Reconstruction of probabilistic S-N curves under fatigue life following lognormal distribution with given confidence

When the historic probabilistic S-N curves are given under special survival probability and confidence levels and there is no possible to re-test, fatigue reliability analysis at other levels can not be done except for the special levels. Therefore, the wide applied curves are expected. Monte Carlo reconstruction methods of the test data and the curves are investigated under fatigue life following lognormal distribution. To overcome the non-conservative assessment of existent man-made enlarging the sample size up to thousands, a simulation policy is employed to address the true production where the sample size is controlled less than 20 for material specimens, 10 for structural component specimens and the errors matching the statistical parameters are less than 5 percent. Availability and feasibility of the present methods have been indicated by the reconstruction practice of the test data and curves for 60Si2Mn high strength spring steel of railway industry.

Analysis Approach to Durability Based on Material Initial Fatigue Quality and S-N Curve

Based on probabilistic fracture mechanics approach, a new concept of material initial fatigue quality （MIFQ） is developed. Then, the relation between S-N curve and crack propagation curve is studied. From the study, a new durability analysis method is presented. In this method, S-N curve is used to determine crack growth rate under constant amplitude loading and evaluate the effects of different factors on durability and then the structural durability is analyzed. The tests and analyses indicate that this method has lower dependence on testing, and higher accuracy, reliability and generality and is convenient for application.

Combine S-N curve and fracture mechanics for fatigue life analysis of welded structures

Based on the evolution of fatigue cracks in welded structures,the fatigue life of welded structures was defined as the sum of the crack initiation life Ni and the crack propagation life Np.Correspondingly,a fatigue-life analysis method combining S-N curves and fracture mechanics theory was proposed.The equivalent structural stress method and the lower 99%boundary of the master S-N curve were used to evaluate Ni,and cracks at the end of the initiation stage were considered as semi-elliptical surface cracks.Moreover,Paris equation and the stress intensity factor range of the cracks were used to evaluate Np.Furthermore,the fatigue test results obtained from the running girder of cranes were used as a reference for comparison and verification of the results.The results revealed that the equivalent structural stress is a good indicator for the crack initiation behavior of complex welded structures.In addition,the predicted fatigue life corresponded closely to the testing life.

Fatigue Reliability Assessment of Correlated Welded Web-frame Joints

The objective of this work is to analyze the fatigue reliability of complex welded structures composed of multiple web-frame joints, accounting for correlation effects. A three-dimensional finite element model using the 20-node solid elements is generated. A linear elastic finite element analysis was performed, hotspot stresses in a web-frame joint were analyzed and fatigue damage was quantified employing the S-N approach. The statistical descriptors of the fatigue life of a non-correlated web-frame joint containing several critical hotspots were estimated. The fatigue reliability of a web-frame joint wasmodeled as a series system of correlated components using the Ditlevsen bounds. The fatigue reliability of the entire welded structure with multiple web-frame joints, modeled as a parallel system of non-correlated web-frame joints was also calculated.

Hybrid reliability model for fatigue reliability analysis of steel bridges

A kind of hybrid reliability model is presented to solve the fatigue reliability problems of steel bridges. The cumulative damage model is one kind of the models used in fatigue reliability analysis. The parameter characteristics of the model can be described as probabilistic and interval. The two-stage hybrid reliability model is given with a theoretical foundation and a solving algorithm to solve the hybrid reliability problems. The theoretical foundation is established by the consistency relationships of interval reliability model and probability reliability model with normally distributed variables in theory. The solving process is combined with the definition of interval reliability index and the probabilistic algorithm. With the consideration of the parameter characteristics of the S-N curve, the cumulative damage model with hybrid variables is given based on the standards from different countries. Lastly, a case of steel structure in the Neville Island Bridge is analyzed to verify the applicability of the hybrid reliability model in fatigue reliability analysis based on the AASHTO.

