Elliptical Crack Research Articles

Analysis of fatigue degradation process and modelling of an elliptical crack in the locking system of a PET bottle blower

In the dynamic world of Polyethylene Terephthalate (PET) bottle production, ensuring the reliability of blow molding machines is paramount, particularly the locking mechanisms that endure significant cyclic loads during operation. This study investigates the fatigue degradation and crack propagation within the locking system of a two-cavity, 2-liter PET bottle blow molder. By modeling an elliptical crack in the most stressed component, we explore the complex stress distribution and the impact of repeated opening and closing cycles on the system’s integrity. Utilizing advanced finite element analysis (FEA), our research provides a comprehensive understanding of the stress intensity factors and safety margins under varying loading conditions. The results not only enhance predictive maintenance strategies but also offer valuable insights into extending the operational lifespan of these machines, thereby improving safety and reliability in industrial applications. This study opens new avenues in the field of component lifespan prediction. By combining artificial intelligence, machine learning, and innovative materials, it aims to improve the reliability and lifespan of PET blow molders.

Experimental method for internal deformation measurement of 3D solids with embedded cracks based on 3D printing and digital speckle techniques

Quantification of the internal deformation of fractured solids such as rock masses under external loads, especially the deformation around internal fractures, is crucial for understanding and predicting the failure of fractured solids. However, it is very difficult to achieve the goal using conventional experimental methods. In this study, we proposed a novel internal deformation measurement method based on three-dimensional (3D) printing and digital speckle techniques. The 3D printing technology was applied to fabricate a 3D transparent model with an embedded elliptical crack and to set a speckle pattern on the internal section of the transparent model. The digital image correlation (DIC) method was used to determine the internal deformation field of the 3D fractured model. The measured displacements and strains of the internal sections in the fractured model were compared with the numerical simulation results. The comparison indicates that the proposed experimental method can well determine the deformation inside the 3D model. This built-in speckle method can realize real-time observation of the internal deformation of a 3D solid model in a non-contact and non-destructive manner.

Effects of Surface Crack Shape on Fracture Behavior of Oil Pipelines Based on the MMC Criterion.

This study employs a hybrid numerical-experimental calibration method based on phenomena to determine the fracture parameters of the Modified Mohr-Coulomb (MMC) model. Using a self-developed VUMAT subroutine and the element deletion technique, the fracture process of a wide plate pipeline is thoroughly analyzed. This study investigates the impact of various crack shapes on the fracture response under tensile loading and the influence of surface crack size on the initiation location of a wide plate. These results demonstrate the calibrated MMC fracture model's accurate prediction of the toughness fracture behavior of X80 pipeline steel. Under equal area conditions of the dangerous section, circular cracks exhibit lower bearing capacity compared to elliptical cracks. Elliptical cracks predominantly propagate in the thickness direction, whereas circular cracks show nearly uniform growth in all directions. Furthermore, when the crack depth is less than half of the wall thickness, the damage accumulation value at the midpoint of the crack front is maximized; conversely, when the crack front is closer to the internal measurement point of the wide plate, the damage accumulation value is maximized.

A study on three coalescence modes of non-collinear parallel elliptical double cracks

Based on the Gurson-Tvergaard-Needleman (GTN) damage model, this study focused on the coalescence modes of non-collinear parallel elliptical double cracks in a homogeneous plate, and the coalescence modes of elliptical double cracks under different horizontal distances and vertical distances were investigated. The ratio of horizontal distance s to crack length a was taken as the horizontal axis, the ratio of vertical distance h to crack length a was taken as the vertical axis to plot the graph, then the coalescence modes were summarized and compared with the coalescence modes of linear double cracks. It was found that the non-collinear parallel elliptical double cracks exhibited three coalescence modes: crack tip to crack tip coalescing, crack interval to crack interval coalescing, and crack tip to crack interval coalescing. Each coalescence mode had its own characteristics. The three coalescence modes were distributed regularly in three regions in the graph with s/a and h/a as coordinates. When the horizontal distance s and the vertical distance h between the double cracks were equal respectively, there were significant differences in the crack propagation process and coalescence modes between elliptical double cracks and linear double cracks.

