•Energy density exhaustion model for creep-fatigue life prediction is extended.•Mean stress effect is considered in the present model.•A correction-factor of oxidation is used to describe oxidation damage.•A three-dimensional creep-fatigue-oxidation interaction diagram is proposed.The aim of the present work is to propose a generalized strain energy density exhaustion model to predict the creep-fatigue lives. The oxidation damage, which is described by a correction factor representing the non-linear oxidation damage mechanism, is considered in the proposed model. All the 77 experimental data sets of GH4169 superalloy at 650 °C, Inconel 738 superalloy at 850 °C and P91 steel at 550 °C in both tension-hold-only and compression-hold-only tests are used to validate the prediction capabilities of the model. The fatigue, creep and oxidation damages per cycle are separately calculated. Then a three-dimensional damage interaction diagram combined with a suitable enveloping surface is proposed.

•Fatigue and creep-fatigue tests are carried out for GH4169 superalloy at 650 °C.•Σ3 CSL boundaries play an important role in inhomogeneous effect.•Tensile dwells show intergranular damage caused by precipitate-assist micro-voids.•Compressive dwells show oxidation-assisted damage and slip-band-induced cracks.The aim of the present paper is to identify the effects of sampling locations and loading waveforms on high-temperature low-cycle fatigue (HTLCF) and creep-fatigue life of a forged and precipitation hardened nickel-based GH4169 superalloy. Both the deformation and failure mechanisms are considered here. It has been revealed that HTLCF and creep-fatigue life of specimens were influenced by inhomogeneous microstructures at different locations. Compared with the HTLCF tests, the presence of dwell times in creep-fatigue tests tended to reduce number of cycles to failure. Intergranular damage was observed at both crack initiation and propagation stages. For the dwell times under tension, the intergranular damage was mainly associated with precipitate-assist voids. However, oxidation accounted for the presence of intergranular damage for the dwell times under compression.

•Modified strain energy density exhaustion is considered in the present model.•The present model is more accurate by using the cycle-by-cycle concept.•Nickel-based GH4169 superalloy at 650 °C is employed to verify the proposed model.•The history-dependent accumulated damage is monitored in the interaction diagram.The purposes of the present work are to extend the previous energy-based model on the basis of strain energy density exhaustion and to estimate creep-fatigue endurance and accumulated damage using cycle-by-cycle concept in tension-hold-only tests. The nickel-based GH4169 superalloy at 650 °C is employed to fit material constants and to verify the prediction capacity of the present model under various loading conditions. The present model exhibits a higher accuracy than some existing models, especially for certain loading waveforms, where the half-life cycle cannot be considered as a representative one. In addition, the trajectory for time-dependent accumulated damage during the operating period can be monitored in the creep-fatigue interaction diagram.

The fatigue crack growth behavior of the newly developed GH4169 nickel-based alloy at a maximum stress of 700 MPa and different stress ratios was investigated in the present work employing the specimens with a single micro-notch at a frequency of 129 Hz at room temperature. The results demonstrate a typical three-stage process of fatigue crack propagation processing from the microstructurally small crack (MSC) stage to the physically small crack (PSC) stage, and finally to the long crack stage. The crack growth rate in the MSC stage is relatively high, while the crack growth rate in the PSC stage is relatively low. A linear function of crack-tip reversible plastic zone size was proposed to predict the crack growth rate, indicating an adequate prediction solution.

•Sharper pit formed under proportional loading compared with non-proportional loading.•Pit density is strongly influenced by different direction of principle stress plane.•Pit to crack transition mechanisms were addressed under different loading path.Multiaxial corrosion fatigue tests with interruption were carried out on 304 stainless steel in 6 wt.% FeCl3 solution at room temperature. Pit initiation, growth and pit to crack transition behavior under proportional and non-proportional loading were investigated. Under proportional loading, significant sharper pits, higher initial pit density and growth rate were observed in comparison with non-proportional loading. The pit depth growth rate under proportional loading was larger than those under non-proportional loading and without loading. Pit to crack transition mechanism was mainly controlled by mechanical assisted local dissolution under proportional loading while additional hardening under non-proportional loading.