Evaluation of the Fatigue Characteristics of Laser-processed Hot Work Tool Steel Based on Reliability

It is reported that laser-processing is effective to repair the heat checks, which are fine shallow cracks on a surfaceof die-casting dies. In this study, the rotating bending fatigue tests have been carried out to evaluate the fatiguecharacteristics of laser-processed hot working tool steel. Because test results are scattered, S-N curves are decidedbased on the evaluation of fatigue strength distribution. As a result, the fatigue strength of the laser-processedspecimens decreases remarkably in comparison with that of base metal. However, it can be recovered to almostinitial value by heat treatment at secondary hardening temperature. This procedure is also effective to decrease thescatter of fatigue strength. The laser-processing can be carried out at low cost and this method is effective for theextension of the work life of dies.

A Model of the Fatigue Life Distribution of Composite Laminates Based on Their Static Strength Distribution

The reasons of the static strength dispersion and the fatigue life dispersion of composite laminates are analyzed in this article. It is concluded that the inner original defects, which derived from the manufacturing process of composite laminates, are the common and major reason of causing the random distributions of the static strength and the fatigue life. And there is a correlative relation between the two distributions. With the study of statistical relationship between the fatigue loading and the fatigue life in the uniform confidence level and the same survival rate S-N curves of material, the relationship between the static strength distribution and the fatigue life distribution through a material S-N curve model has been obtained. And then the model which is used to describe the distributions of fatigue life of composites, based on their distributions of static strength, is set up. This model reasonably reflects the effects of the inner original defects on the static strength dispersion and on the fatigue life dispersion of composite laminates. The experimental data of three kinds of composite laminates are employed to verify this model, and the results show that this model can predict the random distributions of fatigue life for composites under any fatigue loads fairly well.

WEIGHTED LEAST SQUARE METHOD FOR S-N CURVE FITTING

An S-N curve fitting approach is proposed based on the weighted least square method, and the weights are inversely proportional to the length of mean confidence intervals of experimental data sets. The assumption coincides with the physical characteristics of the fatigue life scatter. Two examples demonstrate the method. It is shown that the method has better accuracy and reasonableness compared with the usual least square method.

A GENERAL CONSTITUTIVE RELATION FOR FATIGUE CRACK GROWTH ANALYSIS OF METAL STRUCTURES

Crack growth rate curves are the fundamental material property for metal structures under fatigue loading. Although there are many crack growth rate curves available in the literature, few of them showed the capability to explain various special phenomena observed in tests. A modified constitutive relation recently proposed by McEvily and his co-workers showed very promising capability. This modified constitutive relation is further generalized by (1) introducing an unstable fracture condition; (2) defining a virtual strength to replace the yield stress; and (3) defining an overload and underload parameter. The performances of this general constitutive relation for fatigue crack growth is extensively studied and it is found that this general constitutive relation is able to explain various phenomena observed with particular strong capability on load sequence effect.

Temperature-dependence of acoustic fatigue life for thermal protection structures

Acoustic fatigue life evaluation is essential for thermal protection struc- tures due to the severe thermo-acoustic load in service. A study on temperature- dependence of acoustic fatigue life for a C/SiC panel is presented in this paper. Effects of temperature on both the structural responses and the S-N curves are investigated. The Dirlik method is adopted to predict the fatigue life of a C/SiC panel at three different temperatures respectively. Significant differences are ob- served from the results of numerical simulations between the fatigue lives of the panel in the three cases. The temperature-dependence of acoustic fatigue life of a C/SiC panel is verified, and fatigue test of the material needs to be more atten- tively performed.

High-cycle Fatigue Fracture Behavior of Ultrahigh Strength Steels

The fatigue fracture behavior of four ultrahigh strength steels with different melting processes and therefore different inclusion sizes were studied by using a rotating bar two-point bending fatigue machine in the high-cycle regime up to 107 cycles of loading. The fracture surfaces were observed by field emission scanning electron microscopy （FESEM）. It was found that the size of inclusion has significant effect on the fatigue behavior. For AtSI 4340 steel in which the inclusion size is smaller than 5.5 μm, all the fatigue cracks except one did not initiated from inclusion but from specimen surface and conventional S-N curve exists. For 65Si2MnWE and Aermet 100 steels in which the average inclusion sizes are 12.2 and 14.9 μm, respectively, fatigue cracks initiated from inclusions at lower stress amplitudes and stepwise S-N curves were observed. The S-N curve displays a continuous decline and fatigue failures originated from large oxide inclusion for 60Si2CrVA steel in which the average inclusion size is 44.4 pro. In the case of internal inclusion-induced fractures at cycles beyond about 1×10^6 for 65Si2MnWE and 60Si2CrVA steels, inclusion was always found inside the fish-eye and a granular bright facet （GBF） was observed in the vicinity around the inclusion. The GBF sizes increase with increasing the number of cycles to failure Nf in the long-life regime. The values of stress intensity factor range at crack initiation site for the GBF are almost constant with Nf, and are almost equal to that for the surface inclusion and the internal inclusion at cycles lower than about 1×10^6. Neither fish-eye nor GBF was observed for Aermet 100 steel in the present study.

