Effects of orientation on the fatigue crack growth behaviors of the ZK60 magnesium alloy in air and PBS

Strong anisotropic corrosion and mechanical properties caused by specimen orientations greatly limit the applications of wrought magnesium alloys.To investigate the influences of specimen orientation,the corrosion tests and(corrosion)fatigue crack growth tests were conducted.The rolled and transverse surfaces of the materials show distinct corrosion rate differences in the stable corrosion stage,but the truth is the opposite for the initial stage of corrosion.In air,specimen orientations have a significant influence on the plastic deformation mechanisms near the crack tip,which results in different fatigue fracture surfaces and cracking paths.Compared with R-T specimens,N-T specimens show a slower fatigue crack growth(FCG)rate in air,which can be attributed to crack closure effects and deformation twinning near the crack tip.The corrosion environment will not significantly change the main plastic deformation mechanisms for the same type of specimen.However,the FCG rate in phosphate buffer saline(PBS)is one order of magnitude higher than that in air,which is caused by the combined effects of hydrogen-induced cracking and anodic dissolution.Owing to the similar corrosion rates at crack tips,the specimens with different orientations display close FCG rates in PBS.

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.

Statistical learning prediction of fatigue crack growth via path slicing and re-weighting

Predicting potential risks associated with the fatigue of key structural components is crucial in engineering design.However,fatigue often involves entangled complexities of material microstructures and service conditions,making diagnosis and prognosis of fatigue damage challenging.We report a statistical learning framework to predict the growth of fatigue cracks and the life-to-failure of the components under loading conditions with uncertainties.Digital libraries of fatigue crack patterns and the remaining life are constructed by high-fidelity physical simulations.Dimensionality reduction and neural network architectures are then used to learn the history dependence and nonlinearity of fatigue crack growth.Path-slicing and re-weighting techniques are introduced to handle the statistical noises and rare events.The predicted fatigue crack patterns are self-updated and self-corrected by the evolving crack patterns.The end-to-end approach is validated by representative examples with fatigue cracks in plates,which showcase the digital-twin scenario in real-time structural health monitoring and fatigue life prediction for maintenance management decision-making.

Probability estimation method for fatigue crack growth rate based on a∼t data from service

Purpose–The study aims to provide a basis for the effective use of safety-related information data and a quantitative assessment way for the occurrence probability of the safety risk such as the fatigue fracture of the key components.Design/methodology/approach–The fatigue crack growth rate is of dispersion,which is often used to accurately describe with probability density.In view of the external dispersion caused by the load,a simple and applicable probability expression of fatigue crack growth rate is adopted based on the fatigue growth theory.Considering the isolation among the pairs of crack length a and crack formation time t(a∼t data)obtained from same kind of structural parts,a statistical analysis approach of t distribution is proposed,which divides the crack length in several segments.Furthermore,according to the compatibility criterion of crack growth,that is,there is statistical development correspondence among a∼t data,the probability model of crack growth rate is established.Findings–The results show that the crack growth rate in the stable growth stage can be approximately expressed by the crack growth control curve da/dt=5 Q•a,and the probability density of the crack growth parameter Q represents the external dispersion;t follows two-parameter Weibull distribution in certain a values.Originality/value–The probability density f(Q)can be estimated by using the probability model of crack growth rate,and a calculation example shows that the estimation method is effective and practical.

STOCHASTIC MODELLING OF FATIGUE CRACK GROWTH UNDER CONSTANT AMPLITUDE LOADING

Two stochastic models of fatigue crack growth under constant amplitude cyclic loading are proposed and studied by using the stochastic averaging method and total probability theorem to account for high frequency component and low frequency component, respectively, of the irregular nature of fatigue crack growth observed in Virkler's experiment. Particular attention is paid to the prediction performance of the models under a change in the initial crack length. It is shown that the models proposed in the present paper yields better agreement with experimental data than other models available in literature.

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.

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.

Fatigue Crack Growth Rate of Ti-6Al-4V Considering the Effects of Fracture Toughness and Crack Closure

Fatigue fracture is one of the main failure modes of Ti-6A1-4V alloy,fracture toughness and crack closure have strong effects on the fatigue crack growth（FCG）rate of Ti-6A1-4V alloy.The FCG rate of Ti-6A1-4V is investigated by using experimental and analytical methods.The effects of stress ratio,crack closure and fracture toughness on the FCG rate are studied and discussed.A modified prediction model of the FCG rate is proposed,and the relationship between the fracture toughness and the stress intensity factor（SIF）range is redefined by introducing a correcting coefficient.Notched plate fatigue tests（including the fracture toughness test and the FCG rate test）are conducted to investigate the influence of affecting factors on the FCG rate.Comparisons between the predicted results of the proposed model,the Paris model,the Walker model,the Sadananda model,and the experimental data show that the proposed model gives the best agreement with the test data particularly in the near-threshold region and the Paris region,and the corresponding calculated fatigue life is also accurate in the same regions.By considering the effects of fracture toughness and crack closure,the novel FCG rate prediction model not only improves the estimating accuracy,but also extends the adaptability of the FCG rate prediction model in engineering.

