Methods for fatigue-life estimation: A review of the current status and future trends

Fatigue analysis has been widely studied by many scholars worldwide, and this has resulted in the accumulation of large amounts of experience and theoretical data. In recent years, the understanding of fatigue problems has developed significantly, and this has been widely applied to diverse fields, including highways, aerospace, and automobiles.^1–5 With the development of modern industry, many types of equipment are moving toward high speed and high precision; fatigue failure is thus an important factor restricting the development of machinery and equipment, reducing its working life, and affecting processing accuracy and safe production.^6–8 Accidents due to fatigue failure also emerge from time to time. The Meudon railway accident in 1842, the Aloha Airlines Flight 243 Boeing 737 accident in 1988, and the Delta Air Lines Flight 1288 MD-88 accident in 1996 were all caused by fatigue failure of key components.⁹ The severity and importance of fatigue damage is thus being increasingly recognized.

In engineering applications, more than 80% of the failure damage to parts is the result of fatigue, and this causes incalculable economic losses. As such, index parameters such as the fatigue life and reliability of parts are receiving increasing attention.^10–13 Fatigue analysis can be used to estimate the working life of parts and materials, predict the time of fatigue failure, and potentially avoid the failure of machinery and equipment due to the failure of individual parts. In addition, fatigue analysis can help to avoid overengineered designs which increase costs and waste materials. For example, Chen et al.¹⁴ carried out fatigue analysis of the cutter-head shaft of a sugarcane harvester for the purpose of decreasing its weight and reducing its working life so as to avoid excessive design allowances and reduce energy consumption. It is of great importance to carry out more research on fatigue-life prediction methods and establish a complete and accurate theory of fatigue analysis.

This article reviews and summarizes the current development status of fatigue analysis, presents relevant research results, and provides a technical overview of the subject. The remainder of the article is structured as follows. In Sec. II, an introduction to the theory of fatigue analysis is presented. Sections III and IV discuss analysis and estimation methods, respectively, while Sec. V considers fatigue design methods. Recent research hotspots and the future development of fatigue analysis are considered in Sec. VI, and summary of conclusions is given in Sec. VII.

During their working life, structural members will be subjected to complex loads and stress changes. The progression of load or stress changes with time is called a load spectrum or stress spectrum, and this can be used to reflect the load that a component experiences during its functioning. Before fatigue analysis can be conducted, the fatigue load spectrum must first be determined, and the accuracy of this load spectrum will affect the accuracy of the fatigue analysis. In 1935, Gassner proposed the load spectrum in the form of a spectrum block and applied it to analyzing the reliability of an aircraft structure. After Miner’s theory of cumulative fatigue damage was proposed in 1945, Gassner’s proposed load spectrum was verified. With the rise of computer technology in the 1970s, the pace of research and development of load spectra in fatigue analysis rapidly accelerated.¹⁵ Over the next few decades, the payload spectrum was slowly standardized, and this was initially used in the aerospace industry. The development of the aviation load spectrum included standardized load histories such as TWIST, MiniTWIST, and FALSTAFF. By the 1980s, the use of standard load spectra was also developing in fields such as automobiles, wind power, and offshore engineering.¹⁶ 

The compilation of a load spectrum is divided into three steps: the collection of load signals and their processing, the discarding of unsuitable load signals with large errors, and the final compiling of the load spectrum. There are two common ways to obtain a load signal. One is to acquire the full load signals of parts using measurements and then compile the fatigue load spectrum after processing. This method is accurate, but it takes a long time. The other approach is to obtain a load history through finite-element simulation software such as Ansys, ADAMS, or other software. The accuracy of load spectra obtained by this method is relatively low, but the process is inexpensive and requires relatively little time and effort. Chen et al.¹⁷ used astrain gauge on the stabilizer bar of a passenger car to obtain load signals and imported them into nCode for data processing to obtain a load spectrum. Huang¹⁸ compiled the fatigue load spectrum of the flat grid structure of a suspension crane, obtained the load history of a stress point using Ansys, and then processed the load signal using the rainflow counting method to obtain the fatigue load spectrum of the grid structure. This eliminated the tedious and laborious process of obtaining measurements from experiments. Wu¹⁹ used ADAMS to obtain the time–stress history of an engine’s camshaft and then imported this into nCode to process the load signal. He then used stress-fatigue analysis in nCode to obtain the fatigue life of the camshaft.

