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The axial-connected bolts of the thin-walled cylinder structure product failed under random vibration loading acted in the transverse direction. The failure modes include pull-off of the thread on the nut as well as fracture of the bolt. The fracture appearance in fractographic study shows that the failure mechanisms of the bolt connections are shear strength failure of the thread on the nut and fatigue fracture of the bolt respectively. The FEM random vibration analysis was conducted on the overall structure, and the Power Spectral Density(PSD) of the axial force on the bolt was considered as the input loading of the shear strength failure life analysis on the nut as well as the fatigue life analysis on the bolt. Finally the fatigue experiment was conducted on the simplified bolt-connected structure for verification, which showed that the failure conditions and fatigue lives of the specimens were basically the same as those of the original product. Both the results of the fracture appearance analysis and the theoretical analysis are in accordance with those of the fatigue verification experiment, which confirms the failure mechanism of the product. • The failure of the bolt connections occurred in a thin-walled cylinder structure product. • The failure causes of the bolt connections were determined by fractographic analysis as well as theoretical analysis. • The PSD of the axial load was obtained from FEM as the input of shear strength failure analysis and fatigue analysis. • Pull-off of nut thread resulted from shear strength failure, and fracture of the bolt resulted from fatigue fracture. • The results of failure analysis and failure process of the product were confirmed by the verification experiment. [ABSTRACT FROM AUTHOR]

Highlights • Establish the model to calculate critical energy release rate of sandwich panels. • Derive the equation to calculate critical energy release rate. • Calculate G IC and G IIC for facesheet/core delamination of sandwich panels. • Validate the results by comparing with previous work. Abstract Critical energy release rate is one of the basic material parameters to evaluate interfacial performance. This paper presents a method to calculate the critical energy release rate for interfacial delamination of sandwich panels. This method can be applied to the calculation of the critical energy release rate of the interface between different materials. Double Cantilever Beam (DCB) test and Cracked Sandwich Beam (CSB) test have been studied in this paper. Carbon fiber/Nomex honeycomb sandwich panels and aluminum/foam sandwich panels are used for DCB tests to determine G IC. Glass fiber/balsa sandwich panels are used for CSB tests to determine G IIC. The comparison between this paper and previous work has verified the validity of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract In order to study the nonlinear dynamic behaviors of Thermal Protection System (TPS) and the nonlinear dynamic strength of the strain-isolation-pad (SIP), a two degree-of-freedom nonlinear dynamic theoretical model was presented under the acoustic excitation and base excitation. The tile is simplified as a mass point, a linear spring and a damping element, and the SIP is simplified as a mass point, a nonlinear spring and a damping element. On this basis, the solving process of the nonlinear theoretical model and the iterative process of the equivalent linear stiffness coefficient of SIP were derived by the statistical linearization method. The dynamic responses analyzed by the nonlinear theoretical model and linear theoretical model are compared. The nonlinear stiffness of SIP shows obvious influence on behaviors of TPS and dynamic stress of SIP, and the equivalent linear stiffness of SIP is related to the types of excitations. Finally, the influences on above dynamic responses by the nonlinear stiffness level of SIP were studied. The equivalent linear stiffness coefficient of SIP, acceleration of TPS and dynamic stress of SIP decrease with the increase of the nonlinear level for the stiffness of SIP. Highlights • Nonlinear dynamic theoretical model is presented for TPS. • Nonlinear stiffness of SIP is considered. • Iterative process of equivalent linear stiffness coefficient of SIP is derived. • Effects on dynamic responses by nonlinear stiffness level of SIP are studied. [ABSTRACT FROM AUTHOR]

