Creep-fatigue Loading Conditions Research Articles

A phase-field fracture model for creep-fatigue behavior

A phase-field fracture model for creep-fatigue behavior is proposed. The fatigue and creep behavior are simulated by modifying the free energy functional through a total degradation function that diminishes fracture toughness with the accumulation of the relevant history variable. Specifically, strain energy density and creep strain serve as the chosen fatigue and creep history variables, respectively. To model the creep-fatigue interaction, we propose several total degradation function formulations comprising fatigue and creep degradation functions. Numerical experiments demonstrate the capability of our model to reproduce the strain-lifetime relationship and crack growth behavior under creep-fatigue loading conditions with varying hold times. Moreover, we simulated examples of plates with holes, demonstrating the capability of our model for complex crack paths.

System-level creep-fatigue reliability evaluation by engineering damage mechanics incorporating cumulative damage-damage threshold interference

Reliability assessment for structural system is of great significance in ensuring system safety, providing a scientific guidance for life management. In this work, a creep-fatigue reliability modeling method is developed for system-level perspective on the basis of cumulative damage-damage threshold interference. Probabilistic damage accumulations to given loading cycles are associated with the creep-fatigue models considering multi-source uncertainties and the damage threshold is regarded as a random variable. Particularly, a numerical procedure is proposed for practical application in engineering by combining the Monte Carlo simulation with Gaussian process regression-based surrogate model. Furthermore, a low-pressure turbine disk under creep-fatigue loading condition is taken as an instance to evaluate its reliability considering multiple weakness sites. Results show that the proposed method is better than the independent treatment because it is capable of avoiding the overly-conservative reliability estimation. In addition, the influence of damage summation rules and damage threshold on reliability is quantitatively analyzed in terms of the developed method. The effect of random parameters in structural system on computational efficiency of the proposed numerical procedure is investigated.

Investigation of creep-fatigue crack initiation by using an optimal dual-scale modelling approach

In this work, three dual-scale modelling approaches containing sub-modelling approach, coupled modelling approach and full-field crystal plasticity finite element (CPFE) approach are implemented for notched structures under creep-fatigue loading conditions. Based on the comprehensive comparisons, the sub-modelling approach is determined to be an optimal simulation strategy among them. Furthermore, the combined effects of grain orientation and stress concentration on crack initiation are investigated by adopting the sub-modelling approach. Under low stress concentration factor, the most potential positions of crack initiation randomly locate at the root of geometric discontinuities owing to the influence of grain orientation distribution. With the increase in stress concentration factor and decrease in the number of grains at hotspots, the cooperative relation between grain orientation and stress concentration factor for creep-fatigue crack initiation is revealed through a sequence of simulation results, followed by the competitive relation. On this basis, a feature region map is constructed to distinguish the factor-dominated crack initiation. Finally, a case study of turbine disk is provided to illustrate the engineering meanings of the dual-scale modelling approach. The link from scientific problem to engineering application for the crack initiation prediction is bridged by the damage mechanics approach, which is also expected to be promoted in many high-temperature components.

Oxidation-involved life prediction and damage assessment under generalized creep-fatigue loading conditions based on engineering damage mechanics

The object of this paper is to develop numerical procedures for creep-fatigue-oxidation life prediction and damage assessments based on engineering damage approach, in response to high-reliability and long-life design requirement that supports low-carbon and new-energy technologies. In order to achieve the prediction results in terms of cycle-dependent stress–strain responses, crack initiation life prediction and multi-damage evolutions, the generalized creep-fatigue loading conditions including tension-hold-only, compression-hold-only and tension-compression-hold-both, which are abbreviated as CP, PC, and CC types, are conducted for IN 718 at 650 °C. Results show that creep-fatigue deformation behaviors are well depicted through the evolutions of hysteresis loops, cyclic softening curves and stress responses. With incorporating into oxidation damage especially under long-life conditions, both error band and probability density function for life prediction are quantitatively improved. In addition, the cycle-dependent roles in multi-damage evolutions are clearly observed in a set of radar graphs, where fatigue, creep and oxidation damage are manifested as different evolutionary features. Finally, the technical route in the transition from deterministic to probabilistic multi-damage assessments is discussed based on the established creep-fatigue-oxidation diagram.

