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Conscious efforts on reduction of greenhouse gas emissions have led to an energy transition to renewable energy, however uncertainties of renewable energy production have resulted in higher thermal cycling demands from conventional power plants. Thermal load cycling at high temperature regions of steam turbine components leads to enhanced creep-fatigue damage accumulation. It is well established that such damage mechanism is numerically best predicted by unified constitutive modeling including damage as a variable as per the formalism of continuum damage mechanics at an expense of considerable computational efforts using finite element analysis. In this paper, the non-iterative Asymptotic Numerical Method (ANM), currently limited to partial cycle analysis with linear hardening plasticity model, is proposed for the first time to address cyclic viscoplasticity problems including damage capable of handling multiple cycles and most generalized loading conditions. Regularization techniques additionally necessary to implement loading-unloading-reloading criteria and advanced constitutive models etc. are presented. The constitutive model chosen for the formulation includes the non-linear multiple back stress variable modified Chaboche model to include damage combined with modified Chaboche-Rousselier isotropic hardening model to include damage, power law for viscoplasticity, Lemaitre's damage potential and Kachanov-Rabotnov's creep damage law. The method is verified with defined error measures and then applied to two high pressure steam turbine rotors, one with and another without thermal stress relief groove (TSRG) at the inlet under service type loading conditions to study the beneficial effect of the TSRG on creep-fatigue damage evolution. The accumulated errors of the proposed ANM and computational time are compared to a conventional Newton-Raphson solution. [ABSTRACT FROM AUTHOR]

Performing online damage evaluation of blades subjected to complex cyclic loads based on the operating state of a gas turbine enables real-time reflection of a blade's damage condition. This, in turn, facilitates the achievement of predictive maintenance objectives, enhancing the economic and operational stability of gas turbine operations. This study establishes a hybrid model for online damage evaluation of gas turbine blades based on their operational state. The model comprises a gas turbine performance model based on thermodynamic simulation, a component load calculation model based on a surrogate model, an updated cycle counting method based on four-point rainflow, and an improved damage mechanism evaluation model. In the new model, the use of a surrogate model for the estimation of blade loading information based on gas turbine operating parameters replaces the conventional physical modeling methods. This substitution enhances the accuracy of blade loading calculations while ensuring real-time performance. Additionally, the new model introduces an updated cycle counting method based on four-point rainflow and an improved damage mechanism evaluation model. In the temperature counting part, a characteristic stress that represents the stress information during the cyclic process is proposed. This inclusion allows for the consideration of the impact of stress fluctuations on creep damage, thereby enhancing the accuracy of the fatigue damage assessment. In the stress counting part, the model incorporates time information associated with each cycle. This concept is subsequently applied in determining the identified cyclic strain information, thereby improving the accuracy of the fatigue damage evaluation. Finally, this study applies the new model to an online damage evaluation of a turbine stationary blade using actual operating data from a micro gas turbine. The results obtained from the new model are compared with the EOH recommended by the OEM, validating the accuracy and applicability of the new model. [ABSTRACT FROM AUTHOR]

In mechanical structures exposed to high temperatures, such as turbine blades for power generation, cracks are detected during in-service inspections. However, there is a risk of fracture owing to the relatively rapid rate of crack propagation, even when a large safety factor is in force. Therefore, a technique is required to estimate the creep-strain distribution before crack initiation and to predict the remaining service life. An inverse analysis method, based on the eigenstrain methodology, has been proposed to estimate the three-dimensional creep-strain distribution using non-destructively measured surface displacements. Three-dimensional creep-strain distributions can be estimated even when the relationship between the creep strain and displacement is non-linear. Through iterative calculations, this method converges to a solution with relatively high estimation accuracy, however, a method for estimating actual complex creep-strain distributions is needed. In this study, a method was proposed to improve the convergence of the iterative calculations. Its effectiveness was demonstrated by numerical analysis using a torsional geometry model that could be used to describe an actual turbine blade. Many unknown values were assumed so that relatively complex creep-strain distributions could be estimated. Convergence calculations were performed to improve the estimation accuracy through iterative calculations, even when displacement measurement errors were considered. The estimation accuracy was improved by using more actual measurements in the inverse analysis.

