Meso approaches for the creep damage behavior of nickel-base directionally solidified superalloys

IntroductionNickel-basehightemperatureresistancesuperalloysarsewidelyusedingasturbinesandjetengines.DireetionallysolidificationwasintroducedtoenhancecreepsbengthbyelindnahnggrainboundariesnormaltotheappliedstresswherevoidsarelikelytOoccurundercreepload.Inpractice,however,theappliedstressmaynotbeuniaxialnordirectedparalleltOthegrainboundaries.Singlecrystalswerethusdeveloped.CongregationoflowtempefAnremeltingelementsongrainboundaries,grainboundaryoxidation)etc.,areadditionalfactorsthatwoulddeg…     

沉淀相的尺寸与形态对镍基合金蠕变行为的影响

镍基合金具有优良的高温力学性能,广泛应用于涡轮叶片等热端部件。沉淀相的尺寸和形态是影响镍基合金力学性能的重要因素。本文在考虑应变梯度的镍基合金晶体塑性本构模型的基础上,引入了各向异性损伤张量,研究了包含两种不同尺寸和三种不同长细比的沉淀相形态的镍基合金蠕变行为。结果表明,该模型能够很好地反映沉淀相的尺寸对镍基合金蠕变行为的影响,与实验结果符合较好。同时,沉淀相的形态也对镍基合金的力学性能产生重要影响,随着沉淀相长细比的增加,镍基合金的蠕变寿命延长,这体现了粗化和形态对镍基合金蠕变行为影响的一种竞争的机制。     

A model for high temperature creep of single crystal superalloys based on nonlocal damage and viscoplastic material behavior

A model for high temperature creep of single crystal superalloys is developed, which includes constitutive laws for nonlocal damage and viscoplasticity. It is based on a variational formulation, employing potentials for free energy, and dissipation originating from plasticity and damage. Evolution equations for plastic strain and damage variables are derived from the well-established minimum principle for the dissipation potential. The model is capable of describing the different stages of creep in a unified way. Plastic deformation in superalloys incorporates the evolution of dislocation densities of the different phases present. It results in a time dependence of the creep rate in primary and secondary creep. Tertiary creep is taken into account by introducing local and nonlocal damage. Herein, the nonlocal one is included in order to model strain localization as well as to remove mesh dependence of finite element calculations. Numerical results and comparisons with experimental data of the single crystal superalloy LEK94 are shown.     

Experimental and computational studies of low cycle fatigue crack nucleation in a polycrystal

Low cycle fatigue tests were carried out on a model ‘two-dimensional’ polycrystalline nickel-base alloy; that is, a directionally solidified material with near prismatic grains. Grain morphology and orientation were determined using electron back scatter diffraction (EBSD), and polycrystal plasticity analyses carried out for the characterised microstructure with, in principle, identical conditions to the experiment tests.     

A coupled kinetic-constitutive approach to the study of high temperature crack initiation in single crystal nickel-base superalloys

A rate-dependent crystallographic constitutive theory coupled with a mass diffusion model has been used to study crack initiation in single crystal nickel-base superalloys, exposed to an oxidising environment and subjected to mechanical loading. The time to crack initiation under constant load has been predicted using a strain-based failure criterion. A notched compact tension (CT) specimen containing a single casting defect, idealised as a cylindrical void close to the notch surface, has been studied. Finite element analysis of the CT specimen revealed that, due to the strong localisation of inelastic strain at the void, a microcrack will initiate in the vicinity of the void rather than at the notch surface. The numerical results have also shown that the time to crack initiation depends strongly on the void location. The coupled diffusion-deformation studies have revealed that environmental effects reduce the time to crack initiation due to the oxidation-induced material softening in the vicinity of the notch and void. The applicability of a failure assessment approach, based on the linear elastic stress intensity factor, K, to predict the crack initiation time under creep loading is examined and a probabilistic framework for prediction of component lifetime is proposed.     

Transversely isotropic viscoplasticity model for a directionally solidified Ni-base superalloy

A transversely isotropic continuum viscoplasticity model has been formulated to capture the fatigue and creep responses of a directionally solidified (DS) polycrystalline Ni-base superalloy used mainly in turbine blades. This model has been implemented as an ABAQUS User MATerial (UMAT) subroutine using a semi-implicit integration scheme. Isothermal uniaxial fatigue data from tests conducted with and without hold times and creep data are used to characterize the stress–strain response at temperatures ranging from 427 °C to 1038 °C. The scheme leads to reduction of the associated computational costs when compared to a crystal viscoplasticity model that explicitly considers 3-D grain structure. The macroscopic elastoviscoplastic model is shown to simulate the homogenized deformation response of the polycrystalline DS alloy for various isothermal histories. The predictive capability of this model is verified using both in-phase and out-of-phase TMF data, and is compared to the results of analysis of a single crystal in terms of stress concentration and stress distribution for a model problem of a plate with a central hole.     