The S–N curve of material is the relationship between stress and fatigue life, which can be measured by a fatigue test. A complete S–N curve can be divided into the low-cycle fatigue zone, high-cycle fatigue zone, and sub-cycle fatigue zone.^20–24 The curve can be obtained using standard samples on a fatigue testing machine, on which different stress ratios are used to carry out cyclic loading until sample failure. According to the number of cycles and the maximum stress, this can be used to draw an S–N curve. S–N curves can also be obtained by formula estimation or using materials standards.

Figure 1 shows a typical S–N curve, in which the area to the left of N₁ is the low-cycle fatigue region. Low-cycle fatigue is usually the fatigue generated by 10²–10⁵ cycles; it will produce large plastic deformations, so it is usually described by strain. Between N₁ and N₂ is the high-cycle fatigue zone. Generally, loading of more than 10⁵ cycles is referred to as high-cycle fatigue, and it is usually described by stress. Beyond N₂ is the fatigue-limit zone, where no damage will occur to the material, regardless of the number of cycles. The principle of infinite-life design is to ensure that the stress will always be less than the fatigue limit S_f, and in theory, no damage will occur to the parts; their working life can thus be called infinite. Strain-based fatigue analysis, stress-based fatigue analysis, and infinite-life fatigue design are described in detail in later sections.

A nonlinear mathematical model of the S–N curve has been used to calculate the S–N curves of components; the parameters of this nonlinear model have been determined by using fatigue-test data so that an appropriate S–N curve could be constructed.²⁶ In the fatigue analysis of a section roller, Chen et al. carried out fatigue tests, added cyclic loads of different stress ranges, obtained the number of cycles to failure, and created the S–N curve of the material.²⁷ 

Miner’s linear cumulative damage theory is commonly applied in fatigue-damage estimation. Miner proposed that equal-radial cyclic loads and variable-amplitude cyclic loads will cause different damage to materials. In the case of a constant amplitude, each cycle will cause the same damage; in the case of a variable amplitude, each cycle will cause relatively independent damage.²⁹ 

Miner’s theorem is simple in form and easy to understand, but it has some drawbacks. For example, it does not consider the sequence of loading, and there will be small differences in the damage accumulation value when the loading levels are different. Therefore, some researchers have put forward nonlinear fatigue-damage accumulation approaches. For example: the Marco–Starkey theory obtains the nonlinear cumulative damage based on a damage curve;³⁰ Kommers and Henry used the change of the fatigue limit as a damage measure; and Chaboche applied the concept of damage to the study of fatigue.³¹ 

The fatigue-crack formation process in metals is usually divided into three stages: crack initiation, crack propagation, and final failure. The crack propagation can be divided into microcrack propagation and macrocrack propagation. As summarized in Fig. 2, the formation mechanism proceeds as follows:

1. Crack initiation: cracks are generated under the action of alternating stresses, macroscopic defects, or stress concentration.

2. Microcrack propagation: after the initiation of a crack, it will continue to expand. This will first occur along the shear-stress plane at an angle of 45° to the principal stress. At this stage, most cracks will soon stop expanding, while a few cracks can expand to the length of dozens of micrometers.

3. Macrocrack propagation: the direction of macrocrack propagation will gradually become perpendicular to the principal stress axis, and a microscopic feature, namely a fatigue fringe, will appear on the fatigue crack surface. Microscopic and macroscopic crack propagation are also called phases I and II of crack propagation.

4. Final destruction: when a crack expands to a critical size at which the component can no longer bear its required load, instantaneous fracture and final failure will occur.

The Paris formula can be expressed in the stable region of the crack-growth curve. This is shown in Fig. 3, in which the longitudinal crack growth rate is plotted on the vertical axis and the abscissa is the amplitude of the stress intensity factor. In region 1, there is a fatigue threshold value; when the stress intensity factor is greater than this threshold value, the crack will continue to expand. In the fatigue-life design method, the fatigue threshold value is usually a condition for infinite-life design. In region 2, the crack propagates steadily, and the Paris formula is applied in this part. At the start of region 3, the crack is about to expand to the critical value and the component is about to fracture.

There are many factors influencing the fatigue of metal materials. The fatigue of metal parts is not caused by a single factor but is generally the result of the comprehensive action of many factors. The common factors are as follows.³⁴ 

Metal components are prone to fatigue and fracture when the stress is greater than the fatigue limit due to overloading with non-cyclic loads or the application of fluctuating loads over an extended period.

