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Bolted connections are crucial in joining mechanical assemblies and ensuring the integrity and reliability of structural components. This study proposes a method for estimating bolt loosening life by practically applying material fatigue life prediction methods. First, the study employed the linear cumulative damage rule to predict the loosening life of single bolts under two-block loading conditions. Second, a test device with two bolt attachment points on a single structure was fabricated to model the multi-bolted structure, and tests were conducted. Finite element analysis (FEA) analysis was employed to identify vulnerable points. The loosening life of single bolts predicted using the linear cumulative damage rule exhibited enhanced accuracy within a ±1.2× error band compared with the experimental data despite variations in bolt types and test conditions. The FEA results for the multi-bolt structure demonstrated that the loosening life could be predicted by identifying vulnerable points and estimating the displacements. This study effectively predicts the bolt loosening life, offering valuable data for the reliability assessment of bolted structures.

Holes and their effects on the fatigue behavior and damage propagation of thin-walled structural components remain objects of research. In this paper, the previously untreated effect of round holes in thin plain-woven carbon fiber-reinforced plastic plates subjected to simple block loading is examined, and the implication on both damage propagation and residual tensile strength is investigated. Using three-dimensional digital image correlation, the damage propagation in the performed experimental tests is acquired, and the damage size is quantified. The evaluations reveal a relationship between the damage propagation and applied load level, for which an empirical model has been previously established by the authors. As the number of cycles increases, a saturation behavior is found. Once the increased load is imposed on the plate, damage propagation resumes, leading to further damage propagation that can be described with the same empirical model as the initial damage propagation, including renewed saturation behavior. The subsequent experimental tests to determine the residual tensile strength reveal a positive effect of the existing damage size, as the ultimate load significantly exceeds the ultimate load of the non-damaged plate.

This paper contains a proposition of a new method of determining the fatigue life of elements subjected to non-stationary loads. The model was based on the determination of the time-variable equivalent weighted amplitude. This amplitude is derived on a continuous basis as the arithmetic mean of nth root of the amplitudes that occur up to a given time. The analysis of the proposed model was carried out on the basis of selected literature insights based on specimens made of P91 and P92 steels. The experimental tests were performed under block loading with a zero mean value in the conditions of tension-compression with a small number of cycles.

This paper discusses whether the principal response features of composites subjected to fatigue loadings, including residual strength and lifetime statistics under variable amplitude (VA) loadings, can be resolved based on constant amplitude (CA) fatigue life data. The approach is based on the strength-residual strength-life equal-rank assumption (SRSLERA), providing a statistical correspondence between the static strength, residual strength, and fatigue life distribution functions under CA loadings. Under VA loadings, the strength degradation progression and then the fatigue lifetime are calculated by dividing the loading spectrum into a sequence of CA block loadings of given extents (including one cycle), and assuming that the strength at the end of a generic block loading equals the strength at the start of the consecutive one, namely the equivalent residual strength assumption (ERSA). The consequences of SRSLERA and ERSA are first discussed by re-elaborating a series of uniaxial, statistically sound CA residual strength and fatigue life data obtained under different loading ratios, R, ranging from pure tension to mixed tension–compression to pure compression. It is shown that the static strength Weibull’s shape and scale parameters, as well as the fatigue formulation parameters recovered under pure compression or tension loadings, represent the fingerprint of composite materials subjected to fatigue and characterize their uniqueness. The residual strength statistics, fatigue probability density functions (PDFs), and constant life diagram (CLD) construction are theoretically reported. Then, based on ERSA, the statistical lifetimes under VA loadings and the cycle-by-cycle damage progressions of block repeated loadings are analyzed, and a residual strength-based damage rule is compared to Miner’s rule.

The paper presents results of calculation for modelling of the stressstrain relationship in the case of block loads with mean load value. A model, based on the stable hysteresis loops, was assumed and modified to use for block loading analysis. For stress history calculation, the proposed model and two other constitutive models were used. Results of fatigue test of specimens made of S355J0 steel subjected to bending block loading with mean load value are presented and used to verify the proposed model. In the tests, the mean load was increased and decreased in subsequent blocks. The changes of strain recorded during the tests shown in the paper indicate a different behavior of the material. Damage accumulation degree for block sequence was used to compare the results of calculations. It was shown, that stress history parameters (stress amplitude and mean stress value in this case) are similar for all investigated models.

A numerical analysis of the influence of a corrective function on the calculated durability is presented. The boundaries of variation of arguments have been formed: the limits of endurance and maximum stress amplitudes of the destructive load block. Paradoxical results presented in the graphs were obtained under the boundary conditions provided in the references.