Performing online damage evaluation of blades subjected to complex cyclic loads based on the operating state of a gas turbine enables real-time reflection of a blade’s damage condition. This, in turn, facilitates the achievement of predictive maintenance objectives, enhancing the economic and operational stability of gas turbine operations. This study establishes a hybrid model for online damage evaluation of gas turbine blades based on their operational state. The model comprises a gas turbine performance model based on thermodynamic simulation, a component load calculation model based on a surrogate model, an updated cycle counting method based on four-point rainflow, and an improved damage mechanism evaluation model. In the new model, the use of a surrogate model for the estimation of blade loading information based on gas turbine operating parameters replaces the conventional physical modeling methods. This substitution enhances the accuracy of blade loading calculations while ensuring real-time performance. Additionally, the new model introduces an updated cycle counting method based on four-point rainflow and an improved damage mechanism evaluation model. In the temperature counting part, a characteristic stress that represents the stress information during the cyclic process is proposed. This inclusion allows for the consideration of the impact of stress fluctuations on creep damage, thereby enhancing the accuracy of the fatigue damage assessment. In the stress counting part, the model incorporates time information associated with each cycle. This concept is subsequently applied in determining the identified cyclic strain information, thereby improving the accuracy of the fatigue damage evaluation. Finally, this study applies the new model to an online damage evaluation of a turbine stationary blade using actual operating data from a micro gas turbine. The results obtained from the new model are compared with the EOH recommended by the OEM, validating the accuracy and applicability of the new model.

A comparative study on the low-cycle fatigue properties of 316LN austenitic stainless steel with and without a hold period at the maximum tensile strain was performed. Different hold periods (0 s, 60 s, 120 s, 300 s, 1800 s) at a constant strain amplitude of ±0.8% were employed in creep-fatigue tests at 550 °C. Dynamic strain aging (DSA), creep and thermal recovery dominated the deformation and failure behavior. The evolution process of DSA activity and stress relaxation caused by creep presented an opposite trend during cycling. The amount of stress relaxation increased while the associated inelastic strain rate decreased with increasing dwell time, which promoted the accumulation of intergranular damage per cycle and facilitated the formation of dislocation cells. The enhanced process of cross-slip attenuated the DSA activity, which compensated for the increased creep damage; thus, the fatigue life remained almost constant after the introduction of a hold period of 300 s. Interestingly, the fatigue life showed a slight increase when the hold period increased to 1800 s due to the increased thermal recovery process. [ABSTRACT FROM AUTHOR]

In this paper, the time-dependent damage evolution in carbon fiber-reinforced silicon carbide ceramic-matrix composites (C/SiC CMCs) under creep fatigue loading at elevated temperature was analyzed using a micromechanical approach. Synergistic effects of creep fatigue peak stress level and damage in the matrix and the interface on time-dependent damage evolution in C/SiC composites were analyzed. Next, relationships of time-dependent creep fatigue damage mechanisms, damage parameters, environmental temperature and duration were determined. Then, the effects of composite constituent properties, creep fatigue damage state, environmental temperature, and duration on time-dependent damage evolution in C/SiC composites were analyzed. Furthermore, time-dependent composite strain response and interface debonding and oxidation state in C/SiC composite under different creep fatigue peak stress levels were predicted. Under creep fatigue loading, the composite internal damage evolution contributed to the increased time/temperature-dependent composite peak strain. Hysteresis-based damage parameters were developed and utilized to monitor C/SiC composite internal damage evolution. Under creep fatigue loading, the hysteresis area and width increased with oxidation duration to a peak value and remained constant, and the hysteresis modulus decreased with oxidation duration. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Online damage evaluation based on monitored complex cyclic loadings has become an important technique for reliability assessment, especially in high-temperature environments where creep occurs in addition to fatigue. Accuracy and rapidity of calculation are basic requirements for online damage evaluation methods. However, current creep damage evaluation methods seldom consider the fluctuation in stress, which leads to inaccuracy in life-consumption estimates. In addition, traditional cycle-counting methods are not applicable to online use. In this study, an online creep-fatigue damage evaluation method is proposed that accounts for the creep behavior that occurs under fluctuating loads. The cycle-counting method is modified from a rainflow-counting algorithm; it broadens the counting of half-cycles and adopts a new equivalent temperature in the stress-strain response calculation. The proposed method is explained in detail and demonstrated with a case study. The application of this method to a high-temperature, high-pressure pipe demonstrates its online applicability and accuracy. A time-matching algorithm is developed to display the damage evolution in real time, thus revealing the link between the incremental damage and the current load conditions, and yielding an intuitive demonstration of a given component's state of health. [ABSTRACT FROM AUTHOR]