Parts with steps, grooves, and rounded corners, are prone to the stress-concentration phenomenon. In the stress-concentration phenomenon, the local stress is far greater than the nominal stress, and regions in which the stress is concentrated are the most prone to cracking. Research has also shown that the larger the size of a part with the same material shape, the lower its fatigue strength; the size of parts also affects their fatigue life.

The surface state of parts often affects their fatigue life. If the surface roughness is high, there will be intermittent small gaps on the surface; these gaps will result in stress concentration, and they will thus affect the fatigue life.

Harsh environmental conditions, such as high or low temperatures or corrosive environments, will affect fatigue life. Temperature variations will cause expansion and contraction of parts, resulting in changes in their internal structure and affecting their fatigue strength.

For a part to have good fatigue performance, it should have a uniform internal composition in terms of material structure, and there should be no intrinsic continuous defects. If there are nonmetallic material inclusions or continuous defects in the material structure, this will reduce the fatigue strength of a part.

Fatigue analysis is generally divided into two types of method that approach the problem from different perspectives: time-domain and frequency-domain approaches. The cumulative damage obtained by time-domain methods is relatively accurate. However, if a cumulative damage calculation is large, it can take a long time to obtain. In contrast, frequency-domain analysis methods can reduce the number of calculations required and save computation time.^35–37 

Time-domain fatigue analysis is usually carried out through experimental monitoring or finite-element software simulations to obtain the time–stress course. Then, the rainflow counting method is used to obtain stress amplitudes and numbers of cycles for conversion into a fatigue load spectrum. Finally, fatigue-life prediction methods and the linear fatigue cumulative damage rule are used to calculate a component’s fatigue life. The time–stress history, rainflow counting method, and cumulative damage theory have been described in detail above. Fatigue-life prediction methods include the nominal-stress method, local stress–strain method, and stress-field-strength method. These will be described in detail in Sec. IV.

There is a set of very mature theoretical models for time-domain fatigue analysis, as this has been the subject of much research. Fatigue failure of mast structures, transmission tower line structures, automobile bodies, and wind turbine support structures caused by wind vibration has been extensively studied using time-domain fatigue analysis.^38–40 Huang et al.⁴¹ used a time-domain method to study the fatigue life of a communication tower; they obtained the stress–time history using the finite-element method and obtained the fatigue life by combining the S–N curve and Miner’s rule, putting forward improvement measures according to their analysis results. Li et al.⁴² carried out fatigue analysis of a ship side-shell structure in the time domain; they proposed a fatigue-evaluation method and discussed two local-stress methods, analyzing their differences. Meng⁴³ conducted a time-domain fatigue analysis on the support structure of an offshore wind turbine; the stress–time history of the support structure was calculated under the combined and individual actions of wind and waves using finite-element software, and the fatigue damage was obtained using a fatigue-life prediction method.

Frequency-domain fatigue-analysis methods generally use the power spectral density (PSD) function of strain or stress as the excitation condition. First, the PSD of a structure is obtained using the material characteristics and time–stress history. Then, using the PSD, fatigue-damage accumulation method, and the S–N curve of the material, the fatigue damage and fatigue life of the structure are obtained using finite-element analysis software.

Frequency-domain fatigue analysis is widely used for structures under random loads. This is because in the frequency domain, these random loads can be described by the PSD, which can be used in combination with the fatigue-accumulation method and finite-element simulation software to directly calculate the fatigue life.⁴⁴ Frequency-domain fatigue analysis has been widely used for vehicles, motor vibrations, wind vibrations, airborne electronics, deep-water pipes, and other mechanical systems.^45,46 Wang et al.⁴⁷ suggested that the spare-tire bracket of a vehicle bears large loads in performing its task, and they carried out a fatigue analysis to examine this. By using frequency-domain analysis, the position distribution of fatigue damage was obtained, and verification tests were carried out. Xue et al.⁴⁸ conducted a fatigue analysis of submarine pipelines. In the frequency domain, a virtual excitation method was combined with Ansys to solve this problem, and the Dirlik method was used to obtain the fatigue life.

In practical engineering applications, there are many kinds of fatigue-life prediction methods. Among these, the most commonly used are the stress-life analysis method, strain-life analysis method, and stress-field intensity method. Each of these has its own advantages and disadvantages; they do not exist alone, but are related to each other, and they have been created through continuous development and application. Because each method has its own characteristics, to make the fatigue-life prediction more accurate and more reliable, it is necessary to choose the most appropriate method for each application environment according to its characteristics.