High-cycle fatigue behavior of Mg-8Li-3Al-2Zn-0.5Y alloy under different states

In this study,the tensile and high-cycle fatigue properties of as-cast,solid solution treated and as-extruded Mg-8Li-3Al-2Zn-0.5Y alloy are investigated.The results show that the yield strength and ultimate tensile strength of as-cast alloy is 198.1 MPa and 222.5 MPa,which are improved to 274.7 MPa and 321.7 MPa,282.4 MPa and 319.3 MPa after solid solution and extrusion treatment,respectively.The high-cycle fatigue strength(at 10^(7)cycles,R=-1)of as-cast studied alloy is 65 MPa,which is improved to 90 MPa and 105 MPa after solid solution and extrusion treatment,respectively.The improvement of fatigue property of the solid solution treated alloy is mainly due to the lattice distortion caused by solid solution hindering the crack propagation.However,the improvement of fatigue property of the as-extruded alloy is mainly due to that the refined grains,stacked dislocations and dispersed secondary particles impede the crack propagation.

Fatigue Strength Evaluation of Resin-Injected Bolted Connections Using Statistical Analysis

Different strategies can be used to perform reparations and reinforcements of ancient bolted and riveted metallic bridges. As the riveting process is not currently a common practice, it requires proper equipment and skilled workers. Another solution is the use of welding. However, the weldability of old steels is poor. Bolts are very attractive alternative solutions, and are most commonly used to repair old metallic bridges. Fitted bolts are expensive solutions; the alternative is the use of resin-injected bolts. The behavior of bolted joints with preloaded resin-injected bolts has been studied using quasi-static and creep tests; however, few studies on the slip and fatigue behavior of these joints can be found in the literature. This paper presents an overview of a few experimental programs that were carried out by several authors aiming at evaluating the fatigue behavior of single and double shear resin-injected bolted connections. A comparison between the experimental data of joints with preloaded standard bolts and preloaded resin- injected bolts shows a fatigue strength reduction in the latter. Since Eurocode 3 （EC3） suggests the same fatigue strength curve for joints made of resin-injected bolts and standard bolts, this may raise some con- cerns. Furthermore, research on the feasibility of using both bonded and bolted connections is shown. This last study was performed with high-strength low-alloy structural steel plates and an acrylic struc- tural adhesive for metal bonding. For both case studies, a statistical analysis is performed on fatigue experimental data using linearized boundaries and the Castillo and Fernandez-Canteli model. Fatigue design curves are proposed and compared with the design suggestions of several European and North American standards,

Fatigue Topology Optimization Design Based on Distortion Energy Theory and Independent Continuous Mapping Method

Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.

Statistical Analysis Methods of Fatigue Crack Growth Rate

The standard center-cracked tensile specimens M （T） with different widths made of aluminum alloy were designed for fatigue crack growth rate experiments, and the effect of specimen size on the fatigue crack growth rate was discussed. The firing equation and the p-da/dN-△K curve of fatigue crack growth rate （with different confidence and reliability levels） were obtained by one-side tolerance factor analysis. In order to reasonably reflect the dispersion of material properties on the fatigue crack growth rate and fatigue crack propagation life, two novel statistical analysis methods were proposed, which can be used to describe the probability distribution of fatigue crack growth rate. Compared with the traditional statistical analysis method of probabilistic fatigue crack growth rate, the fitted curves from the novel statistical analysis methods yield more objective description on the probability distribution of crack growth rate.

