PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates (da/dN) of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-ΔK relations, the confidence-based da/dN-ΔK relations, and the probabilistic- and confidence-based da/dN-ΔK relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression

Machine learning(ML)has powerful nonlinear processing and multivariate learning capabilities,so it has been widely utilised in the fatigue field.However,most ML methods are inexplicable black-box models that are difficult to apply in engineering practice.Symbolic regression(SR)is an interpretable machine learning method for determining the optimal fitting equation for datasets.In this study,domain knowledge-guided SR was used to determine a new fatigue crack growth(FCG)rate model.Three terms of the variable subtree ofΔK,R-ratio,andΔK_(th)were obtained by analysing eight traditional semi-empirical FCG rate models.Based on the FCG rate test data from other literature,the SR model was constructed using Al-7055-T7511.It was subsequently extended to other alloys(Ti-10V-2Fe-3Al,Ti-6Al-4V,Cr-Mo-V,LC9cs,Al-6013-T651,and Al-2324-T3)using multiple linear regression.Compared with the three semi-empirical FCG rate models,the SR model yielded higher prediction accuracy.This result demonstrates the potential of domain knowledge-guided SR for building the FCG rate model.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates （da/dN） of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-△K relations, the confidence-based da/dN-△K relations, and the probabilistic- and confidence-based da/dN-△K relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

Simple Predicting Method for Fatigue Crack Growth Rate Based on Tensile Strength of Carbon Steel

Three types of fatigue tests for an annealed carbon steel containing carbon of 0.42%were carried out on smooth specimens and specimens with a small blind hole in order to investigate the fatigue crack growth law.A simple predicting method for crack growth rates has been proposed involving strengthσband the relation between cyclic stress and strain.The validity of proposed method has been confirmed by experiments on several carbon steels with different loadings.

Effects of precipitates on fatigue crack growth rate of AA 7055 aluminum alloy

The effects of precipitates on the fatigue crack growth rate of AA 7055 Al alloy subjected to different ageing treatments were investigated using transmission electron microscope and fatigue crack growth testing.The results show that the T77 treated samples exhibit the lowest crack growth rate,while the crack growth rate of over-aged samples is the highest.In terms of the model based on the reversibility of dislocation motion within the plastic zone close to the crack tip,the improved crack growth resistance is attributed to many precipitates that are coherent with Al matrix in the under-aged and T77 treated samples.When the precipitate is coherent with the Al matrix,the larger the precipitate is,the slower the fatigue crack grows.The effects of grain boundary precipitates and precipitate free zone on the fatigue crack growth resistance are less significant than those of precipitates within grains of the alloy.

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 fitting equation and the p-da/dN-ΔK 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.

FACTORS AFFECTING FATIGUE CRACK GROWTH RATES OF FIBER REINFORCED METAL LAMINATES

Based upon an analytical model for predicting the crack growth in fiber reinforced metal laminates (FRMLs), some factors affecting the fatigue crack growth rates of FRMLs were analyzed, including the lay up of FRMLs, the modulus of the fibers, the residu

EFFECTS OF TRACE Zr ON FATIGUE CRACK GROWTH RATE OF HIGH DAMPING Zn-Al ALLOY

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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.

Monte-Carlo Simulation of Surface Crack Growth Rate for Offshore Structural Steel E36-Z35

The Monte- Carlo method is used to simulate the surface fatigue crack growth rate for offshore structural steel E36-Z35, and to determine the distributions and relevance of the parameters in the Paris equation. By this method, the time and cost of fatigue crack propagation testing can be reduced. The application of the method is demonstrated by use of four sets of fatigue crack propagation data for offshore structural steel E36-Z35. A comparison of the test data with the theoretical prediction for surface crack growth rate shows the application of the simulation method to the fatigue crack propagation tests is successful.

