Linear Elastic Fracture Mechanics Research Articles

Effect of shot peening parameters on fretting fatigue lifetime

Fretting fatigue pertains to the behavior of engineering components subjected to cyclic loading while in contact with each other. This challenging contact-related phenomenon often leads to premature failure compared to typical fatigue issues. To extend the lifespan of components experiencing fretting fatigue, surface strengthening is crucial. One well-established method for enhancing the durability of these components is the application of compressive residual stress to the material's surface, achieved through a process called Shot Peening (SP). Numerous parameters in SP, such as shot speed, ball material, ball diameter, and coverage, must be carefully controlled to make beneficial compressive residual stress. These parameters significantly affect the residual stress distribution, containing the maximum residual stress, the depth of the residual stress area, and the depth of the maximum residual stress. The Critical Plane (CP) approach is used to calculate the damage parameter, and the Theory of Critical Distance (TCD) method is utilized to average the damage parameter due to the stress concentration resulting from the contact problem to investigate the impact of residual stress distribution on crack initiation behavior. Additionally, Linear Elastic Fracture Mechanics (LEFM) criteria, specifically the Extended Maximum Tangential Stress (E-MTS) criterion, are used to study how the residual stress affects crack propagation lifetime under fretting conditions. It is found that the maximum residual stress plays the most important role in improving crack initiation and propagation lifetimes, as well as the depth of the residual stress region. However, an increase in the depth of the maximum residual stress has a negative impact on crack initiation lifetime, and it has little effect on crack propagation lifetime. Furthermore, the enhanced lifetime diminishes as the applied loads increase.

Additive manufacturing of ULTEM 9085: Weak interface-enriched multi-toughening mechanisms and fracture resistance optimization

Modulating the fracture toughness can be used to tailor or enhance the mechanical performances in the design of specific additively-manufactured engineering structures. In this research, we explored the fracture behavior of ULTEM 9085 materials fabricated by material extrusion (MEX) 3D printing technique, with a particular emphasis on the effect of weak interfaces between deposited beads. Under quasi-static bending condition, the MEX-fabricated ULTEM 9085 exhibits brittle and quasi-brittle fracture behaviors by adjusting the print orientations and raster angles. Several intrinsic toughening mechanisms are identified, including crack deflection and twisting, fibril bridging, constrained microcracking and delamination of the weak interface. Notably, the samples that experienced delamination along the weak interface displayed the highest performance in terms of the fracture toughness. To achieve high fracture toughness, we employed an analytical model based on linear elastic multilayers fracture mechanics to understand the crack onset and predict the crack propagate orientation. Based on the insight gained from this model, we proposed an intuitive optimal strategy to enhance the fracture resistance by fine turning the bonding strength and layer height to trigger the crack deflecting towards and propagating at the weak interface consistently. By implanting this approach, we achieved an increase of over 35% in fracture resistance while effectively preventing the catastrophic failure, demonstrating exceptional fracture-resistant performance. Overall, our study elucidates the impact of layer-by-layer MEX-induced weak interfaces on the fracture resistance of MEX-fabricated high temperature engineering materials. The findings of this research hold potential for engineering applications, particularly in optimizing the design of additive manufactured products aiming at high fracture resistant.

Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect Aspects

This paper presents an extension of the validation domain of a previously validated three-dimensional probabilistic semi-explicit cracking numerical model, which was initially validated for a specific concrete mix design. This model is implemented in a finite element code. The primary objective of this study is to propose a function that enables the estimation of the critical fracture energy parameter utilized in the model and validate its effectiveness for various concrete mix designs. The model focuses on macrocrack propagation and introduces significant aspects such as employing volume elements for simulating macrocrack propagation and incorporating two key factors in governing its behavior. Firstly, macrocrack initiation is linked to the uniaxial tensile strength (ft). Secondly, macrocrack propagation is influenced by a post-cracking dissipation energy in tension. This energy is taken equal to the mode I critical fracture energy (GIC) based on the linear elastic fracture mechanics theory. Importantly, both ft and GIC are probabilistic properties influenced by the volume of concrete under consideration. Consequently, in the numerical model, they are dependent on the volume of the finite elements employed. To achieve this objective, numerical simulations of fracture mechanical tests are conducted on a large double cantilever beam specimen. Through these simulations, we validate the proposed function, which is a crucial step towards expanding the model’s applicability to all concrete mix designs.