A two degree-of-freedom uncertainty dynamic theoretical model under the acoustic and base excitations was presented to analyze the uncertainty dynamic behaviors of thermal protection system (TPS) and the uncertainty dynamic strength of strain-isolation-pad (SIP). The tile and SIP are both simplified as the combination of a mass point, a linear spring and a damping element, and all the dynamic parameters obey the normal distribution. The probability distributions of responses were derived from adopting the perturbation method. The difference method is used to analyze the sensitivity of the mean responses to random parameters, and the reasonable sensitivity values are obtained under a difference step which is equal to the standard deviation of the random parameter. The probability distributions calculated by the uncertainty theoretical model match well with the Monte Carlo numerical results, so the accuracy of the uncertainty dynamic theoretical model is verified. The researches in this paper provide a theoretical foundation for studying the uncertainty dynamic behaviors of TPS, analyzing uncertainty dynamic strength of SIP and intensifying the integrity and security of TPS. [ABSTRACT FROM AUTHOR]

In this paper an experimental investigation on damage evolution in cross-ply glass fiber reinforced plastic (GFRP) laminates under quasi-static and fatigue loading is presented. Four configurations of lay-up ([0 2 /90 4 ] s , [0 2 /90 2 ] s , [0/90 4 ] s and [0/90 3 /0/90 3 ] s ) with different thicknesses of cracking plies were selected to study the in-situ behavior in the damage initiation, evolution and saturation. Combined with the imaging features of different damages and the characteristic of damage evolution in the laminates, light transmission method was employed to observe the damage state and to record matrix crack density. In fatigue tests, eight stress levels were chosen for each configuration of laminates, including four lower stress levels below the stress level corresponding to the first transverse crack initiation. A conclusion was drawn from the comparison of the results that the fatigue loading with lower stress level accelerates the process of damage evolution and generates damages more thoroughly at failure. [ABSTRACT FROM AUTHOR]

The fatigue test of composite honeycomb sandwich panels has been carried out under random vibration load in this investigation. The test results show that, the failure mode of the honeycomb sandwich structure under random vibration load is the same as that under constant-amplitude load, both of which are core shear failure and the resulting face-core delamination. Based on the test results and the S-N curve of honeycomb sandwich panel under constant-amplitude load, a method has been proposed to predict the fatigue life of composite honeycomb sandwich structures under random vibration load. The core shear stress is taken as the fatigue damage parameter. The validity of the proposed method has been verified by comparing the predicted results with the test results. [ABSTRACT FROM AUTHOR]

Abstract: The mechanical properties of composite materials degrade progressively with the increasing of the number of cyclic loadings. Based on the stiffness degradation rule of composites, a phenomenological fatigue damage model is presented in this paper, which contains two material parameters. They are proportional to the fatigue life of materials and inversely proportional to the fatigue loading level. Thirteen sets of experimental data of composite stiffness degradation were employed to verify the presented model, and the statistical results showed that this model is capable of describing the damage evolution of composite materials. The characteristics of damage development and accumulation of composite materials subjected to variable loading were studied in this paper. Four sets of two-level loading experimental data were cited to verify the damage model, and the results showed that the predicted life is in good agreement with the experimental ones. [Copyright &y& Elsevier]

Abstract: This paper is to simulate the fatigue damage evolution in composite laminates and predict fatigue life of the laminates with different lay-up sequences on the basis of the fatigue characteristics of longitudinal, transverse and in-plane shear directions by finite element analysis (FEA) method. In FEA model, considering the scatter of the material’s properties, each element was assigned with different material’s properties. The stress analysis was carried out in MSC Patran/Nastran, and a modified Hashin’s failure criterion was applied to predict the failure of the elements. A new stiffness degradation model was proposed and applied in the simulation and then a strength degradation model was deduced, which is coupled with the presented stiffness degradation model. The reduced or discounted elastic constants were determined based on the failure mechanism of the laminates and the restrictive conditions of orthotropic property. The fatigue behavior and fatigue life of six kinds of E-glass/epoxy composite laminates with different lay-up sequences were experimentally studied, and the S–N curves and stiffness degradation models in longitudinal, transverse and in-plane shear direction were obtained. These fatigue data were adopted in the simulation to simulate fatigue behavior and estimate life of the laminates. The simulation results, including the fatigue life predicted and the residual stiffness, were coincident with the experimental results well except for the quasi-isotropic laminate for the lack of consideration of the out-of-plane fatigue character in the simulation. [Copyright &y& Elsevier]