• The extended A-F crystal plasticity model is used to simulate macroscopic and microscopic deformations of 316RF steel. • Effect of micro-defects of different sizes on the LCF and CFI behavior is examined at 650 °C. • Geometric sizes effects of micro-defect on fatigue accumulation is analysed by three fatigue index parameters. The main purpose of this study is to explore and discuss the effect of micro-defects of different sizes on the low cyclic fatigue (LCF) and creep fatigue (CF) behavior in 316FR stainless steel. From the crystal plasticity finite element (CPFE) perspective, representative volume element (RVE) models including different micro-defect sizes are systematically developed, and an extended Armstrong-Frederick (A-F) nonlinear kinematic hardening rule is used to capture the LCF and CF behavior of the 316FR stainless steel. Statistical probability analysis shows that the relative errors between the macroscopic stress–strain simulation results and the experimental data ranged from 0.24% to 16.52%, indicating that the model has high accuracy. Three fatigue index parameters (FIPs) are used to characterize the degree of fatigue of the material: the standard deviation of strain increases with increasing micro-defect size, and the standard deviation of the maximum strain at CF loads exceeds that at LCF loads by 0.0173; the larger the size of the micro-defects are, the coarser the persistent slip band (PSB) around the defects is; the strain distribution under CF loading is wider than that of LCF, and the strain at 99% of the strain accumulation frequency at CF loading exceeds that at LCF loading by 0.078. These results indicate that the larger the defect sizes are, the higher the degree of fatigue accumulation in 316FR stainless steel is, and that the deformation behavior of the material is more complex under CF loading. [ABSTRACT FROM AUTHOR]

Reliability and security of the fusion device are severely affected by the failure of the divertor. It is necessary to have a reliable life prediction for heat sink in W/CuCrZr divertor target, especially during long-term high heat flux operation in future fusion devices in which the high temperature creep accelerates its fatigue failure. In this study, a new approach to creep life was applied to creep-fatigue damage accumulation model for CuCrZr heat sink. It is proved that the results of new method for CuCrZr creep life calculation is more consistent with the experimental results than the previous empirical formula. Then the temperature and stress/strain results were calculated for two types of ITER-like monoblock using thermal–mechanical analysis which shows that high temperature creep could not occur on EAST divertor heat sink of current operating conditions. Based on creep-fatigue damage accumulation model, the predicted life of monoblock for DEMO divertor are given under different operating mode respectively. The model provides theoretical basis and guidance for the divertor engineering design of future fusion reactor like CFETR and DEMO in which the high temperature creep in heat sink must be taken into account due to long-term operation.

To adjust the oscillation of renewable energy sources in the discontinuous generation of electricity,power plants will be used to stabilize the fluctuations. Power plants will start and stop frequently in the fluctuations,which exacerbated the fatigue creep damage of turbine rotor material,thus shorted the life of the power plants. In this paper,the progress in research onturbine rotor material have been introduced,and it is summarized that the damage evolution of rotor steel under low cyclic creep-fatigue loading and thermomechanical loading during start-up and shut-down process of ultra-super critical（ USC） steam turbine. In addition,several life assessment models used widely in engineering practice have been proposed. It provides a theoretical basis for optimizing the design,re-engineering and monitoring of the USC power plant components.

Fatigue damage, time‐dependent creep damage and their interaction are considered as the main failure mechanisms for many high temperature structural components. A generalized methodology for predicting both the high temperature low cycle fatigue (HTLCF) and creep‐fatigue lives by using the hysteresis energy density rate (HEDR) and fatigue damage stress concepts was proposed. Experimental data for HTLCF and creep‐fatigue in Alloy 617, Haynes 230 and P92 steel were respectively collected to validate the method. A better prediction capacity and most of the data points that fall within a 1.5 scatter band were obtained compared with the traditional energy‐based method, time fraction rule and ductility exhaustion model. Moreover, a creep‐fatigue damage diagram was also constructed by using the proposed approach. [ABSTRACT FROM AUTHOR]

