In engineering, many structural components, such as steam turbines, boilers and steam mains in thermal power generation equipment, and reaction vessels and high-temperature, high-pressure piping in petrochemical systems, operate under high-temperature conditions for long periods of time. periods of time. time.
These components not only have to withstand normal working stresses, but also face additional stresses arising from cyclic stresses and rapid temperature fluctuations over a wide range.
As a result, their service life is often affected by creep fatigue and the interaction between creep and fatigue.
The main cause of equipment failure under cyclic loading in high temperature environments is fatigue creep interaction. Accurately predicting its service life is essential for the proper selection, design and safety assessment of high-temperature equipment.
Both the engineering and academic communities have been concerned with this question for a long time, resulting in numerous life prediction models proposed by scholars.
In this post, we provide a brief overview of methods commonly used to estimate the service life of equipment affected by fatigue creep interaction.
Lifetime Fraction Method
The Linear Cumulative Damage Method, also known as the Lifetime Fraction Method, is widely used to estimate the useful life of equipment affected by fatigue creep interaction.
This method assumes that the damage caused by the interaction between fatigue and creep is the result of the linear accumulation of both fatigue damage and creep damage, as expressed in the following equation:
In the above formula, N f represents the fatigue life, n i represents the number of fatigue cycles, tr is the creep failure time, and t is the creep retention time.
The Lifespan Fraction Method simply adds the calculated fatigue damage and creep damage to arrive at the total damage. Although the calculation is simple, it requires obtaining test data for both pure creep and pure fatigue under the relevant temperature conditions.
However, this method has limitations because it does not take into account the interaction between fatigue and creep. As a result, calculation results and accuracy are limited. To address these shortcomings and improve accuracy, researchers have proposed several improved forms of this method.
For example, Xie's correction formula is as follows:
The change proposed by Lagneborg is as follows:
The formula presented above includes the interaction creep damage index (n), the interaction fatigue damage index (1/N), and the interaction coefficients (a and B).
The interaction term is added to the modified expressions, allowing adjustments in the error between the cumulative damage method prediction results and the experimental results. This results in a significant improvement in the reliability of forecast results.
Frequency correction method (FM method) and frequency separation method (FS method)
Currently, most of the fatigue creep life estimation methods used in engineering are based on the strain control mode. One of these methods is the Frequency Correction Method, proposed by Coffin.
The main cause of low-cycle fatigue damage is believed to be plastic deformation.
Eckel proposed the following formula on this basis:
Where: t f is the failure time, K is the temperature-dependent material constant, ϑ is the frequency, ∆ε p is the plastic deformation range.
By incorporating the above formula into the Manson Coffin formula, an expression that takes frequency correction into account can be derived as follows:
The Frequency Separation Method is another improvement of the Frequency Correction Method. This method assumes that the cause of fatigue damage is inelastic deformation and takes into account the effect of retention time on service life under high temperatures.
It introduces the concepts of tensile retention frequency and compression retention frequency and expresses fatigue life as an exponential function of inelastic deformation and retention frequency. This approach highlights the impact of loading frequency on fatigue life more effectively.
As follows:
Where, ϑ C is the compression carrier frequency, ϑ t is the tensile load retention frequency, ∆ε in is the inelastic deformation.
Both the Frequency Correction Method and the Frequency Separation Method are based on a fatigue life estimation model, but effectively incorporate loading frequency to account for creep in the fatigue life estimation model. This makes the new models suitable for estimating the fatigue creep interaction lifetime.
Strain Range Splitting (SRP) and Strain Energy Splitting (SEP)
The strain range division method was proposed by Manson and is based on the idea that even if the amount of strain is the same, the damage caused by time-dependent and time-independent strains is not equal.
Taking into account the interaction between creep and fatigue, the inelastic strain range in a stress-strain cycle is divided into two components: pure mechanical strain range and time-dependent strain range. The damage dealt by each component is then determined based on its unique qualities, and the total damage is calculated by adding up the damage of each component.
Which has the following expression, Cij, β i j is the material constant.
The strain band division method is widely used in the field, but it requires different types of cyclic test data to be effective. The strain energy division method is built on the basis of the strain range division method and establishes a relationship between the strain energy of each deformation and the service life of the material.
Where, C i j , β i j is the material constant determined by the test;
∆U i j is the strain energy;
α i j is the tensile strain energy and the rectangular area σ max. ∆ε P .
According to the linear cumulative damage method, the following life estimation formula is obtained, and F i j is the weight coefficient.
