Fatigue Crack Propagation Estimation Based on Direct Strain Measurement during a Full-Scale Fatigue Test.

Military aircraft are subjected to variable loads, which are the main cause of initiation and propagation of cracks in the most stressed locations of the airframe. The aim of a Full-Scale Fatigue Test (FSFT) is to represent actual load conditions in such a way that the results obtained are a good representation of the actual loads and may be used as data that give insight into the development of real fatigue damage in critical locations. The FSFT load spectrum is a generalized depiction of the expected service loads and is designed to give an overall good representation of loads exerted on the airframe's structural elements during operation. Moreover, the discrete method of load application on the structure (exerting loads with hydraulic actuators rather than pressure fields or inertia loads expected in actual operation) may cause some local effects, which may not be present in operation. The proposed usage of direct strain data from the test include such local effects. Moreover, operational loads may vary between individual aircraft, therefore it is crucial to understand the whole process of fatigue crack onset and development in order to determine safe inspection intervals and thereby mitigate risk. This paper presents crack propagation calculations regarding the development of a crack in a critical location of the PZL-130 "Orlik" TC-II aircraft, discovered during FSFT. The discussed crack was found already developed, hence the information about nucleation and initial propagation of the crack was not available. Therefore, there was a need to recreate the whole propagation process by means of numerical estimations using the FSFT results like location of the crack and total life for model validation. Moreover, in order to gather real load data for calculations a dedicated stain gage was installed on the damaged load path to monitor the actual remote strain in the element during the FSFT. This allowed for the definition of load sequence exerted on the damaged element directly during the test rather than estimating it from the general load conditions of the wing. The calculations allowed for the estimation of crack propagation curves from initiation to critical crack length causing fatal damage. The obtained curves allowed to visualize the crack behavior due to applied load and furthermore define initial and recurring inspection intervals for the entire fleet during operation, which allowed to define which cracks could be found before they reach critical size in order to carry out mitigation actions like repair or replacement of the damaged part. The authors present the methodology for load spectrum development based on direct strain measurements and furthermore crack propagation curves estimation, validated with the actual FSFT results, which allowed to propose nondestructive inspection intervals for future operation.

A Crack Propagation Method for Pipelines with Interacting Corrosion and Crack Defects.

Corrosion and crack defects often exist at the same time in pipelines. The interaction impact between these defects could potentially affect the growth of the fatigue crack. In this paper, a crack propagation method is proposed for pipelines with interacting corrosion and crack defects. The finite element models are built to obtain the Stress Intensity Factors (SIFs) for fatigue crack. SIF interaction impact ratio is introduced to describe the interaction effect of corrosion on fatigue crack. Two approaches based on extreme gradient boosting (XGBoost) are proposed in this paper to predict the SIF interaction impact ratio at the deepest point of the crack defect for pipelines with interacting corrosion and crack defects. Crack size, corrosion size and the axial distance between these two defects are the factors that have an impact on the growth of the fatigue crack, and so they are considered as the input of XGBoost models. Based on the synthetic samples from finite element modeling, it has been proved that the proposed approaches can effectively predict the SIF interaction impact ratio with relatively high accuracy. The crack propagation models are built based on the proposed XGBoost models, Paris' law and corrosion growth model. Sensitivity analyses regarding corrosion initial depth and axial distance between defects are performed. The proposed method can support pipeline integrity management by linking the crack propagation model with corrosion size, crack size and the axial distance. The problem of how the interaction between corrosion and crack defects impacts crack defect growth is investigated.

An External Circular Crack in an Infinite Solid under Axisymmetric Heat Flux Loading in the Framework of Fractional Thermoelasticity.

In a real solid there are different types of defects. During sudden cooling, near cracks, there can appear high thermal stresses. In this paper, the time-fractional heat conduction equation is studied in an infinite space with an external circular crack with the interior radius R in the case of axial symmetry. The surfaces of a crack are exposed to the constant heat flux loading in a circular ring R

[Numerical simulation study of fracture mechanics of the atherosclerotic plaque].