In the present exploration, it was attempted to understand the creep‐fatigue (CF) deformation micromechanisms of alloy CM 247 DS LC by conducting low‐cycle fatigue (LCF) and CF tests employing strain amplitude ranging from 0.6% to 1.0% at T = 850°C in the air and performing extensive electron microscopic examinations. The cyclic life of the alloy lessens for all CF tests conducted at 1 and 5 minute dwell time in comparison to LCF tests. Transmission electron microscopy (TEM) examinations confirmed that during CF tests substructure consists of dislocation loop, mixed dislocations, and γ' rafting, a typical creep deformation signature of nickel‐base superalloys, it also consists of features observed during fatigue deformation such as anti‐phase boundary (APB)‐coupled dislocations inside γ' precipitates and local tangles of dislocations. This confirms that the deformation of CF‐tested specimens is ascribed to the synergistic effect of both creep and fatigue. This fact was further verified by scanning electron microscopic (SEM) examinations. [ABSTRACT FROM AUTHOR]

Fatigue crack growth (FCG) and creep-fatigue crack growth (CFCG) in austenitic stainless-steel Fe-25Ni-20Cr (Alloy 709) were measured experimentally and simulated using the finite element method. Temperature conditions investigated were 550°C, 600°C and 700°C, with load hold times of 0 s, 60 s and 600 s. Fracture surface was investigated using scanning electron microscopy and optical imaging. Experiments indicated that crack growth exhibits minimal sensitivity to the various loading conditions evaluated. At 600°C, crack growth rates were independent of hold time or loading frequency. At 700°C, there was a small increase in crack growth rate as a function of hold time, with a 600s hold time causing a factor of 2 increase in crack growth rate over FCG. Finite element simulations were performed to compute plasticity-induced crack closure in the presence of creep deformations at the crack tip. The simulations produced FCG and CFCG rates similar to the experimental results. [ABSTRACT FROM AUTHOR]

Many components operate under creep‐fatigue loading causing an increasing need to learn the knowledge about creep‐fatigue crack growth (CFCG). The stress and microstructural evolution around the crack tip of G115 steel after CFCG were investigated. According to the finite element simulations, the variations of equivalent stress and stress triaxiality in the crack tip zone are presented. Furthermore, the evolutions of martensitic laths, dislocations, and precipitates were systematically studied through electron backscatter diffraction and transmission electron microscopy observations. The laths at the crack tip or under a larger hold time are wider than those remote from the crack tip or under a shorter dwell time. Meanwhile, the dislocation densities reduced significantly at the crack tip or under a larger hold time. The different variations of laths' width and dislocation densities resulted from the different stress triaxiality and creep strain. W‐rich Laves and Cu‐rich phases appeared during CFCG. The Laves phase coarsened rapidly because of the stress‐accelerated diffusion. [ABSTRACT FROM AUTHOR]

• Hold time during creep-fatigue loading decreases plasticity-induced crack closure. • Hold time increases crack surface displacements and reduces crack opening stresses. • Longer creep hold times lead to faster crack growth rates during cyclic loading. • Hold time effect on crack closure highlights the interaction of creep and fatigue. A strip-yield model was formulated to simulate creep-fatigue crack growth and to quantify the influence of hold time on plasticity-induced crack closure during creep-fatigue crack growth. Creep-fatigue experiments have shown that longer creep hold times result in faster crack growth rates in subsequent fatigue cycles. This model advances the idea that a decrease of plasticity-induced crack closure is experienced by the crack during fatigue loading when a longer hold time is applied each creep-fatigue cycle. Consequently, the crack tip experiences an increase in the effective stress intensity factor range causing faster growth rate during the fatigue loading. The weight function method was used to compute stress intensity factors and surface displacements for cracks embedded in a material experiencing elastic, plastic and creep deformations at elevated temperatures. It is shown that the longer the hold time, the larger the creep deformation and crack opening displacements in the near crack-tip region. In turn, this leads to a decrease in the crack-tip opening stress/load and faster crack growth rates during the subsequent fatigue cycle. The model was used to perform simulations of creep-fatigue crack growth at elevated temperatures in a nickel-base superalloy and AISI 316 austenitic steel. [ABSTRACT FROM AUTHOR]