Abstract: Very high cycle fatigue (VHCF) test of 82 aluminum alloy LC4CS specimens was done by piezo-electric fatigue testing machine and fatigue life data were obtained. The obtained fatigue life data showed that the fatigue life distribution of the alloy under VHCF has a characteristic of duplex peak, which is related to the locations of fatigue crack initiation. The crack initiation site was found near the specimen surface in each fracture surface, but some defects such as inclusions and voids were found at the crack initiation site for the specimens with shorter life, whereas no defect was found at the crack initiation origin for the ones with longer life. This characteristic makes staircase method measuring the fatigue limit inconsequential, and the fatigue life scatter of the VHCF is far larger than those of low cycle fatigue (LCF) and high cycle fatigue (HCF). The fatigue life data were statistically analyzed and a mixed probability distribution function of two lognormal distribution functions was proposed in the present paper, and results showed that the mixed function is suitable to describe the fatigue life distribution of aluminum alloy LC4CS in the VHCF region. [Copyright &y& Elsevier]

[Display omitted] • Critical plane direction determined by maximum shear stress amplitude. • Spectral multiaxial fatigue damage model proposed based on Susmel's criterion. • Mean stress effect considered by the Goodman's formula. • Random vibration fatigue experiment on the notched plate specimens. • High accuracy achieved on both fatigue hotspot and fatigue lives. A spectral method for the determination of the critical plane is proposed for metallic material under random vibration loadings based on the criterion of maximum shear stress amplitude, where the direction of critical plane is obtained by solving the maximum value of a function using mathematical optimization method and the fatigue critical location of the structure can be determined. A multiaxial fatigue damage parameter is proposed for combined random vibration loading and mean stress loading cases based on Susmel's criterion, which is a Power Spectral Density (PSD) of the equivalent shear stress and can be adopted for fatigue life evaluation. The fatigue life estimation of structures under multiaxial random vibration loadings with mean stresses in the frequency domain could be carried out based on this damage parameter constructed at the fatigue critical location with the spectral method for random vibration fatigue life. The multiaxial random vibration fatigue experiment with mean stress loadings is conducted on the notched plate specimens made of 2297-T87 aviation grade aluminum alloy, and the initiation sites of the fatigue cracks as well as the experimental fatigue lives are compared with those calculated by the proposed models, where satisfactory prediction capabilities on both the fatigue crack initiation locations and fatigue lives of the models are demonstrated. [ABSTRACT FROM AUTHOR]

• Strain history of variable amplitudes is caused by constant repeated impacts. • Mean stress compensation on the Manson-Coffin equation by Morrow's method. • Stress gradient effect considered by the Theory of Critical Distance. • Impact fatigue experiment on the plate specimens of two types of notches. • Critical distance method for impact fatigue life estimation on notched structures. A fatigue life estimation method is proposed for the notched specimens under low-velocity repeated impact loadings. The stress concentration effect at the notch root is taken into account by the implementation of the Theory of Critical Distance, and the continuous variation of strain ranges at the critical point due to the plastic strain accumulation is considered by the mean strain modification. The impact fatigue experiment is conducted on the notched plate specimen of material S45C with the pendulum-type test machine, and the comparison with the numerical analysis results indicates that the proposed model gives a satisfactory prediction on the impact fatigue lives. [ABSTRACT FROM AUTHOR]