Numerical Simulation and Experimental Studies on Elastic-Plastic Fatigue Crack Growth

A elastic-plastic fatigue crack growth(FCG)finite element model was developed for predicting crack growth rate under cyclic load.The propagation criterion for this model was established based on plastically dissipated energy.The crack growth simulation under cyclic computation was implemented through the ABAQUS scripting interface.The predictions of this model are in good agreement with the results of crack propagation experiment of compact tension specimen made of 304 stainless steel.Based on the proposed model,the single peak overload retardation effect of elastic-plastic fatigue crack was analyzed.The results shows that the single peak overload will reduce the accumulation rate of plastic energy dissipation of elements at crack tip plastic zone,so that crack growth will be arrested.The crack growth rate will not recover until the crack tip exceed the affected region.Meanwhile,the crack growth rate is mainly determined by the amplitude rather than the mean load under the condition of small scale yielding.The proposed model would be helpful for predicting the growth rate of mode I elastic-plastic fatigue crack.

EFFECIS OF TEMPERATURE AND OVERLOAD RETARDATION ON CORROSION FATIGUE CRACK GROWTH OF HIGH STRENGTH STEEL

The fatigue crack growth rate (CGR) of ultra high strength steel 30CrMnSiNi2A in distilled water at 18,35 and 55℃ were measured.It was confirmed that the temperature is strongly af- fected on the corrosion fatigue CGR of ultra high strength steel.An expression concerning the effects of Δ K and temperature on the CGR was proposed.The fact that the apparent activation energy (36.6 kJ/mol) resulted from regressive analysis of CGR data was similar to the activation energy of hydrogen diffusion in γ-Fe,strongly supporting the theory of hydrogen-assisted crack growth.The overload retardation effect was greatly reduced in cor- rosion fatigue crack growth,especially at lower frequency,e.g.,0.1 Hz.This phenomenon might be due to the increase of the SCC component of CGR after an overload.

Fatigue Crack Growth Behavior of Different Zones in an Annealed Automatic Gas Tungsten Arc Weld Joint of TA16 and TC4 Titanium Alloys

Based on the investigated microstructure of different zones in the annealed automatic gas tungsten arc weld joint of TA16 and TC4 titanium alloys,the mechanical property of them was assessed under fatigue crack growth rate tests.For evaluation of fatigue crack growth rate,three points bending specimens were used.The correlation between the range of stress intensity factor and crack growth rate was determined in different zones of the annealed weld joint.Fatigue crack growth rates were obviously different in different zones of weld joint of dissimilar titanium alloys,due to their different microstructures.Scanning electron microscope examinations were conducted on the fracture surface in order to determine the relevant fracture mechanisms and crack growth mechanisms with respect to the details of microstructure.

The Effects of Fatigue Cracks on Fastener Loads during Cyclic Loading and on the Stresses Used for Crack Growth Analysis in Classical Linear Elastic Fracture Mechanics Approaches

High strength threaded fasteners are widely used in the aircraft industry, and service experience shows that for structures where shear loading of the joints is significant, like skin splices, fuselage joints or spar caps-web attachments, more cracks are initiated and grow from the edges of the fastener holes than from features like fillets radii and corners or from large access holes. The main causes of this cracking are the stress concentrations introduced by the fastener holes and by the threaded fasteners themselves, with the most common damage site being at the edge of the fastener holes. Intuitively, it is easy to visualize that after the crack initiation, during the growth stages, some of the load transferred initially by the fastener at the cracked hole will decrease, and it will be shed to the adjacent fasteners that will carry higher loads than in uncracked condition. Using currently available computer software, the method presented in this paper provides a relatively quick and quantitatively defined solution to account for the effects of crack length on the fastener loads transfer, and on the far field and bypass loads at each fastener adjacent to the crack. At each location, these variations are determined from the 3-dimensional distribution of stresses in the joint, and accounting for secondary bending effects and fastener tilt. Two cases of a typical skins lap splice with eight fasteners in a two rows configuration loaded in tension are presented and discussed, one representative for wing or fuselage skins configurations, and the second case representative for cost effective laboratory testing. Each case presents five cracking scenarios, with the cracks growing from approx. 0.03 inch to either the free edge, next hole or both simultaneously.