Dong Zhaoqin and He Jinrui used the frequency separation method to modify the relationship between strain energy and life, called the SEFS method, and obtained the following expression, where C, β, m, K is a constant.
The strain range division method and the strain energy division method need a large number of reliable test data as a basis, and many material parameters and mechanical variables need to be considered.
Therefore, it is a long-term work to use this method for life estimation.
Stress Relaxation Band Method
In strain control mode, the interaction between creep and fatigue over a long period of time results in greater stress relaxation. Stress relaxation and creep effect are the main factors contributing to reduced creep fatigue life over prolonged periods.
With this in mind, Nam Soo Woo and colleagues introduced the concept of stress relaxation range into their creep fatigue life prediction model.
The normalized life prediction method is derived based on the relationship between life and retention time, and the relationship between retention time and stress relaxation range, as follows:
In between, Φ, f is the material constant.
The stress relaxation range, being a function of factors such as retention time, initial stress, strain level, temperature, and others, allows the above formula to predict life under various retention times, waveforms, and strain ranges. The Coffin-Manson curve obtained under different conditions can be normalized to produce a primary curve.
The stress relaxation range approach is appropriate for predicting the fatigue creep interaction life in strain control mode.
Loss of ductility method
The method for estimating the fatigue life of ductile materials is based on the ductile exhaustion theory.
According to this theory, fatigue and creep cause damage to components through viscous flow. Fatigue leads to reduced intracrystalline ductility, while creep contributes to reduced grain boundary ductility. These two processes accumulate and worsen over time until they reach a critical value, leading to material failure.
Goswami has conducted extensive research on the interaction between fatigue and creep in CrMo steel and proposed a new model to predict the service life of ductile materials under these conditions.
Where Δσ is the stress range, Δε P is the plastic strain range, Δεt is the total strain range, ε is the strain rate, Δσ is the saturated stress at half-life, and K, A, men are constants of the material.
This model is based on the concepts of strain control mode, strain rate and viscous flow, and is suitable for predicting the service life of CrMo steel under the combined effects of fatigue and creep under strain control and plastic strain dominance.
In addition to the ductility depletion model, there are two other methods for estimating fatigue creep life: the fatigue creep life estimation method based on stress control mode and the mean strain rate estimation model .
The ductility depletion model, on the other hand, is more suitable for stress control mode and can comprehensively reflect the impact of factors such as stress rate, loading rate, retention time, average strain rate and others component life, resulting in high prediction accuracy.
Metallographic life prediction method
Nam Soo Woo and his team introduced a new damage parameter based on the nucleation and growth of creep holes in austenitic stainless steel.
This damage parameter has been proven to effectively describe the damage of materials that have creep holes at grain boundaries.
To implement this method, it is necessary to have micro-level information such as pore area, grain boundary thickness, grain boundary diffusivity, and creep atomic volume.
Damage mechanics prediction method for fatigue creep life
The idea of damage mechanics was first introduced by Kachanov and later developed by Lemaitre and colleagues, who applied it to predict the fatigue life and creep behavior of materials.
Classical damage theory states that the damage variable D represents the reduction in the effective support area of a material due to the formation and growth of microcracks and microvoids. As these microcracks and voids expand, the cross-sectional area of the sample decreases, leading to a decrease in the effective support area (a*) and an increase in stress.
Based on the definition of damage mechanics, it can be concluded that total damage can be expressed as the sum of the increments of fatigue damage and creep damage.
The expression for the increment of fatigue damage and the increment of creep damage is based on the Lemaitre model. The specific form of the damage increment of the fatigue-creep interaction is as follows:
The above formula demonstrates that the damage accumulation described by the damage mechanics model is not linear and takes into account the interaction between fatigue and creep.
In addition to Lemaitre's damage model, Shang and colleagues developed a nonlinear uniaxial fatigue damage accumulation model based on Chaboche's continuous fatigue damage theory. This model takes into account the interdependence of fatigue limit, mean stress, damage variable and loading parameters, as well as the impact of the loading sequence.
Jing and colleagues presented a nonlinear continuum damage mechanics model for the fatigue life of steam turbine rotors. This model considers the influence of complex multiaxial stresses and the interaction between fatigue and creep, and includes the nonlinear evolution of damage.
Fracture mechanics prediction method
Fracture mechanics is divided into two life prediction stages: crack formation and crack propagation.
Since the 1970s, many scholars have proposed using the C* integral to describe the local stress field and strain rate field at the crack apex of an object under creep conditions at any time.
The C* integral is also known as the creep fracture parameter, making the measurement and calculation of the C* integral a crucial research direction in the fatigue creep life estimation method.