Atherosclerotic plaque rupture is the main cause of many cardiovascular diseases, and biomechanical factors play an important role in the process of plaque rupture. In the study of plaque biomechanics, there are relatively few studies based on fatigue fracture failure theory, and most of them mainly focus on the whole fatigue propagation process from crack initiation to plaque rupture, while there are few studies on the influence of crack on plaque rupture at a certain time in the process of fatigue propagation. In this paper, a two-dimensional plaque model with crack was established. Based on the theory of fracture mechanics and combined with the finite element numerical simulation method, the stress intensity factor (SIF) and related influencing factors at the crack tip in the plaque were studied. The SIF was used to measure the influence of crack on plaque rupture. The results show that the existence of crack can lead to local stress concentration, which increases the risk of plaque rupture. The SIF at the crack tip in the plaque was positively correlated with blood pressure, but negatively correlated with fibrous cap thickness and lipid pool stiffness. The effect of the thickness and angle of lipid pool on the SIF at the crack tip in the plaque was less than 4%, which could be ignored. This study provides a theoretical basis for the risk assessment of plaque rupture with cracks.

Determining the Fracture Process Zone Length and Mode I Stress Intensity Factor in Concrete Structures via Mechanoluminescent Technology.

The mechanoluminescent (ML) technology that is being developed as a new and substitutive technology for structural health monitoring systems (SHMS) comprises stress/strain sensing micro-/nanoparticles embedded in a suitable binder, digital imaging system, and digital image processing techniques. The potential of ML technology to reveal the fracture process zone (FPZ) that is commonly found in structural materials like concrete and to calculate the stress intensity factor (SIF) of concrete, which are crucial for SHMS, has never been done before. Therefore, the potential of ML technology to measure the length of the FPZ and to calculate the SIF has been demonstrated in this work by considering a single-edge notched bend (SENB) test of the concrete structures. The image segmentation approach based on the histogram of an ML image as well the skeletonization of an ML image have been introduced in this work to facilitate the measurement of the length of ML pattern, crack, and FPZ. The results show ML technology has the potential to determine fracture toughness, to visualize FPZ and cracks, and to measure their lengths in structural material like concrete, which makes it applicable to structural health monitoring systems (SHMS) to characterize the structural integrity of structures.

Fracture Mechanism and Fracture Toughness at the Interface Between Cortical and Cancellous Bone.

The microstructure at the interface of cortical and cancellous bone is quite complicated. The fracture mechanisms at this location are necessary for understanding the comprehensive fracture of the whole bone. The goal of this study is to identify fracture toughness in terms of J integral and fracture mechanism at the interface between cortical and cancellous bone. For this purpose, single edge notch bend (SENB) specimens were prepared from bovine proximal femur according to ASTM-E399 standard. Bone samples were prepared such that half of the sample width consists of cortical bone and other half of the width was cancellous bone; this interfacial bone is referred as a corticellous bone. Elastic-plastic fracture mechanics was used to measure fracture toughness. The J integral (both elastic and plastic) was used to quantify the fracture toughness. The plastic part of J integral value (Jpl) of corticellous specimen was 9310 J m-2, and shown to be 27 times of the J integral of the elastic part (Jel), 341 J m-2. The total J integral of the corticellous bone was found to be 9651 J m-2, which is close to two times of the cortical bone, 4731 J m-2. This study observed that J integral of corticellous bone is higher than the cortical bone since more energy is required for plastic deformation of corticellous bone due to crack branches and slowdown at the interface between cortical and cancellous bone.

Theoretical and Numerical Study on Stress Intensity Factors for FRP-Strengthened Steel Plates with Double-Edged Cracks.

This paper presents a theoretical and numerical study on the stress intensity factors for double-edged cracked steel plates strengthened with fiber reinforced polymer (FRP) plates. Based on the stress intensity factor solution for infinite center-cracked steel plates strengthened with FRP plates, expressions of the stress intensity factors were proposed for double-edged cracked steel plates strengthened with FRP plates by introducing two correction factors: ß and f. A finite element (FE) simulation was carried out to calculate the stress intensity factors of the steel plate specimens. Numerous combinations of the specimen width, crack length, FRP thickness and Young's modulus, adhesive thickness, and shear modulus were considered to conduct the parametric investigation. The FE results were used to investigate the main influencing factors of the stress intensity factors and the correction factor, ß. The expression of the correction factor, ß, was formulated and calibrated based on the FE results. The proposed expressions of the stress intensity factors were a function of the applied stress, the crack length, the ratio between the crack length and the width of the steel plate, the stiffness ratio between the FRP plate and steel plate, the adhesive thickness, and the shear modulus. Finally, the theoretical results and numerical results were compared to validate the proposed expressions.

