Calculation Of Stress Intensity Factors Research Articles

Physics-informed neural networks for V-notch stress intensity factor calculation

This paper proposes a physics-informed neural networks (PINNs) based approach for elastic structures with a V-notch, by which the displacement field, stress field as well as the V-notch stress intensity factor (NSIF) can be obtained through artificial neural networks. A PINN model is established for V-notch structures, integrating physical information into a deep neural network to ensure adherence to physical laws while fitting observational data. Subsequently, an adaptive local sampling strategy for V-notch structures is adopted, generating locally dense Gaussian points sampling around regions of stress concentration. Based on this, a sequential PINNs approach for V-notch structures is then established to calculate the NSIF for V-notch structures with arbitrary notch angles. Finally, the effectiveness of the proposed method is validated through three numerical examples. The results demonstrate the method can accurately predict the NSIFs for V-notch structures across a spectrum of opening angles. Compared to the traditional data-driven method, the proposed method is able to more effectively compute the NSIF of V-notch structures due to the integration of physical information and observational data.

Fatigue mechanisms at 450°C of a highly twined (>70%) and HIP-densified IN718 superalloy additively manufactured by laser beam powder bed fusion

Fatigue resistance at elevated temperatures is crucial for certifying aerospace structures additively manufactured by the laser beam powder bed fusion (PBF-LB) method with IN718 superalloy. This study employed a multi-step, supersolvus heat treatment process with hot isostatic pressing (HIP), called RHSA, to minimize pores and brittle phases. Stress intensity factor (△K) calculations using data from X-ray computed tomography and shape factors referencing finite element analysis (FEA) studies confirmed the suppression of △K below the threshold of conventional IN718 (∼5 MPa√m), shifting fatigue behavior to grain-structure-dominated. Despite a very high twin boundary (TB) fraction (>70%), fatigue tests at 450°C and R = 0.1 demonstrated low scatter. Slip trace analysis and high-resolution electron backscatter diffraction (EBSD) revealed that TB-induced strain concentration became prominent only at high △K, causing cracking at 45⁰ to the loading direction. The randomly oriented TBs with higher angles (60⁰) compared to high-angle grain boundaries (HAGBs) (30–40⁰) likely enhanced slip resistance and provided a net strengthening effect, which can explain the lower-than-average TB% along fracture paths. These insights suggest that a high TB fraction is not detrimental if fatigue stress is not excessive, alleviating concerns about annealing twins during defect minimization in AM IN718, allowing novel processes to improve fatigue resistance in PBF-LB IN718.

Research on the stress intensity factor calculation of multi-elliptical hole-edge crack

Research on the stress intensity factor calculation of multi-elliptical hole-edge crack

Investigation of individual lack-of-fusion defects in the fatigue performance of laser-powder bed fusion Ti6Al4V alloys: A finite element analysis

Laser-Powder Bed Fusion (L-PBF) techniques have revolutionized the production of Ti6Al4V alloys across various industries. However, the widespread adoption of L-PBF Ti6Al4V alloys is impeded by their inadequate fatigue performance, particularly in high cycle regimes. A significant contributing factor to this limitation is the presence of internal defects inherent to the L-PBF process, act as sites for fatigue crack initiation. Previous investigations have focused on the fatigue performance of L-PBF Ti6Al4V alloys with gas porosities, while research on lack-of-fusions (LOFs) which are recognized as the most detrimental defects, remains limited. In order to deepen our understanding of the factors influencing the reduced fatigue performance observed in L-PBF Ti6Al4V alloys associated with inherent LOFs, this study employed three-dimensional (3D) finite element analysis approaches. Such approaches allow to assess fatigue indicator parameters to evaluate fatigue life and predict fatigue crack propagation. A 3D average Smith-Watson-Topper method has been proposed, which is able to rationally estimate the fatigue life of L-PBF Ti6Al4V. In addition, a novel finite element method has been developed to accurately calculate stress intensity factors along irregular shaped crack front of a notch-like feature embedded on a LOF. Additionally, parametric studies were conducted to gain further insights into the influence of LOFs on fatigue performance. The results shown the presence of embedded humps and notch-like features, and their topologies play key roles in the fatigue performance of LOF predominated L-PBF Ti6Al4V alloys.

