Phase Transformation Behavior and Microstructural Control of High-Cr Martensitic/Ferritic Heat-resistant Steels for Power and Nuclear Plants: A Review

The martensitic/ferritic steels have been used as boiler and turbine materials in power plants, and also been selected as potential materials for structural materials in nuclear reactors. In this paper, the kinetic analysis of the martensite formation and microstructural control of high-Cr martensitic/ferritic steels are reviewed. A modular approach, incorporating Fisher partitioning nucleation and anisotropic growth for impingement, was proposed to describe the martensite formation kinetics under different cooling rates.The kinetic analysis suggested a thermal-activated growth feature occurring during the martensitic transformation of martensitic steels. The microstructure can be tuned by composition optimization and various combinations of heat treatment parameters(temperature, time, severe and minor deformation).For the application in power plant, the potential of boundary-design, refinement of original austenite grain size and the final martensitic lath, pinning effect of stable carbides, in improving the performances of martensitic/ferritic steels at elevated temperatures should be investigated more thoroughly.Furthermore, efforts should be made to explore the effects of retained austenite on the improvement of high-temperature creep strength. For the application of nuclear plants, attempts should also be made to produce Fe powders with uniformly distributed oxide particles by chemical reactions.     

Long-term creep strength predictions from short-term creep test data for high Cr creep-resistant steels and microstructural evolution origin of over-predictions

A new tensile creep model that integrates the tensile strength at creep temperature is investigated for its generic applicability in predicting the long-term creep strengths from short-term creep test data for high Cr creep-resistant steels using creep and tensile strength data measured for a grade of 11Cr steel. The results show that, when the long-term creep strengths are specified by stresses producing the required minimum creep rate, they can be accurately predicted using short-term creep test data. However, when they are specified by stresses giving the required creep rupture time, using only short-term creep test data will lead to over-predictions. The microstructure evolution origin of such over-predictions is traced to the Z-phase precipitation during creep in creep-resistant steels with more than 9 wt.% Cr. The conventional concept on the relationship between creep test stress and creep mechanisms is also re-evaluated in light of the new results.     

沥青砂粘弹塑蠕变损伤本构模型实验研究

针对沥青砂的非线性材料特性,结合连续损伤力学理论,对传统Burgers模型进行改造,提出了粘弹塑蠕变损伤本构模型,通过对不同实验条件下沥青砂单轴蠕变试验结果的非线性拟合,获得模型参数,然后利用模型进行预测分析,得到了不同应力水平与环境温度下的蠕变曲线和损伤演化曲线,通过比较发现该文模型能够更合理地反映沥青砂加速蠕变的非线性特征,而且蠕变过程中损伤演化的速度受蠕变时间、应力水平与环境温度的影响很大。     

Effect of time and temperature on nonlinear constitutive equation in polypropylene

In order to investigate viscoelastic-plastic properties and discuss a constitutive equation at finite strains in polymer solids, uniaxial compression tests were executed at different temperatures using polypropylen (PP) rods under conditions of constant strain rate, abrupt change of strain rate, stress relaxation, creep loadings and their combination. Several viscoelastic-plastic properties which must be taken into account in the constitutive equation of PP are pointed out, and the experimental data are compared with the numerical results based on the concept of an over stress model. It is found that the model describes the stress-strain behaviours of PP well in the case where the current strain is not below the previous one.     

Analysis of creep rupture in a notched tensile bar

For circumferentially notched, round tensile bars the creep rupture behaviour is analysed, based on constitutive relations that account for the nucleation and growth of grain boundary cavities in polycrystalline metals at high temperatures. Both diffusive cavity growth and growth by dislocation creep of the surrounding grains is incorporated in the model, and in some cases free grain boundary sliding is assumed. Failure by cavity coalescence is predicted at small overall strains in the range where cavity growth is constrained by the rate of dislocation creep of the grains, whereas outside this range large occur prior to failure.In the analyses for notched specimens, where the stress fields are strongly non-uniform, first failure occurs at the notch tip, and subsequently a macroscopic crack grows into the material. Various combinations of material parameters are considered, and in most cases the crack is found to grow in the plane of the notch. The results are related to earlier experimental and computational investigations of creep rupture in notched bars.     