EFFECTS OF MICROSTRVCTURE ON FATIGUE CRACK GROWTH BEHMIOR IN Ni-BASE SUPERALLOY GH586

Threshold stress values, muging from ～8 to 16MPa·m1/2 can be obtained in a Ni-base alloy GH586 by varying the microstructure through heat treatments. The threshold and low crack growth rate behaviors at room temperature, with varying groin size and γ'-distribution, have been investigated. The results indicate that grain size is an important microstructurol parameter that affects fatigue crack growth threshold and propagation behaviors, as the values of △Kth increase with increasing grain size, but the γ' -distribution also has important effect. Analyses show that the effects of groin size on threshold and low crack-growth rate behavior result from heterogeneous deformation and roughness-induced crack closure due to crystallographic slipping and cracking in coarse microstructure. The higher △Kth and lower fatigue crack growth rate with increasing amounts of fine γ' phases are closely related to less damage accumulation level in deformation zone of crack-tip resulted from heterogeneous deformation due to dislocations' shearing γ' precipitates.

EFFECTS OF STRESS RATIO AND FREQUENCY ON CORROSION FATIGUE CRACK GROWTH MECHANISM IN LOW ALLOY STEELS

Based on theoretical analysis about local strain,strain rate and dissolving rate at crack tip, the corrosion fatigue crack growth rate of steels ZG20SiMn and SM50B-Zc in fresh water and 3.5% NaCl solution were measured experimentally,and the PH and electrode potential within crack were also measured continuously along with crack propagating.It showed that the increase of crack growth rate,caused by both decreasing frequency and raising stress ratio,was mainly accelerated by hydrogen embrittlement.

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.

Residual stress relaxation in typical weld joints and its effect on fatigue and crack growth

Many factors influence the fatigue and crack growth behavior of welded joints. Some structures often undergo fairly large static loading before they enter service or variable amplitude cyclic loading when they are in service. The combined effect of both applied stress and high initial residual stress is expected to cause the residual stresses relaxation. Only a few papers seem to deal with appropriate procedures for fatigue analysis and crack growth by considering the combined effect of variable amplitude cyclic loading with residual stresses relaxation. In this article, some typical welded connections in ship-shaped structures are investigated with 3-D elastic-plastic finite element analysis. The effect of residual stress relaxation, initial residual stress, and the applied load after variable amplitude cyclic loading is revealed, and a formula for predicting the residual stress at hot spot quantitatively is proposed. Based on the formula, an improved fatigue procedure is introduced. Moreover, crack growth of typical weld joints considering residual stresses relaxation is studied.

Fractographic analysis of the overload effect on fatigue crack growth in 2024-T3 and 7075-T6 Al alloys

The effect of single overload on the fatigue crack growth in 2024-T3 and 7075-T6 Al alloys was analyzed.Fatigue tests under constantamplitude loading with overload peak were carried out on V-notched specimens.Fractographic analysis was used as a principal approach to explain the crack growth retardation due to the overload.Scanning electron microscopy(SEM)analyses were conducted on the fractured surface of failed specimens to study the retardation effect.The obtained results show that the overload application generates a plastic zone in both aluminum alloys.The generated plastic zone is three times larger in the case of 2024-T3 compared to 7075-T6,and thus,a significant crack retardation was induced for 2024-T3.The retardation effect due to the overload for 2024-T3 and 7075-T6 lasted for about 10 mm and 1 mm,respectively,from the point of overload application.

Fatigue Crack Growth Behavior of Eutectoid Steel Rail

The fatigue crack behavior of U75V rail under different quenching rates was studied using SEM and CLSM.The results show that the pearlite interlayer spacing and fatigue crack growth rate decrease,and the deflection path of cracks and the number of branching cracks of U75V rail increases with an increase of cooling rate.The tearing edge of unstable region transites from pearlite lamellae to dimple.The fatigue crack growth path is closely related to the orientation of lamellae in pearlite microstructure.There are three modes direction of fatigue crack growth path and pearlite lamellar,which are parallel,vertical and 45°angle,and most of the branch cracks occur at an angle of 45°between the lamellar direction and the crack direction.More specifically,the deflection paths of cracks and branching crack have a relaxation effect on the stress intensity at the crack tip,which restrains the fatigue crack growth rate.

Fatigue crack growth behaviors of a new burn-resistant highly-stabilized beta titanium alloy

This article presents the fatigue crack growth （FCG） behaviors of a new bum-resistant highly-stabilized beta Ti40 alloy. The FCG rates were analyzed. The fracture surfaces and the side surfaces of the test samples were explored. The results show that frequency affects the cracking behaviors of Ti40 alloy. Temperature also plays an important role in Ti40 alloy cracking. At room temperature （25℃）, when the frequency increases, the cracking rate changes a little in the range of low stress intensity factor （△K）, while it changes significantly when △K is high. At 500℃, the cracking rate of Ti40 alloy changes significantly during all the course of cracking. The fi＇equency also affects the microstructure patterns of Ti40 alloy. A number of secondary cracks appear in the area more than 200μm from the main crack at a high △K when the frequency is 1 Hz, but only a few secondary cracks exist when the frequency is 10 Hz. Facet image is the main image of the fracture surfaces when the frequency is 1 Hz. While, ductile striation occupies most of the area of fracture surfaces when the frequency is 10 Hz.