A physics knowledge-based neural network method for three-dimensional fracture mechanics of attachment lugs

The lug type joint serves as a critical connecting structure in aerospace vehicles, allowing for convenient assembly and disassembly, and transfer the load during service. However, cracks often initiate at the stress concentration location near the lugs hole, posing a significant threat to the safety of the aircraft structure. Therefore, evaluating the stress intensity factors for complex lug structures is of great significance. In this study, a physics knowledge-based neural network method of calculating the stress intensity factors of attachment lugs is proposed. Three types of cracked lug structures are analyzed: through-thickness crack in straight lug, quarter elliptical corner crack in straight lug and quarter elliptical corner crack in tapered lug. Various complex influencing factors in actual situations are also considered, such as the impact of the interference fit between the pin and the lug, as well as different loading directions and crack positions of tapered lugs. The stress intensity factor dataset generated by 3D finite element method, and then the neural network with its powerful learning ability and prior physical knowledge are used to achieve accurate fitting of the data. The results demonstrate that incorporating physical knowledge features significantly improves the model performance of the neural network. This method can be extended to analyze crack in structures with arbitrary geometry and complex loading conditions.

Research on the influence of rock fracture toughness of layered formations on the hydraulic fracture propagation at the initial stage

Deep underground rocks exhibit significant layered heterogeneity due to geological evolution and sedimentation. Rock fracture toughness, as one of the important indicators of hydraulic crack propagation, also exhibits heterogeneous distribution. In order to investigate the influence of non-uniform fracture toughness of layered rocks on hydraulic crack propagation, this paper establishes a planar three-dimensional hydraulic crack propagation model. The model is numerically solved using the 3D displacement discontinuity method (3D-DDM) and the finite difference method. The calculation results indicate that when the distribution of the fracture toughness of layered rocks changes from uniform to non-uniform, the fracture morphology develops from a standard circular crack to an elliptical crack. When the difference of the rock fracture toughness between adjacent rock layers and the middle rock layer (pay zone) is large enough, the fracture morphology will develop towards a rectangular shape. In addition, when the fracture toughness of rock layers is non-uniformly distributed, the hydraulic crack not only rapidly expand in the softening layer (rock layer with lower fracture toughness), but also slowly propagate in the strong layer (rock layer with higher fracture toughness). However, the propagation speed in the softening layer is much faster than that in the strong layer. The results indicate that the heterogeneity of rock fracture toughness has an important impact on the morphology, propagation speed, and direction of hydraulic fractures.

SIF formula based on exact SIF distribution for semi‐elliptical surface cracks subjected to mode I, II, III uniform loading

AbstractThe stress intensity factor (SIF) distribution of a semi‐elliptical surface crack is often used for evaluating the fatigue strength of structures. Virtually exact distributions of SIFs can be provided along the crack front by solving the hypersingular integral equation of the body force method. In this paper, to create a very accurate SIF variation formula, the elliptical crack SIF solutions , , are used and the SIF ratios , , are mainly focused. Paying attention to the corner point singularity, by applying the least squares method to the ratio , in the whole range of parametric angle , and formulas can be proposed. Instead, formula can be proposed by applying the method of least squares to the ratio of in the range but applying directly to in the range . In this way, all of formulas proposed in this paper provide the SIFs with better than 1.0% accuracy.

Resonances of Fluid‐Filled Cracks With Complex Geometry and Application to Very Long Period (VLP) Seismic Signals at Mayotte Submarine Volcano