An in-depth analysis of the Radial Point Interpolation Method’s parameters in relation to the accuracy of fracture problem

The fracture problem has been modeled using Radial Point Interpolation Method (RPIM) to examine the effects of support domain size and shape parameter value on the calculation of Stress Intensity Factor (SIF). The study focuses on an edge crack problem subjected to normal load and shear loads, determining that the support domain size of ‘ α ≥ 3.5 and shape parameter value between ‘ n = 1.9 -2.1’ yield results of accuracy with error % ≤ 3 % . Additionally, research extended by varying the problem domain size and crack location to verify consistency. The findings indicate that selecting the optimal shape parameter value will ensure better accuracy over the enrichment techniques with lesser computational cost.

Study on the influence of rock vertical heterogeneity on the vertical extension law of hydraulic fractures

The vertical expansion of fractures during hydraulic fracturing in low-permeability bottom-water oil and gas reservoirs is a crucial factor that significantly influences stimulation effectiveness. Fractures propagate concurrently in three dimensions; however, as operation time for fracturing and fracture length increase, there is a gradual reduction in fracture height. In the absence of a barrier layer or with inadequate strength and thickness, fractures may extend vertically or oscillate through it leading to an “unyielding” fractured state that impedes successful operations. This study introduces a mathematical model delineating the vertical expansion of hydraulic fractures (HFs) while computing stress intensity factors at upper and lower tips of each individual fracture. We use numerical methods to examine how vertical heterogeneity within reservoir rocks impacts laws governing vertical fracture propagation while conducting sensitivity analysis for making informed decisions on design parameters for hydraulic fracturing operations. The research results indicate that an escalation in stress disparity and increased toughness results in diminished height for HFs. Hydraulic fracturing augments fracture lengths along their respective axes. Nevertheless, if gap stress disparity surpasses net fluid pressure, a reduction in fracture length is observed. With an increasing ratio between local stress gradient versus fluid gravity gradient, HFs persistently advance vertically across cap and bed formations.

3D analysis of crack propagation in nuclear graphite using DVC coupled with finite element analysis

The initiation and propagation of cracks within nuclear graphite components compromise the lifespan of advanced gas-cooled reactors and even lead to safety incidents. A thorough understanding of fracture properties in nuclear graphite is crucial for the effective management and design of graphite structural components. In this work, an in-situ test of a double cleavage drilled compression (DCDC) specimen was conducted using X-ray tomographic imaging to fully analyze the 3D crack propagation behavior in IG-11 nuclear graphite. “Subvolume Splitting” digital volume correlation (SS-DVC) was employed to accurately quantify the displacement fields surrounding the crack. The entire 3D crack propagation and crack surface around the crack front were precisely captured through 3D imaging processing of the gray level residual (GLR) field. Additionally, crack opening displacements (CODs) and stress intensity factors (SIFs) were determined using finite element (FE) analysis with extended finite element method (XFEM). Experimental results indicate that although mode I crack remains predominant throughout the whole process, complex crack propagation exists around the crack front. The utilization of irregular crack surfaces in FE analysis helps to obtain refined displacement fields and accurate SIFs of the crack front. This work provides comprehensive insights into crack propagation and reveals the influence of complex crack morphology on SIF calculations, facilitating accurate prediction of structural integrity and rational design of graphite components.

A New Semi-Analytical Method for the Calculation of Multi-Crack Stress-Intensity Factors under Hydro-Mechanical Coupling

A New Semi-Analytical Method for the Calculation of Multi-Crack Stress-Intensity Factors under Hydro-Mechanical Coupling

A combined displacement discontinuity-interaction integral method for computing stress intensity factors and T-stress

In this paper, the displacement discontinuity method (DDM) is combined with interaction integral to simultaneously evaluate stress intensity factors and T-stress for analyzing two-dimensional mixed-mode crack problems. The displacement discontinuity method has been proved to be one of the most efficient boundary element methods for solving crack problems with boundary-only discretization character. However, there is a lack of efficient methods collaborating with the displacement discontinuity method to evaluate fracture parameters. The available geometrical extrapolation method and J-integral technique for calculating fracture parameters in combination with the displacement discontinuity method are imprecise and difficult to be implemented into mixed-mode crack analysis. The present combined displacement discontinuity method and interaction integral approach can easily extract stress intensity factors and T-stress for mixed-mode crack problems without needing any decomposition of elastic field into symmetric and antisymmetric components. The fundamental basis lies in introducing auxiliary fields for the proper defined single mode crack, then calculating fracture parameters by evaluating the formulated interaction integral in terms of displacement discontinuity solutions and auxiliary elastic fields. In this paper, the basis of the displacement discontinuity method is illustrated firstly, then the explicit expressions for auxiliary fields of displacement gradients are derived. Next, the interaction integral can be determined by being converted to an equivalent area integral. Finally, several numerical examples are examined to demonstrate the correctness of the present method.

