Stress Intensity Research Articles

Analysis of load distribution on the plate and lateral hinge of a valgus opening high tibial osteotomy during weight-bearing: a finite element analysis

IntroductionValgus high tibial osteotomy (HTO) is indicated for managing isolated medial knee osteoarthritis in a young patient with a metaphyseal deformity of the proximal tibia. In a medial opening HTO, maintaining the integrity of the lateral hinge is crucial for ensuring proper healing and correction retention. Using a locked plate to stabilize an HTO is common practice, allowing for earlier weight-bearing. The objective of this study was therefore to measure and track the mechanical load distribution on a locked fixation plate and the lateral hinge of an HTO using a finite element (FE) model simulating single-leg stance loading. HypothesisThe working hypothesis was that during weight-bearing, the plate and the lateral hinge absorb stress asymmetrically, predominantly on the plate. Material and methodsA numerical model of an HTO stabilized with a locked plate was developed based on the actual geometry of a healthy proximal tibia (using Autodesk Fusion 360 and Altair HyperWorks software). In this finite element simulation of loading, a mesh convergence study was conducted to optimize the accuracy of the numerical model results. The primary outcome measure was the maximum stress value in the affected areas (Von Mises stress, in MPa) of the plate and the lateral hinge. ResultsThe maximum stress intensity in the plate was approximately 20.29 MPa. The maximum stress intensity in the bony hinge was about 5.6 MPa. The results of the mesh convergence study for the hinge and the plate enabled defining the most suitable model for future FE studies: a 4 mm mesh for all model elements except for the high-stress area in the plate and the hinge, which were meshed with a 0.7 mm element size. This adaptation provided greater precision in the study. DiscussionThere is a distribution and allocation of stress both on the plate and the hinge, underlining the significance of the plate and the absolute necessity of preserving the hinge. Predictably, the plate absorbs the majority of the load, more than three times that of the hinge. ConclusionThe hypothesis is confirmed; however, additional studies would be necessary to validate these numerical results: an experimental component on instrumented cadaveric bones, as well as comparative studies of different fixation plates. Level of EvidenceV, expert opinion; controlled laboratory study.

Finite element analysis of characterization parameters the double cracks in linear elastic DCFEM

In fracture mechanics, the lifespan of structures plays an important and effective role in terms of rigidity and resistance to secondary effects linked to direct friction and the effects of the atmosphere, in order to avoid any danger that could end to the life of the work. structure, and among these effects are those linked to internal and external cracks. Sometimes the structure may be exposed to double cracks resulting from external loads and influences, such as our study that we present in this paper. We must also not forget the structures which contain holes, which play an important role in tension with other elements and have an essential function in operation and resistance. We don't forget the basic dimensions between the crack and the other. These days, numerical modeling techniques, such the finite element method which is the most popular approach for determining characterisation parameters at the bottom of a crack are the foundation for fatigue problem analysis. This work aims to investigate the impact of two-dimensional parameters (b, c) and the crack length (a) on crack parameters, including the J-integral and stress intensity factor (SIF), of an aluminum alloy structure with a double starting fracture. The finite element method (DCFEM) has been used to study these characteristics under uniform tensile loading. After that, rupture happens in plane stress under mode I loading, and the modeling is done using 4-node CPS4R quadratic elements. Numerous instances have been provided. The optimal rupture resistance solution for plates with two cracks on each sides will be developed using the results obtained.

Structure, microstructure, mechanical and luminescent properties of (Y0.96Еu0.01Sm0.01Tb0.01Er0.01)NbO4 ceramics obtained by uniaxial hot pressing

Fine powders of yttrium orthoniobate activated by Eu, Sm, Tb, Er have been synthesized by the sol-gel. The synthesized powders have been calcined at different temperatures (1000, 1100 and 1180 °C). Luminescent ceramics (Y0.96Еu0.01Sm0.01Tb0.01Er0.01)NbO4 were prepared from fine powders by uniaxial hot pressing (UHP) via various technological modes. For the first time, the crystal structure, microstructure, spectral composition, photoluminescence properties of (Y0.96Еu0.01Sm0.01Tb0.01Er0.01)NbO4 ceramics have been studied depending on the temperature conditions of the synthesis of powders and UHP conditions during sintering of ceramics. The mechanical properties of these ceramics (Young's modulus, microhardness and critical stress intensity factor for the mode I KIC) have been evaluated.

Source-sink relationships during grain filling in wheat in response to various temperature, water deficit and nitrogen deficit regimes.