Couple effects of temperature and fatigue, creep-fatigue interaction and thermo-mechanical loading conditions on crack growth rate of nickel-based alloy

The ambient and high-temperature fatigue crack growth behaviors in C(T) and SENT specimens of Ni-based superalloy for turbine disk application were studied in a wide interval of temperatures 25–750°C using a combination a electro- and servohydraulic test systems and fractographic investigations. The fatigue, creep-fatigue interaction and thermo-mechanical in-phase fatigue (TMF IP) crack growth tests are performed under isothermal and dynamic waveforms loading conditions. The interpretation of the experimental results is given in terms of the traditional stress intensity factors and C-integral as well as new normalized cyclic fracture diagrams. It is found that there are definite temperature-sensitive regions separate for harmonic fatigue and creep-fatigue interaction loading conditions in which the crack growth rate of Ni-based alloy increases sharply. Scanning electron microscopy in longitudinal sections containing cracks revealed the mechanisms responsible for fatigue crack initiation and growth. The couple effect of temperature ranging and isothermal and dynamic waveforms loading conditions on fatigue life was discussed.

Effect of creep-fatigue loading condition on crack tip fields of grade 91 steel at crack initiation and growth

In this paper, the effect of creep-fatigue loading condition on crack tip deformation and stress fields of Grade 91 steel at 600 °C at crack initiation and growth is studied. By using finite element debond analysis method, creep-fatigue crack growth tests using C(T) specimens under various load ratios and hold times are simulated, and the effect of creep-fatigue load ratio and hold time on the crack opening profile, equivalent stress, crack-opening stress and triaxiality at crack initiation and growth is presented. It is found that the crack tip deformation and stress fields under tension–compression creep-fatigue loading are overall different from those under tension-tension creep-fatigue and pure creep loading, due to re-sharpening of the crack tip.

Semi-quantitative creep-fatigue damage analysis based on diffraction-based misorientation mapping and the correlation to macroscopic damage evolutions

A large number of strain-controlled creep-fatigue tests under wide loading waveforms are conducted at 650 ℃ in nickel-based forged GH4169 superalloy. Comprehensive characterizations, including scanning electron microscope (SEM), electron backscatter diffraction (EBSD) and transmission electron microscope (TEM), are observed from the post-test examinations. Particular focus is brought to the physical understanding of damage mechanisms under wide creep-fatigue loading conditions using EBSD analysis. The representative misorientation parameters are calculated for constructing diffraction-based misorientation mapping. Semi-quantitative analysis of longitudinal EBSD observations is conducted to prove that strain ratio has little influence on creep-fatigue damage degrees, while dwell time causes noticeable changes to damage progressions. In particular for geometrically necessary dislocation (GND) map explored in this work, more fundamental information based on failure physics is obtained to analyze the creep-fatigue crack initiation mechanism.

Evolution of principal stress of a turbine rotor under cyclic thermo-mechanical loading

The target of the present study is to analyze the local variation of stress and strain state in a steam turbine rotor under cyclic service-type thermo-mechanical creep-fatigue loading conditions. Toward this end, a Chaboche model based material constitutive model is applied to simulate the multi-axial stress-strain behavior in the rotor. Comparison of von Mises stress, stress tensors and principal stresses is carried out to demonstrate the importance of the stress state which is very useful to the optimization of the components and operation, and then principal stress and strain during a whole cyclic loading condition is analyzed to illustrate the variation of tension and compression states. Both the temperature and rotating speed related centrifugal force influence the evolution of the principal stresses and strain, but the influential extent has a large difference at different locations; furthermore, the discrepancy of cyclic softening/hardening behavior and ratcheting behavior due to creep at different locations is also significant. This outcome can be used to carry out the optimization or damage assessment in the rotor.