The last few decades have witnessed an increasing emphasis on the development of strain-based approach for predicting the creep life or damage of components operating at elevated temperatures. Creep ductility, as a key parameter in this approach, may vary with a number of factors including strain rate, state of stress, operating temperature, material microstructure, etc. The present paper, however, is focused on reviewing the state-of-the-art understanding of the effects of stress level and stress state on the creep ductility. Mechanisms involving the void growth and coalescence are presented to describe the role of stress level in the variation of uniaxial creep ductility. The prediction capacity of existing empirical ductility models is also assessed in light of uniaxial test data. On the other hand, a vast body of multiaxial creep test data, collected from open literature, is utilized to examine the influence of the state of stress on the creep ductility. Then, a variety of multiaxial ductility factor models are introduced and evaluated with the available experimental data. Finally, a brief discussion on the dependence of creep ductility on the stress triaxiality and Lode parameter, predicted by numerical methods, is provided.

•A holding time at 600 °C during brazing is designed to reduce the residual stress.•The holding time has been determined by a thermal-elasto-plastic-creep simulation.•The simplified method for brazing simulation can underestimate the residual stress.•The simulation method is verified by neutron diffraction experiment.Bonded compliant seal is a new sealing design for planar solid oxide fuel cell. During brazing, large residual stresses are generated which have a great effect on failure of the brazing connection. Therefore, how to decrease the residual stresses is a critical issue for structure integrity. This paper presents a study on decreasing residual stresses by using short-time creep relaxation effect. A sequential-coupled calculation model is developed based on finite element method. The brazing temperature field is firstly obtained by simulating the convection and radiation heating, and then the residual stress is calculated by a thermal-elasto-plastic-creep model. The calculated results are verified by neutron diffraction measurements. During cooling, a short holding time at 600 °C is designed to relax the residual stress by creep effect. The results show that this effect has a remarkable impact on decreasing the residual stress. The stresses in cell, Ag–CuO and foil have been reduced by about 26.9%, 13.6% and 22.1%, respectively, as the holding time increases up to 40 h. When the holding time exceeds 40 h, the residual stresses remain almost unchanged. It is thus suggested that the holding time should be reasonably determined to allow sufficient stress relaxation.

•Creep damage in BCS structure is simulated using a continuum damage model.•The effect of the multi-axial stress on the creep and damage has been considered.•Failure is not located in the region of the maximum creep for the multi-axial effect.•Reducing the thickness of filler metal and foil decreases the creep and damage.•The BCS structure meets the requirement of long-term operation.Planar solid oxide fuel cell (SOFC) operates at high temperature and requires a good creep strength to ensure the structure integrity. This paper presents a creep and damage analysis of a bonded compliant seal (BCS) structure of a planar SOFC considering the effect of as-bonded residual stress and thermal stress, as well as the effect of filler metal and foil thickness. A modified continuum creep-damage model is used in the finite element simulation. It demonstrates that the BCS structure meets the requirement of the long-term operation at the high temperature of 600 °C with an appropriate braze bonding process. The results show that the failure location is not in the region of maximum creep deformation due to the effect of high level multi-axial stress which drastically decreases the multi-axial ductility. Reasonably reducing the thickness of filler metal and foil can decrease the damage of the BCS structure. Based on the consideration of creep and damage, it is proposed that the thickness of filler metal and foil should not exceed 0.1 and 0.05 mm, respectively.

In recent years, the need for high temperature heat exchangers to improve the efficiency of power and chemical conversion systems has been growing. However, the creep design of the high temperature compact heat exchangers has been a primary concern because the working temperature can be well above the creep limit of the materials. To establish the high temperature design criterion for compact heat exchangers, creep behavior of the plate-fin structures and brazed joints are investigated in this paper. The time-dependent deformation and bending stress of the plate-fin structures are obtained analytically by simplifying the fins to elastic springs. The creep damage evolution inside the brazed joint is studied by coupling the finite element method with a damage constitutive equation. The significant effect of creep property mismatch in the brazed joint on the creep strength is demonstrated.

Micro-fatigue tests were performed on 316LSS vacuum diffusion bonded joints to investigate the interfacial fatigue crack growth behavior with discrete micro-voids located ahead of a pre-existing crack tip. In situ observation of the interfacial fatigue crack propagation and micro-voids evolution was carried out during the whole fatigue testing. SEM of the fracture surface was analyzed. The results showed that the interface failure mechanism of similar diffusion bonded joints is different from that of dissimilar materials joints. A brittle mode is observed in the main crack growth. And the ridge interface formed in diffusion bonded joints due to surface roughness can be a resistance to the crack growth. The location of the fatigue crack initiation and the crack propagation direction derived from SEM observation of the fracture surface of the specimen are in consistent with those obtained from the in situ observation by using the optical microscope.