Uniaxial ratchetting in steels with different cyclic softening/hardening behaviours

The cyclic deformation of three structural steels, SS316L stainless steel, 40Cr3MoV bainitic steel and 25CDV4.11 steel, were studied experimentally by uniaxial cyclic straining or stressing tests at room temperature. The cyclic softening/hardening behaviours of the steels were discussed first by cyclic straining tests; and then the effects of cyclic softening/hardening behaviours on the uniaxial ratchetting of the materials were investigated by asymmetrical cyclic stressing tests. It is concluded from the experimental results that the ratchetting greatly depends on the cyclic softening/hardening behaviours of the materials, as well as the loading history. Different ratchetting and failure behaviours are observed for the prescribed steels. It is also stated that the proposed unified visco‐plastic constitutive model can provide a fairly reasonable simulation of the uniaxial ratchetting of SS316L stainless steel and 25CDV4.11 steel; but cannot simulate the ratchetting of 40Cr3MoV bainitic steel since the dependence of cyclic softening behaviours on the applied inelastic strain amplitude cannot be reasonably described in the discussed constitutive model. Some significant conclusions are obtained, which are useful to construct constitutive model to describe the ratchetting of the materials with different cyclic softening/hardening behaviours.     

Modeling and experimental study of long term creep damage in austenitic stainless steels

One of the main challenges for some reactors components in austenitic stainless steels at high temperature in-service conditions is the demonstration of their behavior up to 60 years. The creep lifetimes of these stainless steels require on the one hand to carry out very long term creep tests and on the other hand to understand and to model the damage mechanisms in order to propose physically-based predictions toward 60 years of service. Different batches of austenitic stainless steels like-type 316L with low carbon and closely specified nitrogen content, 316L(N), are subjected to numerous creep tests carried out at various stresses and temperatures between 525 °C and 700 °C up to nearly 50 • 10³ h.Interrupted creep tests show an acceleration of the creep deformation only during the last 15% of creep lifetime, which corresponds to macroscopic necking. The modeling of necking using the Norton viscoplastic power-law allows lifetime predictions in fair agreement with experimental data up to a transition time of about ten thousand hours which is temperature dependent. In fact, one experimental result together with literature ones, shows that the extrapolation of the ‘stress–lifetime’ curves obtained at high stress data leads to large overestimations of lifetimes at low stress. After FEG–SEM observations, these overestimates are mainly due to additional intergranular cavitation as often observed in many metallic materials in the long term creep regime. The modeling of cavity growth by vacancy diffusion along grain boundaries coupled with continuous nucleation proposed by Riedel is carried out. For each specimen, ten FEG–SEM images (about 250 observed grains) are analyzed to determine the rate of cavity nucleation assumed to be constant during each creep test in agreement with many literature results. This measured constant rate is the only measured parameter which is used as input of the Riedel damage model. Lifetimes for long term creep are rather fairly well evaluated by the lowest lifetime predicted by the necking model and the Riedel model predictions. This holds for experimental lifetimes up to 200,000 h and for temperatures between 525 °C and 700 °C. A transition time as well as a transition stress is defined by the intersection of the lifetime curves predicted by the necking and Riedel modelings. This corresponds to the change in damage mechanism. The scatter in lifetimes predicted by the Riedel model induced by the uncertainty of some parameter values is less than a factor of three, similar to experimental scatter. This model is also validated for various other austenitic stainless steels such as 304H, 316H, 321H (creep rupture data provided by NIMS). A transition from power-law to viscous creep deformation regime is reported in the literature at 650 °C–700 °C for steel 316H. Taking into account the low stress creep rate law, it allows us to predict lifetimes up to 200,000 h at very high temperature in fair agreement with experimental data.     

On the initiation of wedge-type cracks at grain-boundary triple junctions during high-temperature creep

The typical grain boundary cracks are often formed at the grain-boundary triple junction as a result of blocking of grain-boundary sliding. However, a theoretical discussion has not fully been made on the nucleation of grain corner cracks at high temperatures where diffusional recovery occurs. In this study, a continuum mechanics model which incorporated the recovery effect by diffusion of atoms has been developed to explain the initiation of wedge-type cracking during high-temperature creep. A good agreement was found between the result of calculation based on this model and experimental results in austenite steels. It was considered that there is a critical creep rate for wedge-type cracking. The model was also applied to the prediction of the rupture life in creep.     

Self-consistent Constitutive Modeling of the Creep Damage Behaviour of Nickel-base Directionally Solidified Superalloys with Different Grain Orientations

A self consistent creep damage constitutive model is developed for nickel-base directionally solidified superalloys. Grain degradation and grain boundary voiding are considered. The model parameters are determined from the creep test data of single crystal and directionally solidified superalloy with a special grain orientation. The numerical analysis shows that the model creep damage behaviours of nickel-base directionally solidified superalloys with difFerent grain orientations are in good agreement with the experimental data.     