Reliability assessment of cracked pipes subjected to creep-fatigue loading

The reliability analysis of defective pipes, which operate under creep-fatigue loading conditions has been studied. An austenitic stainless steel pipe containing an axially external semi-elliptical surface crack, subjected to variable internal pressure at elevated temperature has been considered as the benchmark problem. Different parameters in material behavior, geometry parameters, and operational condition have been assumed as random variables in the probabilistic assessments. The reliability of the cracked pipes have been evaluated at various operation times, using different reliability methods. Sensitivity analyses have been conducted to investigate the importance measure of the random variables involved in the problem. Moreover, the effects of reducing the scattering of the random variables on the variations of the reliability index, β, has been examined.

Crack growth behavior, fracture mechanism, and microstructural evolution of G115 steel under creep–fatigue loading conditions

Creep–fatigue crack growth (CFCG) behavior, fracture mechanism, and microstructural evolution of G115 steel under different hold times and initial stress intensity factor ranges (ΔKin) were investigated. The crack propagation durations increased significantly with decreasing ΔKin and increasing dwell time. In da/dN vs. ΔK plots, a “hook” was formed, and it entered the fast crack growth zone at approximately ΔK=36MPam, which corresponds to σref = σ0.2 under plane stress. In (da/dt)avg vs. (Ct)avg plots, data for a specific hold time in a wide load range exhibited a unique relationship. It appears that the parameter D0 in this relationship is affected by hold time and constraint, while φ is independent of these factors. Scanning electron microscopy analyses revealed that with increasing hold time (60–600 s), the fracture mode changed from transgranular-dominated to intergranular-dominated. Meanwhile, the fracture mode changed from intergranular-dominated to predominantly transgranular with high ductility when ΔKin increased (17–29 MPam). According to electron backscatter diffraction observations, many substructured and recrystallized grains formed after CFCG and the deformed grains further decreased as ΔKin increased. The increased crack resistance with decreased deformation grains may combine with the ductility fracture effect to decrease the CFCG rates under high load levels. Additionally, the local misorientation angle reduced significantly after CFCG, and the differences among various load levels were limited.

Notch Effect on Structural Strength of Components at Elevated Temperature Under Creep, Fatigue, and Creep-Fatigue Loading Conditions: Phenomenon and Mechanism

Structural discontinuities (e.g., nozzle, hole, and groove) widely occur in many high temperature components of nuclear and fossil power plants. In general, the notched component is used for simplified tests and analyses due to the complexity of the introduction of a practical component. In the previous work, the effects of the notch on failure life of the components have been reported experimentally, including the strengthening and weakening effects; however, the internal mechanisms have not been clearly demonstrated. This work reviews the notch effects on the structural strength of the notched components at elevated temperatures under creep, fatigue, and creep-fatigue loading conditions. Experimental phenomena (i.e., strengthening or weakening effects) for typical notched specimens subjected to the above three loading conditions are summarized, and the related factors for notch effects on creep rupture life or cycle to failure of the components are discussed. The mechanisms for the strengthening or weakening effects induced by a notch are described. Evaluation procedures for notch effect analysis under complex loading conditions are also included, and the primary challenges concerning the notch effect are provided for further investigations.