Analysis based on stress fatigue is the most common and basic form of fatigue estimation, and it is widely used in high-cycle fatigue situations. The main cause of fatigue failure is alternating stress, which can be divided into uniaxial and multiaxial stress.⁴⁹ Uniaxial stress occurs when a part or material is subject to cyclic stress changes only in one direction.^50,51 Multiaxial stress is a complex stress process in which a part or material is subjected to two or more stresses.^52–54 The process of stress-fatigue analysis under random loads is depicted in Fig. 4.

The stress-fatigue-analysis method, also called the nominal-stress-life analysis method, was the first fatigue-life prediction method to be developed. In this process, the locations of potentially problematic areas of a part are first determined, and then a stress–time load history is obtained, either through actual measurements or using finite-element software. A stress–time history can be simplified to obtain a stress spectrum or load spectrum. The most commonly used method for this processing is the rainflow counting method. Finally, the fatigue life is calculated according to the S–N curve of the material and the cumulative damage theory. The basic assumption of stress-life analysis is that the fatigue life of members of the same material is the same if the stress concentration factor and the loading history are the same. The precondition of fatigue-life calculations based on stress-life analysis is that the average stress under external load is zero. Because the S–N curve is expressed as the relationship between zero mean characteristic stress and fatigue life, when the average stress under external load is not zero, a fatigue-life study of the S–N curve cannot be carried out. However, in engineering practice, a large fraction of the average stress is not zero. Therefore, there are several formulae that are commonly used to correct the average stress. These include the Goodman linear model, the Gerber parabola model, the von Mises–Hencky ellipse model, and the broken-line model.

As noted above, stress-fatigue analysis was the first approach to be developed, and it is still used now.⁵⁵ Xu and Guo⁵⁶ used this method to analyze the life of an automobile wheel rim under the condition of a bending moment load. They carried out finite-element analysis and used theoretical calculations to verify the accuracy of their assessment. Hang et al.⁵⁷ studied the fatigue load of wind turbine blades under the effects of bend–twist coupling (BTC). Based on the stress method, the correctness of the model and the influence of the BTC were verified.

Strain fatigue-life prediction is mainly used in the cases of low-cycle fatigue and large plastic deformations.⁵⁸ Strain fatigue-life estimation is based on the strain curve of the material; stress and strain analysis of potentially problematic locations on a part is carried out with the help of some engineering methods, and then the fatigue damage is obtained through cyclic counting so as to obtain the fatigue life.⁵⁹ An outline of this approach is shown in Fig. 5.

The strain-fatigue-life analysis method is also called the local stress–strain-life analysis method, and it was proposed after the 1960s. In this approach, a potentially problematic region of a part is first identified, and a stress or load spectrum of this area is then obtained using the strain curve of the material. Finally, the fatigue life of the region is calculated according to the strain-life curve and the cumulative damage theory. The basic assumption of the local stress–strain method is that the fatigue life of components of the same material under the same cyclic load will be the same as the local strain. The local stress–strain method can calculate the fatigue life of notched parts, making up for the shortcomings of the nominal-stress method. It considers the influence of plastic deformation on the fatigue life, as well as the mutual influences among the load history, geometric shape, and material properties, and it improves the accuracy of fatigue-life analysis. Xiong et al.⁶⁰ used the local stress–strain method to study the fatigue life of steel wire rope; they verified the accuracy of the approach for predicting the fatigue life through comparison using results obtained from the finite-element method. Zhang et al.⁶¹ used the local stress–strain method to evaluate the life of a crane crack. First, the modified Neuber method and strain curve were used to transform the nominal stress spectrum of the component into a local stress and strain spectrum of the dangerous position. The Neuber method is an approximate method for estimating the relationship between the nominal stress and the local stress and strain. The fatigue life was obtained from the strain-life curve and cumulative damage theory.