金属塑性变形的本构模型研究

根据位错动力学理论,忽略动态应变时效因素,将塑性变形的流变应力分解为非热应力、热激活应力和粘拽阻力3部分,建立了一个基于物理概念的本构模型。对HSLA-65结构钢的力学行为进行了研究,试验温度为77～700K,应变率为0.001～0.1s-1,真实塑性应变超过60%。结果表明,塑性流变应力随温度的降低、应变和应变率的增加而增大;在一定的温度和应变率范围发生动态应变时效现象,并且随应变率的提高,该现象将移向更高的温区。通过模型预测与试验结果的比较可知,所给本构关系能很好地描述较宽的温度与应变率范围内的塑性流变应力。     

Normally distributed free energy model and creep behavior of ferroelectric polycrystals at room and high temperatures

A constitutive model that can be used to predict creep behavior of ferroelectric polycrystals at room and high temperatures is proposed. The model consists of the Gibbs free energy function with normal distribution and a switching evolution law with critical driving force. Linear moduli in the free energy function and switching parameters in the switching law are assumed to be linearly dependent on temperature. A ferroelectric polycrystal is modeled by an agglomerate of 210 single crystallites. Compressive stress and electric field-induced creep behavior as well as polarization hysteresis and strain butterfly responses of the model are calculated and compared with experimental observations.     

A coupled creep damage evolution model and creep life evaluation

Due to the damage accumulation during creep deformation, creep failure after a certain service time is the most important failure mode for metal structures working at high temperatures. Considering the coupled damage evolution of geometric and material’s damage, a creep life evaluation method based on continuum damage mechanics has been proposed and examined. It is found that the geometric damage evolution model can be deduced theoretically from the creep constitutive equation, while the material’s damage evolution can be assumed in the same way as that for static fatigue problems. Through solving the coupled damage evolution models, creep lives under various stress levels and temperatures can be evaluated in a unified way, just by several material constants which can be determined by some creep tests only.     

Steady-state creep of a pressurized thick cylinder in both the linear and the power law ranges

Summary The classical solution of the steady-state creep problem for a pressurized thick-walled cylinder is based on the power law constitutive equation. Several heat resistant steels show, however, the linear dependence of the creep rate on the applied stress within a certain stress range. In this paper we apply an extended constitutive equation which includes both the linear and the power law stress dependencies. The material constants are identified for the 9Cr1MoVNb steel at 600 °C. We recall the boundary value problem of steady-state creep for the thick cylinder under the plane strain condition. We present an approximate solution illustrating the stress redistributions as a result of the creep process. The analysis shows that for the certain range of the internal pressure both the linear and the power law creep must be taken into account. In this case the results according to the extended constitutive model essentially differ from the classical ones. The obtained solution is also applied to verify the developed user-defined creep material subroutine inside a commercial finite element code. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

A micromechanics model of creep deformation in dispersion-strengthened metals

A micromechanics model, in which work-hardening caused by second-phase particles and a recovery process by diffusion of atoms were taken into account, has been proposed for explaining the creep deformation of dispersion-strengthened metals in high-temperature creep. A constitutive equation of the projection was employed to describe the whole creep curves from the onset of loading to rupture. The results of the calculations based on the present model have been compared with those of experiments on the carbon steels containing spherical cementite particles. There was a correlation between the experimental creep curves and the calculated ones. The changes in the calculated creep strain and creep rate with time have also been compared with the experimental results on carbon steels. The micromechanics model was found to be applicable to any kind of two-phase material, if the constitutive equation was appropriately chosen.     

Meso-scale analysis of the creep behavior of hydrogenated Zircaloy-4

During dry storage, creep is the most likely degradation mechanism for spent Zircaloy fuel cladding. The fuel cladding integrity during dry storage depends on the amount of oxidation, irradiation hardening and hydrogen-uptake during in-reactor operation. In this paper, the effect of hydrogen on the creep behavior of Zircaloy-4 cladding material was investigated at different temperatures. Depending on temperature, hydrogen can be found in the sample in solid solution and/or hydride. To capture this phenomenon, a numerical mesoscale model of the hydrogenated material has been built using the Finite Element (FE) Method. The numerical setup explicitly describes the hydrides as an inclusion in a hydrogenated Zircaloy-4 matrix. The matrix creep behavior follows a combined Norton-Bailey and Norton creep rules whereas the hydrides are considered to be elastic material. The creep law was defined in FE Code ABAQUS using the user subroutine CREEP. The comparison of predicted creep behavior obtained from numerical modeling showed good agreement with the results reported in literature. The predicted creep behavior shows a significant effect of hydrides morphology. Particularly, our model is able to seize the competition between the creep strain rate enhancement induced by hydrogen in solid solution and its reduction due to precipitated hydrogen.     