Mechanical strength of nanoporous graphene as a desalination membrane.

Recent advances in the development of nanoporous graphene (NPG) hold promise for the future of water supply by reverse osmosis (RO) desalination. But while previous studies have highlighted the potential of NPG as an RO membrane, there is less understanding as to whether NPG is strong enough to maintain its mechanical integrity under the high hydraulic pressures inherent to the RO desalination process. Here, we show that an NPG membrane can maintain its mechanical integrity in RO but that the choice of substrate for graphene is critical to this performance. Using molecular dynamics simulations and continuum fracture mechanics, we show that an appropriate substrate with openings smaller than 1 µm would allow NPG to withstand pressures exceeding 57 MPa (570 bar) or ten times more than typical pressures for seawater RO. Furthermore, we demonstrate that NPG membranes exhibit an unusual mechanical behavior in which greater porosity may help the membrane withstand even higher pressures.

Research on Crack Propagation of Nitrate Ester Plasticized Polyether Propellant: Experiments and Simulation.

To understand the fracture properties of the nitrate ester plasticized polyether (NEPE) propellant, single-edge notched tension (SENT) tests were carried out at room temperature (20 °C) under different tensile rates (10-500 mm/min). The mechanical response, crack morphology, evolution path, and crack propagation velocity during the fracture process were studied using a combination of a drawing machine and a high-speed camera. The mode I critical stress intensity factor KIc was calculated to analyze the tensile fracture toughness of the NEPE propellant, and a criterion related to KIc was proposed as a means of determining whether the solid rocket motors can normally work. The experimental results demonstrated that the NEPE propellant exhibited blunting fracture phenomena during crack propagation, resulting in fluctuating crack propagation velocity. The fracture toughness of the NEPE propellant exhibited clear rate dependence. When the tensile rate increased from 10 mm/min to 500 mm/min, the magnitude of the critical stress intensity factor increased by 62.3%. Moreover, numerical studies based on bond-based peridynamic (BBPD) were performed by modeling the fracture process of the NEPE propellant, including the crack propagation speed and the load-displacement curve of the NEPE propellant. The simulation results were then compared with the experiments.

Experimental Study on Fracture Behavior of Adhesive-Bonded Structure with V-notch Based on Digital Gradient Sensing Method.

In this paper, a comparative study of the mode-I fracture behaviors of two types of specimens with a V-notch defect under plane stress conditions was performed using the digital gradient sensing (DGS) method. First, two types of specimens (namely one-piece specimen and bonded specimen) with the same V-notch defect were both made of polymethyl methacrylate (PMMA), and three different V-notch angles' defect were considered for each type of specimen. Then, three-point bending tests were performed on both types of specimens. The angular deflection field of light near the V-notch region was recorded using a CCD during the experiments. Finally, by utilizing the relationship between the stress gradient and angular deflection as established by the elasto-optic effect, in conjunction with the principles of linear elastic fracture mechanics theory, the stress intensity factors (SIFs) of two types of specimens under different stress conditions were calculated using the least square method. According to the experimental results, the influence of V-notch angle on fracture load and fracture toughness of two kinds of specimens was discussed. Meanwhile, the experimental results show the significant differences in the fracture behaviors of the two types of specimens under mode-I loading conditions.

Determination of Fracture Mechanic Parameters of Concretes Based on Cement Matrix Enhanced by Fly Ash and Nano-Silica.