单晶高温材料中铸造微孔洞的扩长

基于有限变形晶体塑性本构关系及三维体胞模型,采用有限元的方法,分析了在不同应力三维度、不同罗德参数、不同滑移系开动及不同加载取向下,单晶高温合金中铸造微孔洞扩长的力学行为。分析结果表明:累积剪切应变在铸造微孔洞的扩长中起着很重要的作用,大的累积剪切应变对应高含量的铸造微孔洞;开动滑移系族的类型对铸造微孔扩长的影响不容忽视,故准确的确定开动滑移系的类型,对于评估单晶热端部件的寿命至关重要。由于不同的取向具有不同的Schmid因子、弹性模量及开动滑移系,单晶高温合金中的铸造微孔洞的扩长还与取向密切相关,因此根据热端部件工况,合理的选择其取向是有必要的。     

Creep,plasticity, and fatigue of single crystal superalloy

Single crystal components in gas turbine engines are subject to such extreme temperatures and stresses that life prediction becomes highly inaccurate resulting in components that can only be shown to meet their requirements through experience. Reliable life prediction methodologies are required both for design and life management. In order to address this issue we have developed a thermo-viscoplastic constitutive model for single crystal materials. Our incremental large strain formulation additively decomposes the inelastic strain rate into components along the octahedral and cubic slip planes. We have developed a crystallographic-based creep constitutive model able to predict sigmoidal creep behavior of Ni base superalloys. Inelastic shear rate along each slip system is expressed as a sum of a time dependent creep component and a rate independent plastic component. We develop a new robust, computationally efficient rate-independent crystal plasticity approach and combined it with creep flow rule calibrated for Ni-based superalloys. The transient variation of each of the inelastic components includes a back stress for kinematic hardening and latent hardening parameters to account for the stress evolution with inelastic strain as well as the evolution for dislocation densities. The complete formulation accurately predicts both monotonic and cyclic tests at different crystallographic orientations for constant and variable temperature conditions (low cycle fatigue (LCF) and thermo-mechanical fatigue (TMF) tests). Based on the test and modeling results we formulate a new life prediction criterion suitable for both LCF and TMF conditions.     

Anisotropic continuum damage modeling for single crystals at high temperatures

In single crystals, the process of creep damage is generally anisotropic. Indeed, the damage evolution does not only depend on the loading conditions, but also on the lattice orientation. And the current state of damage has an anisotropic influence on the effective stress state, so that it is represented by a tensorial damage variable. Based on the continuum damage mechanics theory, a creep damage model for F.C.C. single crystals has been developed and implemented in a three-dimensional anisotropic creep model. It is shown that the resulting material model is capable of describing the orientation dependence of the creep and damage evolution of nickel-based superalloys in the high temperature regime.     

Relationship between fatigue life in the creep-fatigue region and stress-strain response

On the basis of mechanical tests and metallographic studies, strain-range partitioned lives were predicted by introducing stress-strain materials parameters into the universal slopes equation. The method was developed by correlating fatigue-damage mechanisms and deformation mechanisms operating at elevated temperatures. Correlation between high-temperature fatigue and stress-strain properties for nickel-base superalloys and stainless steel substantiated the method. Parameters which must be evaluated for PP-and CC-life are the maximum stress achievable under entirely plastic strains, and the elastic modulus. For plasticity/creep interaction conditions (PC and CP) two more pairs of stressstrain parameters must be ascertained.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland OR on June 5–10.     

Crystallographic failure analysis of film near cooling hole under temperature gradient of nickel-based single crystal superalloys

In this paper, a unit cell model with a film cooling hole has been set up to analyze the crystallographic stress characterization and failure behavior under temperature gradient of nickel-base single crystallographic superalloys (SC). The aim of this work is to study the failure behavior of SC blades with film cooling. The distribution of cooling air pressure on the hole side surface and the distribution of the temperature around the hole are obtained from the fluid analysis. The result of the temperature distribution is then transferred to the finite element model (cell model) by the interpolation method. The cell model is analyzed by the crystallographic rate dependent finite element method (FEM). Special attention is put on the influence of temperature gradient. The influence of the loading boundaries, i.e. displacement loading and stress loading, on the stress characterization around hole is also taken into consideration. The results show that temperature gradient hole has much influence on the stress characterization. Different types of loading boundaries result in different types of stress and strain distributions. There is clear stress concentration near the hole under displacement loading, while there is clear strain concentration under stress loading. The failure characterization has been studied by the strain energy density criterion. It is shown that the temperature gradient has influence on the failure behavior.     