Simulation of crack propagation in piping components using phase field approach

Understanding the fracture behaviour in pipelines transporting steam and other resources is vital for its longevity and structural integrity. The prediction of crack initiation and propagation, involving crack branching, and the nucleation of new cracks, etc. in fracture processes are challenging tasks. The phase field method (PFM), based on variational formulation, emerged as a competitive mathematical tool to address fracture mechanics problems. PFM does not require the presence of predefined cracks, handles the crack initiation and propagation within the same system. This feature provides an added advantage to PFM and overcomes the limitations of Griffith’s approach-based linear elastic fracture mechanics (LEFM). In the present work, simulation of the crack propagation in the piping components by employing phase field methodologies has been carried out. Two parameters namely; a phase field parameter (ϕ) that varies between 0 and 1 differentiating between broken and intact material, and a length scale parameter (l_0) that approximates the sharp crack into the diffused crack with exponential distribution are introduced in the mathematical modeling. Numerical modeling is solved using the staggered algorithm in three layered scheme defining the displacement field and phase field within a 3-D finite element framework and implemented in Abaqus via user-defined element (UEL) subroutine codes. PFM simulates the crack path and predicts the load-displacement response, which is validated with benchmark problems, and extended for piping components under monotonic loading. The proposed study accurately captures the crack growth behaviour as observed in experiments on SA312 Type 304LN stainless steel pipes and hence, demonstrated the robustness of the proposed formulation.

Stress ratio effect on fatigue crack growth assessment via thermoelastic stress analysis

The fatigue performance of welded joint is strongly dependent on welding residual stresses as well as the local geometry of the weld toes. To ensure the structural integrity over time of such components, fine predictive models must be proposed together with efficient experimental methods for their assessment.This study introduces a model based on linear elastic fracture mechanics to forecast fatigue life in service of high strength steel welded joints. This model considers the effect of the local stress ratio (dependent on stabilized residual stresses) on the crack growth rate through the definition of an effective stress range. The use of Thermoelastic Stress Analysis (TSA) is used to perform in-situ monitoring of fatigue cracks on welded joints to experimentally characterize the crack-closure phenomenon at different load ratios. Indeed, under adiabatic conditions, the temperature's first harmonic at the surface of a structure submitted to cyclic loading is proportional to the stress tensor's first invariant's amplitude. As a result, the presence of a surface crack and the non-linearity induced by the alterative opening and closing within one loading cycle can be observed in the immediate temperature response. This phenomenon is used to evaluate a crack-opening rate that is related to the fatigue life of the welded joints.

Экспериментальная оценка адекватности численного моделирования межслоевой трещиностойкости слоистого стеклоэпоксикомпозита при комбинированной моде нагружения I/II

The reliability of numerical simulation of crack growth in a laminate glass-epoxy composite under mixed-mode loading by opening (mode I) and shear (mode II) of an interlayer crack is verified. According to the experimentally determined standard (DCB and ENF) and nonstandard (SLB and OLB) methods, the values of the parameters of interlayer crack resistance under individual and mixed-mode loading modes I and II calculated the exponent in the Benzeggagh-Kenane equation as a material constant of the laminate epoxy glass composite. Using this parameter and the ANSYS software package, within the framework of linear elastic fracture mechanics and the method of virtual crack closure, numerical finite element modeling of the growth of interlayer cracks in samples of a laminate glass-epoxy composite of the SLB and OLB types was carried out under a mixed-mode loading with a different fraction of modes. With the optimal number of elements in the finite element mesh per given length of the crack growth trajectory, numerical simulation provides sufficient accuracy of calculations of the limit load of the beginning of crack growth with a minimum amount of calculations and good agreement between the experimentally determined and calculated crack resistance parameters.