Recent advances in creep-resistant steels for power plant applications

The higher steam temperatures and pressures required to achieve increase in thermal efficiency of fossil fuel-fired power-generation plants necessitate the use of steels with improved creep rupture strength. The 9% chromium steels developed during the last three decades are of great interest in such applications. In this report, the development of steels P91, P92 and E911 is described. It is shown that the martensitic transformation in these three steels produces high dislocation density that confers significant transient hardening. However, the dislocation density decreases during exposure at service temperatures due to recovery effects and for long-term creep strength the sub-grain structure produced under different conditions is most important. The changes in the microstructure mean that great care is needed in the extrapolation of experimental data to obtain design values. Only data from tests with rupture times above 3,000 h provide reasonable extrapolated values. It is further shown that for the 9% chromium steels, oxidation resistance in steam is not sufficiently high for their use as thin-walled components at temperatures of 600°C and above. The potential for the development of steels of higher chromium contents (above 11%) to give an improvement in steam oxidation resistance whilst maintaining creep resistance to the 9% chromium steels is discussed.     

基于Eshelby等效夹杂理论的沥青混合料有效粘弹性质分析

利用Eshelby 等效夹杂理论研究了沥青混合料的单轴压缩蠕变行为。通过时间域内的Laplace 变换将问题线性化, 得到了沥青混合料的蠕变本构关系。开展了不同温度、应力水平条件下沥青砂的单轴压缩蠕变实验, 根据数据拟合了沥青砂四参量流变模型的模型参数。在此基础上, 预测了沥青混合料在不同温度、应力水平下的蠕变曲线, 分析了温度、应力水平对沥青混合料蠕变行为的影响。结果表明:在相同的应力水平下, 沥青混合料的应变和应变率都随温度的升高而增大, 并且在沥青软化点附近发生明显突变;在相同的温度下, 沥青混合料的应变和应变率都随加载应力的增加而增大。     

A thermovisco-hyperelastic constitutive model of HTPB propellant with damage at intermediate strain rates

The uniaxial compressive tests at different temperatures (223–298 K) and strain rates (\(0.40\mbox{--}63~\mbox{s}^{-1}\)) are reported to study the properties of hydroxyl-terminated polybutadiene (HTPB) propellant at intermediate strain rates, using a new INSTRON testing machine. The experimental results indicate that the compressive properties (mechanical properties and damage) of HTPB propellant are remarkably affected by temperature and strain rate and display significant nonlinear material behaviors at large strains under all the test conditions. Continuously decreasing temperature and increasing strain rate, the characteristics of stress-strain curves and damage for HTPB propellant are more complex and are significantly different from that at room temperature or at lower strain rates. A new constitutive model was developed to describe the compressive behaviors of HTPB propellant at room temperature and intermediate strain rates by simply coupling the effect of strain rate into the conventional hyperelastic model. Based on the compressive behaviors of HTPB propellant and the nonlinear viscoelastic constitutive theories, a new thermovisco-hyperelastic constitutive model with damage was proposed to predict the stress responses of the propellant at low temperatures and intermediate strain rates. In this new model, the damage is related to the viscoelastic properties of the propellant. Meanwhile, the effect of temperature on the hyperelastic properties, viscoelastic properties and damage are all considered by the macroscopical method. The constitutive parameters in the proposed constitutive models were identified by the genetic algorithm (GA)-based optimization method. By comparing the predicted and experimental results, it can be found that the developed constitutive models can correctly describe the uniaxial compressive behaviors of HTPB propellant at intermediate strain rates and different temperatures.     

A temperature dependent creep damage model for polycrystalline ice

We present a continuum damage model for the temperature dependent creep response of polycrystalline ice under a multiaxial state of stress, suited for ice in polar regions. The proposed model is based on a thermo-viscoelastic constitutive law for ice creep and a local orthotropic damage accumulation law for tension, compression and shear loadings. Orthotropic damage is represented by a symmetric second-order damage tensor and its effect on creep is incorporated through the effective stress concept. The unknown model parameters are first calibrated using published experimental data from constant uniaxial stress tests and then predictions are made for constant strain rate and multiaxial loadings. The predicted results are in good agreement with both experimental and numerical results in the literature illustrating the viability of the proposed model. The model is mainly intended for studying the failure mechanisms of polar ice at low deformation rates with depth varying temperature profiles.     

A cyclic viscoplastic and creep damage model for lead free solder alloys

The reliability of microelectronic components under cyclic thermomechanical loading is an important problem especially for new leadfree solder alloys. To investigate the low cycle fatigue strength of solder joints, material models are required, that can describe the constitutive inelastic deformation and damage behavior of solder materials. Such models form the basis for advanced numerical analyses by the finite element method. In the present contribution an appropriate material model that combines the viscoplastic constitutive model of Chaboche-type with the damage law of A.C.F. Cocks for porous creep will be introduced. The algorithm is reported for an implementation as a user defined material subroutine into the FEM-code ABAQUS®. The necessary parameters of the material model are identified using results of miniaturized double lap-shear experiments and tensile tests for a Sn96Ag3Cu1 solder alloy at various temperatures. The comparison of experimental and numerical results shows a good agreement with respect to strain rate sensitivity, relaxation and damage behavior of the investigated solder material. Finally, some numerical applications to surface mounted microelectronic devices are presented.