Characterization crack growth behavior in creep-fatigue loading conditions through different specimen geometries

Creep-fatigue interaction would accelerate crack growth behavior and change crack growth mode, which is different from that presenting in pure creep or fatigue regimes. In addition, the constraint ahead of crack tip affects the relationship between crack growth rate and fracture mechanics parameter and thus influences the accuracy of the life prediction for defected high-temperature components. For the aim of revealing the role of various specimen geometries in the creep-fatigue regimes, crack growth behaviors were investigated using five different types of cracked specimens (including C-ring in tension CST, compact tension CT, single notch tension SENT, single notch bend SENB, middle tension MT). The crack growth and damage evolution were simulated using finite element method coupled with a non-linear creep-fatigue interaction damage model. Moreover, the solutions of (Ct)avg for different specimen geometries were given to expand the range of testing specimens. By analysing crack growth behavior with various specimen geometries under creep-fatigue conditions, CT and CST showed the highest crack growth rates, which were eight times as the lowest crack growth rates in MT. This revealed that distinctions in specimen geometry influenced the in-plane constraint level ahead of crack tip. Furthermore, a load-independent constraint parameter Q* was introduced to correlate the crack growth rate. The sequence of crack growth rate at a given value of (Ct)avg was same to the reduction of Q*. A normalized constraint level was employed to correlate with the normalized crack growth rate for the aim of transferring lab results into engineering issues.

Creep-fatigue damage simulation at multiple length scales for an aeroengine titanium alloy

Aeroengine titanium alloys such as Ti-6Al-4V experience creep-fatigue loading conditions during the critical fighter aircraft operations. To ensure and enhance the reliable application of such alloys, mechanical behaviour across multiple length scales need renewed attention. Hence, in the present investigation, an attempt has been made to study creep-fatigue damage across multiple length scales (microstructure to component level) using damage mechanics methodology for Ti-6Al-4V alloy. This involves ambient creep, fatigue and creep-fatigue experimentation; identification of various parameters for creep and fatigue models; developing a creep-fatigue model and finally application of this model for damage simulation at specimen, component and microstructure levels. At specimen level, creep-fatigue damage has been obtained from simulations and compared with experimental values. A very good comparison has been observed for the applied maximum peak stress range of 925–975 MPa. The creep-fatigue model has also been successful in mapping damage and identifying critical damage locations in component as well as in the microstructure.

Predicting creep-fatigue crack growth rates in Alloy 709 using finite element simulations of plasticity and creep-induced crack closure

This paper reports on a computational study and experimental validation of creep-fatigue crack growth rates at high temperature in two structural materials. The objectives are to develop a methodology to predict creep-fatigue crack growth rates using plasticity-induced crack closure under creep-fatigue loading conditions by characterizing the effect of hold time on crack growth rates during cyclic loading. In this study, the computation of fatigue crack growth rates is based on the crack closure phenomenon. The total crack growth rate during creep-fatigue loading is based on the addition of fatigue crack growth rate during cyclic loading and creep crack growth rate during hold time. The study identifies the effects of frequency and shape of loading cycle on crack-tip opening stresses induced by the combined action of the plasticity-induced crack closure and creep relaxation at the crack tip. Two-dimensional finite element analyses of compact tension specimens are performed to simulate crack growth under cyclic and time-dependent loading conditions. Elastic-plastic-creep material behavior is considered in these simulations. Closure levels are computed for high temperature structural materials such as 9Cr-1Mo steel and Alloy 709. The numerical predictions provide satisfactory agreement with experimental data of creep-fatigue crack growth rates in modified 9Cr-1Mo and Alloy 709 steels at high temperatures.

Degradation of the Strength of Grains and Grain Boundaries of Ni-Base Superalloy under Creep and Creep-Fatigue Loadings

The degradation process of the micro texture of Ni-base superalloys was observed under fatigue and creep-fatigue loading conditions at elevated temperatures higher than 700oC by applying electron back-scatter diffraction (EBSD) analyses. The local distribution of the crystallinity of a grain and a grain boundary was defined quantitatively by analyzing the Kikuchi pattern obtained from each electron-beam-irradiated area with a diameter of 50 nm. The calculated image quality value was used for the analysis. It was found that the crystallinity of grain boundaries degraded seriously under creep-fatigue loading conditions due to the acceleration of anisotropic strain-induced diffusion of component elements. Since the initial finely-controlled strengthened micro texture disappeared due to the anisotropic diffusion of component elements, this degradation was found to cause the drastic decrease of the strength of grains and grain boundaries and thus, lifetime of the material. The decrease of the strength of both grains and grain boundaries was measured by micro tensile test system in a scanning electron microscope by making a small sample from bulk specimen using focused ion beam. The strength of a grain and a grain boundary varied drastically depending on their crystallinity, in other words, the image quality value.