The simplicity of the Engelmaier equation is highly attractive; however, it suffers from two critical flaws: (i) it is incapable of modeling the full range of creep fatigue, from pure fatigue to pure creep; and (ii) the embedded creep function is inconsistent with the constitutive equation of creep. As such, the fitting constants in the Engelmaier equation are not material constants but have limited window of applicability. In this manuscript, three novel creep-integrated fatigue equations that are capable of modeling the full range of creep fatigue and that are embedded with the creep constitutive equations of Dorn, Larson-Miller, and Manson-Haferd are established. The equations are validated and benchmarked against the Engelmaier equation using the experimental creep fatigue data of Sn37Pb and An3.5Ag solders. The fitting constants in these creep-integrated fatigue equations are material constants and therefore can be used with confidence to accelerate creep fatigue testing. The acceleration factors for temperature cycle testing of solder joints in electronic assemblies have been established for these novel creep-integrated fatigue equations. • Novelty: fatigue equation embedded with creep constitutive equation • Superior accuracy: validated with creep fatigue data of Sn37Pb and Sn3.5Ag solders; benchmarked with Engelmaier equation • Novelty: fitting constants of the equation are material constants, independent of design and test conditions. • Usefulness: reliable life prediction for new design; reliable acceleration of temperature cycling test [ABSTRACT FROM AUTHOR]

Fatigue damage, creep damage, and their interactions are the critical factors in degrading the integrity of most high-temperature engineering structures. A reliable creep-fatigue damage interaction diagram is a crucial issue for the design and assessment of high-temperature components used in power plants. In this paper, a new three-dimensional creep-fatigue-elasticity damage interaction diagram was constructed based on a developed life prediction model for both high-temperature fatigue and creep fatigue. The total tensile strain energy density concept is adopted as a damage parameter for life prediction by using the elastic strain energy density and mean stress concepts. The model was validated by a great deal of data such as P91 steel at 550 °C, Haynes 230 at 850 °C, Alloy 617 at 850 and 950 °C, and Inconel 625 at 815 °C. The estimation values have very high accuracy since nearly all the test data fell into the scatter band of 2.0.

Background-Creep-fatigue damage is generally identified as the combined effect of fatigue and creep. This behaviour is macroscopically described by crack growth, wherein fatigue and creep follow different principles. Need-Although the literature contains many studies that explore the crack-growth path, there is a lack of clear models to link these disparate findings and to explain the possible mechanisms at a grain-based level for crack growth from crack initiation, through the steady stage (this is particularly challenging), ending in structural failure. Method-Finite element (FE) methods were used to provide a quantitative validation of the grain-size effect and the failure principles for fatigue and creep. Thereafter, a microstructural conceptual framework for the three stages of crack growth was developed by integrating existing crack-growth microstructural observations for fatigue and creep. Specifically, the crack propagation is based on existing mechanisms of plastic blunting and diffusion creep. Results-Fatigue and creep effects are treated separately due to their different damage principles. The possible grain-boundary behaviours, such as the mismatch behaviour at grain boundary due to creep deformation, are included. The framework illustrates the possible situations for crack propagation at a grain-based level, particularly the situation in which the crack encounters the grain boundary. Originality-The framework is consistent with the various creep and fatigue microstructure observations in the literature, but goes further by integrating these together into a logically consistent framework that describes the overall failure process at the microstructural level. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background--Creep-fatigue behavior is identified as the incorporated effects of fatigue and creep. One class of constitutive-based models attempts to evaluate creep and fatigue separately, but the interaction of fatigue and creep is neglected. Other models treat the damage as a single component, but the complex numerical structures that result are inconvenient for engineering application. The models derived through a curve-fitting method avoid these problems. However, the method of curving fitting cannot translate the numerical formulation to underlying physical mechanisms. Need--Therefore, there is a need to develop a new creep-fatigue formulation for metal that accommodates all relevant variables and where the relationships between them are consistent with physical mechanisms of fatigue and creep. Method--In the present work, the main dependencies and relationships for the unified creep-fatigue equation were presented through exploring what the literature says about the mechanisms. Outcomes--This shows that temperature, cyclic time and grain size have significant influences on creep-fatigue behavior, and the relationships between them (such as linear relation, logarithmical relation and power-law relation) are consistent with phenomena of diffusion creep and crack growth. Significantly, the numerical form of "1 -- x" is presented to show the consumption of creep effect on fatigue capacity, and the introduction of the reference condition gives the threshold of creep effect. Originality--By this means, the unified creep-fatigue equation is linked to physical phenomena, where the influence of different dependencies on creep fatigue was explored and relationships shown in this equation were investigated in a microstructural level. Particularly, a physical explanation of the grain-size exponent via consideration of crack-growth planes was proposed. [ABSTRACT FROM AUTHOR]