Strain-fatigue-analysis methods include elastic (high cycle) and elastoplastic (low cycle) approaches.⁶² There are many theoretical methods under this umbrella, including the advanced mean-value method,⁶³ the complete-probability fast-integration method, and the local-strain method.⁶⁴ Strain-fatigue analysis has a wide range of applications. Ni and Chen⁶⁵ conducted strain-fatigue analysis on automobile stabilizer bars and used HyperMesh, NASTRAN, and nCode DesignLife co-simulation to obtain the fatigue life of the parts. Qiao et al.⁶⁶ carried out a multi-axial strain-fatigue analysis of a compressor cylinder and studied the influence of the cylinder structure and bolt-tightening force on its fatigue life. Li et al.⁶⁷ fitted the strain curve of GH3030 alloy using the Manson–Coffin model and strain-fatigue formula and verified that the fatigue life of the alloy at 800 °C is the lowest when compared with that at 700 °C and 600 °C.

In 1984, Zheng proposed the stress-field intensity method. The basic idea of the stress-field intensity method is that the fatigue life of parts is mainly controlled by the locations of notches, and the fatigue damage is related to the material properties, the maximum stress at the root of the notch, the state of stress and strain at each point in the local damage area, and the stress gradient at each point.⁶⁸ The basic assumption of the stress-field intensity method is that if notched and smooth specimens of the same material have the same stress-field intensity history and smooth parts, then their fatigue life will also be the same.

The location of the faulty area of a component is obtained by finite-element analysis combined with the fatigue load spectrum method, and the stress field of the gap can then be calculated according to the cyclic stress–strain curve. Finally, the material curve and the fatigue life of the component are calculated using the cumulative damage theory. A schematic of the fatigue-analysis process of the stress-field intensity method is shown in Fig. 6.

The stress-field intensity method has many applications in engineering practice. Yao⁷¹ described applications of the stress-field intensity method, including the S–N prediction curve and fatigue design of aircraft structures under complex loading. The stress-field intensity method has good potential for application in fatigue-life prediction; it compensates for the low prediction accuracy and large errors relating to some fatigue behaviors obtained by the nominal-stress and local stress–strain methods. Li et al.⁷² used the stress-field intensity method to evaluate the fatigue of a compressor wheel and provided a calculation method and process for each parameter in the method. They compared the results with those from the nominal-stress method and showed that the stress-field intensity method had better accuracy for predicting fatigue life. Tang et al.⁷³ examined the fatigue of a pumping unit horsehead using the nominal-stress and stress-field intensity methods; they presented the steps of the two methods separately, using the fatigue load spectrum and Ansys to calculate the stress–time history of the vulnerable parts. Finally, they compared the fatigue life with the actual service life of a horsehead, and the two methods were analyzed. The results showed that the stress-field intensity method was more accurate. Guo and Wu⁷⁴ applied the stress-field intensity method to estimate the life of a flat flange weld joint; they presented the basic concepts of the stress-field intensity method, calculated the time history of the stress field of the welded joint, and used the S–N curve and cumulative damage theory to estimate its fatigue life. Comparing the test results with those from a local stress–strain gauge, they concluded that the prediction accuracy of the stress-field intensity method was higher.

There are many kinds of fatigue-life prediction methods. In this section, the nominal-stress method, the local stress–strain method, and the stress-field intensity method have been introduced. These three methods are the most commonly used fatigue-life prediction methods. In addition to these, other approaches include the critical plane/distance method and methods based on fracture mechanics.^75–77 Each method has its own appropriate application scenarios, and the most accurate analysis results can be obtained by selecting the appropriate method according to different structures and scenarios. For example, Wei et al.⁷⁸ proposed a fatigue-life analysis method combining the S–N curve and fracture situation mechanics theory to examine the evolution of fatigue cracks in welded structures, and they verified the accuracy of their method using experiments. Miner’s criterion does not consider the effect of the loading sequence on fatigue life; for this reason, Zhang and Cui⁷⁹ proposed a method combining damage mechanics and the finite-element method that can be used to predict the fatigue life of components under variable-amplitude loading. Thus, in the selection of fatigue-analysis methods, it is necessary to select or combine different fatigue-life prediction methods for fatigue analysis according to the material of the target structure, the loading method, and the degree of crack evolution.

