Random Load History Research Articles

Multi-layer statistical analysis and surrogate model based fatigue crack growth reliability assessment of lifting lug structure under random load history

The reliability of fatigue crack growth (FCG) in lifting lug structures is a critical component of overall aircraft operational reliability. Assessing the FCG reliability of these structures poses a classic time-dependent challenge, necessitating the consideration of dynamic changes in load distribution, strength distribution, and failure correlations. To address these complexities, a novel FCG reliability assessment method for lifting lug structures has been developed, drawing upon multi-layer statistical analysis theory, artificial neural networks (ANN), and the concept of the minimum order statistic distribution of equivalent strength (Sequ). The introduced variable Sequ enables a direct comparison with applied loads to ascertain structural integrity. Findings suggest that the rate of FCG reliability change is governed by the load and Sequ distributions at any given moment. The predicted Sequ distribution from the new method closely aligns with experimental data, and it offers a more thorough characterization of random load histories. The reliability assessment outcomes of the new method are deemed more rational compared to those of traditional approaches.

Fatigue life estimate of metallic chain links of mooring systems assuming out of plane bending: From constant amplitude to random loading

In this work, a numerical and analytical study of the fatigue life of chains in the mooring system of FPSO platforms is carried out. Initially, analytical equations are proposed to calculate the stress at the hotspot of the critical chain link, considering axial stresses generated by axial loads and out-of-plane bending (OPB). The analytical equations consider the operating angle of the mooring systems as well as the interlink angle of the links. Thus, the validation of the equations is done by comparing the stress values obtained through numerical simulations of the mooring-fairlead system, where a satisfactory correlation was observed. In addition, loads with constant and variable amplitude are generated as well as random load histories, always between the maximum and minimum operating load of the system, which represent 1/3 and 1/6 of the minimum breaking load (MBL) of the chain link. Based on the Smith-Watson-Topper (SWT) approach, the fatigue life of the chain was estimated, considering the analytical value of the stress at the hotspot based only on the axial contribution and later, due to the axial and OPB contributions. Finally, it was verified that the analytical equations were able to determine the stress values at the hotspot and that the effect of normal stress at the hotspot due to OPB can cause a severe loss in the fatigue life of the mechanical component.

A probabilistic fatigue life prediction method under random combined high and low cycle fatigue load history

In this paper, a probabilistic high and low cycle fatigue (H-LCF) life prediction framework is proposed to consider random load history into fatigue life prediction of structures. First, the random load history is generated and quantified by finite element analysis (FEA) and Monte Carlo simulation (MCS). Subsequently, based on the quantification approach and an improved H-LCF damage curve, the framework of probabilistic H-LCF life prediction is then established. A turbine shaft is analyzed by the proposed method, which confirms the superior accuracy of the proposed method than the existing ones. Overall, the proposed method provides an effective way for structures’ fatigue life and reliability assessment.

Pseudo‐dynamic hybrid simulations of steel eccentrically braced frames equipped with cast steel replaceable modular yielding links

AbstractPrevious studies have underlined the importance of establishing a database of high‐fidelity benchmark experimental test results under random loading histories such as earthquake excitations for both existing structural systems as well as newly proposed ones. Such experimental results are useful for understanding the limitations of previously developed numerical models, proposing new numerical models for more recently developed structural systems, better assessing the ultra‐low cycle fatigue (ULCF) life of energy dissipative components, and improving the loading protocols used for element assessments or developments of numerical model. This paper presents experimental results from pseudo‐dynamic hybrid simulations on steel eccentrically braced frames (EBF) equipped with novel cast steel replaceable modular yielding links. The first set of experiments are carried out on a four‐story EBF, with the first‐floor yielding link physically tested in the laboratory. The second set of experiments are performed on a two‐story EBF where the second‐floor link is physically tested in the laboratory, while considering axial loads due to the imbalanced distribution of the seismic weight in the building. Each building structure is subjected to three Maximum Credible Event (MCE) level earthquakes. A framework for performing hybrid simulations on EBFs is proposed where the response of the yielding link is physically captured in a single degree of freedom control system, with or without axial loads. A substructuring strategy is proposed in conjunction with a modeling approach in the integration module. The results confirm the effectiveness of the hybrid simulation framework, which can be adopted in similar studies. Two numerical models are proposed for capturing the response of cast steel links using a simplified and a more advanced approach. The models are first calibrated using incremental reversed‐cyclic experimental test results, and then refined using the hybrid simulation test results. The effects of this calibration improvement are quantified through critically comparing the response prediction for different response parameters before and after improving the calibration with the experimental results. The numerical model which captures the physical mechanism of the cast steel links provides a more accurate response prediction compared to the simplified numerical model using a phenomenological truss with calibrated force‐deformation. The remaining ULCF life of the tested yielding links is experimentally investigated after having sustained three MCE level earthquakes, which indicates a large reserve ductility capacity which is more than twice the required plastic rotation capacity for cast steel links after seismic events.

