Fatigue Life Distribution Research Articles

A framework for fatigue reliability analysis of high-pressure turbine blades

Fatigue evolution under continued stresses is a process of degradation of material performance with many uncertainties. In order to quantify the uncertainties of materials and working conditions, a probabilistic method is utilized to estimate the reliability of structures by considering scatter of the fatigue life prediction model, in which improvements are provided to model the accumulation of the damage. Firstly, the fatigue parameters are modeled by the Bayesian theory and the finite element analysis. Secondly, the distributions of parameters are transformed by the probabilistic method into the distribution of fatigue life by using the fatigue life prediction model, and a damage accumulation model is chosen to characterize regulation evolution of properties. Finally, the probability distribution function transformation approach is employed to expound distribution of fatigue damage by the known distribution of fatigue life, and a general probabilistic method is then used to estimate the reliability. By combining the above methods, the framework for reliability analysis is established and then is used to calculate the reliability for high-pressure turbine blades in a low cycle fatigue region under variable amplitude loadings.

Fatigue life prediction of hot-riveted shear connections using system reliability

Before bolts were invented, hot-riveting was employed as technological process to produce built-up structural members of steel structures. Nowadays, these structures being still in service and susceptible to fatigue failure, they need to be assessed for their remaining service life. To estimate the fatigue life distribution of riveted connections is, therefore, a topic of relevance. A system reliability model for estimating the probabilistic fatigue life of riveted shear connections is proposed in this paper. Similarly to other models available in the literature, the failure of the connection is modelled by evaluating potential failure at identified critical locations. In addition to these existing models, the proposed formulation is able to consider: (1) the dependency between failure at different critical locations by updating the state of stress given that a failure has occurred and evaluate the residual fatigue life considering the cumulated damage, and (2) the fail-safe behaviour of the connection by using system reliability. Thus, it is possible to evaluate the effect of the position and the number of the rivets on the fatigue life of the connection. The stress and strain field is obtained using the finite element method and the fatigue life estimation is performed using the strain-life approach. The fatigue resistance of the plain material, the rivet clamping force, and the friction coefficient are considered as stochastic quantities. The constant amplitude fatigue life predicted by the reliability model is compared with three datasets of riveted double shear connection having different geometries. In addition, several analyses are performed: (1) a sensitivity study to determine the relationship between the input parameters and the fatigue life, (2) a comparison with other reliability models, and (3) a comparison with a similar connection having a different number of rivets.

P-S-N Curve Description of Laser Metal Deposition Ti-6.5Al-2Zr-1Mo-1V Titanium Alloy after Duplex Annealing.

Fatigue tests were conducted on standard smooth laser metal deposition (LMD) Ti-6.5Al-2Zr-1Mo-1V titanium alloy specimens under three constant-amplitude stresses. The mixed failure behaviors and the influence of internal pores on the fatigue life were discussed in detail. The double-peak characteristics of the fatigue life distribution have been observed, and a bimodal lognormal distribution (BLG) with five variables can be used to describe the fatigue life variation. A parameter estimation method based on the maximum likelihood estimation (MLE) method was proposed to estimate the BLG distribution parameters, and the Newton–Raphson algorithm was used to solve the nonlinear equations derived from the likelihood functions. A P-S-N curve description of LMD titanium alloy was established based on the BLG and verified by fatigue life data obtained from a fatigue test.

Research on Drill Pipe’s Fatigue Life Prediction Based on Reliability

Fatigue life of drill pipe is studied systematically based on reliability analysis. Calculation results show that bending and tensile stress in drill pipe body is significantly greater than that in the tool joint during drilling process. Drill pipe body’s fatigue strength is about 500MPa under the condition that the stress ratio is -1. The fatigue strength of tool joint is about 360MPa under the condition that the average tensile stress is 496MPa. The fatigue fracture position of drill pipe is concentrated on pipe body, and most fatigue cracks originate from pipe’s outer surface. Compared with material fatigue life, the fatigue life of whole drill pipe is significantly lower. Under the condition that the confidence level is 95% and deviation is 5%, drill pipe’s fatigue life distribution is normal distribution while the stress amplitude is 660MPa, 620MPa, 580MPa and 540MPa respectively. With the decreasing of stress amplitude, the peak of logarithmic fatigue life’ probability density distribution curve decreases gradually, and its dispersion increases gradually. Drill pipe’s fatigue life prediction equations whose reliability are 50%, 90%, 99% and 99.9% are calculated separately.