The literature in the area of material fatigue indicates that the fatigue properties may change with the number of cycles. Researchers recommend taking this into account in fatigue life calculation algorithms. The results of simulation research presented in this paper relate to an algorithm for estimating the fatigue life of specimens subjected to block loading with a nonzero mean value. The problem of block loads using a novel calculation model is presented in this paper. The model takes into account the change in stress–strain curve parameters caused by mean strain. Simulation tests were performed for generated triangular waveforms of strains, where load blocks with changed mean strain values were applied. During the analysis, the degree of fatigue damage was compared. The results of calculations obtained for standard values of stress–strain parameters (for symmetric loads) and those determined, taking into account changes in the curve parameters, are compared and presented in this paper. It is shown that by neglecting the effect of the mean strain value on the K′ and n′ parameters and by considering only the parameters of the cyclic deformation curve for εm = 0 (symmetric loads), the ratio of the total degree of fatigue damage varies from 10% for εa = 0.2% to 3.5% for εa = 0.6%. The largest differences in the calculation for ratios of the partial degrees of fatigue damage were observed in relation to the reference case for the sequence of block n3, where εm = 0.4%. The simulation results show that higher mean strains change the properties of the material, and in such cases, it is necessary to take into account the influence of the mean value on the material response under block loads.

Understanding the composite damage formation process and its impact on mechanical properties is a key step towards further improvement of material and higher use. For its accelerated application, furthermore, practice-related modeling strategies are to be established. In this collaborative study, the damage behavior of carbon fiber-reinforced composites under cyclic loading with load reversals is analyzed experimentally and numerically. The differences of crack density evolution during constant amplitude and tension-compression block-loading is characterized with the help of fatigue tests on cross-ply laminates. For clarifying the evolving stress-strain behavior of the matrix during static and fatigue long-term loading, creep, and fatigue experiments with subsequent fracture tests on neat resin samples are applied. The local stress redistribution in the composite material is later evaluated numerically using composite representative volume element (RVE) and matrix models under consideration of viscoelasticity. The experimental and numerical work reveals the strong influence of residual stresses and the range of cyclic tension stresses to the damage behavior. On the microscopic level, stress redistribution dependent on the mean stress takes place and a tendency of the matrix towards embrittlement was found. Therefore, it is mandatory to consider stress amplitude and means stress as inseparable load characteristic for fatigue assessment, which additionally is influenced by production-related and time-dependent residual stresses. The phenomenological findings are incorporated to a numerical simulation framework on the layer level to provide an improved engineering tool for designing composite structures.

Adhesive joints in real-world conditions often experience variable or step loading rather than constant-amplitude fatigue. This study addresses this gap by examining the influence of load sequence and block loading on fatigue damage in adhesive joints of fiber-reinforced polymer (FRP) composites. A novel bilinear traction-separation law based on the Fatigue Crack Growth Rate (FCGR) rule is introduced to predict fatigue failure under step/variable loads, accounting for load history, sequence, and interaction effects. This model was validated using a double-lap joint model under step/variable loading across four experimental scenarios. The proposed model outperformed existing fatigue damage-accumulation models, significantly reducing the Relative Error of Prediction (REP). Notably, the proposed model significantly reduced the Relative Error of Prediction (REP), achieving reductions from 81.10% to as low as 0.013% in certain cases. The proposed bilinear law exhibited an accelerated damage accumulation rate per cycle for low-to-high loading situations and a decelerated rate for high-to-low loading scenarios, aligning more closely with experimental observations. The proposed model offers practical benefits by improving fatigue life predictions, enabling optimized FRP composite designs, and minimizing overengineering. These advancements are particularly relevant in industries such as aerospace, automotive, and wind energy, where structural durability and safety are paramount. This research represents a significant step forward in the fatigue analysis of composite adhesive joints, paving the way for more reliable engineering solutions.

The paper presents results of calculation for modelling of the stressstrain relationship in the case of block loads with mean load value. A model, based on the stable hysteresis loops, was assumed and modified to use for block loading analysis. For stress history calculation, the proposed model and two other constitutive models were used. Results of fatigue test of specimens made of S355J0 steel subjected to bending block loading with mean load value are presented and used to verify the proposed model. In the tests, the mean load was increased and decreased in subsequent blocks. The changes of strain recorded during the tests shown in the paper indicate a different behavior of the material. Damage accumulation degree for block sequence was used to compare the results of calculations. It was shown, that stress history parameters (stress amplitude and mean stress value in this case) are similar for all investigated models.