Structural integrity technology has been widely used with great success for the design, manufacture and failure prevention of modern constructions such as chemical and petrochemical plants, power generation and energy conversion systems, as well as space and oceanic exploration. The modern needs of structural integrity technology are largely attributed to the increase of service temperature of the structures that results in the efficiency improvement in energy conversion and chemical processing technologies. Besides the needs arising from large-scale high-temperature plants, the high tech developments, such as micro chemo-mechanical systems and high-power electronics, provide new challenges to structural integrity technology. The present paper summarizes the recent technical progresses in large process plants and the aviation industry, micro chemo-mechanical systems, fuel cells, high-temperature electronics, and packaging and coating technologies. The state-of-the-art of structural integrity technology for high temperature applications is reviewed. Suggestions are provided for the improvement of current design and assessment methods.

A probabilistic model for prediction of bonding time in diffusion bonding is presented based on the stochastic characteristics of surface finish of bonded area. The probabilistic distribution of surface roughness is introduced into a deterministic model of diffusion bonding by taking the parameters of void radius and height as random variables. Monte Carlo simulation technique in conjunction with numerical integration is used to calculate the bonding time and its probabilistic distribution. The sensitivity analysis of parameters is then performed to evaluate the effects of creep exponent and surface roughness on the bonding time. Comparison is also made between the theoretical predictions and available experimental results from previous work on Ti–6Al–4V alloy in order to validate the probabilistic model. The proposed model showed a good agreement with the experimental results.

Small specimen test methods have distinct advantages in life prediction of components operating at high temperatures. Yet some factors which can be ignored in traditional bulk material creep tests should be considered in the small specimens. In the present paper four different miniature specimens used to evaluate high-temperature creep properties of materials, such as small punch, impression, three-point bending and cantilever beam specimens, are discussed. Combined with Kachanov–Rabotnov creep damage constitutive equations, finite element models are established and applied to analyze the creep properties of small specimens. The effect of friction on the steady and tertiary creep properties is further investigated for four different small specimen tests. The results show that the friction existing between the specimen and clamp has a significant influence on the evaluation of creep properties and is more pronounced than that between the specimen and punch. In comparison with the small punch, impression, and three-point bending specimens with friction constraints the three-point bending specimens with fixed ends and the cantilever beam specimens give better results. Smaller ratio of characteristic punch size to gauge length, fixed constraint and smaller or no sliding between the punch and specimen are accordingly recommended.

For small-specimen bending creep tests, large deformation occurs inevitably when the specimen under a large load or a long creep time. In such a circumstance, the conventional method for creep property evaluation, which is based on the small deformation assumption, may fail to attain a sufficiently high accuracy. Three typical specimens including circular ring, three-point bending and cantilever-beam specimens, are therefore examined. Based on the limit load approach, a critical load method is proposed to control the large deformation effect. Analytical solutions of the critical loads of the specimens are derived. Finite element method is used to quantitatively assess the effect of large deformation. The results show that the predicted creep curves of all the three specimens are significantly affected by the large deformation. Creep properties can only be accurately regressed when the applied load is below the critical load. The critical loads calculated by finite element method agree well with the analytical solutions. Furthermore, the analytical solutions are validated by the experimental results. The effect of creep time on the critical load has also been discussed.

•Small fatigue crack initiation and growth mechanisms of GH4169 at 650 °C were investigated.•The effect of δ phase on fatigue resistance and crack growth was discussed.•ΔK might be applicable to correlate the small crack and long crack growth rates.•Two three-stage models are proposed to describe the crack initiation and propagation process.The aim of this paper is to identify the fatigue crack initiation and small crack growth mechanisms of GH4169 at 650 °C in air. Results show that fatigue cracks tend to initiate at oxidized inclusions. The crack incubation period takes up more than 90% of the fatigue lifetime. The δ phase can improve the crack initiation life and the total fatigue lifetime. The similarity between small crack and long crack growth data at relatively high ΔK can be attributed to the similarity of propagation mode. Two three-stage models are proposed to describe the cracks initiation and propagation processes.

•The 3-D creep crack-tip constraint of cracked pipes and test specimens were analyzed.•Correlation of creep constraint between cracked pipelines and specimens was studied.•Single-edge notched tension specimen provides a closely matched constraint with pipes.•The results provide a strong support for use of constraint-designed specimens.Three-dimensional creep crack-tip constraints of axially cracked pipes and conventional test specimens have been characterized and analyzed by a load-independent creep constraint parameter R∗ proposed by authors. An average measure of constraint over the crack front is utilized to correlate the creep constraint between the 3-D axially cracked pipelines and test specimens. It was found that single-edge notched tension specimens provide a closely matched creep crack-tip constraint with axially cracked pipes. The investigation results provide a strong support for use of constraint-designed specimens in creep life assessment of pressurized pipes.