AbstractFluid‐filled cracks sustain a slow guided wave (Krauklis wave or crack wave) whose resonant frequencies are widely used for interpreting long period (LP) and very long period (VLP) seismic signals at active volcanoes. Significant efforts have been made to model this process using analytical developments along an infinite crack or numerical methods on simple crack geometries. In this work, we develop an efficient hybrid numerical method for computing resonant frequencies of complex‐shaped fluid‐filled cracks and networks of cracks and apply it to explain the ratio of spectral peaks in the VLP signals from the Fani Maoré submarine volcano that formed in Mayotte in 2018. By coupling triangular boundary elements and the finite volume method, we successfully handle complex geometries and achieve computational efficiency by discretizing solely the crack surfaces. The resonant frequencies are directly determined through eigenvalue analysis. After proper verification, we systematically analyze the resonant frequencies of rectangular and elliptical cracks, quantifying the effect of aspect ratio and crack stiffness. We then discuss theoretically the contribution of fluid viscosity and seismic radiation to energy dissipation. Finally, we obtain a crack geometry that successfully explains the characteristic ratio between the first two modes of the VLP seismic signals from the Fani Maoré submarine volcano in Mayotte. Our work not only reveals rich eigenmodes in complex‐shaped cracks but also contributes to illuminating the subsurface plumbing system of active volcanoes. The developed model is readily applicable to crack wave resonances in other geological settings, such as glacier hydrology and hydrocarbon reservoirs.

A novel damage identification algorithm by combining the boundary element method and a series connection neural network

A novel damage identification approach based on a model-driven and a data-driven combined algorithm is developed. By using this approach with only boundary strains, the existence, location, classification as well as the extent of the damage in a plate can be predicted at once with high accuracy and efficiency. To accumulate the data, the boundary element method (BEM) is applied as a model-driven in modeling plates with one or multiple damages in the forms of circular or elliptical holes or cracks and for solving the boundary strains of the defective plates. The dimensionality reduction and semi-analytical characteristics of BEM not only can compress the feature data also can improve the accuracy of the database for the data-driven algorithm. The boundary strains are obtained directly from BEM models, which are also easily collected through the use of strain gauges mounted on the surfaces of structures being monitored in real applications. A series connection neural network algorithm is established to accomplish the novel damage identification assignments with deep learning. The number of the existing damages is firstly detected by a classification neural network model, then the extracted features are transmitted to the corresponding regression neural network model to prognosis the location, classification as well as the extent of each flaw. A high accuracy of about 99.86 % is achieved by the present combined neural network algorithm, which is promising in applications of actual structural health monitoring.

Численное исследование направления роста трещины в квазихрупком материале в градиентном поле температуры

The elliptical crack growth in a quasi-brittle material located in a gradient field of temperature next to the melting temperature for the thermodynamic phases of the material is studied. The elastic properties of the material are assumed to have an obvious dependence on temperature. This is typical for materials located close to the melting point. To determine the direction of crack growth, a gradient strain criterion is introduced, which assumes crack growth from the point of maximum elastic strain of the material toward its minimum. Depending on the orientation of the crack axis relative to the direction of the temperature gradient, the crack retardation, the change of the crack growth direction, or the appearance of secondary lateral cracks in the vicinity of the main crack tip are possible. The calculated results and the admissibility of applying the introduced criterion have been successfully validated by an experiment with thermal fracture of freshwater ice blocks. As a result, the phenomena predicted by finite element calculations have also been discovered experimentally.

Stress Intensity Factor equations for incipient transverse external annular eccentric cracks contained in a shaft under bending

One of the most common failures in rotating machines is the apparition and propagation of fatigue cracks in one of its main elements: the shafts. These cracks can cause catastrophic failures and lead to costly maintenance or repair processes. Most of the studies in relation to cracks contained in shafts have focused on straight or elliptical transverse cracks. However, although it is less common, the shaft breaks also occur with cracks whose fronts are approximately circumferential, that are more difficult to analyze. These cracks are transverse with circular shape that extend over a complete circumference and that have a certain eccentricity. This work presents the equations that provide the value of the Stress Intensity Factor (SIF) of an incipient crack with circumferential shape contained in a shaft subjected to bending, along the front, as a function of the characteristics of the crack, size and eccentricity. For this, an exhaustive numerical study has been carried out, using the Finite Element Method (FEM), to determine the SIF value along the circumferential front for different sizes and eccentricities of the annular crack.