Advances in Machine Learning Techniques Used in Fatigue Life Prediction of Welded Structures

In the shipbuilding, construction, automotive, and aerospace industries, welding is still a crucial manufacturing process because it can be utilized to create massive, intricate structures with exact dimensional specifications. These kinds of structures are essential for urbanization considering they are used in applications such as tanks, ships, and bridges. However, one of the most important types of structural damage in welding continues to be fatigue. Therefore, it is necessary to take this phenomenon into account when designing and to assess it while a structure is in use. Although traditional methodologies including strain life, linear elastic fracture mechanics, and stress-based procedures are useful for diagnosing fatigue failures, these techniques are typically geometry restricted, require a lot of computing time, are not self-improving, and have limited automation capabilities. Meanwhile, following the conception of machine learning, which can swiftly discover failure trends, cut costs, and time while also paving the way for automation, many damage problems have shown promise in receiving exceptional solutions. This study seeks to provide a thorough overview of how algorithms of machine learning are utilized to forecast the life span of structures joined with welding. It will also go through their drawbacks and advantages. Specifically, the perspectives examined are from the views of the material type, application, welding method, input parameters, and output parameters. It is seen that input parameters such as arc voltage, welding speed, stress intensity factor range, crack growth parameters, stress histories, thickness, and nugget size influence output parameters in the manner of residual stress, number of cycles to failure, impact strength, and stress concentration factors, amongst others. Steel (including high strength steel and stainless steel) accounted for the highest frequency of material usage, while bridges were the most desired area of application. Meanwhile, the predominant taxonomy of machine learning was the random/hybrid-based type. Thus, the selection of the most appropriate and reliable algorithm for any requisite matter in this area could ultimately be determined, opening new research and development opportunities for automation, testing, structural integrity, structural health monitoring, and damage-tolerant design of welded structures.

An effective free-meshing and linear Step-Wise procedure to predict crack initiation and propagation

An automated procedure is proposed to calculate fracture initiation and propagation in two-dimensional structures. The application uses and enriches the Hybrid Semi-Analytical Method to calculate mixed-mode stress intensity factors in linear elastic fracture mechanics framework. The strategy does not necessitate prior knowledge of the starting crack tip location within the structure, resulting in suitable for analyzing structures without initial defects. When neither a priori invitation nor pre-existing notch is provided, the fracture initiation is assumed to occur when the structure reaches its elastic limit, and a non-linear analysis is conducted under the prescribed load to identify the first occurrence of permanent strain and to locate where the crack opening occurs. As the crack propagates, solely linear elastic analyses are performed to calculate the stress intensity factors. Relying upon these parameters, the procedure implements an evolutionary algorithm based on a step-by-step evaluation of the crack increment and direction. A global–local energy-based criterion is employed to drive fracture propagation. Neither local refinement nor mapped meshes around the crack tip are required, resulting in a streamlined and efficient free-meshing strategy.The calculation has been implemented in a standard finite element environment, and several numerical examples have been investigated, both from a qualitative and quantitative point of view. Qualitative crack paths have been shown for a square hollow plate under pure tensile and shear loads, and a modified Single Edge Notched specimen in bending, as a function of the mutual void positions, distance from the plate edges, and different notch lengths. Finally, an effective comparison in terms of forces-displacement curves has been presented between the proposed procedure, and a lab test for a modified Compact Tension specimen under tensile loading, demonstrating the overall accuracy and reliability of the presented strategy.It is felt that the proposed procedure could pave the way for designing hollowed structures and investigating the corresponding evolutionary laws that relate structural geometries to the insurgence and spread of fractures, and envisaging crack initiation and propagation within inhomogeneous media.