Study on Multi-scale Time-frequency Analysis of Cutting Force Based on EMD Method

A method for establishing the multi-scale cutting force spectrum under complex random load history is presented according to the non-stationary random characteristics of the cutting force-time history. The IMF components of different time scales are obtained by EMD decomposition of complex random cutting force-time history data. The probability density distribution of cutting force in certain frequency band is obtained as the load spectrum on this time scale. This method avoids the disadvantage of the conventional method that the load or stress is regarded as a constant or variable amplitude load under one frequency to establish the load spectrum. The method for establishing the multi-scale load spectrum can provide a basis for fatigue life calculation and fatigue reliability analysis of mechanical components.

Prognostic Health Monitoring Method for Fatigue Failure of Solder Joints on Printed Circuit Boards Based on a Canary Circuit

Devices mounted on printed circuit boards (PCBs) are subject to temperature variations resulting from power switching and ambient temperature changes, and may be subject to random dynamic load histories from sources such as vibration. Since solder material is mechanically the most ductile part, fatigue failure may occur in solder joints. Health monitoring for fatigue life under field conditions is a key issue for improving availability and serviceability for maintenance. We have developed a failure precursor detection technology and a fatigue life estimation method for ball grid array (BGA) solder joints, based on a canary circuit. This method estimates fatigue failure life of an actual circuit by detecting failure connections in a canary circuit (a dummy circuit of daisy-chained solder joints). The canary circuit is designed to fail before the actual circuit under the same failure mode by using accelerated reliability testing and inelastic stress simulation. A feasibility study of the failure probability estimation method is conducted by applying the method to a PCB on which a BGA component is mounted. It is confirmed that the fatigue life under a thermal cyclic load can be estimated from a canary circuit, that estimation of fatigue life under a random dynamic load is feasible, and that the estimation results are consistent with results from actual random vibration tests. The proposed method is found to be useful for prognostic health monitoring of solder joint fatigue failure.

A modified accumulation damage algorithm for predicting corrosion fatigue life by considering load interaction for aluminum alloys

Fatigue tests were conducted on centrally notched aluminum alloys 2524-T3 and 7050-T7451 under constant-amplitude and actual random spectrum loading in dry air and in 3.5% NaCl sodium chloride solution, and fatigue damage mechanisms under the load interaction and the corrosion effect on fatigue crack initiation and propagation were deduced from fractographic analysis. Pure and corrosion fatigue lives under actual random spectrum load history were modelled based on a modified accumulation damage algorithm accounting for the load interaction. More reasonable predictions were achieved from the modified algorithm proposed in the paper than from the Palmgren–Miner rule.

11.21: Experimental evaluation and explicit fracture simulations of stainless steel seismic dampers

ABSTRACTSeismic dampers with high post‐yield stiffness were recently proposed by the authors as the main energy dissipative system in a seismic‐resistant steel frame. The dampers are hourglass‐shaped pins made of duplex stainless steel and their high post‐yield stiffness significantly reduced the residual drifts of the frame after the design earthquake. This work evaluates the cyclic behaviour of the proposed dampers both experimentally and numerically. Two different geometries of full‐scale prototype dampers were tested under various standard and random cyclic loading protocols in a configuration that reproduced the damper‐brace connection in the actual steel frame. The results of fourteen tests showed that the proposed dampers possess excellent hysteresis and fracture capacity. Following the tests, explicit numerical simulations were carried out using the Abaqus software. Geometry‐independent fracture criteria were calibrated using the results of monotonic and cyclic tests on coupon specimens made of duplex stainless steel, and explicitly included in the numerical simulations of the dampers. The finite element models are able to accurately capture the initiation and evolution of fracture in the prototype dampers subjected to both standard and random cyclic loading histories. The results can be used to calibrate reliable macro‐models for seismic collapse simulations of the proposed frame.