ИССЛЕДОВАНИЕ ПОВЕДЕНИЯ ЦИЛИНДРИЧЕСКИХ ТЕЛ В УСЛОВИЯХ СОВМЕСТНОГО РАСТЯЖЕНИЯ И КРУЧЕНИЯ ПРИ НЕПРОПОРЦИОНАЛЬНОМ НАГРУЖЕНИИ

The work is devoted to studying the behavior of cylindrical bodies of structural steels in the conditions of joint tension and torsion under complex loading. The study is aimed at studying and subsequent modernization of the method of increasing the fatigue life of cylindrical products. It consists in creating the product favorable axial compressive residual stresses in the near-surface area due to the successive elastoplastic deformation, first by tension, and then, during fixation of the longitudinal deformation obtained by tension, by torsion. A mathematical model of elastoplastic deformation by joint tension and torsion of a homogeneous cylindrical body, which allows to calculate the distribution of residual stresses created in the body, is constructed. To check the adequacy of the obtained solution and determine the required material parameters of the model, tests were performed on cylindrical samples of steel 15Cr2MnMoV. The necessary studies were carried out at the Center for Experimental Mechanics of Perm National Research Polytechnic University using the Instron 8850 universal two-axis servo-hydraulic test system, which allows for loading by joint tension and torsion. According to the results of the experiments, graphs of the longitudinal force and torque versus the twist angle were obtained with the deformation sequences studied. By comparing the experimental and calculated dependencies, the adequacy of the developed model was confirmed and the range of deformation modes was established, in which it reflects the behavior of the material with an accuracy acceptable for practice. Instead of the existing method of deformation, which includes a single torsion of a product in a state of tension, a new method is considered, consisting in reversional (alternating) torsion of a cylindrical body in a state of tension. Deformation by sequential tension and reversional torsion allows to provide a favorable (from the standpoint of increasing fatigue life) distribution of residual axial stresses over the cross section of the body with minimum values of residual shear stresses.

Probabilistic modelling of notch and size effect of components under fatigue loadings

For ensuring structural integrity and reliability of engineering components, it is vital to accurately model notch and size effects on fatigue behavior of materials. Based on the highly stressed volume approach, this paper proposes a methodology considering both effects of notch and size to predict the fatigue life distribution of specimens with different geometries. In detail, under Weibull distribution, a dynamic model coefficient vary with different maximum local stresses is proposed by quantifying the highly stressed volumes of different sizes. Experimental data of two alloys are applied for model validation and comparison. Fatigue life distributions of two materials with different geometries are predicted respectively, and estimated P-S-N curves indicate that proposed model predictions agree well with the probabilistic scatter band of experimental results.

The fatigue limit of metals as a characteristic of the multimodal fatigue life distribution for structural materials

Based on the concept of physical mesomechanics, the sequence of damage accumulation mechanisms was considered in accordance with stress level increasing. It was shown that metals behavior evolution takes place in the direction from micro- to meso- and then macroscale level in accordance with introduced bifurcation diagram. It was explained why metals mechanical characteristic named “fatigue limit” cannot be used for simulation of structure durability and in-service lifetime. The problem of bimodal fatigue life distribution for different types of metals was discussed when bifurcation transition from one to another scale level of metals evolution takes place. Test data for “fatigue limit” determination in accordance with the standard technique of more than 250 aviation structural materials were reviewed. Influence of mechanical characteristics on the “fatigue limit” value was analyzed. It was demonstrated that the major part of materials realized all three scale level during stress level increasing. Realization of low-cycle-fatigue is not designed case for operating complex structures when the mesoscale level of metal fatigue does not exist.