Critical thrust force prediction in unidirectional CFRP drilling: An analytical modeling approach

In recent trends, unidirectional carbon fiber laminates have been extensively used in the aviation sector due to their remarkable material properties. Delamination is a major damage introduced during drilling in composite laminates. One of the prime contributing factors for delamination-induced damages is considered as the thrust force. A mathematical model is proposed using an analytical approach for accurate prediction of the thrust force for the last lamina, which experience the most damage. The linear elastic fracture mechanics (LEFM), the classical bending plate theory (CPT) and the theory of elastic behavior of composite lamina are taken into consideration for the proposed analytical model because numerical prediction greatly depends on material properties and the nature of force as well. In the current research, the mathematical equation is proposed based on assumption of combined loading of drill tip and chisel edges for the elliptical delaminated area. The Mode-I interlaminar fracture toughness of unidirectional CFRP (CTC1-FUD160/CT-E556) is experimented with as per ASTM D5528 for better experimental substantiation of the proposed model. When the outcomes of the proposed model are compared with the experiment results and available literature as well, a plausible relationship between the suggested analytical model and the experimental results is found. The result also reveals that the contribution of the drill tip is more profound than the chisel edges of drill bit in drilling operations.

Nanofracture of graphyne family with geometrical distortions of crack fronts

The static fracture of α-, β-, γ-, and 6,6,12-graphyne under mixed-mode I/II loading in boundary layer models is studied by molecular dynamics and linear elastic fracture mechanics. We find that the crack front undergoes distinct lattice distortions before cracking, which is closely related to the geometric composition of lattices (hexagonal and triangular) in graphynes. Distorted lattices intensify stress concentration around the crack tip during loading. Furthermore, the fracture toughness varies with the graphyne types, among which γ-graphyne shows the highest critical stress intensity factor of 2.0–2.9 MPa·√m, while α-graphyne exhibits the largest critical energy release rate of 8.3–8.9 J/m2. Upon cracking, the crack tends to propagate along the zigzag surface, aligning with the direction of atomic maximum circumferential stress or the local maximum energy release rate. However, the T-stress criterion is limited in determining the cracking direction due to the local anisotropy in graphynes. This study provides plenty insights into the lattice fracture of the graphyne family.

Structural integrity analysis with crack propagation for reactor pressure vessel nozzles based on XFEM

Structural integrity analysis for reactor pressure vessel (RPV) nozzles has been a vital issue due to the irradiation embrittlement and especially the discontinuity of geometry in RPV nozzles, which may cause a higher stress concentration and influence the structural integrity of RPV nozzles. For the linear elastic fracture mechanics (LEFM) analysis of the RPV nozzle, a postulated crack with a specific crack depth is presumed to evaluate the stress intensity factors (SIFs) whose crack depth does not grow during LEFM analysis. Thus, this paper would discuss the crack propagation for the postulated crack with a specific crack depth under the different reference temperature of nil-ductility transition (RTNDT), and the SIFs on the specific crack depth are also calculated. In recent research, the extended finite element method (XFEM) was developed, which is based on the enrichment solution space to simplify the computational fracture mechanics with the crack propagation of various discontinuities, and can be used to evaluate the crack propagation of RPV nozzle with a specific crack depth under RTNDT of −23.89, −10.89, 0.89, 2.69, and 2.89 °C. To investigate the crack propagation and structural integrity of RPV nozzles, the finite element analysis of Taiwan domestic boiling water reactor (BWR) nozzles containing the postulated circular corner crack with depths of one-fourth and one-tenth thickness along the 45° path from the tip of the nozzle corner is engaged. The present result shows that the crack was growing when the RTNDT was 0.89 °C and. In addition, the XFEM calculation of the SIFs for the specific crack depth is similar to the LEFM results.