Analytical verification of FFT-based micromechanical simulations near an elliptical crack tip by using composite voxels

In this paper, we make use of composite voxels in elasto-viscoplastic formulations based on fast Fourier transforms (EVPFFT) to calculate the stress field around an elliptical crack. The predicted stress field at the vicinity of the crack is verified against recently developed analytical solutions. The representation of an elliptical crack in the image-based method is stair-stepped, resulting in oscillations that are mitigated by the use of partially-filled, i.e. composite voxels. Dependencies of the oscillations in the predicted stress fields based on minor changes in the crack size crack size and aspect ratio are discussed and quantified. New understanding is gained of the factors that affect the oscillations, such as the aspect ratio of the ellipse, and the effect of minor changes in the crack interface location. The results show that the use of composite voxels significantly reduces the spurious oscillations in predicted stress fields, and consequently improves the agreement between the EVPFFT simulations and analytical solutions.

Deterministic Stress Intensity Factor of a Railway Axle under Adverse Running Condition

Although railway axles are a crucial part of railway vehicles, they are susceptible to long-term failure because of repeated loads. The aim of this research is to investigate the stress intensity factor (SIF) of a surface elliptical crack on a high-speed railway axle under various operating conditions. The study employs numerical analysis to explore the impact of press-fitting, rotary bending, stable and adverse running conditions on the SIF solutions. The main findings demonstrate that adverse running conditions, such as the press-fitting force, asymmetric vehicle weight, lateral force and wheel-rail contact force, can significantly increase the SIF values and result in axle failure. The press-fitting effect and rotary bending also have a significant impact on the SIF values, highlighting their importance in the railway axle design and analysis. The outcome of this research emphasizes the significance of accurately estimating SIF values to ensure the safe and reliable performance of railway axles in adverse operating conditions.

Elliptic crack problem under shear mode in one-dimensional hexagonal quasicrystals with crack surface parallel to the quasiperiodic axis

In this work we are concerned with a special elliptic crack problem in one-dimensional hexagonal quasicrystals. The crack surface is assumed to be parallel to the quasiperiodic axis. A couple of anti-symmetrical uniform shear loadings is applied on the crack surfaces. Taking advantage of the potential theory method, we develop the governing integral equation and obtain the phonon–phason field in terms of simple integrals. The crack slip displacement and the stress intensity factor are derived explicitly. Based on the analytical solution, we investigate the effects of phason field, crack orientation and the eccentricity of elliptic crack on the important fracture parameters. The solutions obtained in this work are helpful to understand the fracture behavior of one-dimensional hexagonal quasicrystals, especially for the situations in which the cracks are not located on the isotropic planes.

Analysis of three-dimensional cracks horizontally placed in transversely isotropic FGMs under interior compressive stresses

This paper develops the dual boundary element method (DBEM) using a new fundamental singular solution. This new solution is the elastic fields of transversely isotropic multilayered materials of infinite extent under point concentrated loads. The discretization technique is utilized to approximate arbitrary variations of functionally graded materials (FGMs) with transverse isotropy in a graded direction. The proposed DBEM is used to analyze the three-dimensional crack problems in FGM halfspaces. The penny-shaped and elliptical cracks are horizontally placed on the interface between the FGM layer and homogeneous halfspace and are subjected to uniform compressive stresses on crack surfaces. The stress intensity factors are provided to understand the fracture behaviors of transversely isotropic FGMs. An influential factor is defined to describe the influence of the anisotropy of the FGMs on stress intensity factors. Results show that the anisotropy and heterogeneity of materials exert an obvious influence on the fracture properties of crack problems.

Stress intensity factors of elliptical cracks at the weld toe

The paper takes into account the assessment of the stress intensity factor (SIF) of defects similar to elliptical cracks located at the weld toe. By assuming a second order approximation of the Oore-Burns equations the SIF has been evaluated with simplified equations. The analytical results are compared with those evaluated by means of the finite elements method. As an example, the SIF is calculated for a defect located in the neighborhood of the weld toe of full penetration cruciform joints under mode I loading.