• The CPFEM was constructed as a life evaluation tool and calibrated by LCF hysteresis loop. • Porosity-related fatigue damage parameters were evaluated and the GCF parameter is the best in this study. • A new porosity-related fatigue damage parameter distinguishing fracture modes was proposed. • The proposed method has improved the life prediction ability compared with the GCF parameter. Microporosity is one of the most common defects in nickel base single crystal (N-SC) superalloys, which is a great threat to fatigue performance. In this paper, nine porosity-related fatigue damage parameters for N-SC superalloys were selected by referring to those parameters originally proposed for casting and 3D printing metal materials as well as the critical plane damage parameters commonly used in N-SC superalloys. According to the plastic constitutive model of single crystals, a crystal plastic finite element (CPFE) model was established to evaluate these different fatigue damage parameters, and the parameters of CPFE were calibrated by the low cycle fatigue (LCF) hysteresis loop obtained from the fatigue test. The evaluation results showed that the geometric mean of stress–strain concentration factor (GCF) k g was a satisfactory parameter to quantify the effect of porosity defects on fatigue. Inspired by the discovery and considering the slip systems characteristics of N-SC superalloys, the geometric mean of resolved stress–strain concentration factor (GRCF) k rg on slip systems was proposed, and it was found that the max (k rg , k g) could be used to predict the fracture modes of N-SC superalloys. Based on the max (k rg , k g) , a porosity-related fatigue life prediction method which can distinguish the fracture modes was put forward. The prediction results showed that the fracture mode prediction results were consistent with the test results, and the life prediction results were also improved compared with the GCF parameter. [ABSTRACT FROM AUTHOR]

The fatigue damage of composite sandwich panels is divided into two parts: the face sheet damage and the core damage. Both the two kinds of damage cause the performance degradation of panels, however only the core damage results in the ultimate failure. In this paper, a fatigue damage model of the face sheet and the core is proposed and three-point bending tests are carried out to obtain the deflection evolution curves. With the proposed model, the fatigue damage can be predicted accurately, which proves the validity of the fatigue damage model proposed in this paper. [ABSTRACT FROM AUTHOR]

The fiber reinforced polymer/plastic (FRP) laminates are often subjected to random block spectrum loading in engineering. The simplified regular load in the laboratory fatigue tests is not sufficient to describe the actual fatigue damage history of FRP laminates. In order to explore the fatigue damage evolution of FRP laminates characterized by the residual stiffness degradation under complex random loads, some random block spectra are compiled based on the real engineering fatigue loads, and the fatigue tests of two FRP laminates, the E-glass/YPX-3300 glass fiber laminate and T700/YPX-3001 carbon fiber laminate, were conducted under the random block spectra. Four kinds of differently stacked laminates were prepared for each material. The residual stiffness degradation curves are obtained from the experiments. A stiffness degradation model proposed by the authors are used to correlate the residual stiffness evolution data. The results show that the residual stiffness degradation curves of different specimens can reach satisfactory consistency after correlation, though the original experiment data show a large dispersion. The residual stiffness degradation law of FRP laminates under random block spectrum is the same as that under constant amplitude spectrum. The proposed model can well characterize the residual stiffness degradation law of RRP laminates under random block spectrum. • The stiffness degradation law of FRP laminates under random block spectrum is investigated. • The random block spectra are compiled based on engineering loading. • The fatigue tests of two FRP laminates were conducted under the random block spectra. • The stiffness degradation law of RRP laminates under random block spectrum can be characterized by the proposed model. [ABSTRACT FROM AUTHOR]

• The plane passing through the FCP and experiencing the MVRSS is defined as NCP. • The relevant elastic stress fields around the notch root are obtained. • The relation between critical distance l and fatigue damage D b is proposed. • Multiaxial VA fatigue data were collected to check the accuracy of these approaches. In the present paper, the notch critical plane method proposed by the authors is extended from 2D- to 3D-cases. The plane passing through the assumed critical point and experiencing the maximum variance of the resolved shear stress is defined as the the notch critical plane. The linear-elastic stress fields around the notch root are fitted via polynomial functions. The relationship between critical distance, l, and fatigue damage, D b , under variable amplitude loading blocks is proposed. Susmel's parameter and a specific multiaxial cycle counting method are incorporrated into this approach to estimate multiaxial variable amplitude fatigue life. Numerous fatigue data generated by testing five different notched metallic materials were collected from the literature to check the accuracy of the proposed approach. This validation exercise allowed us to demonstrate that this method is highly accurate, with the majority of the predicted experimental results falling within an error band of 2. [ABSTRACT FROM AUTHOR]