Testing and assessment of cracking in P91 steels under creep-fatigue loading conditions

Abstract Future green energy options dictate that renewable energy source must be utilized when available. This poses a challenge to conventional power plant, which has generally been designed for base-load conditions, as they now need to operate in a ‘flexible’ manner. This flexible operation, in high temperature power plant components, could lead to a combination of creep and fatigue crack growth failure. Thus a better characterization of interactive creep-fatigue crack growth behaviour is required especially for assessing long term failure in plant. The industrial codes, such as R5 or BS7910, treat this interaction using linear accumulation of damage. However, this does not consider the degradation of properties and reduction in creep ductility in long term operations and their effect on the subsequent creep/fatigue behaviour. In this work creep-fatigue crack growth (CFCG) tests were performed on compact tension specimen of P91 steel in the as received and ex-service conditions at temperatures ranging between 600 °C to 625 °C, with the hold-times ranging from static to 600 s. The experimental results in addition to appropriate data from the literature have been analysed using stress intensity factor range, Δ K appropriate under fatigue control and the creep fracture mechanics parameter C* relevant under creep control. Scanning electron macroscopy (SEM) analysis confirms the influence of frequency on the mode of cracking. Within the scatter of experimental data for the present short term accelerated tests a linear cumulative damage rule can still predict the creep/fatigue interaction. However the effects due to low frequency cyclic loading as well as degraded the steel under ex-service conditions tending to reductions in creep ductility show factors of two or more faster cracking rates compared to as received static testing. Unavailability of long term tests at low stresses may pose additional problems under creep since creep is stress state controlled but fatigue in not. However using plane strain predictions of crack initiation and growth data using the NSW multiaxial ductility creep crack growth model suggest that conservative predictions of long term cracking can still be made under creep/fatigue and when there is a marked reduction creep failure ductility.

Near-tip strain ratchetting and crack growth at elevated temperature

In this work, we have extended our earlier work on the concept of ratchetting strain as a crack driving force (Tong et al., 2013), to examine the crack growth of a nickel-based superalloy at selected temperatures in vacuum under both fatigue and fatigue-creep loading conditions. The parameters of a unified constitutive model were calibrated against the material data obtained at selected temperatures from 550 to 775°C, and a finite element model was developed to simulate the near-tip stress–strain responses under fatigue and creep-fatigue loading conditions at the experimental temperatures. Both ratchetting strain and accumulated inelastic strain near the crack tip were utilised in the prediction of the crack growth rates collected in vacuum. It seems that, although both ratchetting strain and accumulated inelastic strain correlate with the crack growth rates obtained under fatigue and fatigue-creep loading conditions, the predictions based on accumulated plastic strain are particularly close to the experimental results at all temperatures and loading conditions examined.This is the first time the concept of ratchetting strain has been used to predict the crack growth rates of an engineering alloy at elevated temperature in vacuum, where the influence of oxidation on crack growth is removed.

High-temperature fatigue behaviour of a second generation near-γ titanium aluminide sheet material under isothermal and thermomechanical conditions

The high-temperature deformation behaviour of a second generation γ-TiAl sheet material with near-γ microstructure was characterised under tensile, creep, isothermal and thermomechanical fatigue (TMF) loading conditions. Test temperature ranged from 500 to 750°C in isothermal tests and these temperatures were also used as minimum and maximum temperature of in-phase (IP) and out-of-phase (OP) thermomechanical fatigue tests. Under tensile loading, a ductile-to-brittle transition temperature (DBTT) of about 650°C was observed. At this temperature the material experiences a temperature dependent change in the fracture morphology. Creep tests carried out in the temperature range from 650 to 800°C under true constant stress conditions revealed a temperature and stress dependence of the Norton stress exponent n and the apparent activation energy for creep Qapp. With increasing temperature, isothermal fatigue life at constant strain amplitude decreased in vacuum, but increased in air indicating an abnormal (inverse) environmental effect. Under IP loading, fatigue is characterised by cyclic softening due to dynamic recrystallisation. OP loading drastically reduces fatigue life and turned out to be an extremely critical loading situation for γ-TiAl alloys.