A new paradigm for fatigue analysis - evolution equation based continuum approach

A very general continuum based approach to model both low- and high cycle fatiguebehaviour is described. The approach allows for both isotropic and anisotropic properties undervery general random multiaxial loading histories.

Damaging fatigue cycles determination for random service loadings using mixed Weibull analysis

This paper investigates the fatigue damage behaviour of random service loading histories and suggests a criterion to determine fatigue damaging cycles by using probability values. The rainflow strain range distribution is often used in fatigue damage prediction. The existence of very small amplitude of cycles that do not significantly contribute to damage makes the prediction process unnecessarily complex. Therefore, a criterion to determine the size of damaging cycles that contribute significantly to total damage values is desired. In this study, two datasets were compared, i.e. the standard SAE road profile for the suspension system and an experimental data recorded using a strain gauge installed on a vehicle component. Fatigue damage was determined using the Coffin–Manson, Morrow and Smith–Watson–Topper models. The distribution of strain ranges was identified by distribution fitting process. The relation between strain range magnitude and RMS values was explored using the probability of damage occurrence values. The results show that both sets of strain histories data fit well to a mixed Weibull distribution with n subpopulations. The probability of damage occurrence values obtained were very high, i.e. 0.9362 and 0.9987, indicating very high chances of damage incurred by these damaging cycles. Therefore, 2 RMS values is suggested as a criterion for damaging cycles determination.

A practical approach for evaluating safe fatigue life of hydraulic actuator in helicopter based on a nominal force concept and minimal datasets

A practical approach was developed to evaluate fatigue lives of hydraulic actuators in helicopter. The approach is informed by the paucity of experimental dataset for structural fatigue characteristics of hydraulic actuator. On the basis of available fatigue design knowledge, the structural fatigue characteristics of hydraulic actuator was depicted based on a nominal force concept from the paucity of experimental dataset, and safe fatigue life of hydraulic actuator subjected to actual random spectrum load history was modelled based on a reliability concept. Fatigue tests were conducted on three hydraulic actuators subjected to step constant amplitude loading. Finally, the concepts were applied to experimental data, demonstrating the practical and effective use of the proposed method.

Fatigue life prediction of low‐alloy steel samples undergoing uniaxial random block loading histories based on different energy‐based damage descriptions

ABSTRACTFatigue damage of low‐alloy steel samples tested earlier under uniaxial random loading spectra was evaluated using energy‐based models of Smith–Watson–Topper, Macha (M), Ellyin and Varvani‐Farahani with different descriptions in damage assessment. Damage over peak‐valley events of block loading histories was accumulated by means of these models. Smith–Watson–Topper approach involved stress and strain components on the maximum principal plane to evaluate fatigue life. M model related the life of samples to damage values calculated from the applied stress and strain histories. Ellyin model assessed damage of samples on the basis of dissipated hysteresis energy generated over fatigue cycles. Varvani‐Farahani damage approach assessed fatigue life on the basis of tensile and shear energies acting on critical plane over peak‐valley events of block histories. The predicted lives based on these approaches were compared with those of experimental data reported by M and coworkers. The choice of energy‐based models in damage assessment of steel samples was discussed on the basis of model description and terms of damage models.

Measurement and Simulation of Random Vibro-Impact Responses at Brake Guide Pins

This study firstly conducted measurement of load history profiles at brake guide pins using strain gages subject to random road load history obtained from vehicle durability tests. Then, this study developed a simple mathematical model capable of estimating guide pin load history using the principle of energy conservation for a given road load profile. The model took into account the effect of impact that occurs from a range of acceleration levels and frequency content of the road input. The mathematical model also utilized the measured stiffness of the guide pin specimens and strain versus load relationship to increase the accuracy of the predictions. The estimated loads at a brake guide pin subject to a given random road load history were then computed using the mathematical model and compared to the load history obtained from the measurement. This study also compared cumulative fatigue damages calculated using Smith-Watson-Topper equation with the measured and predicted load profiles at the guide pin. The comparison study showed that the developed simple model is applicable to predict load profiles for fatigue life calculation at brake guide pins.