Gigacycle fatigue behaviors of two SNCM439 steels with different tensile strengthes

Gigacycle fatigue behaviors of two SNCM439 steels with different tensile strengthes were experimentally studied by rotating bending tests,to investigate the effects of the tensile strength obtained by different heat treatment processes on very high cycle fatigue failure mechanisms.The material with higher tensile strength of 1 710 MPa exhibited typical gigacycle fatigue failure characteristics,whereas one with lower tensile strength of 1 010 MPa showed only traditional fatigue limit during the tests and no gigacycle failure could be found even when the specimen ran up to more than 10 8 cycles.Metallographic and fractographic analysis were carried out by an optical microscope （OM） and scanning electron microscope （SEM）.It showed two different crack initiation mechanisms that for the specimen with lower tensile strength the crack prefers surface initiation and for that with higher strength the crack initiates from subsurface inclusions revealed by a fish-eye like microstructure.

Very high cycle fatigue behavior of bridge steel welded joint

Very high cycle fatigue（VHCF） behaviors of bridge steel（Q345） welded joints were investigated using an ultrasonic fatigue test system at room temperature with a stress ratio R = -1. The results show that the fatigue strength of welded joints is dropped by an average of 60% comparing to the base metal and the fatigue failure still occurred beyond 10~7 cycles.The fatigue fracture of welded joints in the low cycle regime generally occurred at the solder while at the heat-affected zone（HAZ） in the very high cycle regime.The fatigue fracture surface was analyzed with scanning electron microscopy（SEM）,showing welding defects such as pore,micro-crack and inclusion were the main factors on decreasing the fatigue properties of welded joints.The effect of welding defects on the fatigue behaviors of welded joints was discussed in terms of experimental results and finite element simulations.

A Rapid Estimation Method of Structural Fatigue Analysis for a 17k Ton DWT Oil Tanker

Fatigue cracks and fatigue damage have been important issues for ships and offshore structures for a long time.However,in the last decade,with the introduction of higher tensile steel in hull structures and increasingly large ship dimensions,the greater attention should be paid to fatigue problems.Most research focuses on how to more easily access the fatigue strength of ships.Also,the major classification societies have already released their fatigue assessment notes.However,due to the complexity of factors influencing fatigue performances,such as wave load and pressure from cargo,the combination of different stress components,stress on concentration of local structure details,means stress,and the corrosive environments,there are different specifications with varying classification societies,leading to the different results from different fatigue assessment methods.This paper established the Det Norske Veritas（DNV） classification notes ＂fatigue assessment of ship structures＂ that explains the process of fatigue assessment and simplified methods.Finally,a fatigue analysis was performed by use data of a real ship and the reliability of the result was assessed.

Fatigue Damage Assessment by Considering Mean Value Effect in Frequency Domain

Fatigue damage assessment is carried out considering mean value effect by applying four criteria of failure. Three frequency domain methods, i.e., level crossing counting(LCC), range counting(RC) and a new proposed method, are applied. The core of frequency domain method is the construction of probability density function for the mean stress and stress range of the stress process. The applicability of these frequency domain methods are inspected by comparing with time domain method. Numerical simulations verify the applicability of LCC and the proposed method, while RC gives poor estimations.

Effect of Varying Carbon Content and Shot Peening upon Fatigue Performance of Prealloyed Sintered Steels

The aim of the work was to find out how the modification of surface treatment and microstructures affect the fatigue characteristics of the considered sintered materials. Two different systems were prepared： as-sintered and shot peened prealloyed sintered （Astaloy CrL based） steels with addition of 0.5% and 0.7% C. Sintering was carried out in laboratory tube furnace in an atmosphere of pure gases 75%N2＋25%H2. The sintering temperature was 1180℃ and sintering time was 60 min. Heating and cooling rates were 10℃/min. Fatigue tests were carried out in symmetric plane bending at stress ratio R=-1 with frequency of about 24 Hz. The presented experimental results showed that prealloyed water-atomised steels, with surface modification, exhibit positive effects on the fatigue failure resistance, and for that reason are suitable for high-performance applications.