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.

Remaining Useful Life for Heavy-Duty Railway Cast Steel Knuckles Based on Crack Growth Behavior with Hypothetical Distributions

The current research on the integrity of critical structures of rail vehicles mainly focuses on the design stage,which needs an effective method for assessing the service state.This paper proposes a framework for predicting the remaining useful life(RUL)of in-service structures with and without visible cracks.The hypothetical distribution and delay time models were used to apply the equivalent crack growth life data of heavy-duty railway cast steel knuckles,which revealed the evolution characteristics of the crack length and life scores of the knuckle under different fracture failure modes.The results indicate that the method effectively predicts the RUL of service knuckles in different failure modes based on the cumulative failure probability curves for different locations and surface crack lengths.This study proposes an RUL prediction framework that supports the dynamic overhaul and state maintenance of knuckle fatigue cracks.

Fatigue crack growth investigation on offshore pipelines with three-dimensional interacting cracks

Due to high cost of full-scale experimental setup, this study presents a numerical model on fatigue behaviours of offshore pipeline with multiple coplanar cracks under cyclic tensile loadings. The validation on numerical results is made by other researchers' experimental results, and significant parameters affecting fatigue crack growth are studied.

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.

Fracture of two three-dimensional parallel internal cracks in brittle solid under ultrasonic fracturing

Similar to hydraulic fracturing(HF), the coalescence and fracture of cracks are induced within a rock under the action of an ultrasonic field, known as ultrasonic fracturing(UF). Investigating UF is important in both hard rock drilling and oil and gas recovery. A three-dimensional internal laser-engraved crack(3D-ILC) method was introduced to prefabricate two parallel internal cracks within the samples without any damage to the surface. The samples were subjected to UF. The mechanism of UF was elucidated by analyzing the characteristics of fracture surfaces. The crack propagation path under different ultrasonic parameters was obtained by numerical simulation based on the Paris fatigue model and compared to the experimental results of UF. The results show that the 3D-ILC method is a powerful tool for UF research.Under the action of an ultrasonic field, the fracture surface shows the characteristics of beach marks and contains powder locally, indicating that the UF mechanism includes high-cycle fatigue fracture, shear and friction, and temperature load. The two internal cracks become close under UF. The numerical result obtained by the Paris fatigue model also shows the attraction of the two cracks, consistent with the test results. The 3D-ILC method provides a new tool for the experimental study of UF. Compared to the conventional numerical methods based on the analysis of stress-strain and plastic zone, numerical simulation can be a good alternative method to obtain the crack path under UF.

Discrete Element Modeling of Asphalt Concrete Cracking Using a User-def ined Three-dimensional Micromechanical Approach

We established a user-defined micromechanical model using discrete element method （DEM） to investigate the cracking behavior of asphalt concrete （AC）. Using the ＂Fish＂ language provided in the particle flow code in 3-Demensions （PFC3D）, the air voids and mastics in asphalt concrete were realistically built as two distinct phases. With the irregular shape of individual aggregate particles modeled using a clump of spheres of different sizes, the three-dimensional （3D） discrete element model was able to account for aggregate gradation and fraction. Laboratory uniaxial complex modulus test and indirect tensile strength test were performed to obtain input material parameters for the numerical simulation. A set of the indirect tensile test were simulated to study the cracking behavior of AC at two levels of temperature, i e, -10 ℃ and 15 ℃. The predicted results of the numerical simulation were compared with laboratory experimental measurements. Results show that the 3D DEM model is able to predict accurately the fracture pattern of different asphalt mixtures. Based on the DEM model, the effects of air void content and aggregate volumetric fraction on the cracking behavior of asphalt concrete were evaluated.

THREE-DIMENSIONAL ELLIPTIC CRACK UNDER IMPACT LOADING

The dynamic stress intensity factor of a three-dimensionalelliptic crack under impact loading is determined with the finiteelement method. The computation results can take into account theinfluence of time and the ratio of the wave speeds on the stressintensity factor. The present method is suitable not only forthree-dimensional dynamic crack, but also for three-dimensionaldynamic contact.

Three-Dimensional and Cross-sectional Characteristics of Normal Grain Growth Based on Monte Carlo Simulation

An appropriate Monte Carlo method was developed to simulate the three-dimensional normal grain growth more completely. Comparative investigation on the three-dimensional and the cross-sectional characteristics of normal grain growth was done. It was found that the time exponent of grain growth determined from cross-section exhibits the same rule of increasing slowly with time and approaching the theoretical value n = 0.5 of steadygrain growth as the three-dimensional (3-D) system. From change of the number of grains per unit area with timemeasured in cross-section, the state of 3-D normal grain growth may be predicted. The gtain size distribution incross-section is different from that in 3-D system and can not express the evolution characteristic of the 3-D distribution. Furthermore, there exists statistical connection between the topological parameters in cross-section and thosein three-dimensions.

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.