Grain filling is a critical process for improving crop production under adverse conditions caused by climate change. Here, using a quantitative method, we quantified post-anthesis source-sink relationships of a large data set to assess the contribution of remobilized pre-anthesis assimilates to grain growth for both biomass and nitrogen. The data set came from 13 years' semi-controlled field experimentation, in which six bread wheat genotypes were grown at plot scale under contrasting temperature, water, and nitrogen regimes. On average, grain biomass was ~10% higher than post-anthesis aboveground biomass accumulation across regimes and genotypes. Overall, the estimated relative contribution (%) of remobilized assimilates to grain biomass became increasingly significant with increasing stress intensity, ranging from virtually nil to 100%. This percentage was altered more by water and nitrogen regimes than by temperature, indicating the greater impact of water or nitrogen regimes relative to high temperatures under our experimental conditions. Relationships between grain nitrogen demand and post-anthesis nitrogen uptake were generally insensitive to environmental conditions, as there was always significant remobilization of nitrogen from vegetative organs, which helped to stabilize the amount of grain nitrogen. Moreover, variations in the relative contribution of remobilized assimilates with environmental variables were genotype-dependent. Our analysis provides an overall picture of post-anthesis source-sink relationships and pre-anthesis assimilate contributions to grain filling across (non-)environmental factors, and highlights that designing wheat adaption to climate change should account for complex multi-factor interactions.

SINGULAR INTEGRAL EQUATIONS FOR A CRACK SUBJECTED NORMAL STRESS IN A HEATED PLATE

In this paper, a crack in a heated plate is investigated, subjected to normal stress. Employing the relationship between the uniform and perturbation fields, as well as complex potential functions and stresses, the problems of heat conduction and heat stress are modeled as singular integral equations. The derivatives of the crack opening displacement function and the temperature jump function serve as the unknown functions. Gauss integration rules are applied to solve the obtained equations numerically. Analysis of the stress intensity factors(SIFs) for some particular crack configurations is presented.

Spatiotemporal Evolution in the Thermal Environment and Impact Analysis of Drivers in the Beijing–Tianjin–Hebei Urban Agglomeration of China from 2000 to 2020

As urbanization advances, the issue of urban heat islands (UHIs) grows increasingly serious, with UHIs gradually transitioning into regional urban heat islands. There is still a lack of research on the evolution and drivers of the thermal environment in urban agglomerations; therefore, in this study, we used trend analysis methods and spatial statistical analysis tools to investigate these issues in the Beijing–Tianjin–Hebei (BTH) urban agglomeration. The results demonstrated the following: (1) The land surface temperature (LST) exhibited low fluctuation, while the relative land surface temperature (RLST) fluctuated significantly. In Zhangjiakou and Chengde, the LST and RLST evolution trends were complex, and the results differed between daytime and nighttime, as well as between the annual and seasonal scales. In other regions, the trends of LST and RLST evolution were more obvious. (2) During the daytime, the high UHI clusters centered on “BJ–TJ–LF” and “SJZ–XT–HD” formed gradually; during the nighttime, the high UHI clusters were mainly observed in built-up areas. The distribution range and direction of UHIs showed greater degrees of evolution during the daytime in summer. (3) The total UHI area showed an increasing trend, and the intensity of heat stress suffered by the BTH agglomeration was increasing. (4) In BTH and Hebei, aerosol optical depth, surface solar radiation, population density, and gross domestic product were the dominant factors influencing UHIs; moreover, in Beijing and Tianjin, all factors showed an basically equal impact. The methodology and findings of this study hold significant implications for guiding urban construction, optimizing urban structure, and improving urban thermal comfort in the BTH urban agglomeration.

Local carotid stiffness, hemodynamic forces and blood viscosity in patients with cerebral lacunar infarctions.

The carotid stiffness is an important factor in the pathogenesis of cerebrovascular small vessel disease. Our study aimed to evaluate the relation of the local arterial stiffness of the common carotid artery (CCA) to the hemodynamic forces and blood viscosity in patients with cerebral lacunar infarctions (LI). Twenty-two patients with chronic LI and 15 age-matched controls were examined. An ultrasound examination of the CCA intima-media thickness (IMT), the parameters of local CCA stiffness: distensibility (DC) and compliance coefficients (CC), α and β stiffness indices and pulse wave velocity (PWV) was performed. The local hemodynamic forces were calculated: circumferential wall tension (CWT) and wall shear stress (WSS). Whole blood viscosity (WBV) and shear stresses at shear rates of 0.277 s-1 to 94.5 s-1 were measured in patients and controls. Higher values of IMT, a significant decrease of DC and CC and an increase of α and β stiffness indices and PWV in the LI patients compared to the controls were obtained. A parallel significant increase in CWT and a decrease in WSS was found. An increase in WBV and a significant increase in shear stresses were detected. In the LI patients, the increased stiffness indices were associated with an increase in age, cholesterol and WBV at higher shear rates in the left CCA. In the controls, the IMT and stiffness indices correlated significantly with the hemodynamic factors and WBV in both CCAs, while the stiffness indices correlated with the hemodynamic forces in the left CCA. The results of the present study demonstrate different associations of the local carotid stiffness indices with the hemodynamic forces and WBV in patients with LI and controls.