• Microscopic observation and statistical investigation of cracks are carried out. • A bimodal distribution model of matrix crack density is established. • VHCF life distribution model of braided CFRP is established. • Fatigue life of CDS is obtained and the life distribution model is verified. The microscopic observation and statistical investigation of matrix cracks are carried out through the ultra-high cycle bending fatigue experiment of braided CFRP (Carbon Fiber Reinforced Plastic) in this paper, and the matrix crack development law of CFRP under ultra-high cycle fatigue load has been studied. It is found that there are two different forms of matrix cracks under the ultra-high cycle fatigue load, and a bimodal distribution model of matrix crack density is established based on the distribution law of matrix crack density. At the same time, the ultra-high cycle fatigue life distribution model of braided CFRP is established based on the matrix crack density distribution model. At last, the corresponding fatigue life of CDS (Characteristic damage state) is obtained through the crack density evolution curve, and the life distribution model is verified. [ABSTRACT FROM AUTHOR]

In this paper, the bending fatigue tests of honeycomb sandwich panels are carried out by using an improved three-point bending test fixture, and the S-N curves at different stress ratios are obtained. Through the records of fatigue damage in the experiment, the failure mode of the honeycomb sandwich panels and the source of fatigue damage are determined. At the same time, through the calculation of the shear stress distribution on the honeycomb wall, the reasons for the difference in the failure morphology of the L-direction and W-direction sandwich panels are clarified. Besides, a life prediction method is proposed and its effectiveness in predicting the fatigue life of sandwich panels has been verified. • Complete three-point bending test of sandwich panels. • Determine the fatigue failure modes of composite sandwich panels. • Observe the growth process of fatigue damage in the core of composite sandwich panels. • Analyze differences of failure modes between L and W direction specimens. [ABSTRACT FROM AUTHOR]

• The multiaxial critical-plane damage parameters are adopted for life evaluation. • The stress energy parameters are proved the most effective in this analysis. • A new method considering the interaction of slip systems is proposed. • The proposed method has achieved an improvement of correlation ability. Fifteen multiaxial critical-plane fatigue damage parameters of isotropic metal materials are applied to the life evaluation of nickel-base single crystal superalloys. These parameters are classified into stress-, strain- and strain-energy parameters, and their predictive abilities are evaluated by 12 groups of single crystal fatigue data obtained from mainly an intermediate temperature range (500–760 °C) where the slip deformation is the main damage mode. The results show that the strain energy group exhibits the best fitting characteristics with correlation coefficients. A topologized resolved shear stress method (TRSS) considering the interaction of main slip systems is further proposed. The dispersion degree of resolved shear stress among the main slip systems is quantified by a dispersion factor, and the real driving capacity of resolved shear stress is amended according to the topology of driving force. The obtained results show that the proposed method has achieved an improvement of correlation ability. [ABSTRACT FROM AUTHOR]

• The matrix crack evolution and its fractal dimension in cross-ply GFRP laminates were studied. • The fractal dimension of matrix crack could be an appropriate damage state parameter. • Fractal dimension failure criterion of cross-ply GFRP laminates is D bf = 1.90. Damage evolution and failure criterion are the focus of structural strength research in fiber reinforced plastic (FRP) composites. In this paper, quasi-static tests and fatigue tests at different stress levels of cross-ply glass fiber reinforced plastic (GFRP) laminates were carried out to obtain the stiffness degradation curves and matrix damage images. Based on the discovery that the matrix damage morphology has statistical self-similarity, the evolution of the matrix damage and its fractal dimension were studied. It is found that the evolution of matrix damage's fractal dimension can be divided into three stages, and the fractal dimension of matrix damage corresponding to the characteristic damage state is independent of load type and stack sequence. When transverse crack initiation, transverse crack saturation and laminate failure occur, the fractal dimensions are D bi = 1.39, D bs = 1.81, D bf = 1.90 respectively. Due to these advantages, the fractal dimension of matrix crack could be an appropriate damage state parameter. [ABSTRACT FROM AUTHOR]