Investigation of crack recognition and spatio-temporal evolution pattern in coal samples damage

Understanding the evolution mechanism of cracks helps to evaluate the behavior and performance of rock masses and provides a theoretical basis for the mechanism of crack propagation and instability. For this purpose, a rock mechanics testing system and an acoustic emission monitoring system were used to conduct acoustic emission positioning experiments on coal samples under uniaxial compression. According to clustering theory, the distribution pattern of microcracks and the dynamic evolution process of multiple cracks were studied. Subsequently, the reasons for the change in the spatio-temporal entropy (H) and fractal dimension (D) of a single crack were revealed. The research results show that microcracks present a statistical equilibrium distribution, the Gaussian distribution model is applicable to cluster crack distribution patterns, and a machine learning method can effectively identify cracks. The fractal dimension reflects the spatial characteristics of three-dimensional elliptical cracks, and low-dimensional cluster cracks are more likely to develop into macroscopic cracks. The change of H is related to the formation process of cracks, and an abnormal H (sudden increase and sudden decrease) could provide precursor information for the instability of coal samples. This research provides a new method to study crack distributions and formations and shows the competitiveness of the method in evaluating the damage state of coal.

Reliability analysis of plate parts with multiple interacting hole-edge cracks using complex variable function

In this paper, a successive conformal mapping technique is used to propose an analytical method for solving the stress intensity factor (SIF) of asymmetrical hole-edge cracks on the basis of Muskhelishvili's complex variable function analysis method. Based on this analytical solution, the superposition method is used to get the SIF under the interaction of multiple cracks. Subsequently, according to the plastic collapse criterion, the residual strength under the interaction of two collinear asymmetric elliptical hole-edge cracks with different sizes on the side rail of a dumper's frame is analyzed through the method established. The failure probability of the plate part is obtained by the Kriging meta-model. This study provides a theoretical guide for the operation and maintenance plan of plate parts with multiple cracks.

Degradation analysis of horizontal steam generator tube bundles through crack growth due to two-phase flow induced vibration

A correct understanding of vibration-based degradation is crucial from the standpoint of maintenance for Steam Generators (SG) as crucial mechanical equipment in nuclear power plants. This study has established a novel approach to developing a model for investigating tube bundle degradation according to crack growth caused by two-phase Flow-Induced Vibration (FIV). An important step in the approach is to calculate the two-phase flow field parameters between the SG tube bundles in various zones using the porous media model to determine the velocity and vapor volume fraction. Afterward, to determine the vibration properties of the tube bundles, the Fluid-Solid Interaction (FSI) analysis is performed in eighteen thermal-hydraulic zones. Tube bundle degradation based on crack growth using the sixteen most probable initial cracks and within each SG thermal-hydraulic zone is performed to calculate useful lifetime. Large Eddy Simulation (LES) model, Paris law, and Wiener process model are considered to model the turbulent crossflow around the tube bundles, simulation of elliptical crack growth due to the vibration characteristics, and estimation of SG tube bundles degradation, respectively. The analysis shows that the tube deforms most noticeably in the zone with the highest velocity. As a result, cracks propagate more quickly in the tube with a higher height. In all simulations based on different initial crack sizes, it was observed that zone 16 experiences the greatest deformation and, subsequently, the fastest degradation, with a velocity and vapor volume fraction of 0.5 m/s and 0.4, respectively.

Experimental and Numerical Prediction of Surface Crack Growth in Fatigue in a Finite Width Plate

In the thick components such as gas turbine disks, the cracks usually manifest in the form of part-through or embedded elliptical cracks. The shape of surface crack varies during the crack propagation and significantly affects the fatigue life predictions of the surface cracked components. In present work, crack propagation of semi-elliptical cracks in a finite width specimen of a gas turbine material subjected to fatigue load has been studied experimentally and numerically. The numerical simulation was accomplished by first extending the applicability of available stress intensity factor empirical equation for semi-elliptical cracks to finite width solid. Using this empirical equation for stress intensity factor, the effect of change in the crack shape on the crack propagation life is simulated by numerical models. Also, in order to include the effect of crack closure in the numerical prediction of growth of surface cracks, a ratio of crack closure factor between depth and surface locations of a semi-elliptical crack was obtained by experiments. The experimental observations were used in correlating the numerical predictions for crack shape progression and crack propagation life.