Investigation on uniaxial compression and fracture damage mode of prefabricated parallel double-jointed red sandstone.

As a special type of joint fracture, the fracture evolution characteristics of parallel double joints have important engineering significance for the stability analysis of fractured rock mass. In this work, a new method for calculating stress intensity factor of parallel double-jointed fractures was importantly proposed. Physical uniaxial compression tests were carried out on parallel double jointed red sandstone filled with cement mortar under different geometric parameters, and the macroscopic mechanical properties and failure characteristics of red sandstone are deeply analyzed. The results show that the larger the connectivity rate is, the smaller the peak stress and strain are. The increase of connectivity rate will affect the change rate of transverse strain in the center of rock bridge. The closer the dip angle of the joint is, the lower the peak stress is and the shorter the failure time is. The damage mode of joint tip encroachment affects the lateral displacement of the rock bridge center, and the displacement is always close to the first damage section. The closer the joint tip is to the load, the easier the end-face penetrating cracks occur. The research content can provide basic support for guaranteeing the stability of underground engineering rock mass.

Calculation of Stress Intensity Factor for Annular Double Cracks on Inner Surface of Pipeline

Calculation of Stress Intensity Factor for Annular Double Cracks on Inner Surface of Pipeline

Model for Calculating Stress Intensity Factors for an Inclined Crack at the Leading Edge of a Gas Turbine Engine Blade Under the Influence of Centrifugal Forces

The study is devoted to the issue of the destruction of a body with an inclined crack during rotation. A mathematical model for calculating stress intensity factors in a rectangular plate with an inclined crack under the influence of centrifugal tensile forces during rotation around an axis lying in the plane of the plate is constructed in the article. Based on the equations of the theory of elasticity and the principles of brittle fracture mechanics, relationships were obtained that relate the stress intensity factors of type I and II, the rotation speed and geometry of the plate, as well as the parameters of the crack: length, angle of inclination to the axis of rotation, distance from the axis of rotation to the crack. The complexity of the study is because the plate in question with an inclined crack is under the action of mass forces. Therefore, the values of the effective stresses are not the same along the crack edge. Accordingly, stress intensity factors will depend on the location of the crack relative to the axis of rotation. The influence of the crack location and plate rotation speed on the change in stress intensity factor values is analyzed based on the results obtained. As the distance from the axis of rotation to the crack increases, the values of the stress intensity factors decrease. As the plate rotation frequency increases, the stress intensity coefficients increase according to a parabolic law. The results of the study can be used to assess the limit state of the rotating blades of a gas turbine engine in the presence of an inclined crack. The mathematical model can find practical application for assessing the critical speed regime of blade rotation in the presence of cracks of various lengths and angles of inclination to the rotation axis.

Analytical computation of stress intensity factor for multi-physics problems

This work presents a methodology for the analytical calculation of the stress intensity factor when the stress distribution on the crack surfaces is non-homogeneous. At first, a polynomial function is used to express the non-homogenous stress distribution. Subsequently, the principle of superposition of effects is applied, and the stress intensity factor is computed by multiplying each polynomial term by its respective geometric factor. Finite element fracture model is used to compute the geometric factor of the single polynomial grade. To explain the method, a spherical body is considered, with central and superficial cracks. Each geometric factor depends on a normalized geometrical parameter (the ratio between the crack length and sphere radius). The proposed methodology is applied to determine the stress intensity factor in the case of a crack driving force caused by diffusive fields, such as the concentration gradient in particles of electrodes active material in lithium-ion batteries. The methodology allows to speed up the fracture computation, then it is used to give electrode design guidelines to limit the fracture likeliness and mechanical degradation in lithium-ion batteries, as well as it is the basis for the development of algorithms assessing the capacity loss and the remaining useful life of lithium-ion batteries in real-time.