Interactions of penny-shaped cracks in three-dimensional solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

Three-dimensional-arterial spin labeling perfusion correlation with diabetes-associated cognitive dysfunction and vascular endothelial growth factor in type 2 diabetes mellitus rat

BACKGROUND Type 2 diabetes mellitus(T2DM) has been strongly associated with an increased risk of developing cognitive dysfunction and dementia.The mechanisms of diabetes-associated cognitive dysfunction(DACD) have not been fully elucidated to date.Some studies proved lower cerebral blood flow(CBF) in the hippocampus was associated with poor executive function and memory in T2DM.Increasing evidence showed that diabetes leads to abnormal vascular endothelial growth factor(VEGF) expression and CBF changes in humans and animal models.In this study,we hypothesized that DACD was correlated with CBF alteration as measured by three-dimensional(3D) arterial spin labeling(3D-ASL) and VEGF expression in the hippocampus.AIM To assess the correlation between CBF(measured by 3D-ASL and VEGF expression) and DACD in a rat model of T2DM.METHODS Forty Sprague-Dawley male rats were divided into control and T2DM groups.The T2DM group was established by feeding rats a high-fat diet and glucose to induce impaired glucose tolerance and then injecting them with streptozotocin to induce T2DM.Cognitive function was assessed using the Morris water maze experiment.The CBF changes were measured by 3D-ASL magnetic resonance imaging.VEGF expression was determined using immunofluorescence.RESULTS The escape latency time significantly reduced 15 wk after streptozotocin injection in the T2DM group.The total distance traveled was longer in the T2DM group;also,the platform was crossed fewer times.The percentage of distance in the target zone significantly decreased.CBF decreased in the bilateral hippocampus in the T2DM group.No difference was found between the right CBF value and the left CBF value in the T2DM group.The VEGF expression level in the hippocampus was lower in the T2DM group and correlated with the CBF value.The escape latency negatively correlated with the CBF value.The number of rats crossing the platform positively correlated with the CBF value.CONCLUSION Low CBF in the hippocampus and decreased VEGF expression might be crucial in DACD.CBF measured by 3D-ASL might serve as a noninvasive imaging biomarker for cognitive impairment associated with T2DM.

Simulation of three-dimensional tension-induced cracks based on cracking potential function-incorporated extended finite element method

In the finite element method,the numerical simulation of three-dimensional crack propagation is relatively rare,and it is often realized by commercial programs.In addition to the geometric complexity,the determination of the cracking direction constitutes a great challenge.In most cases,the local stress state provides the fundamental criterion to judge the presence of cracks and the direction of crack propagation.However,in the case of three-dimensional analysis,the coordination relationship between grid elements due to occurrence of cracks becomes a difficult problem for this method.In this paper,based on the extended finite element method,the stress-related function field is introduced into the calculation domain,and then the boundary value problem of the function is solved.Subsequently,the envelope surface of all propagation directions can be obtained at one time.At last,the possible surface can be selected as the direction of crack development.Based on the aforementioned procedure,such method greatly reduces the programming complexity of tracking the crack propagation.As a suitable method for simulating tension-induced failure,it can simulate multiple cracks simultaneously.

Analysis of Three-dimensional Crack Propagation by Using Displacement Discontinuity Method

A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.

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.

A modified maximum tangential tensile stress criterion for three-dimensional crack propagation

The three-dimensional （3D） crack propagation is a hot issue in rock mechanics. To properly simulate 3D crack propagation, a modified maximum tangential tensile stress criterion is proposed. In this modified criterion, it is supposed that cracks propagate only at crack front in the principal normal plane. The tangential tensile stress at crack front in the principal normal plane in local coordinates is employed to determine crack propagation, which is calculated through coordinate transformation from global to local coordinates. New cracks will propagate when the maximum tangential tensile stress at crack front in the principal normal plane reaches the tensile strength of rock-like materials. Compared with the previous crack propagation criteria, the modified crack propagation criterion is helpful in calculating 3D crack stress intensity factor, and can overcome the limitations of propagation step determined by individual experiences in previous studies. Finally, the 3D crack propagation process is traced by element-free Galerkin method. The numerical results agree well with the experimental ones for a frozen resin sample with prefabricated 3D cracks.

INTERFACIAL CRACK ANALYSIS IN THREE-DIMENSIONAL TRANSVERSELY ISOTROPIC BI-MATERIALS BY BOUNDARY INTEGRAL EQUATION METHOD

The integral-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions, in which the displacement discontinuities across the crack faces are the unknowns to be determined. The interface is parallel to both the planes of isotropy. The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method. The stress intensity factors were expressed in terms of the displacement discontinuities. In the non-oscillatory case, the hyper-singular boundary integral-differential equations were reduced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials.

A STUDY ON STRESS INTENSITY FACTORS AND SINGULAR STRESS FIELDS OF THREE-DIMENSIONAL INTERFACE CRACK

By using the finite-part integral concepts and limit technique,the hypersingular inte- grodifferential equations ofthree-dimensional(3D)planar interface crack were obtained; then thedominant-part analysis of 2D hypersingular integral was further usedto investigate the stress fields near the crack front theoretically,and the accurate formulae were obtained for the singular stressfields and the complex stress intensity factors.

CONVOLUTION OF THE IMPACT THREE-DIMENSIONAL ELASTO-DYNAMICS AND DYNAMIC STRESS INTENSITY FACTOR FOR AN ELLIPTIC CRACK

This paper presents a formulation for three-dimensional elasto-dynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral equation method.

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)--THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper,three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program.The results reveal that the constraints along the thickness direction are obviously separated into two parts:the keeping similar high constraint field(Z_(1))and rapid reducing constraints one(Z_(2)).The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively.So the three dimensional stress structure of Mode I specimens can be derived through discussing the two fields respectively.The distribution of the Crack Tip Opening Displacement(CTOD)along the thickness direction and the three dimensional distribution of the void growth ratio(V_(g))near the crack tip are also obtained.The two fracture parameters are in similar trends along the thickness direction,and both of them can reflect the effect of thickness and that of the loading level to a certain degree.

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.