Fatigue is a common form of part damage. To avoid the economic losses caused by fatigue damage, the concept of anti-fatigue design has been proposed. There are different design methods for anti-fatigue analysis, and different approaches are selected for different circumstances to ensure the greatest possible accuracy and applicability. The most commonly used fatigue design methods include infinite-life design, safe-life design, damage-tolerance design, and durability design.⁸⁰ 

As noted earlier, the principle of infinite-life design is to ensure that the stress level is always less than the fatigue endurance limit. According to the S–N curve, when this condition is met, fatigue cracks will not appear in a part. In fracture mechanics, when the stress intensity factor inside a material is less than a critical value, a fatigue crack will not continue to expand, and theoretically, infinite life can be achieved.⁸¹ The infinite-life fatigue design method was first proposed in the former Soviet Union, and it was the earliest method for fatigue design.⁸² In 1991, Fu et al. from the Beijing University of Aeronautics and Astronautics published an infinite-life reliability-analysis method, pointing out that some products that are not easy to maintain usually adopt an infinite-life design so that any cracks do not continue to expand.⁸³ Although infinite-life design is simple and widely applicable, the designed products are usually bulky and large. For some product components with short service times, an infinite-life design will waste material and be expensive. The current trend toward mechanical parts being lightweight and miniaturized has thus meant that there are limitations to the application of infinite-life design.

Safe-life design does not seek to make parts have an infinite service life, but rather to make them have a limited fatigue life during which they will not experience fatigue damage. This design method is based on Miner’s cumulative damage theory and the S–N curve. As described above, Miner’s principle considers that each stress applied to a component and its resulting damage will be independent, and these stresses will gradually accumulate. When the accumulation reaches a certain level, damage will occur. Safe-life design is mainly based on the oblique part of the S–N curve of a material, while infinite-life design used the horizontal part. Safe-life design is the most commonly used fatigue design method, and it is widely applied in the fatigue-life design of aircraft, ships, and vehicles. Safe-life design can make better use of a material across a limited component lifespan; it can ensure the quality of a part while also keeping it lightweight.

Damage-tolerance design is proposed on the basis of fracture mechanics and the crack-propagation equation. This approach considers a critical value of an initial crack in a part and then estimates the remaining life of that cracked part while ensuring that the crack will not expand within a certain period of time. Damage-tolerance theory describes the stress field at the tip of a crack using the stress intensity factor, and the initial defect and critical size of a crack are determined through nondestructive testing. The remaining life of a part is then calculated, and the fracture is controlled to guarantee that the part can work safely within a certain service period.^84,85 The determination of crack size, the detection of the initial crack, and the determination of residual life are the key problems in damage-tolerance design.

Durability design is a comprehensive development of the research on fatigue-fracture control in the 21st century;⁸⁶ it considers safety, function, economy, and other factors to make an overall evaluation.

The previous three sections discussed different methods for fatigue analysis, prediction, and design. Table I provides a summary of the advantages and disadvantages of these methods. In this section, we consider the challenges in this field and the future directions for research.

With the ongoing and rapid development of the machinery industry, the structures of parts and products are also continuously changing. If the theoretical formulae for standard specimens are applied to parts with different shapes and structures, calculation errors will be increased, and the accuracy of fatigue analysis will be affected. A set of suitable fatigue-analysis models has been developed for different parts and products, and these can save time and economic cost. Taking simply supported beams as an example, Luo⁸⁷ analyzed the applicability and limitations of traditional fatigue-analysis methods. He explained that complex vibration forces are not applicable to traditional static stress analysis, and this can be solved through dynamic analysis. Cheng and Zhong⁸⁸ studied the applicability of fatigue-analysis methods used in the evaluation of steam turbines and pointed out that some experts and scholars ignore the material factors in this analysis, which is not appropriate; they explained the influence of the material characteristics on fatigue evaluation and considered some factors affecting fatigue characteristics. They suggested that these influencing factors should be considered in the process of fatigue analysis and gave examples to show that there are great errors between the fatigue life obtained without considering these influencing factors and the actual fatigue life.

One of the difficulties of fatigue tests is that some fatigue parameters are difficult to obtain, and there are few corresponding national or industrial standards. This means that it may not be possible to carry out fatigue tests, or their results may not be accurate. Therefore, it is important to formulate countermeasures to solve the problems of fatigue parameters as soon as possible. There should be more tests of fatigue-analysis methods, and the results of these should be used to verify theoretical and simulation calculations to improve the accuracy of fatigue analysis. Only when theoretical calculations, simulations, and experimental verification are combined can these methods be given more credibility, and this will promote the development and progress of technology. Cao⁸⁹ used SolidWorks to build a three-dimensional model, Ansys Workbench to conduct finite-element analysis, and nCode to predict fatigue life, finally carrying out topology optimization according to the analysis results. The results were found to meet the optimization objectives. However, this work did not include tests to verify whether the fatigue-analysis and optimization results were accurate and matched the practical engineering application. Similarly, Liu et al.⁹⁰ carried out fatigue analysis and optimization of a bagpipe mounting bracket, but they did not conduct fatigue tests to verify the results of the simulation analysis.