含与不含晶界空穴的双晶体蠕变行为研究

基于晶体滑移理论,建立了各向异性镍基合金双晶体的蠕变本构模型和蠕变寿命预测模型,通过MARC用户子程序CRPLAW将上述本构模型进行了有限元实现,并对双晶体蠕变行为进行了计算分析,考虑了:(1)晶体取向的影响;(2)垂直、倾斜和平行于外载方向的三种位向晶界情况;(3)晶界处引进空间空穴的影响。结果表明,双晶体上特别是微空穴和晶界附近区域的蠕变应力应变呈现不同的变化规律,对此晶粒晶体取向和晶界位向有较大的影响;微空穴的存在削弱了双晶体的承载能力,显著地影响了双晶体蠕变持久寿命;相同条件下,垂直晶界对双晶体模型的蠕变损伤影响最为强烈,倾斜晶界次之,平行晶界最小;微空穴的生长与晶界位向和晶体取向有强烈的依赖关系,其中垂直晶界更有利于晶体滑移和微空穴生长。     

单晶高温合金中铸造微孔洞的扩长

基于有限变形晶体塑性本构关系及轴对称体胞模型,采用有限元的方法,分析了在不同取向偏角及不同滑移系开动,单晶高温合金中铸造微孔洞扩长的力学行为。分析结果表明:取向偏角对铸造微孔洞的扩长具有重要的意义,但对铸造微孔洞的形状改变影响不大,为改善单晶高温合金热端部件的疲劳、蠕变性能,控制晶体的取向偏角是很必要的;滑移系族开动的类型对铸造微孔洞的扩长有很大的影响,这种影响与Schmid因子、加载的取向相关,为更加准确地分析单晶高温热端部件的寿命,确定滑移系族开动类型至关重要。     

镍基单晶高温合金定向粗化行为及高温蠕变力学性能研究进展

镍基单晶高温合金是一种广泛应用于航空发动机和工业燃气轮机的两相叶片材料,由软的$\gamma $ 基体相和均匀镶嵌在其中的立方状 $\gamma'$ 沉淀强化相组成.它有个显著的特征,即在高温施加应力条件下, $\gamma '$沉淀相会发生定向粗化, 形成筏状.这种筏化行为直接影响了合金的蠕变疲劳寿命,是镍基单晶高温合金强化机制研究的重点. 此外,镍基单晶高温合金无晶界, 不存在高温晶界弱化、纵向晶界裂纹等问题.因此, $\gamma$/$\gamma'$相界面的位错运动、微观结构以及在载荷和温度作用下的演化决定了其蠕变力学性能.本文从镍基单晶高温合金的微观强化机制出发对定向粗化行为及蠕变力学性能进行了综述.重点介绍了定向粗化行为发生的微观机理、驱动力、影响因素和蠕变过程中界面微结构演化、蠕变力学模型以及定向粗化对高温蠕变力学性能的影响,指出了高温蠕变力学性能研究的发展方向和仍待解决的问题.      

Multiaxial creep and cyclic plasticity in nickel-base superalloy C263

Physically-based constitutive equations for uniaxial creep deformation in nickel alloy C263 [Acta Mater. 50 (2002) 2917] have been generalised for multiaxial stress states using conventional von Mises type assumptions. A range of biaxial creep tests have been carried out on nickel alloy C263 in order to investigate the stress state sensitivity of creep damage evolution. The sensitivity has been quantified in C263 and embodied within the creep constitutive equations for this material. The equations have been implemented into finite element code. The resulting computed creep behaviour for a range of stress state compares well with experimental results. Creep tests have been carried out on double notched bar specimens over a range of nominal stress. The effect of the notches is to introduce multiaxial stress states local to the notches which influences creep damage evolution. Finite element models of the double notch bar specimens have been developed and used to test the ability of the model to predict correctly, or otherwise, the creep rupture lifetimes of components in which multiaxial stress states exist. Reasonable comparisons with experimental results are achieved. The γ^′ solvus temperature of C263 is about 925 °C, so that thermo-mechanical fatigue (TMF) loading in which the temperature exceeds the solvus leads to the dissolution of the γ^′ precipitate, and a resulting solution treated material. The cyclic plasticity and creep behaviour of the solution treated material is quite different to that of the material with standard heat treatment. A time-independent cyclic plasticity model with kinematic and isotropic hardening has been developed for solution treated and standard heat treated nickel-base superalloy C263. It has been combined with the physically-based creep model to provide constitutive equations for TMF in C263 over the temperature range 20–950 °C, capable of predicting deformation and life in creep cavitation-dominated TMF failure.     