Fitness for service of welded components under creep and creep–fatigue loading

The welded materials are prone to damage particularly in heat-affected zones in base metal as well as in fusion line and weld metal. Therefore the treatment of welded components operating in the creep and creep–fatigue regime is of immediate industrial interest. It needs to be addressed by a methodology that will be developed and incorporated into design codes such as ASME, as well as in Fitness-for-Service assessment procedures. Assessment of welded components for Fitness-for-Service is addressed in fragments in various procedures. This is due to the complex microstructures of weldments that include base metal, heat-affected zone and weld metal. The R5 high temperature assessment procedure, produced by BE in the UK, formalized the methods for base metals loaded in static and creep–fatigue with sections describing the treatment of welds. Subsequently, procedures for assessing defects at high temperature, similar to those in R5, have been included in British Standards, the French A16 procedure and in API 579. Section 8 of the recent European thematic network FITNET Fitness-for Service procedure which is incorporated into R5, specifies methods for assessing defects in structures operating at high temperatures and subject to creep and creep–fatigue loading conditions. The reliability of the structural assessments following the codes depends strongly on availability of reliable data required as input data. Most of the data obtained to date on high temperature materials has been reported on creep crack growth (CCG), ignoring the creep crack initiation (CCI) where as creep–fatigue data is scarce. Recent European and international collaborative effort included EC projects CRETE and ECCC, and ESIS TC11, WG on High Temperature Testing of Welds concentrated on CCI as well as CCG testing and analysis of industrial specimens and assessment. This has led to development of a Code of Practice for High Temperature Testing of Weldments via Int. Institute of Welding (IIW) to be presented to ISO for standardization. The present paper gives an overview of the high temperature assessment procedures with recent developments in procedures. Experimental and analytical test results are presented following the codes and assessment procedures. The experimental work on deformation and crack behavior of similar welds of ferritic steel P22, studied at 550 °C are reported. P22 materials are commonly used by power generation and chemical processing industrial applications since couple of decades.

A perspective on creep and fatigue issues in sodium cooled fast reactors

Development of advanced materials alongwith improved high temperature mechanical properties, particularly creep and fatigue are important and play a major role for the successful development of robust, safe and economical sodium cooled fast reactor (SFR) technology. The components of SFRs operate in demanding environments at high temperatures under complex creep, fatigue and creep-fatigue loading conditions. Based upon the service requirements in terms of different environments, temperature and loading conditions, different materials are chosen for different components. Ti modified 15Cr-15Ni austenitic stainless steel is chosen for clad and wrapper tubes in the reactor core, which experience high fast neutron flux of ∼ 1015 ncm−2s−1 along with high temperatures. Type 316L(N) SS is used for out-of-core structural components like main and inner vessels, and sodium pipelines. For steam generators, modified 9Cr-1Mo steel is chosen for all the components, where liquid sodium and steam/water coexist. Some of the important experiences and exciting achievements in the areas of in-house materials development and its characterization in terms of creep, low cycle fatigue and creep-fatigue properties important to design of reactor components for core, out-of-core and steam generator applications are described in the paper. Future directions for materials research and development activities involving critical issues like radiation damage resistance along with improved mechanical properties for advanced clad and wrapper materials necessary for achieving high fuel burnup and design life up to 60 years for out-of-core structural components leading to economical nuclear energy have been highlighted.