cemented prosthetic joints subjected to cyclic loading

Polymers such as polymethyl-methacrylate (PMMA) surgical cement undergo elastic and viscoelastic deformation (creep) in response to physiological cyclic loading. Theoretically, the effect of gradual creep deformation on the stresses, strains, and displacements of a prosthetic joint can be evaluated by running a finite element analysis (FEA) model through a large number of loading cycles. However, with complex (i.e. realistic) models, this approach may require extensive computational time, and may accumulate unacceptably large numerical errors over the many iterations of the model. The present study utilized a Fourier series to represent a periodic stress and incorporated it in the linear viscoelastic constitutive equation. It was demonstrated that, for a linear viscoelastic material, the time average (i.e. the constant in the Fourier series) of the cyclic stress determined the accumulated creep strain and the sinusoidal components of the stress produced the periodic creep strain with a zero average and negligible amplitude. For a geometrically linear FEA model, the solution based on a cyclic stress can be readily applied to an external cyclic load, that is, the creep strain is determined by the time average of the cyclic load. While femoral component models were considered as geometrically non-linear, an FEA model of a femur implanted with an Exeter hip prosthesis showed that there was only a minor difference between the profile of the applied sinusoidal load and that of the resulting displacement. In such cases, applying the time average of a cyclic load to calculate the resulting creep strain with a given duration of loading should expect to provide acceptable accuracy, with a marked reduction in the computational time.     

Cyclic loading of beams based on the Prager and Frederick–Armstrong kinematic hardening models

The kinematic hardening theory of plasticity based on the Prager and Frederick–Armstrong models are used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. The beam material is assumed to follow non-linear strain hardening property. The material's strain hardening curves in tension and compression are assumed to be both identical for the isotropic material and different for the anisotropic material. A numerical iterative method is used to calculate the stresses and plastic strains in the beam due to cyclic loadings. The results of the analysis are checked with the known experimental tests. It is concluded that the Prager kinematic hardening theory under deformation controlled conditions, excluding creep, results into reversed plasticity. The load controlled cyclic loading under the Prager kinematic hardening model with isotropy assumption results into reversed plasticity. Under anisotropy assumption of tension/compression curve, this model predicts ratcheting. On the other hand, the Frederick–Armstrong model predicts ratcheting behavior of the beam under load controlled cyclic loading with non-zero mean load. This model predicts reversed plasticity under the load controlled cyclic loading with zero mean load, and deformation controlled cyclic loading.