The approach to distinguish crack initiation and crack propagation. • The advanced volumetric approaches are reviewed briefly. • A method is proposed to distinguish crack initiation and crack propagation. • Direction of crack initiation and lives of notches can be predicted by NCP approach. • NCP approach explains the reason why crack initiation in notches is mixed mode. The advanced volumetric approaches are reviewed briefly to state the stress/strain-based or energy-based parameters of fatigue damage region are critical. A new approach is proposed to distinguish crack initiation and propagation stage. The angles of crack initiation are predicted by notch critical plane (NCP) approach (Luo et al. Fatigue Fract Eng Mater Struct , 2019, 42(4): 854–870). NCP is the plane which passes through the fatigue critical point (FCP) and undergoes the maximum shear stress amplitude. The experiment of thin-walled round tube components is conducted to check these approaches. The direction of crack initiation is basically the same as that of NCP. Most of the predicted lives fall within an error factor of 3. [ABSTRACT FROM AUTHOR]

• The micromechanics based model was verified for composite laminates under fatigue loading in this paper, and mechanical behavior of composite laminates with transverse matrix cracks was modelled based on micromechanics theory. • The initiation of matrix cracks in cracked plies was predicted with the definition of the initial matrix crack initiation life, which was considered as a fatigue property of composite materials in this paper, and the equation between the initial matrix crack initiation life and maximum load stress in cracked plies was deduced. • The evolution of matrix crack density in cracked plies was predicted with the distribution of the initial matrix crack initiation life in cracked plies, and the distribution was obtained based on the distribution of critical energy release rate in quasi static model, which ensures the consistency in fatigue model and quasi static model. • The experiment of cross-ply laminates under fatigue loading with four stress levels was conducted, several material parameters were determined based on the experimental results, and the prediction results were compared with the experimental results, including the degradation of normalized longitudinal modulus and evolution of matrix cracks density, and the comparison shows a good agreement. An analytical model for prediction of transverse matrix cracks in composite laminates under fatigue loading was proposed. The micromechanics method was utilized to characterize the damaged behavior of composite laminates. The initial matrix crack initiation life was defined and deduced based on micromechanics method. Then the relation between initial matrix crack initiation life and critical energy release rate was established to obtain the distribution of initial matrix crack initiation life in cracked plies, and the evolution of matrix crack density and stiffness degradation were predicted. The prediction results were compared with experimental results and the comparison shows good agreement. [ABSTRACT FROM AUTHOR]

• Propose a theoretical natural frequency reduction model of woven fibric composite subjected to very high cycle vibration load. • Design a very high cycle bending fatigue test of woven fibric composite. • Verified the saturated state of cracks (CDS). • Propose an on-line natural frequency measurement test. Based on the matrix crack density evolution, a theoretical model is proposed to study the natural frequency degradation of woven fabric composite subjected to very high cycle vibration loading. A very high cycle bending fatigue test of woven fabric composite is designed, and the existence of crack saturated state is verified. An on-line natural frequency measurement test is proposed, which proved the validity of the proposed natural frequency degradation model. [ABSTRACT FROM AUTHOR]