Fatigue Failure Analysis on Precracked 304 Stainless Steel Components Repaired by Laser with Addition of Nanocomposites

Abstract The service life of components can be extended by repairing fatigue crack with laser so as to improve resource utilization rate. However, the effect of laser repair may be influenced by the instability of laser treatment. To investigate the addition of nanocomposites on the laser repairing effect, fatigue test under uniaxial tension was carried out to evaluate the fatigue life of precracked 304 stainless steel components repaired by laser. According to the results obtained from fatigue tests, a probabilistic fatigue life distribution model considered the sampling size and discreteness of data was established based on the three-parameter Weibull distribution model and three-parameter stress-life equation. The results of probabilistic fatigue life distribution model show that the fatigue life of components repaired by laser with addition of WC nanocomposites can be enhanced significantly, especially the high cycle fatigue life. Moreover, the microstructure of repaired region show that the WC nanoparticles could refine the recrystallized grains and lead to the improvement of strength and toughness of material around crack tip, which are the main reason of improved fatigue life. Meanwhile, smooth surface of repaired region caused by WC nanoparticles can also prevent the initiation of microcracks.

Statistical Analysis of Two-Parameter Generalized BS-Logistic Fatigue Life Distribution

The logarithmic moment estimations of parameters are proposed for two-parameter generalized Birnbaum-Saunders Logistic fatigue life distribution GBS-Logistic(α, β) under the full sample. The precisions of point estimations are investigated and compared with other point estimations by Monte-Carlo simulations. The approximate interval estimations of parameters are given by using Taylor expansion, and the precisions of approximate interval estimations are investigated by Monte-Carlo simulations. Finally, several examples show the feasibility of the methods.

Experimental study on flexural fatigue performance of rubberised concrete for pavement

ABSTRACT In order to study the probability distribution of flexural fatigue life of self-compacting rubberised concrete (SCRC), the flexural fatigue tests were carried out on 100 × 100 × 400 mm size beam specimens at different stress levels. The test results show that the probability distributions of fatigue life of SCRC can be approximately modelled by two-parameter Weibull distribution, and their fitting correlation coefficients are over 0.9. The shape parameter and scale parameter (two parameters of Weibull distribution) were estimated by different methods, namely the graphical method, the method of moments and the method of maximum likelihood estimates respectively, and it has been showed that the variability of fatigue life distribution of SCRC is higher when compared to plain concrete. The Pf – S – N curve (failure probability Pf , stress level S and fatigue life N) has been generated from the fatigue test data to predict the failure probability and corresponding stress level of the two-million cycle fatigue strength of SCRC. It has been proved that the fatigue performance of SCRC is better than that of the plain concrete by the S – N curve. And the fatigue failure process of SCRC was analyzed by acoustic emission (AE), showing obvious three-stage characteristic with the time.

Statistical analysis of high cycle fatigue life and inclusion size distribution in shot peened 300M steel

In order to fully exploit the benefits of shot peening process in terms of fatigue performance, the proper choice of peening conditions is indispensable, which is largely material specific. In this study, the influence of 3 different peening conditions on the axial fatigue life of high strength 300M steel (modified AISI 4340) was investigated in the high cycle fatigue regime. A statistical estimate of 90% survival life at 95% confidence interval was made to rigorously compare the fatigue performance of the material with different surface conditions. The peening induced roughness, compressive residual stresses and their relaxation during cyclic loading were quantified. It was however revealed, that shot peening had no significant effect on this material when tested at 55% of yield strength (σy,0.2). The fatigue life was dominated by the larger non-metallic inclusions within the bulk material. An empirical relationship between inclusion size and fatigue life was proposed based on this observation. Furthermore, the inclusion size distribution was well described using Gumbel extreme value distribution allowing the largest inclusion to be predicted in a given volume of steel. The prediction results were in good agreement with the experimentally observed value of the largest inclusion size observed at a fatigue crack initiation site.

Deterministic and probabilistic fatigue life calculations of a damaged welded joint in the construction of the trolleybus rear axle

Abstract In trolleybuses in service, fatigue cracks were frequently encountered in a welded structural detail in their rear axle housing. Sufficiently representative stress-time histories for the critical cross section through this part were obtained by measurement during rides with empty as well as fully-loaded vehicles. The fatigue characteristics of the critical location had to be established by estimation. This information was used as the basis for parametric calculations of fatigue life. The main purpose of these calculations was to ascertain whether these in-service failures could have been predicted (and prevented) during the design stage, and what their main cause had been. Furthermore, this investigation explored the feasibility of verifying this structural detail's service life using the fatigue life distribution function. The paper is expanded work published at the 2nd International Conference on Structural Integrity, ICSI 2017, 4-7 September 2017, Funchal, Madeira, Portugal [ 1 ].