This study presents test results and deep discussion regarding measurements of the fracture toughness of new concrete composites based on ternary blended cements (TCs). A composition of the most commonly used mineral additive (i.e., fly ash (FA)) in combination with nano-silica (NS) has been proposed as a partial replacement of the ordinary Portland cement (OPC) binder. The novelty of this article is related to the fact that ordinary concretes with FA + NS additives are most often used in construction practice, and there is a decided lack of fracture toughness test results concerning these materials. Therefore, in order to fill this gap in the literature, an extensive evaluation of the fracture mechanic parameters of TC was carried out. Four series of concretes were created, one of which was the reference concrete (REF), and the remaining three were TCs. The effect of a constant content of 5% NS and various FA contents, such as 0, 15%, and 25% wt., as a partial replacement of cement was studied. The parameters of the linear and nonlinear fracture mechanics were analyzed in this study (i.e., the critical stress intensity factor (KIcS), critical crack tip opening displacement (CTODc), and critical unit work of failure (JIc)). In addition, the main mechanical parameters (i.e., the compressive strength (fcm) and splitting tensile strength (fctm)) were evaluated. Based on the studies, it was found that the addition of 5% NS without FA increased the strength and fracture parameters of the concrete by approximately 20%. On the other hand, supplementing the composition of the binder with 5% NS in combination with the 15% FA additive caused an increase in all mechanical parameters by approximately another 20%. However, an increase in the FA content in the concrete mix of another 10% caused a smaller increase in all analyzed factors (i.e., by approximately 10%) compared with a composite with the addition of the NS modifier only. In addition, from an ecological point of view, by utilizing fine waste FA particles combined with extremely fine particles of NS to produce ordinary concretes, the demand for OPC can be reduced, thereby lowering CO2 emissions. Hence, the findings of this research hold practical importance for the future application of such materials in the development of green concretes.

Enhancing aircraft crack repair efficiency through novel optimization of piezoelectric actuator parameters: A design of experiments and adaptive neuro-fuzzy inference system approach.

This study addressed the critical problem of repairing cracks in aging aircraft structures, a safety concern of paramount importance given the extended service life of modern fleets. Utilized a finite element (FE) method enhanced by the design of experiments (DOE) and adaptive neuro-fuzzy inference system (ANFIS) approaches to analyze the efficacy of piezoelectric actuators in mitigating stress intensity factors (SIF) at crack tips-a novel integration in structural repair strategies. Through simulations, we examined the impact of various factors on the repair process, including the plate, actuator, and adhesive bond size and characteristics. In this work, initially, the SIF estimation used the FE approach at crack tips in aluminum 2024-T3 plate under the uniform uniaxial tensile load. Next, numerous simulations have been performed by changing the parameters and their levels to collect the data information for the analysis of the DOE and ANFIS approach. The FE simulation results have shown that changing the parameters and their levels will result in changing of SIF. Several DOE and ANFIS optimization cases have been performed for the depth analysis of parameters. The current results indicated that optimal placement, size, and voltage applied to the piezoelectric actuators are crucial for maximizing crack repair efficiency, with the ability to significantly reduce the SIF by a quantified percentage under specific conditions. This research surpasses previous efforts by providing a comprehensive parameter optimization of piezoelectric actuator application, offering a methodologically advanced and practically relevant pathway to enhance aircraft structural integrity and maintenance practices. The study innovation lies in its methodological fusion, which holistically examines the parameters influencing SIF reduction in aircraft crack repair, marking a significant leap in applying intelligent materials in aerospace engineering.

X-IGA Used for Orthotropic Material Crack Growth.

In this paper, we propose a new approach for numerically simulating the growth of cracks in unidirectional composite materials, termed extended isogeometric analysis, evaluating the maximum stress intensity factor and T-stress. To validate our approach, we used a small anisotropic plate with two edge cracks, beginning with formulating the governing equations based on the energy integral method, Stroh's Formula, and the Elastic Law describing the behaviour of anisotropic materials, while considering boundary conditions and initial states. A MATLAB code was developed to solve these equations numerically and to post-process the tensile stress and the stress intensity factor (SIF) in the first mode. The results for the SIF closely match those obtained using the extended finite element method (X-FEM), with a discrepancy of only 0.0021 Pa·m0.5. This finding underscores the credibility of our approach. The extended finite element method has demonstrated robustness in predicting crack propagation in composite materials in recent years, leading to its adoption by several widely used software packages in various industries.

Three-Dimensional Fracture Analysis in Functionally Graded Materials Using the Finite Block Method in Strong Form.