• A model is established to calculate CERR of asymmetrical specimen. • The formula to calculate CERR for asymmetrical specimens is deduced. • CERR for delamination of specimen with asymmetric stiffness are calculated. • By comparing with previous work, a smaller dispersion is observed. • Find that inserts in crack tip may reduce CERR during crack initiation stage. The interface debonding is a major failure mode of composite structures. In this paper, the debonding behavior of the structurally asymmetric interfaces is studied, and the calculating method of the critical energy release rate of such debonding interfaces is proposed. The experimental results show that the critical energy release rate calculated in this paper is more in line with its intrinsic physical attribute of being a material constant, which proves the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• A novel damage model for matrix crack damage under fatigue loading is proposed based on damage mechanics at macro level. • The damage model takes into account the 'edge effect' of matrix cracks in composite laminate under fatigue loading. • The model is applicable to laminated composites under fatigue loading with different stress levels. • Experimental validation demonstrated the effectiveness and predictive capability of the model. A damage model for transverse matrix cracks in composite laminates under fatigue loading was presented in this paper. The model was prosed based on the theory of continuum damage mechanics (CDM) at macro level and could capture the 'edge effect' of matrix cracks in composite laminate under fatigue loading. To obtain the constitutive equation of UD lamina containing transverse matrix cracks, a polynomial Gibbs free energy function was derived, and a macro damage parameter was introduced to characterize the influence of matrix cracks on multidirectional stiffness properties of UD composite. To predict the initiation and evolution of matrix cracks, a previously deduced initial crack initiation life function and a Paris-like equation in terms of damage driving force were employed, respectively. Prediction results of two cross-ply laminates under fatigue loading with different stress levels were compared to the experimental results and prediction results obtained from previously proposed model. The comparison results indicate the presented model is more effective and reliable in predicting the initiation and evolution of matrix cracks and the corresponding stiffness degradation in composite laminates under fatigue loading. [ABSTRACT FROM AUTHOR]

• Improvement of nonlinear fatigue cumulative models considering load sequence effect. • Probabilistic model to take into account the uncertainties of load and material character. • Incorporation of load exceedance variation of fatigue load spectrum. • Verification on 2297-T87 aluminum–lithium alloy under spectrum loading. A probabilistic fatigue cumulative damage model that can be applied to the fatigue life prediction of aluminum alloy under spectrum loading is proposed in this paper. The model is constructed by a novel nonlinear cumulative damage model, the P – S – N curve, and the probabilistic load–exceedance curve. It introduces the randomness of the loading process and fatigue resistance of the material to the deterministic model. In this model, it is derived that the cumulative damage under fleet spectrum loading exhibits an approximate lognormal distribution, and a method to calculate the distribution parameters is provided. Finally, the validity of the proposed probabilistic model is verified through fatigue tests on 2297-T87 aluminum–lithium alloy specimens under random loading, demonstrating its capability to capture the probabilistic nature of the fatigue behavior of aluminum alloy effectively. [ABSTRACT FROM AUTHOR]

In order to solve the difficulty of predicting very high cycle fatigue (VHCF) life of fiber reinforced plastic (FRP), a prediction method based on surface crack density is presented in this paper. According to the general rule of FRP fatigue damage evolution, the crack density is used to characterize the damage state of FRP in this method and further, the crack density-life evolution model of matrix can be established. The VHCF life prediction can be accomplished after obtaining the parameters in the evolution model through multi-load fatigue tests. The threshold of FRP fatigue strain is also assumed to exist in this paper. If the service strain level is lower than this threshold value, no new damage will occur after the matrix crack density reaches the characteristic damage state (CDS), which implies that FPR bearing below-threshold loads possesses an infinite life expectancy. In this paper, the very high cycle fatigue test of single-layer orthotropic woven CFRP has been carried out. The matrix crack density-life curve and the strain threshold of fatigue have been obtained by providing the rationality of this method. [ABSTRACT FROM AUTHOR]