Analysis of fatigue life of hybrid fibre reinforced self-compacting concrete

This paper presents the results of an investigation conducted to analyse the flexural fatigue life of self-compacting concrete with different proportions of steel fibre (SF) and polypropylene fibre (PPF) reinforcement. An experimental programme was planned to obtain the fatigue lives of approximately 250 beam specimens under four-point flexural loading. Approximately 90 static flexural strength tests were also conducted to facilitate fatigue testing. The proportions of SF and PPF varied in volume but the total volume was kept at 1%. The two-parameter Weibull distribution was used to describe the probability distributions of fatigue life data at different stress levels. The gradual replacement of SF with PPF in the mixes was found to reduce the variability in the distribution of fatigue life significantly. The maximum increase of 62% in the shape parameter for the fatigue life of a mix with 100% PPF as with a mix containing 100% SF was observed at a stress level of 0·85.

Fatigue behavior of ultrafine tabletop ceramic restorations

ObjectiveThe goal of this study was to investigate the fatigue life, failure modes, and stress distribution of partial ultrafine restorations for posterior teeth in different ceramics. MethodsSixty standard tabletop preparations in epoxy resin G10 received lithium-silicate-based zirconia-reinforced (ZLS) or hybrid ceramic (PIC) restorations in 0.5- or 1-mm thickness bonded with resin cement. The same cycling protocol was applied for all specimens, which consisted of 5000 cycles at 200N, followed by 450-N cycles until the specimens’ fracture or the suspension of the test after 1.5×106 cycles. Axial load was carried out with a 4Hz frequency in Biocycle V2 equipment (Biopdi, São Carlos, SP), with samples immersed in water. The presence of cracks and/or fractures was checked every 2.5×105 cycles, and the survival analysis was performed with the number of cycles in which each specimen failed. All specimens were evaluated by stereomicroscopy and scanning electron microscopy (SEM). After data tabulation, Kaplan–Meier and Mantel–Cox (log-rank test) analyses were performed, followed by multiple pairwise comparison, all with a significance level of 5%, and Weibull analysis. Through three-dimensional finite element analysis, stress distribution and maximum principal stresses in the posterior occlusal veneers were evaluated by comparison of different types of substrate (G10, enamel/dentin, enamel), thicknesses, and ceramic materials. ResultsZirconium-reinforced lithium silicate restorations with 0.5-mm thickness (ZLS.5) showed lower fatigue strength compared with that of 1.0-mm hybrid ceramic restorations (PIC1), and both were similar to other restorations (PIC.5 and ZLS1) (log-rank test, χ2=11.2; df=3; p=0.0107<0.05). ZLS groups presented random defects that culminated in fracture, whereas PIC groups presented defects that increased with mechanical fatigue after some cycling time. Stereomicroscope images show radial cracks due to the translucency of the material. There was no damage caused by the applicator. MPS (maximum principal stress) distributions were similar for the different substrate types, but the highest modulus of elasticity showed slightly lower stress concentration. SignificancePIC is more likely to be used in thinner thickness than indicated by the manufacturer, with fatigue strength similar to that of thicker ZLS restorations.

Flexural fatigue behavior of ultra-lightweight cement composite and high strength lightweight aggregate concrete

This paper investigated the fatigue performance of ultra-lightweight cement composite (ULCC) and lightweight aggregate concrete (LWAC) subjected to flexural load. The ULCC having mean density of 1450 kg/m3 contained cenosphere as micro aggregates and 0.9% volume of polyvinyl alcohol (PVA) fibers. The average 28-days cylinder compressive strengths of the ULCC and LWAC were 62 MPa and 63 MPa, respectively. 108 specimens were tested to measure the flexural fatigue strength under third-point loading. All the specimens were sized as 100 × 76 × 406 mm with an effective span of 300 mm. Using the experimental results, S-N curves were plotted and regression analysis was conducted to propose the equations (called Wöhler equations) for predicting the flexural fatigue strength of ULCC and LWAC. Also, the probabilistic distributions of fatigue life of ULCC and LWAC at a given stress level were modeled using the two-parameter Weibull distribution. The distribution parameters were obtained using three different methods. Design fatigue lives were obtained at different stress levels for ULCC and LWAC corresponding to different failure probabilities. The S-N relationship incorporating the failure probability is found more conservative than that found by Wöhler fatigue equation. The flexural fatigue performance of ULCC is better than that of LWAC, both of having similar strength.