With the rapid development of modern industry, many mechanical products have lightweight components as a production goal. The probability of fatigue fracture is greatly increased due to complex structural loads.⁹¹ Therefore, improving fatigue strength and fatigue performance is an urgent problem, and increasing attention is being paid to these areas. Wang et al.⁹² studied the influence of the main shaft structure of a wind turbine on the threaded segment; they showed that the distance between the threaded segment and the main shaft will affect the fatigue strength of the threaded segment. Chen et al.⁹³ used Ansys to study the fatigue strength of a diesel engine crankshaft under the action of cylinder forces, supporting forces, and other factors. Tang⁹⁴ examined the fatigue strength of a wind turbine, analyzed its fatigue status, and obtained the maximum danger point. Sheng⁹⁵ discussed the fatigue performance of automotive radiators and obtained fatigue performance parameters, which are of great significance for fatigue management and the optimal design of radiators.

One of the development directions of fatigue analysis is to combine fatigue technology with optimization technology. An optimization scheme can be put forward to complete the optimization of a design according to the results of fatigue analysis; this enables the achievement of optimization goals such as increasing the working life or reducing the weight of components. Wang et al.⁹⁶ studied the fretting fatigue of a marine diesel engine piston; they calculated the stress distribution using the Smith–Watson–Topper parameter, analyzed some influencing factors, and optimized these parameters to extend the working life of the piston and reduce fretting fatigue. Zhi et al.⁹⁷ proposed a fatigue-reliability analysis approach based on fuzzy design optimization; they constructed an optimal mathematical model for a welding robot in terms of quality and fatigue life and constructed a genetic particle-swarm optimization algorithm and radial basis function neural network proxy model. They used the improved non-dominated sorting genetic algorithm to solve this model. Finally, the fatigue reliability was analyzed using the optimized structure combined with the numerical simulation method. In the study of the fatigue life of a truck cab, Qiu et al.⁹⁸ proposed a hybrid multi-objective robust design optimization method. This used the Taguchi robust parameter design method to refine the intervals of design variables, and they chose a dual kriging method to determine the relationship between mass and fatigue life. The mean and standard deviation were modeled, and a multi-objective particle swarm optimization algorithm was used for robust design. The optimized design was found to increase fatigue life and significantly reduce the mass of the truck cab.

With the ongoing development of science and technology and the rise and wide application of computers, computers have begun to be extensively used in fatigue analysis. Using the rapid-analysis capabilities of computers to predict and analyze fatigue life can save money and time. Many finite-element analysis software packages are equipped with fatigue-analysis modules, including simulation software such as Ansys Workbench, Ansys nCode DesignLife, and Abaqus.^99–103 Ansys nCode DesignLife is a fatigue-durability analysis package developed by HBM nCode; the data is integrated into the Ansys Workbench platform, and it can be used to simulate almost all types of fatigue problems, including high- and low-cycle fatigue, vibration fatigue, and solder-joint fatigue. It can generate data such as load spectra and S–N curves, and it can easily obtain input conditions such as finite-element models and the materials used in fatigue analysis so that users can easily obtain the required results.¹⁰⁴ 

Now, with the ongoing in-depth study of fatigue analysis, fatigue-life prediction is increasingly being applied in diverse engineering fields. To meet the needs of users, the mainstream finite-element software manufacturers will continue to combine fatigue-analysis and finite-element software more closely, and their functions will become increasingly powerful. The fatigue life and fatigue damage obtained from finite-element simulations will become increasingly convenient and rapid, and there will be smaller errors and higher precision.