In this paper, the application of the strong-form finite block method (FBM) to three-dimensional fracture analysis with functionally graded materials is presented. The main idea of the strong-form FBM is that it transforms the arbitrary physical domain into a normalized domain and utilizes the direct collocation method to form a linear system. Using the mapping technique, partial differential matrices of any order can be constructed directly. Frameworks of the strong-form FBM for three-dimensional problems based on Lagrange polynomial interpolation and Chebyshev polynomial interpolation were developed. As the dominant parameters in linear elastic fracture mechanics, the stress intensity factors with functionally graded materials (FGMs) were determined according to the crack opening displacement criteria. Several numerical examples are presented using a few blocks to demonstrate the accuracy and efficiency of the strong-form FBM.

Optimization of Structural Damage Repair with Single and Double-Sided Composite Patches through the Finite Element Analysis and Taguchi Method.

Over the last four decades, numerous studies have been conducted on the use of bonded composite repairs for aircraft structures. These studies have explored the repair of damaged plates through experimental, numerical, and analytical methods and have found that bonded composite repairs are effective in controlling crack damage propagation in thin plates. The use of double-sided composite repairs has been found to improve repair performance within certain limits. This study focuses on these limits and optimizes double-sided composite repairs by varying adhesive bond and composite patch parameters. The optimization process begins with a finite element analysis to determine the stress intensity factor (SIF) for various variables and levels, followed by the application of the Taguchi method to find the optimal combination of parameters for maximizing the normalized SIF. In conclusion, we successfully determined the stress intensity factor (SIF) for various variations and normalized it for optimization. An optimization study was then performed using the Taguchi design and the results were analyzed. Our findings demonstrate the repair performance of bonded composite patches using a cost-effective and energy-efficient approach.

Optimization of Reinforcing Patch Effects on Cracked Plates Using Analytical Modeling and Taguchi Design.

Over the past four decades, the use of composite materials for the repair of cracked structural plates with glued patches has been extensively studied. Attention has been focused on determining a mode-I crack opening displacement, which is important in tension load and in preventing the failure of a structure due to small damages. Therefore, the significance of conducting this work is to determine the mode-I crack displacement of the stress intensity factor (SIF) using analytical modeling and an optimization method. In this study, an analytical solution was obtained for an edge crack on a rectangular aluminum plate with single- and double-sided quasi-isotropic reinforcing patches, using linear elastic fracture mechanics and Rose's analytical approach. Additionally, an optimization technique with the Taguchi design was used to define the optimal solution of the SIF from the suitable parameters and levels. As a result, a parametric study was conducted to assess the mitigation of the SIF using analytical modeling, and the same data were used to optimize the results via the Taguchi design. This study successfully determined and optimized the SIF, demonstrating an energy- and cost-efficient approach to address damage control in structures.

Numerical Analysis of Fracture Behaviour for Cracked Joints in Corrugated Plate Girders Repaired by Stop-Holes.

The efficient crack eliminated stop-hole measure was proposed to repair and reduce the stress concentration associated fracture risk of the corrugated plate girders by setting it at the critical joint of flange plate with tightened bolts and gaskets under preloading. To investigate the fracture behaviour of these repaired girders, parametric finite element analysis was conducted, focusing on the mechanical feature and stress intensity factor of crack stop-hole in this paper. The numerical model was verified against experimental results first, and then the stress characteristics due to the presence of crack open-hole were analysed. It was found that the moderate-sized open-hole was more effective than the over-sized open-hole in the reduction of stress concentration. For the model with prestressed crack stop-hole through bolt preloading, the stress concentration was nearly 50% with the prestress around open-hole increased to 46 MPa, but such a reduction is inconspicuous for even higher prestress. Relatively high circumferential stress gradients and the crack open angle of oversized crack stop-holes were decreased owing to additional prestress effects from the gasket. Finally, the shift from the original tensile area around the edge of the crack open-hole that was prone to fatigue cracking to a compression-oriented area is beneficial for the reduction of stress intensity factor of the prestressed crack stop-holes. It was also demonstrated that the enlargement of crack open-hole has limited influence on the reduction of stress intensity factor and crack propagation. In contrast, higher bolt prestress was more beneficial in consistently reducing the stress intensity factor of the model with the crack open-hole, even containing long crack.