A two-parameter model to predict fatigue life of high-strength steels in a very high cycle fatigue regime

In this paper, ultrasonic （20 kHz） fatigue tests were performed on specimens of a high-strength steel in very high cycle fatigue （VHCF） regime. Experimental results showed that for most tested specimens failed in a VHCF regime, a fatigue crack originated from the interior of specimen with a fish-eye pattern, which contained a fine granular area （FGA） centered by an inclusion as the crack origin. Then, a two-parameter model is proposed to predict the fatigue life of high-strength steels with fish-eye mode failure in a VHCF regime, which takes into account the inclusion size and the FGA size. The model was verified by the data of present experiments and those in the literature. Furthermore, an analytic formula was obtained for estimating the equivalent crack growth rate within the FGA. The results also indicated that the stress intensity factor range at the front of the FGA varies within a small range, which is irrespective of stress amplitude and fatigue life.

CRACK GROWTH BEHAVIOR IN TITANIUM ALLOY TC11 AT ROOM AND HIGH TEMPERATURES

This paper presents some new results of a research on the fatigue crack propagation (FCP) behavior in the titanium alloy TC11. Crack propagation tests were carried out at room temperature by center cracked tension (CCT) specimens under three stress ratios of R=0, 0.5, -1, and at 400 by compact tension (CT) and single edged specimens under stress ratios of R=0.1 and -1, respectively. The crack growth rates were compared by using stress intensity factor and effective stress intensity factor. The results show that the effects of stress ratio and ambient temperature on crack growth rates decreased if they were correlated by using the effective stress intensity factor.

Aspects of Fretting Fatigue Finite Element Modelling

Fretting fatigue is a type of failure that may affect various mechanical components,such as bolted or dovetail joints,press-fitted shafts,couplings,and ropes.Due to its importance,many researchers have carried out experimental tests and analytical and numerical modelling,so that the phenomena that govern the failure process can be understood or appropriately modelled.Consequently,the performance of systems subjected to fretting fatigue can be predicted and improved.This paper discusses different aspects related to the finite element modelling of fretting fatigue.It presents common experimental configurations and the analytical solutions for cylindrical contact.Then,it discusses aspects of fretting fatigue crack initiation,such as crack location,orientation,and length,as well as stress averaging approaches.Then,it deals with the propagation stage;crack face interaction,orientation criteria,and crack growth rate are discussed.Lastly,additional aspects of recent research on fretting fatigue are reviewed:out-of-phase loading,cohesive zone modelling,wear effects,heterogeneity,and crystal orientation.Fretting fatigue is a phenomenon not well understood,and much more research is needed so that its understanding is increased and proper criteria and laws may be available for different cases.

An Improved Solow- Swan Model

In this paper,under the assumption that the labor force function increases strictly and is bounded and the labor force growth rate function decreases monotonically from a positive value to zero,we obtain an improved Solow Swan model. We prove that the per capita capital trends stabilitily to the steady state of the classical Solow Swan model with zero the labor force growth rate. Two comparison theorems,a limited theorem and a stability theorem are given. At the end of this paper,we give an example and discuss the economic meaning of this model and the theorems.

Fatigue Crack Propagation in Steel A131 Under Ice Loading of Crushing,Bending and Buckling

Three types of ice loading, which are most commonly present when ice acts on structures, are chosen and simulated for use of fatigue crack propagation tests on offshore structural steel A131. The three types of ice categorized in accordance with the failure modes when acting on structures called Crushing ice, bending ice, and buckling ice, respectively. This paper presents an experimental investigation on the fatigue crack propagation behavior of widely used high strength steel A131 for offshore jackets in the loading environment of ice crushing, bending, and buckling. The test results of fatigue crack propagation in steel A131 tinder these simulated ice loading at temperature 292K are presented and analyzed in detail in this paper, The amplitude root mean square stress intensity factor is optimized to be the fundamental parameter of fatigue crack propagation for all types of ice loading histories. The results are also compared with constant amplitude fatigue crack propagation conclusions as in wave load mode, and a joint investigation on the results from ice forces, ice-induced vibrations, and ice-induced fatigue crack propagation is conducted. Conclusions are drawn for reference in structural design and material selection for offshore structures in ice environments.