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.

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.

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.

Fatigue crack growth rate test using a frequency sweep method

Fatigue crack propagation characteristics of a diesel engine crankshaft are studied by measuring the fatigue crack growth rate using a frequency sweep method on a resonant fatigue test rig. Based on the phenomenon that the system frequency will change when the crack becomes large, this method can be directly applied to a complex component or structure. Finite element analyses （FEAs） are performed to calibrate the relation between the frequency change and the crack size, and to obtain the natural frequency of the test rig and the stress intensity factor （SIF） of growing cracks. The crack growth rate i.e. da/dN-AK of each crack size is obtained by combining the testing-time monitored data and FEA results. The results show that the crack growth rate of engine crankshaft, which is a component with complex geometry and special surface treatment, is quite different from that of a pure material. There is an apparent turning point in the Paris＇s crack partition. The cause of the fatigue crack growth is also discussed.

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.

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.

An Improved Unique Fatigue Crack Growth Rate Curve Model and Determination of the Model Shape Exponents

It is essential to precisely predict the crack growth,especially the near-threshold regime crack growth under different stress ratios,for most engineering structures consume their fatigue lives in this regime under random loading.In this paper,an improved unique curve model is proposed based on the unique curve model,and the determination of the shape exponents of this model is provided.The crack growth rate curves of some materials taken from the literature are evaluated using the improved model,and the results indicate that the improved model can accurately predict the crack growth rate in the nearthreshold and Paris regimes.The improved unique curve model can solve the problems about the shape exponents determination and weak ability around the near-threshold regime meet in the unique curve model.In addition,the shape exponents in the improved model at negative stress ratios are discussed,which can directly adopt that in the unique curve model.

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.

Correlation of crack growth rate and stress ratio for fatigue damage containing very high cycle fatigue regime

A model is proposed to correlate the crack growth rate and stress ratio containing very high cycle fatigue regime.The model is verified by the experimental data in literature.Then a formula is derived for the effect of mean stress on fatigue strength,and it is used to estimate the fatigue strength of a bearing steel in very high cycle fatigue regime at different stress ratios.The estimated results are also compared with those by Goodman formula.

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.

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

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FACTORS AFFECTING FATIGUE CRACK GROWTH RATES OF FIBER REINFORCED METAL LAMINATES

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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.

Effect of annealing treatment on microstructure and fatigue crack growth behavior of Al–Zn–Mg–Sc–Zr alloy

Al-Zn-Mg-Sc-Zr alloy samples were annealed to four different states （under-aging, peak-aging, over-aging and double-aging） and then thoroughly investigated by means of electron backscatter diffraction （EBSD）, transmission electron microscopy （TEM）, scanning electron microscopy （SEM）, tensile and fatigue crack growth rate tests to explore the influence of annealing treatment on microstmcture and fatigue crack growth behavior. The results indicate that Al3（Sc,Zr） particles can effectively refine grains and enhance tensile properties and fatigue properties. After annealing treatment, the under-aged sample and double-aged sample obtained average grain sizes of 4.9473 and 4.1257 μm, and the maximum value of yield/tensile strength （561 MPa/581 MPa） was obtained in peak-aged state. In the Paris region, fatigue crack growth rate, crack deflection and bifurcation, crack blunting and inter/trans-granular propagation were discussed based on data fitting and Laird model and Griffith theory. And the results show that the under-aged sample possesses the best resistance to fatigue crack propagation and the most tortuous and bifurcated crack path. For all samples, the fatigue crack growth rate in the rupture region was inversely proportional to yield strength.

Effect of stress ratio on fatigue lifetime and crack growth behavior of WC-Co cemented carbide

Two types of fatigue tests, a rotating bending fatigue test and a three- or four-point bending fatigue test, were carried out on a fine grained WC-Co cemented carbide to evaluate its fatigue crack growth behavior and fatigue lifetime. From successive observations of the specimen surface during the fatigue process, it was revealed that most of the fatigue lifetime of the tested WC-Co cemented carbide was occupied with crack growth cycles. Using the basic equation of fracture mechanics, the relationship between the fatigue crack growth rate(da/dN) and the maximum stress intensity factor(Kmax) was derived. From this relation, both the values of the threshold intensity factor(Kth) and the fatigue fracture toughness(Kfc) of the material were determined. The fatigue lifetime of the WC-Co cemented carbide was estimated by analysis based on the modified linear elastic fracture mechanics approach. Good agreement between the estimated and experimental fatigue lifetimes was confirmed.

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.

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.

EFFECT OF Mg AND Zr ADDITION ON CREEP CRACK GROWTH BEHAVIOUR OF A Ni-BASE SUPERALLOY

The creep crack growth(CCG)and the time to carck initiation and rupture of specimen (t_(rc)and t_r)were measured by means of electrical potential method on single edge notched specimens at 700℃.The field near the crack tip under steady-state creep was represented by energy rate integral(C~*),and the CCG rate as a function of C~* has been obtained.The agreement between the predicted and observed t_(rc)values is quite good.It was found that the addition of small amount of Mg and Zr in the alloys causes t_(rc)and t_r of the specimens to in- crease significantly.

EFFECT OF OVERLOAD ON CRACK GROWTH IN FIBER REINFORCED METAL LAMINATES

This paper is concerned with fatigue behavior of glass fiber reinforced aluminium laminates (GLARE) under overload fatigue loading. The effect of single overload on the crack growth rates in GLARE was investigated, and the mechanism of the retardation of crack growth determined. Crack growth retardation by overload was observed in GLARE, but much smaller than monolithic metals. The retardation of crack growth in GLARE is only controlled by the effective stress intensity factor experienced by the constituent metals at crack tips.

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.