Stress intensity factor of a cracked molar restored with different materials and designs: A 3D-FEA.

OBJECTIVE: This work used 3D finite element analysis (FEA) to analyze and directly compare the stress intensity factor (SIF) and stress distribution at the crack tip of identical cracked tooth models restored with different materials and crown parameters. METHODS: A 3D model of the cracked tooth was generated. Then, we applied 25 restorative models, including three parameters (shoulder height, width, and degree of polymerization), five restorative materials (GC, IPS, LU, ZC, VE), and two combinations of types of cement (RMGIC and GIC). An occlusal load of 800N was applied to the spherical part along the longitudinal axis. The stress distribution of the preparation and the SIF of the crack tip was analyzed. RESULTS: The crack tip SIF was minimal for a shoulder height offset of 0.8 mm (P = 0.032), a shoulder width of 0.6 mm (P = 0.045), a crown material of ZC (P < 2e-16), and a cement material of RMGIC (P < 0.05), respectively. In contrast, the effect of different polymerization degrees on SIF was insignificant (P = 0.95). CONCLUSION: Our results suggest that the selection of a larger modulus of elasticity (MOE) material for the crown, the preparation of a smaller shoulder width within a safe range, a reasonable increase in the crown length, and the selection of adhesive materials with high fracture toughness are favorable methods to prevent further crack extension.

Predicting Stress Intensity Factor for Aluminum 6062 T6 Material in L-Shaped Lower Control Arm (LCA) Design Using Extended Finite Element Analysis.

The aim of this study is to solve a practical problem encountered in the automotive industry, especially the failure of a cracked lower control arm made of al 6062 T6 material during static and crash physical tests, and to characterize the behavior of cracked parts made of aluminum materials using the fracture mechanics parameters. As a first step, we carried out a numerical study and simulation using Abaqus/CAE 2020 software and the finite element method to determine the stress concentration and load limit capacity for different car weight cases. The von Mises stress variation shows crack initiation and propagation to be in the area of the lower control arm's attachment to the vehicle platform, where stress is concentrated. These numerical results are consistent with the experimental test results found by automotive manufacturers. Also, we find that the mechanical load that can support this part is below 4900 N for good performance. In the second step, we use the results of the first section to simulate the failure of a lower control arm with a crack defect. This paper investigates the stress intensity factor KI in mode I for different lengths (L) and depths (a) of the crack in the lower control arm using the extended finite element method (XFEM) under Abaqus/CAE. For crack failure initiation and progression, we relied on the traction separation law, specifically the maximum principal stress (MAXPS) criterion. The KI factor was evaluated for the materials steel and Al 6062 T6. The results obtained from the variation of the KI coefficient as a function of crack depth (a) and the thickness (t) show that the crack remains stable even when a depth ratio (a/t = 0.8) is reached for the steel material. However, the crack in the Aluminum 6062 T6 material becomes unstable at depth (a/t = 0.6), with a high risk of total failure of the lower control arm.

Comparison of Various Intrinsic Defect Criteria to Plot Kitagawa-Takahashi Diagrams in Additively Manufactured AlSi10Mg.

Selective laser melting is a form of additive manufacturing in which a high-power density laser is used to melt and fuse metallic powders to form the final specimen. By performing fatigue and tensile tests under various loading conditions, the study sought to establish the impact of internal defects on the specimens' fatigue life. Scanning electron microscopy and finite element simulation were conducted to determine the defect characteristics and the stress intensity factor of the specimens. Four different methods were used to determine the intrinsic defect length of the specimen, using data such as grain size, yield strength, and hardness value, among others. Kitagawa-Takahashi and El-Haddad diagrams were developed using the results. A correction factor hypothesis was established based on the deviation of measured data. Using Paris law, fatigue life was determined and compared to the experimental results later. The study aims to select one or more approaches that resemble experimental values and comprehend how internal defects and loading situations affect fatigue life. This study's findings shed light on how internal defects affect the fatigue life of selective laser-melted AlSi10Mg specimens and can aid in improving the fatigue life prediction method of additively manufactured components, provided an appropriate intrinsic crack criterion is selected.