Tension-shear extension criteria used in PFC2D to reveal a brittle failure of rock bridges in rock slopes with stepped joints

Stepped failure is a typical mode in alpine valleys and usually manifests as brittle fractures determined by joints. Tension-shear extension criteria were proposed to reflect the intrinsic mechanism of this failure mode. These criteria combined the theory of linear elastic fracture mechanics and the Mohr-Coulomb (M−C) strength criterion, including propagation trends and fracture conditions, and reflected the fracture behavior of rock bridges determined by joints. The proposed extension criteria were numerically applied in the 2D Particle Flow Code (PFC2D). The mesoscopic strength parameters were calibrated according to a mathematical relationship, which could satisfy the relationship between stress and strength with the proposed criteria. For massive rock slopes dominated by stepped joints, it is determined through theoretical and experimental analysis that rock bridges undergo tensile failure under low normal stress levels, which gives a reasonable explanation of why rock bridges observed in situ generally undergo tensile fracture. The internal mechanism of rock bridge failure is revealed through mechanical analysis of fracture behavior, which is considered in the numerical method. Taking the Xiaowan Hydropower Station as an example, it is confirmed that the simulation results truly reproduce the mesoscopic mechanism of the stepped failure of the slope.

Fatigue Crack Growth Analysis in Modified Compact Tension Specimen with Varying Stress Ratios: A Finite Element Study

In this study, the primary objective is to analyze fatigue crack propagation in linear elastic fracture mechanics using the SMART crack growth module in the ANSYS Workbench, employing the finite element method. The investigation encompasses several crucial steps, including the computation of stress intensity factors (SIFs), determination of crack paths, and estimation of remaining fatigue life. To thoroughly understand crack behavior under various loading conditions, a wide range of stress ratios, ranging from R = 0.1 to R = 0.9, is considered. The research findings highlight the significant impact of the stress ratio on the equivalent range of SIFs, fatigue life cycles, and distribution of deformation. As the stress ratio increases, there is a consistent reduction in the magnitude of the equivalent range of stress intensity factor. Additionally, a reciprocal relationship is observed between the level of X-directional deformation and the number of cycles to failure. This indicates that components experiencing lower levels of deformation tend to exhibit longer fatigue life cycles, as evidenced by the specimens studied. To verify the findings, the computational results are matched with the crack paths and fatigue life data obtained from both experimental and numerical sources available in the open literature. The extensive comparison carried out reveals a remarkable level of agreement between the computed outcomes and both the experimental and numerical results.

Study on Dynamic Parameters and Energy Dissipation Characteristics of Coal Samples under Dynamic Load and Temperature

Coal and rock dynamic disasters such as rock burst and outburst seriously threaten the sustainable development of the coal mining industry, which are intimately correlated with the nonlinear dynamic response process of the deep coal and rock mass. This study conducts coal dynamic experiments under vibration load from room temperature to 60 °C by using the split Hopkinson bar (SHPB) with a temperature real-time control system and analyzes the variation in stress and strain and the energy dissipation characteristics of coal during the dynamic load process. The expression equation of dissipated energy of coal at different scales is established, and the judgment conditions of the macroscopic mechanical behavior of coal are analyzed theoretically. The stress curves show a multi-stress peak phenomenon when the coal samples are subjected to different temperatures and dynamic loads, and the coal’s dynamic stress and temperature show a polynomial fitting relationship at different stages. When the coal sample is subjected to temperature and dynamic load, the macroscopic changes in incident energy, reflected energy, and dissipated energy are consistent; that is, various energies gradually increase to a fixed value and tend to stabilize with the time of stress wave action. The transmission energy exhibits a rising trend in correlation with the duration of the dynamic load action, but the value is less than 0.1 J. The growth gradients of the different energies, in descending order, are: the growth gradient of incident energy, reflection energy, dissipation energy, and transmission energy. The energy inflection point appears at 60 °C. Based on the linear elastic fracture mechanics and damage mechanics theories, the expression for coal energy dissipation from the nanoscale to the microscale is established, and the relationship between energy dissipation and macroscopic mechanical behavior response of the coal samples is analyzed. The main physical components of the coal sample are calcite and kaolinite. Within the temperature range of 18–60 °C, the macroscopic failure form of the coal is horizontal tensile failure. The study results are introduced into dynamic disaster prevention and control and the surrounding rock system stability evaluation in deep mines.