Determining Stress Intensity Factors at Varied Inclination Angles through Innovative Discontinuous Digital Image Correlation

An innovative method is proposed for determining stress intensity factors at crack tips with different inclination angles, based on the Adaptive Digital Image Correlation (AD-DIC) method. This method involves fitting a set of nonlinear equations with unknown parameters using displacement field data. The initial values for crack tip coordinates and inclination angles, computed through the AD-DIC method, are employed in this process to obtain stress intensity factors at the crack tips. The results demonstrate that this approach accurately captures the crack tip positions and calculates stress intensity factors for cracks at various inclination angles. This addresses the challenge of computing stress intensity factors during the crack propagation stage, where cracks may deviate, making conventional calculations impractical.

Experimental and numerical analysis of the behavior of rehabilitated aluminum structures using chopped strand mat GFRP composite patches

PurposeThis paper comprehensively addresses the influence of chopped strand mat glass fiber-reinforced polymer (GFRP) patch configurations such as geometry, dimensions, position and the number of layers of patches, whether a single or double patch is used and how well debonding the area under the patch improves the strength of the cracked aluminum plates with different crack lengths.Design/methodology/approachSingle-edge cracked aluminum specimens of 150 mm in length and 50 mm in width were tested using the tensile test. The cracked aluminum specimens were then repaired using GFRP patches with various configurations. A three-dimensional (3D) finite element method (FEM) was adopted to simulate the repaired cracked aluminum plates using composite patches to obtain the stress intensity factor (SIF). The numerical modeling and validation of ABAQUS software and the contour integral method for SIF calculations provide a valuable tool for further investigation and design optimization.FindingsThe width of the GFRP patches affected the efficiency of the rehabilitated cracked aluminum plate. Increasing patch width WP from 5 mm to 15 mm increases the peak load by 9.7 and 17.5%, respectively, if compared with the specimen without the patch. The efficiency of the GFRP patch in reducing the SIF increased as the number of layers increased, i.e. the maximum load was enhanced by 5%.Originality/valueThis study assessed repairing metallic structures using the chopped strand mat GFRP. Furthermore, it demonstrated the superiority of rectangular patches over semicircular ones, along with the benefit of using double patches for out-of-plane bending prevention and it emphasizes the detrimental effect of defects in the bonding area between the patch and the cracked component. This underlines the importance of proper surface preparation and bonding techniques for successful repair.Graphical abstract

Determination of stress intensity coefficients using PC LIRA CAD

Today, the issue of involving fracture mechanics approaches to the calculation of structures with cracks is becoming more and more relevant. For the most part, the implementation of such approaches is carried out using software complexes in which the finite element method is implemented. Among them, such software complexes as Abaqus, Ansys, Nastran stand out, where the implementation of fracture mechanics approaches is constantly being improved. However, the cost of licenses for the use of such complexes, especially in the conditions of Ukraine, does not allow most researchers to fully use such programs. Therefore, it is relevant to study the possibility of applying fracture mechanics approaches in software complexes, the use of which is free. In construction, a significant number of structures are isotropic bodies. Operation of most of them is accompanied by elastic deformations. If there are cracks in them, the load-bearing capacity is assessed using stress intensity factors (SIF). This article examines the possibility of determining the TIN based on the results of the specified stress-strain state obtained with the help of the free software package "PC LIRA-SAPR 2016 R5 (non-commercial)". The calculation of SIF is performed by a direct method based on the determined distribution of displacements and stresses around the crack tip. The crack is modeled by setting appropriate boundary conditions. Implementation of the direct method is performed in 2 ways. According to the 1st method, the SIF calculation is performed in the apical area according to the values of stresses and displacements. According to the 2nd method, the SIF is calculated by moving the node closest to the top of the crack. Approbation of the approaches was carried out on the test problem of tension of a plate with a central crack. A study of the influence of the dimensionality of the discrete model and the types of finite elements both outside the apex region and in the apex region itself was conducted. The obtained results showed the possibility of obtaining reliable SIF values in this software complex in two ways, subject to compliance with certain rules for building a discrete model.