•A new multiaxial creep ductility factor based on cavity growth theory is proposed.•Multiaxial creep ductility model is validated by theoretical solutions and test data.•The influence of microcracks is considered in the creep constitutive equations.•2-D and 3-D FE analyses are performed based on the proposed creep-damage model.•The proposed creep-damage model shows an excellent predictive capability.This article presents a concise multiaxial creep-damage model for creep crack growth considering the cavity growth and microcrack interaction. Special emphasis is put on developing and validating the multiaxial creep ductility factor (MCDF) based on power-law creep controlled cavity growth theory. Good agreements with the theoretical and experimental data prove the effectiveness of the proposed MCDF. The application of the proposed creep-damage model through finite element simulation of the creep deformation and crack growth in C-Shaped Tension and Compact Tension specimens of 316H tested at 550 °C confirms the predictive capability of the proposed model.

•Grain size effect on small crack initiation and growth mechanisms was investigated.•Crack initiation mechanism was different between fine and coarse grained material.•Crack driving force was discussed by using stress intensity factor and crack tip displacement.•The scattering of fatigue lives were dependent on the crack initiation mechanisms.The aim of this paper was to identify the grain size effect on the small fatigue crack initiation and growth mechanisms of nickel-based superalloy GH4169. Results showed that there was a transition of fatigue crack initiation mechanism between fine-grained material and coarse-grained material. Small fatigue crack growth rates were almost constant across a wide range of crack lengths. Once the surface crack length reached the critical size of 200 μm, the crack would propagate fairly quickly. At a given experimental condition, the scattering of fatigue lives of the parallel specimens was dependent on the crack initiation mechanisms.

•A load-independent creep constraint parameter R* was proposed.•The R* at steady-state creep can be used to evaluate constraint for whole creep time.•The R* can be used for ranking constraint levels for various specimens or components.•The R* can be used for predicting constraint-dependent creep crack growth rates.A load-independent creep constraint parameter R* was proposed, and its load-independence was validated using finite element results in previous studies. A fixed distance r = 0.2 mm from a crack tip is chosen to define the R*, and the R* at steady-state creep can be used to evaluate constraint level with little conservatism for whole creep time. The R* can be used for ranking constraint levels for different specimens or components, and for predicting constraint-dependent creep crack growth rates. The constraint-dependent creep crack growth rate equations of a Cr–Mo–V steel have been obtained, and it may be used in creep life assessments.

In the present study, a low alloy Cr–Mo steel cylinder subjected to internal pressure at high temperature with a semi-elliptical crack located at the inner surface is considered. The creep crack driving force parameter C∗-integrals calculated by finite element (FE) method, are compared with results from previous studies, which indicates that empirical equations may be inaccurate under some conditions. A total of 96 cases for wide practical ranges of geometry and material parameters are performed to obtain systematic FE results of C∗-integral, which are tabulated and formulated in this paper. It is observed that the maximum C∗-integral may occur neither at the deepest point nor at the surface point when the aspect ratio is large enough and the value of C∗-integral is significantly sensitive to the crack depth ratio. Furthermore, based on the proposed equations for estimating C∗-integrals and a step-by-step analysis procedure, crack profile development, crack depth, crack length and remaining life prediction are obtained for surface cracks with various initial aspect ratios. It is found that when the crack depth ratio is increased, there is no obvious convergence of crack aspect ratio observed. The magnitude of half crack length increment is always minor compared with the crack depth increment. In addition, the remaining life is much more dependent on the surface crack depth than on the surface crack length.Highlights► Existing empirical equations of C∗-integral for surface cracks may be inaccurate. ► Systematic FE results of C∗-integral from 96 cases are tabulated and formulated. ► Maximum C∗-integral may not occur at deepest/surface point if a/c is large enough. ► The value of C∗-integral is significantly sensitive to the crack depth ratio. ► Crack profile development, crack size and remaining life prediction are obtained.

The micro heat exchangers or micro reactors in miniature chemical and thermal systems entail the design know-how of microchanneled plates or miniaturized multichannel passages with fins. With the increase of temperature and pressure in the chemical and thermal systems, the design of the miniature components against creep failure becomes a primary concern. To develop a simplified design method, the time-dependent deformation and stresses of the plate–fin structures are analyzed by assuming the fins as elastic springs. Using the numerical inversion of Laplace transform and the standard linear solid model, the analytic expressions of the deformation and stresses are derived. The feasibility and accuracy of the method are verified by a comparison of the analytical results with finite element simulations.