An efficient computational framework for height-contained growing and intersecting hydraulic fracturing simulation via SGBEM–FEM

An efficient computational framework to model the growth of intersecting height-contained hydraulic fractures is proposed. The fracture in solids is modeled by the classical theory of linear elastic fracture mechanics, whereas the injection flow in hydraulic fractures is treated as channel flow. The governing equations of fracture mechanics are formulated in terms of weakly-singular weak-form boundary integral equations, with the knowledge of the fracture surface geometry exploited to reduce the integral dimension. The fluid flow within the fracture is treated using finite element method as one dimensional flow in an arbitrarily curved channel. The symmetric Galerkin boundary element method and finite element method are coupled with the traction continuity condition. The model is then formulated in a variational form and augmented with Lagrange multipliers to prescribe displacement constraints on intersections of hydraulic fractures, while fluid constraints are enforced by a consolidation of associated pressure degrees of freedom. Pertinent numerical implementation techniques, including spatial and temporal discretizations, special crack tip element, crack propagation criteria and remeshing strategy, are presented. The proposed framework is verified by comparing to the numerical results from a three dimensional hydraulic fracturing simulator and then verified by comparing the stress intensity factors to the XFEM and Murakami’s results for both star shaped cracks and symmetric branched cracks. The verification shows the utility properly enforces the physical constraints on the intersections of fractures. Three numerical examples are shown to demonstrate the capability of the proposed computational framework modeling the intersecting hydraulic fracturing process in a single or separated height-contained pay zones.

Fatigue crack growth and life assessment of full penetration U-rib welded joints considering residual stresses

The combination of cyclic stresses and welding residual stresses (WRS) can significantly contribute to fatigue cracking in steel bridge decks. This study aims to investigate the effect of WRS on the fatigue life and crack propagation of single-sided and full penetration double-sided U-rib welded joints through experimental and numerical methods. Fatigue tests were conducted to study fatigue crack initiation and propagation behavior. Utilizing the ABAQUS software, a thermoelastic-plastic finite element method was employed to determine the residual stress distribution. Subsequently, based on linear elastic fracture mechanics (LEFM), fatigue crack propagation and life assessment were performed using ABAQUS and FRANC3D software under the coupling of residual stresses and external cyclic stresses. Findings reveal that WRS play a crucial role in fatigue life by altering the effective stress ratio during fatigue crack growth. The effective stress ratio ranges from 0.15 to 0.57, while the changing trends differ between single-sided and double-sided U-rib welded joints. The fatigue crack growth rate of double-sided U-rib welded joints is lower compared to single-sided U-rib welded joints with the same deck thickness. Furthermore, the introduction of WRS induces a mixed mode I, II, and III fracture at the outer weld toe of the U rib, with mode I fracture predominating, which leads to a deviation in the crack propagation path. The fatigue life prediction results agree well with experimental findings when considering WRS. Importantly, these predictions tend to be conservative, thereby ensuring safety and reliability in engineering applications.

Comparing linear damage hypothesis to linear elastic fracture mechanics in the estimation of fatigue life in a high speed light craft

Linear elastic fracture mechanics methods provide a more comprehensive representation of crack propagation compared to traditional methods such as the linear damage hypothesis (or SN curve approach). These techniques have been widely adopted in the aerospace industry, however, their usage in the design of marine structures remains limited. The presented research uses full-scale trial data measured onboard a 111 m wave-piercing catamaran to compare the results obtained from linear elastic fracture mechanics and SN curve-based methods. The results reveal significant differences in estimated fatigue life between SN curve-based methods and fracture mechanics methods. These differences are likely due to limitations in the fracture mechanics model during the crack initiation phase. Changes in fracture mechanics parameters also had a significant effect on fatigue life, suggesting that if accuracy is important then material specific parameters are required. Despite the limitations shown, linear elastic fracture mechanics methods have a higher level of tailor-ability when compared to SN curve based methods and could offer benefits in situations such as the tracking of known flaws or in the assessment of changes to vessel configuration, or usage profiles.