Sensitivity analysis on the fatigue life of solid state drive solder joints by the finite element method and Monte Carlo simulation

We proposed a method to determine the probabilistic fatigue-life distribution of solid state drives (SSDs) due under thermal cycling through finite element method and Monte Carlo simulation and the effect of their design and operating variables on failure through sensitivity analysis. In the developed finite element model, we utilized the Anand model to represent the viscoplastic behavior of solder balls and utilized the Prony series to represent the viscoelastic behavior of a polymer material in the underfill. In order to verify the developed finite element model, we compared the simulated strain with that measured in a thermal chamber. Using the developed finite element model, thermal cycling analysis was performed to determine the fatigue life of the SSD using the simulated results and Morrow’s energy-based fatigue model. The finite element analysis results showed that the outermost solder ball at the corner of the dynamic random access memory (DRAM), was the most vulnerable component under thermal cycling. Monte Carlo simulation was performed to analyze the fatigue life distribution according to the manufacturing tolerances of the design and operating variables of the SSD. Sensitivity analysis was also performed to determine the effects of variables on number of cycles to failure. The analysis results showed that the minimum temperature of the thermal cycling profile condition and the diameter of the DRAM solder balls dominantly affected the fatigue life of the SSD.

On the distribution and scatter of fatigue lives obtained by integration of crack growth curves: Does initial crack size distribution matter?

By integrating the simple deterministic Paris’ law from a distribution of initial defects, in the form of a Frechet extreme value distribution, it was known that a distribution of Weibull distribution of fatigue lives follows exactly. However, it had escaped previous researchers that the shape parameter of this distribution tends to very high values (meaning the scatter is extremely reduced) when Paris’ exponent m approaches 2, leading to the exponential growth of cracks with number of cycles. In view of the fact that values close to m = 2 are of great importance in materials for example used for primary aircraft structures as recognized by some certification requirements (and the so-called “lead crack” methodology), we believe this conclusion may have some immediate relevance for damage tolerance procedures, or certification methods where accurate description of scatter is required. Indeed, we extend the result also to the case when Paris’ constant C is distributed, and give also an estimate of the level of scatter expected in propagation life in the most general case when C, m are both random variate alongwith the defect size distribution, based on first transforming them to uncorrelated form C0, m, and validate this with the famous Virkler set of data. We finally discuss that from known typical values of fatigue life scatter of aeronautical alloys, it is very likely that an important contribution comes from short crack growth.

Fatigue-life distributions for reaction time data.

The family of fatigue-life distributions is introduced as an alternative model of reaction time data. This family includes the shifted Wald distribution and a shifted version of the Birnbaum-Saunders distribution. Although the former has been proposed as a way to model reaction time data, the latter has not. Hence, we provide theoretical, mathematical and practical arguments in support of the shifted Birnbaum-Saunders as a suitable model of simple reaction times and associated cognitive mechanisms.

Optimising safety stocks and reorder points when the demand and the lead-time are probabilistic in cement manufacturing

Inventory control is an extremely challenging task, complicated by a probability of demand and lead-time. An inventory system attempts to balance between overstock and understock to reduce the total cost and achieve customer demand in a timely manner. The optimality of inventory policies for a cement industry is still unknown for many types of inventory systems. In this paper, probability distribution of demand during lead-time is considered when the demand and lead-time are probabilistic while extracting the optimal safety stock placement and the reorder point in cement manufacturing. Probability distributions of demand during lead-time include Pearson type 6 four-parameter, log-Pearson 3, fatigue life (Birnbaum-Saunders), and inverse Gaussian three-parameter distributions. The probability distribution of demand during lead-time is established when the demand and the lead-time are probabilistic; each one has a probability distribution function. The safety stock depends on the safety factor under certain service level and the standard deviation of demand during lead-time which can be obtained from the distribution. The quantities of the safety stock and the reorder point represent an optimal value at each position to avoid over or under stock, the most controversial issue in the inventory system.

Parametric calculations of fatigue life of critical part of trolleybus rear axle

The paper describes the application of probability approach when assessing fatigue life of structures. The case study includes an assessment of two components of the rear axle of the trolleybus. The predicted fatigue life distribution functions were compared with service data. The calculations helped to identify and prevent fatigue cracks and fractures.