Chapuliot, Curtit et al. presented an experimental method to determine the C* parameter of a surface crack in a plate subjected to bending moment and derived the calculation formula for C*.
Fookes and Smith demonstrated experimentally that the total displacement rate can be used to determine the parameters.
Yatomi et al. proposed determining the parameters through the use of the numerically calculated creep load line displacement rate.
A new forecasting method based on multivariate statistics
Goswami is a representative of multivariate statistical methods and proposed a general formula to predict the fatigue creep life of high-temperature materials based on extensive experimental data.
He also provided the basic formulas for predicting the fatigue creep life of CrMo steel, stainless steel, and steel alloys containing tin, titanium, and other materials.
A new prediction method based on Neural Network
A Neural Network (ANN) is a sophisticated non-linear analysis tool that has been developed in recent years. It is able to effectively address any complex non-linear relationship.
One of the most significant advantages of Neural Networks is their ability to find solutions in uncertain systems and variable relationships.
Currently, many researchers have applied Neural Network techniques to predict the fatigue life of materials.
For example, Venkatech et al. proposed a backpropagation neural network method to predict the fatigue creep life of materials at a melting point of (0.7 to 0.8).
Similarly, Srinivasan et al. utilized neural network techniques to predict the service life of 316L(N) stainless steel under fatigue creep interaction.
In 2013, Wang et al. proposed the creation of a new type of adaptive network for predicting creep fracture life. This network has a four-layer structure system and can accurately predict the creep fracture life of ferritic steel with 9-12% chromium.
The results indicate that this method is more accurate than the Larsen Miller parameter method and more effective than the Backpropagation Neural Network.
Prediction model based on conservation of energy and conservation of momentum
Many existing models for predicting fatigue creep interaction life require a large amount of diverse test data. Furthermore, models based on strain control are often difficult to apply and cannot be used for stress control.
Jiang et al. developed a new fatigue creep interaction life prediction model based on the principles of conservation of energy and momentum, which reflect the movement of the system. The aim of this new model is to have a stronger theoretical basis and more direct expression, and can be used for fatigue creep interaction under stress control.
The expression is:
The formula used to predict the life of the fatigue creep interaction has a clear physical meaning and is applicable to both strain-controlled and stress-controlled modes. The required test parameters are easily obtained and the number is limited.
To verify the accuracy of the model, Jiang et al. conducted stress-controlled trapezoidal wave loading tests on smooth samples made of 1.25Cr0.5Mo steel at temperatures of 540°C and 520°C. They used the model to predict the life of the fatigue creep interaction under these two temperature environments.
The predicted results were in good agreement with the actual results.
Service Condition Resistance Interference (SCRI) Model
Zhao proposed a service condition creep property interference model (SCRI model) to predict the service life reliability of high-temperature materials. The model is based on the Z parameter method.
When using the Z parameter method, the dispersion of the resistance resistance of high-temperature materials follows a normal distribution. The Monte Carlo method can be used to simulate the dispersion of service conditions caused by fluctuations in temperature and service voltage, allowing a reliability analysis of the useful life of materials that takes into account the dispersion of performance data and fluctuations in service conditions.
Creep fracture data extrapolation model based on dynamic process
Liu, H et al. proposed a model to extrapolate creep fracture data based on the dynamic process. The model describes the relationship between stress and fracture time.
The model has a limited number of expression parameters, making the calculation process relatively simple. The calculated results are in good agreement with the experimental results.
The expression is:
The Larsen Miller constant (C), the activation energy of the creep process (Q) and the Boltzmann constant (R) are used in the model.
The model improves the accuracy of predicting long-term creep life.
Comparison of test data for 2.25Cr1.0Mo steel and Ti Al metal composite showed that this evaluation method is more accurate than the traditional Larsen Miller Parameter (LMP) method.
Conclusion
This article presents a summary of research results on methods for estimating fatigue creep life over the past few decades.
The linear cumulative damage correction formula takes into account the interaction between fatigue and creep, thereby effectively increasing the calculation accuracy.
Service life prediction methods based on damage mechanics and fracture mechanics have a well-established theoretical basis and can effectively solve service life prediction problems for complex or defective components.
The frequency correction method, frequency separation method and strain range division method provide ideal prediction results, while the strain energy division method and strain energy frequency correction method produce results bad.
Multivariate statistical methods and neural networks are new approaches for estimating fatigue creep life.
In particular, the multivariate statistical method can directly predict the life of three types of materials using a basic calculation formula, while the neural network method is used to solve complex or unknown life prediction problems.