Effect of bending stress parallel to the crack plane on J and the limit load of plates with surface cracks

The effect of bending stress parallel to the crack plane on J-integral of plates containing semi-elliptical surface cracks is investigated in this paper. Elastic and elastic–plastic finite element (FE) analyses are used to obtain J values for the surface-cracked plates under membrane stress or through-thickness bending stress normal to the crack plane or under biaxial membrane stresses plus through-thickness bending normal to the crack plane with/without bending stress parallel to the crack plane. The FE results show that, as predicted by linear elastic fracture mechanics, the applied bending stress parallel to the crack plane does not affect the crack tip elastic J. However, it does affect the elastic–plastic J. A limit load (or reference stress) solution for a plate containing a rectangular surface crack under combined biaxial membrane stresses and biaxial bending stresses is developed, which shows good correlation to the elastic–plastic FE J via the reference stress J scheme, for both cases with/without the bending stress parallel to the crack plane. Based on the results of the investigation, a newly-developed local limit load model is updated to include the effects of bending stress parallel to the crack plane for use in structural integrity assessments.

Effect of size and anisotropy on mode I fracture toughness of coal

Obtaining the accurate fracture toughness of coal considering bedding angle and independent of size is of great significance to the evaluation of the initiation pressure in the hydraulic fracturing of coal seam. In this study, the newly proposed modified semi-circular bending test was used to conduct mode I fracture testing of coal samples with different sizes and bedding angles. A four-dimensional lattice spring model (4D-LSM) was established based on the cohesive zone model considering bedding planes to study the effects of specimen size and bedding angle the fracture toughness and fracture pattern of coal. The size effect and anisotropy characteristics of fracture toughness of coal were analyzed by using linear elastic fracture mechanics and Bazant size effect law (SEL) theory. The results show that the fracture toughness of coal has obvious size effect and anisotropy. In quasi-brittle materials, the fracture toughness increases with the increase of specimen size due to the fracture process zone (FPZ). However, the fracture toughness of coal affected by microcracks generally decreases with the increase of specimen size. The size effect of fracture toughness of coal is jointly determined by the FPZ with increasing effect and the microcrack with reducing effect. The fracture toughness of coal increases with the increase of bedding angle. The bedding angle has no influence on the fracture toughness size effect of coal, but the microcracks associated with the bedding plane have a greater influence on the fracture toughness size effect. The specimen size only affects the fracture toughness value, but has no obvious effect on the fracture toughness anisotropy. Based on Bazant SEL theory, a fracture toughness size effect model considering microcracks and bedding angles was established. The research results have reference significance for crack initiation and propagation in hydraulic fracturing of coal seam.

Effect of double cracks merge on fatigue crack propagation life of engine heat shield

To prevent overheating of the airframe, an aero-engine is often designed to play a role in shielding heat radiation heat shield. Since the thermal protection system used in this paper is active, it is subject to a cold gas pressure load on the outside and a thermal radiation load from the combustion chamber on the inside. Therefore, the working environment of the heat shield is very harsh. Taking the heat shield of an aero-engine as the research object, the finite element method (FEM) is used to analyze the thermal-mechanical coupling (TMC) of the actual working process of the heat shield, and the mechanical quantities such as the thermal stresses and mechanical stresses are comprehensively analyzed. According to the finite element simulation results, two stress concentrations are obtained near the connecting lug, and the stress concentrations are set as the initial crack insertion locations. Using the theory related to linear elastic fracture mechanics (LEFM) and the Forman-Newman-de Koning (FNK) model, the fatigue crack propagation life (FCPL) and its law of the merged double cracks of the engine heat shield are calculated. The results show that the FCPL of the heat shield decreases nonlinearly and the critical crack length decreases linearly under different working conditions. This law applies not only to single cracks but also to merged double cracks. In terms of FCPL, the merged double cracks are lower than the single crack with a maximum life reduction rate of 70.9%.