Fracture mechanics approach to TRISO fuel particle failure analysis

Weibull stress-based methods for failure probability assessment have been developed and analyzed to assess the integrity of tristructural isotropic (TRISO) fuel particles during fuel life cycles and accident operating conditions. While simple, these methods entail a number of drawbacks when stress concentrates near crack tips, including finite element mesh size dependency when the Weibull stress is averaged over the finite element domain. Fracture mechanics approaches involving the use of interaction integrals eliminate this lack of mesh convergence and produce consistent fracture predictions. In this work, we use an interaction integral approach to computing stress intensity factors for a crack in the inner pyrolytic carbon layer perpendicular to the silicon carbide layer, which is simplified representation of a failure mode in TRISO particles. The interface between these two TRISO layers has been shown to become porous, which we simulate by considering a transition of mechanical properties over such porous length, i.e. the layers are modeled as a functionally graded material. Aspects such as porosity and thermal and irradiation eigenstrains are considered in computing the stress intensity factor from a fracture mechanics approach and compared with the known Weibull stress failure approach. The methodology introduced in this paper enables a more general fracture probability assessment in TRISO particles and eliminates the need to identify best suited parameters when using local or averaged stress-based failure criterion. Finally, the numerical sensitivity studies show how parameters such as the porous transition zone length, the material stiffness, and creep affect the probability of TRISO fuel particle failure.

Geomechanical analysis of lost circulation control in tight formations

Unconventional oil and gas reservoirs, especially that in tight formations, contribute great parts to the global energy. During drilling in tight formations, lost circulation was one of the major problems, which can cause large amount of non operation time and millions of losses. In order to migrate the problem, lost circulation materials (LCMs) were used to prevent reopening of the fracture by isolating the fracture tip while the calculation of stress intensity factor (SIF) and fracture width is the key to LCMs design. In this paper, a dual porosity medium flow model suitable for tight formation is established to calculate the pressure distribution in fracture, and the fracture width and fracture reopening pressure (FROP) is then calculated by using the semi-analytical fracture mechanics model. Sensitivity analysis of critical parameters, for example, fracture length, wellbore radius, LCMs permeability, viscosity, wellbore pressure, and two rock-mechanics-related properties are implemented. The fracture width is larger in the formation with large horizontal principal stress anisotropy, low Young’s modulus and Poisson’s ratio. The increase in fracture length, wellbore radius and wellbore pressure also contributes to fracture opening. Meanwhile, we compared the situation before and after fracture plugging and the results emphasize that the fracture reopening is less likely to occur under the conditions of high viscosity and low permeability LCMs. The method proposed in this study can be used to calculate fracture width and FROP, which has potential significant application for lost circulation control in tight formation.

Analytical Solution of Ice–Rock-Model Stress Field and Stress Intensity Factors in Inhomogeneous Media

The stress distribution and fracture parameter calibration of ice–rock models are important aspects of studying rock properties at high altitudes and latitudes. However, progress in ice–rock modeling has been slow and singular, and it is limited due to the discrete nature of rocks and the applicability of fracture mechanics. In this study, a circular inhomogeneous ice–rock model is proposed for the first time, and a method is provided for calculating the stress field of the model under biaxial loading. A method for calculating the single-crack stress intensity factor of the model subjected to biaxial compressive loading is also provided. The novelty of this work is that the inhomogeneous ice–rock model is treated as a superposition of two models, namely, a circular pore plate and circular ice, according to the superposition principle. The key is that the stress field distribution law of the ice–rock model is obtained based on the basis of the displacement continuity of the ice–rock interface. The analytical and approximate solutions of the stress intensity factor of a single crack were also obtained by considering the normal phase effect of the crack surface and combining the stress distribution law of the ice–rock model. Comparison with the CAE method was made to verify the correctness of the stress field and stress intensity factor calculation methods. The evolution laws of lateral pressure coefficients, the elastic modulus ratio of ice and rock on the stress field, and the stress intensity factor were analyzed. The effects of lateral pressure coefficients, elastic modulus ratios, and crack distributions on the failure modes were investigated using the extended finite element method (XFEM). This study can provide a theoretical basis for the evaluation of mechanical properties and prediction of the failure modes of frozen rock bodies.

Analysis and calculation of stress intensity factors for type I cracks on the edge of elliptical holes under internal pressure

Analysis and calculation of stress intensity factors for type I cracks on the edge of elliptical holes under internal pressure