A formula for the crack opening level under random loading in 2024-T351 aluminum alloy

Based on the fatigue crack growth results of the previous work for 2024-T351 aluminum alloy, the crack closure behavior under random loading was analyzed, and the correlation between the crack opening ratio and the stress ratio under random loading was discussed. The crack opening ratio under random loading can be expressed as a function of the stress ratio for the largest load cycle in a random load history. The correlation obtained is found to provide good predictions for crack growth under random loading.

Random Load History of Hydraulic Support and Application of Monte Carlo Method

Random Load History of Hydraulic Support and Application of Monte Carlo Method

Fatigue crack growth and closure behavior under random loadings in 7475-T7351 aluminum alloy

Fatigue crack growth and closure behavior under random loadings in 7475-T7351 aluminum alloy is investigated by performing various random loading tests. The effects of random load spectrum, history length, and stress ratio on the crack growth and closure behavior are discussed. The crack opening load was automatically determined by using the normalized-extended ASTM method. The crack opening load is nearly constant during a random loading block and is mainly governed by the largest load cycle in a random load history, irrespective of random load spectrum and history length. The fatigue crack growth under random loading can be well described by the crack closure concept.

Study on Fatigue Life of Pressure Vessels Based on Random Load

The paper discusses the fatigue design theory of pressure vessels. For pressure vessel loads absorbed (pressure, temperature, earthquake, wind, snow, etc.) have significant stochastic dynamic characteristics and coupling characteristics, fatigue life analysis of pressure vessels based on random load history is proposed. Discusses in detail the random load spectrum rain flow counting process, the linear damage theory and fatigue life analysis. The new structure reactor of synthesis system fatigue life is calculated, the results show that the fatigue life and the design life of equipment vary widely, the need to improve pressure fluctuations of the synthesis of system.

Strain‐life approach in thermo‐mechanical fatigue evaluation of complex structures

ABSTRACTThis paper is a contribution to strain‐life approach evaluation of thermo‐mechanically loaded structures. It takes into consideration the uncoupling of stress and damage evaluation and has the option of importing non‐linear or linear stress results from finite element analysis (FEA). The multiaxiality is considered with the signed von Mises method. In the developed Damage Calculation Program (DCP) local temperature‐stress‐strain behaviour is modelled with an operator of the Prandtl type and damage is estimated by use of the strain‐life approach and Skelton's energy criterion. Material data were obtained from standard isothermal strain‐controlled low cycle fatigue (LCF) tests, with linear parameter interpolation or piecewise cubic Hermite interpolation being used to estimate values at unmeasured temperature points. The model is shown with examples of constant temperature loading and random force‐temperature history. Additional research was done regarding the temperature dependency of the Kp used in the Neuber approximate formula for stress‐strain estimation from linear FEA results. The proposed model enables computationally fast thermo‐mechanical fatigue (TMF) damage estimations for random load and temperature histories.

Low-Cycle Bending Fatigue of Steel Bars under Random Excitation. Part II: Design Considerations

In this paper, the low-cycle bending-fatigue strength of square and rectangular steel bars under random loading histories is quantified through an experimental program. Based on the experimental data, and considering the fatigue failure mechanisms, a damage accumulation index formula is established. This formula serves as a foundation for further investigation on structural members with other geometrical shapes, with local buckling effects, and/or with welding residual stress effects, etc. After these effects are considered, design principles for low-cycle bending-fatigue strength of steel members can be developed for earthquake engineering applications.

Probabilistic Fatigue–Creep Life Prediction of Composites

In this paper, a continuum damage mechanics-based model is developed to model the damage evolution of composite materials subjected to fatigue and creep loading. A simulation-based procedure of probabilistic creep fatigue life prediction of composite materials is presented with the proposed damage accumulation model. Uncertainties in loading are considered through simulated random loading histories. Material properties are addressed as random variables to consider the uncertainties in materials. The proposed method is capable of considering the interaction effects between different loading levels and the interaction effect between creep and fatigue. The application of the damage accumulation model and the proposed method for probabilistic life prediction are illustrated with a numerical example.