Crack growth behavior of SRR99 single crystal superalloy under thermal fatigue

The thermal fatigue behavior of a single crystal superalloy SRR99 was investigated. Specimens with V-type notch were tested at the peak temperatures of 900, 1000, and 1100℃. The crack growth curves as a function of the number of cycles were plotted. With the increase of peak temperature, the crack initiation life was shortened dramatically. Through optical microscopy （OM） and scanning electron microscopy （SEM） observation, it was found that multiple small cracks nucleated at the notch tip region but only one or two of them continued to develop in the following thermal cycles. The primary cracks generally propagated along a preferential direction. Microstructure changes after thermal fatigue were also discussed on the basis of SEM observation.

A CATASTROPHE ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

This paper presents an attempt at the application of catastrophe theory to the stability analysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions of J-integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.

Analytical study of subcritical crack growth under mode I loading to estimate the roof durability in underground excavation

The long-term stability of the roof is particularly important in designing underground rock structures.To estimate the durability of roof strata in underground excavation,a computation scheme of subcritical crack growth is proposed in this study.By adopting the proposed method,the potential collapse location of strata is derivable in accordance with a static model,the durability of roof strata can be estimated,a dynamic time step control strategy is achieved to balance the accuracy and speed of computing,and the initial crack size of rock can be estimated.In addition to the above,a mechanical model of underground excavation with non-uniformly distributed loads and partially yielded foundation is presented as the prototypical case.A set of case studies is carried out that showcase a power correlation between applied stress and roof durability.The allowable applied tensile stress for a 100-year life cycle is about 76%of the tensile strength.By using the proposed subcritical crack growth computation scheme,the roof stability in an underground excavation can be identified not only from the spatial view but also from the temporal perspective.

Effect of crystallographic orientation on crack growth behaviour of HSLA steel

In this work,the crack growth behaviours of high strength low alloy(HSLA)steel E690 with three crystallographic orientations(the rolling direction,normal direction,and transverse direction)were investigated and compared from the view of the mechano-electrochemical ef-fect at the crack tip.The results show that the crack growth of the HSLA steel is controlled by the corrosion fracture at the crack tip.The vari-ation of crystallographic orientation in E690 steel plate has no influence on the crack tip electrochemical reaction and crack growth mechanism,but changes the crack growth rate.When the stress loading direction is parallel to the rolling direction and the fracture layer is parallel to the transverse-normal plane,the crack growth rate is the slowest with a value of 0.0185 mm·h^(-1).When the load direction and the fracture layer are parallel to the normal direction and the rolling-transverse plane,respectively,the crack growth rate is the highest with a value of 0.0309 mm·h^(-1).This phenomenon is ascribed to the different microstructural and mechanical properties in the rolling direction,normal direction,and transverse direction of E690 steel plate.

Modeling of Fatigue Crack Growth Closure Considering the Integrative Effect of Cyclic Stress Ratio,Specimen Thickness and Poisson's Ratio

Key components of large structures in aeronautics industry are required to be made light and have long enough fatigue lives.It is of vital importance to estimate the fatigue life of these structures accurately.Since the FCG process is affected by various factors,no universal model exists due to the complexity of the mechanisms.Most of the existing models are obtained by fitting the experimental data and could hardly describe the integrative effect of most existing factors simultaneously.In order to account for the integrative effect of specimen parameters,material property and loading conditions on FCG process,a new model named integrative influence factor model（IIF） is proposed based on the plasticity-induced crack closure theory.Accordingly to the predictions of crack opening ratio（γ） and effective stress intensity factor range ratio（U） with different material under various loading conditions,predictions of γ and U by the IIF model are completely identical to the theoretical results from the plane stress state to the plane strain state when Poisson＇s ratio equals 1/3.When Poisson＇s ratio equals 0.3,predictions of γ and U by the IIF model are larger than the predictions by the existing model,and more close to the theoretical results.In addition,it describes the influence of R ratios on γ and U effectively in the whole region from-1.0 to 1.0.Moreover,several sets of test data of FCG rates in 5 kinds of aluminum alloys with various specimen thicknesses under different loading conditions are used to validate the IIF model,most of the test data are situated on the predicted curves or between the two curves that represent the specimen with different thicknesses under the same stress ratio.Some of the test data slightly departure from the predictions by the IIF model due to the surface roughness and errors in measurement.Besides,based on the analysis of the physical rule of crack opening ratios,a relative thickness of specimen is defined to describe the influence of material property,specimen thickness and so forth on FCG characteristics conveniently.In conclusion,the relative thickness of specimen simplifies the expression of FCG characteristic and provides a general parameter to analyze the fatigue characteristics of different materials with various thicknesses under different loading conditions.The IIF model describes the integrative effect of existing influence factors explicitly and quantitatively,and provides a helpful tool for fatigue property estimation of practical component and experiment design.