A loosely coupled fluid-structural thermal numerical method is introduced for the thermal protection system (TPS) gap thermal control analysis in this paper. The aerodynamic heating and structural thermal are analyzed by computational fluid dynamics (CFD) and numerical heat transfer (NHT) methods respectively. An interpolation algorithm based on the control surface is adopted for the data exchanges on the coupled surface. In order to verify the analysis precision of the loosely coupled method, a circular tube example was analyzed, and the wall temperature agrees well with the test result. TPS gap thermal control performance was studied by the loosely coupled method successfully. The gap heat flux is mainly distributed in the small region at the top of the gap which is the high temperature region. Besides, TPS gap temperature and the power of the active cooling system (CCS) calculated by the traditional uncoupled method are higher than that calculated by the coupled method obviously. The reason is that the uncoupled method doesn't consider the coupled effect between the aerodynamic heating and structural thermal, however the coupled method considers it, so TPS gap thermal control performance can be analyzed more accurately by the coupled method. [ABSTRACT FROM AUTHOR]

This paper presents a FEM model for the simulation of delamination in composite materials under fatigue loads using extended cohesive interface elements. A virtual fatigue damage variable is proposed to continually locate the crack tip elements with local element information only. The proposed method allows for a fully automatic identification of crack tip elements without any global information. Once crack tip elements are identified, the fatigue damage accumulation is determined by a modified Paris-law with a strain energy release rate correction method to reduce mesh sensitivity. The predicted delamination growth rates of different mesh sizes were compared with experimental results from open literature using a mode-I Double Cantilever Beam specimen and a mode-II 4-point End Notch Flexure specimen respectively. In all cases good agreement was obtained with weak mesh dependency. [ABSTRACT FROM AUTHOR]

• A thermal–mechanical-equivalent fatigue load method was proposed. • A fatigue damage distribution model of fastened structure was established. • The distribution distance was defined to describe the difference. • The method was verified by fatigue tests of aluminum alloy/CFRP hybrid joints. It is difficult to verify the fatigue performance of mechanically fastened hybrid-material structures under the complex environment-load spectrum. A thermal–mechanical-equivalent fatigue load method was proposed, so that the structure has the same fatigue damage distribution under the equivalent load and the original thermal–mechanical load. By considering the influence of environmental temperature on the structural fatigue performance and the dispersion of material fatigue property, the calculation model for the fatigue damage distribution of fastened structure was established. The equivalent load could be determined according to the designed tolerance value of distribution difference. The effectiveness of method was verified by 7050-T7451 aluminum alloy/CFRP laminate plate three-bolt single-lapped hybrid fastened specimens. [ABSTRACT FROM AUTHOR]

In this paper, the S 0 -mode Lamb wave phase velocity at low frequency range is chosen to characterize fatigue damages accumulated in composite laminates under cyclic loadings. A stiffness/velocity degradation model is proposed based on three distinctive damage mechanisms: fiber breaks, matrix cracks and delamination, all of which are always involved in fatigue damage process. In order to reduce the complexity of the damage model, fiber damage is treated as an independent damage and delamination is coupled with matrix cracks. An approximation of shear-lag model is then proposed to avoid any direct measurements of crack density for it is highly impractical in real applications. Following this, energy release rate for formation of matrix cracks is extracted based on measured phase velocity and damage evolution is realized by incorporating a modified Paris law. Controlled fatigue experiments were conducted where in-situ phase velocity was measured by a laser ultrasonic system. The fatigue damages were then characterized using the proposed damage model with the measured velocity. Finally, the ability of proposed model to predict residual lives was also validated and good accuracy has been obtained. [ABSTRACT FROM AUTHOR]

• A multiaxial fatigue life prediction method based on single defect is proposed for L-PBF 316L. • Investigated L-PBF 316L shows Mode I crack growth macroscopically under axial and torsional loading. • It is detected that more than 95% of the specimens have defects in the crack initiation zone. A multiaxial fatigue life prediction method based on single defect for 316L stainless steel processed by laser powder bed fusion is studied. Defects are detected in the crack initiation zone of more than 95% of the specimens. A method based on the small crack propagation theory is applied to predict fatigue life under uniaxial and pure torsional loading. The fatigue parameters obtained from the above method are substituted into the Modified Wöhler Curve Method to predict multiaxial fatigue life. The result shows that the predicted fatigue lives are in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]