The prediction of the location of fatigue damage and the determination of fatigue life is being increasingly closely combined with cutting-edge technology, which can simplify and speed up fatigue analysis. These new technologies include neural networks, non-destructive testing, and machine learning. Among these, the application of neural networks in fatigue analysis has been extensive. Chen and Liu¹⁰⁴ summarized the basic background of neural networks and their application in fatigue analysis in their review, and they also summarized some defects and future development trends in the field. They noted that the application of neural networks in fatigue analysis includes five aspects: fatigue-life prediction, fatigue cracks, fatigue-damage diagnosis, fatigue strength, and fatigue loads. Among these, fatigue-life prediction is the most widely used; this combines the consideration of materials and experimental variables as the input conditions, and fatigue life is the output result. Kalayci et al.¹⁰⁵ described the neural-grid method in the first part of their review of soft methods for fatigue analysis. They noted that artificial neural networks are used in 57% of applications and are the most widely used estimation method for material fatigue life in recent years. They also elaborated on some technical methods such as heuristic algorithms, support vector machines, polynomial classifiers, and rough set theory. Ma et al.¹⁰⁶ demonstrated the abilities of neural networks and proposed a new method using them to predict crack growth. Non-destructive testing technology and fatigue analysis are also gradually becoming more widespread; this is because non-destructive testing technology does not damage the material it is being used to examine. Wisner et al.¹⁰⁷ reviewed the non-destructive evaluation methods currently used in fatigue research, including optical, thermal, acoustic, electrical, magnetic, x-ray, and diffraction methods, and they summarized the advantages and disadvantages of each method in fatigue analysis. For example, optical methods and thermal imaging are good at detecting faults at or near surfaces, but they are not as good at detecting fatigue damage in the entire volume. Sakagami¹⁰⁸ described the application status of the detection of fatigue cracks in steel bridges using non-destructive testing technology and proposed infrared thermal imaging for this purpose.

This paper has examined and summarized the current status of fatigue-life prediction methods and the following summary conclusions can be drawn. In terms of fatigue-analysis methods, examining structures in the time and frequency domains have their own advantages and disadvantages. The nominal-stress method and the local stress–strain method are the most widely used classical fatigue-life calculation methods. In terms of fatigue design, using these approaches, we can calculate the structural designs needed to achieve the required design goals.

There are still challenges in the applicability of fatigue-analysis methods and the development of fatigue tests, which should be used to verify the accuracy of the analysis methods. Using finite-element software, neural grids, non-destructive testing techniques, etc., the locations of fatigue damage and the value of the fatigue life of a structure can be quickly and accurately predicted. With the discovery and application of new materials, fatigue analysis can be combined with new technologies to increase the applicability of fatigue-life prediction methods. The combination of fatigue analysis with new technologies will be the main direction of the development of this field.

According to the fatigue-life analysis and prediction methods discussed in this paper, the future development of fatigue analysis is imagined as follows. At present, most of this analysis is carried out on an individual part of a mechanism, and the imposed boundary conditions will inevitably produce errors in comparison with the real boundary constraints, which will in turn lead to inaccuracy in the predicted life. Therefore, in the prediction of fatigue life, not just the key components of a structure should be analyzed and studied, but the minimum life of the entire structure should also be predicted under the overall working environment. In this regard, fatigue analysis has great potential for future development.

In the future development of this field, more effective and accurate methods will be developed with the birth of new technologies. As noted, the combination of fatigue analysis and new technologies will be the main direction of development. Some new areas may be found to be more effective than others, but the discovery and application of new materials will increase the suitability and applicability of fatigue-life prediction methods and other research areas.

The development of new technologies for fatigue analysis should not be limited to the study and application of existing approaches, nor should it be limited to its combination with existing cutting-edge technologies. Instead, there should be a move away from traditional thinking, and new technologies should be developed to challenge the problems currently faced in fatigue analysis and provide more reliable solutions.

This research was financially supported by China Postdoctoral Science Foundation, the National Natural Science Foundation of China (Grant No. 51705132), the Natural Science Project of Henan Provincial Department of Science and Technology (Grant No. 222102220088), and the Natural Science Project of Henan Provincial Department of Education (Grant No. 21A460006).

The authors have no conflicts to disclose.

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Lufan Zhang received a Ph.D. in mechanical engineering from Xi’an Jiaotong University, Xi’an, Shaanxi, China, in 2015. He is currently an Associate Professor with the School of Mechanical and Electrical Engineering, Henan University of Technology, Zhengzhou, Henan, China. His research interest include design, simulation, kinetic analysis, motion control, and ultra-precision positioning motion platforms.

Boshi Jiang is a master’s student. He is currently studying at the School of Mechanical and Electrical Engineering, Henan University of Technology. His main research interest are fatigue analysis, optimization simulation, and ultra-precision positioning motion platforms.

Pengqi Zhang is a master’s student. He is currently studying at the School of Mechanical and Electrical Engineering, Henan University of Technology. His main research directions are piezoelectric drives, control simulation, and ultra-precision positioning motion platforms.