Constitutive modelling of anisotropic creep deformation in single crystal blade alloys SRR99 and CMSX-4

A damage mechanics based model has been developed to model stress rupture and creep behaviour of the first and second generation single crystal superalloys SRR99 and CMSX-4. In this article the creep behaviour of CMSX-4 in several different orientations at 950°C is simulated using finite elements, these simulations are compared with the results of creep tests. In order that the effects of rotation and specimen bending can be accounted for in the analysis the entire creep specimen is modelled. The FE program ABAQUS has been used and the slip system model is written using a User MATerial subroutine (UMAT). EBSD (electron back scattered diffraction) measurements of the lattice rotations occurring during creep indicate that the active slip systems at 950°C are the <101>{111} and <112>{111} systems, our simulations show that the creep results can be explained by activating these two families of slip system. There is strong microstructural evidence that the significant components of the hardening matrix should be those causing self and latent hardening of the <101>{111} systems and latent hardening by the <101>{111} systems on the <112>{111} systems.     

Characterization of Irradiation Damage of Ferritic ODS Alloys with Advanced Micro-Sample Methods

Oxide dispersion strengthened (ODS) steels are candidate materials for advanced electric energy and heat generation plants (nuclear, fossil). Understanding the degradation of mechanical properties of these alloys as a result of service exposure is necessary for safe design. For advanced nuclear applications combinations of temperature, irradiation and stress are important damage conditions. They are studied either with neutron irradiated samples (often highly active) or with ion-irradiated samples (irradiation damage often limited to only a few micrometer deep areas). High activity of samples and limited sample volume claim to subsized samples like nano-indentation, micro-pillar compression or thin strip creep testing. Irradiation hardening and irradiation creep were studied with these methods. Ferritic ODS steels with 19% chromium were investigated. The materials were studied in qualities differing in grain sizes and in sizes of the dispersoids. Irradiation was performed in an accelerator using He-ions. Irradiation damage profiles could be well analyzed with indentation. Yield stress determined with compression tests of single-crystal micropillars was well comparable with tension tests performed along the same crystallographic orientation. Irradiation creep of samples with different sizes of dispersoids revealed only a small influence of particle size being is in contrast with thermal creep but consistent with expectations from other investigations.     

On the accuracy of self-consistent elasticity formulations for directionally solidified polycrystal aggregates

In this work, the elastic properties of directionally solidified (DS) polycrystal aggregates are investigated through a combination of analytical and numerical approaches. The effects of crystallographic misorientations and grain aspect ratios of aggregates with ellipsoidal shaped grains are first examined following a self-consistent approach. Finite element techniques are then used to examine the effects of grain size on the elastic properties of the aggregate and to assess the accuracy of the self-consistent predictions. To that purpose, a finite element procedure is presented to generate numerically realistic 3D DS microstructures from electron back-scatter diffraction (EBSD) lattice orientation measurements on an arbitrary cross-section of a DS material. The elastic stiffnesses predicted numerically and analytically are then compared with experimental data on a Ni-base DS alloy tested uniaxially along arbitrary orientations. The general trend predicted analytically was found to be consistent with the numerical and experimental results. Furthermore, an increase in the misorientation between the [0 0 1] axis of each DS grain with respect to the grain growth direction was found to decrease the elastic anisotropy of the DS material.     

复杂应力状态镍基单晶合金低周疲劳损伤模型

根据连续介质损伤力学理论,采用应变能释放率作为热力学广义力描述正交异性材料的疲劳损伤过程,引入取向函数考虑镍基单晶合金晶体取向对疲劳损伤的非线性影响,提出了一个各向异性疲劳损伤模型。应用多元线性回归分析方法,拟合疲劳试验数据可确定模型参数。从应变能释放率的应变空间表达式出发,导出了含有3个弹性常数的单晶合金应变三轴性因子,它既反映了材料性能的晶体取向相关性,又反映了正应力和剪应力的相互作用,并可退化为各向同性材料的应变三轴性因子。利用该模型对CMSX-2镍基单晶合金在应力控制对称循环拉-扭载荷作用下的低周疲劳寿命进行预测,预测值与试验值吻合的相当好,试验所得数据均落在2.2倍偏差的分布带内。     

A constitutive theory for creep behavior of initially isotropic materials sustaining unilateral damage

The goal of the present work is to modify structure of the creep constitutive equations existing in the literature, and simultaneously to incorporate both damage induced anisotropy and unilateral damage into the constitutive model. The proposed nonlinear-tensor constitutive equation for creep together with the damage evolution equation take into account the secondary and tertiary creep of the initially isotropic materials. The material parameters of the model are determined using basic experiments. It is shown that the creep model is capable of describing available experimental data for the lateral creep responses under uniaxial compression.