Effect of thermal ageing on fatigue crack growth behaviour of forged alloy 617M at elevated temperatures

ABSTRACT Fatigue crack growth (FCG) studies have been conducted on compact tension specimens of alloy 617M for as-received and aged for 1000, 5000 and 10,000 h at 710°C. Effects of thermal ageing on FCG behaviour of alloy 617M forged has been characterised at 27°C, 650°C, 710°C and 750°C. Results reveal that threshold stress intensity factor ( Δ K th ) decreases as temperature increases upto 710°C and then increases at 750°C for all the ageing conditions except for 1000 h aged. The Δ K th value also decreases with an increase in ageing time till 5000 h, but at 10,000 h a reverse trend is observed. The influence of thermal ageing and temperature reflects major deviations for Paris constant (C) and exponent (m). Additionally, thermal ageing and temperature influences on FCG, the effects of dynamic strain ageing, Cr-rich carbides and γ’-phase precipitations have been discussed and corroborated with fractographic and microstructural changes.

Random Dynamic Responses of Two Parallel Interfacial Cracks Between A Functionally Graded Material Strip And Two Dissimilar Elastic Strips

Abstract An analytical approach is presented in this article for the random dynamic study of two parallel interfacial cracks in a functionally graded material (FGM) strip that is bonded between two distinct elastic strips. One of the parallel cracks is placed at the interface of the elastic strip I and the FGM strip, and another is at the interface of the FGM strip and elastic strip II. A stationary stochastic process of time is used to model the dynamic loadings that are applied to the crack faces. To find the solution, the FGM strip is splited into a number of sub-strips, and using an average method, the material properties of each sub-strip are reduced to random variables. A fundamental problem is formulated to find the solution. The boundary conditions are reduced to a set of singular integral equations employing the Fourier sine, Fourier cosine, and Laplace transforms, which are solved by using the Collocation method. Further, the analytical expressions of dynamic stress intensity factors (DSIFs) about the crack tips in the time domain are obtained with the help of the Improved Dubner and Abate's method. Finally, the Monte Carlo method is used to obtain the mathematical expectation and standard deviation of DSIFs. The outcomes of the present study are also verified. The unique aspect of this study is the pictorial illustration of mathematical expectation and standard deviation as functions of the number of sub-strips, functionally graded parameter, thickness of the strips, and length of parallel interfacial cracks.

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.

Fracture of Epoxy Networks Using Atomistic Simulations.

Predicting fracture properties through all-atomistic simulations poses challenges due to classical force field limitations in breaking covalent bonds and the computational demands of reactive force fields like ReaxFF. In addressing this, we propose a scale-bridging method for forecasting the fracture behavior of highly cross-linked epoxy combining classical force fields, the LAMMPS package REACTER, and for bond breaking a parameter based on experimental distance criterion. In our analysis, we anticipate the macroscopic fracture energy GC of the epoxy network through the application of a continuum fracture mechanics model developed for fibrils. In addition, we extract the value of the stress intensity factor KI. This modeling approach is specifically implemented for a frequently used epoxy system that consists of bisphenol F and DETDA hardener. Notably, our results demonstrate a robust correlation with existing literature and experimental studies. Moreover, our approach boasts a substantial computational time advantage, facilitating calculations that are significantly faster compared to those performed using reactive force fields.

Effect of Synthetic Jet on Flow Field over Different Shaped Ribs and Its Impact on Heat Transfer

The present work reports the manipulation of the flow field over different shapes of surface-mounted obstacles using a synthetic jet. A round synthetic jet is placed upstream and downstream of surface-mounted ribs on a flat surface. Particle image velocimetry and hotwire anemometry are used to study the flow field characteristics and features. Heat transfer rate was obtained using transient liquid crystal thermography technique. Experiments are carried out at Reynolds number of 32,000 in a low-speed wind tunnel. Flow field features behind ribs are analyzed using time-averaged velocity, streamline, vorticity Reynolds stress and turbulent intensity. The spanwise average Nusselt number distribution for the downstream rib location is compared for two optimum locations of the synthetic jet relative to the rib. The recirculation bubble length formed downstream of a rib varies with the frequency of the synthetic jet, its location, and the shape of the rib. A drastic reduction in reattachment length is observed at 50 and 80 Hz frequencies for square rib. The highest heat transfer rate is obtained for the square rib at 50 Hz and 4 voltage peak-to-peak excitation amplitude for the upstream location of the synthetic jet relative to the rib.

Dissipation during crack growth in a viscoelastic material from a cohesive model for a finite specimen

AbstractIn the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.

Dissipation during crack growth in a viscoelastic material from a cohesive model for a finite specimen

AbstractIn the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.

The consequences of heatwaves for the reproductive success and physiology of the wingless sub-Antarctic fly Anatalanta aptera

Sub-lethal effects of warming temperatures are an important, yet sometimes overlooked impact of climate change that may threaten the long-term survival of numerous species. This, like many other effects of climate change, is especially concerning for cold-adapted ectotherms living in rapidly warming polar regions. This study examines the effects of warmer temperatures on cold-adapted Diptera, using the long-lived sub-Antarctic sphaerocerid fly, Anatalanta aptera, as a focal species. We conducted two experiments to assess heat stress in adult flies, one varying the intensity of the heat stress (daily heating from 4 °C to 8 °C, 20 °C, or 24 °C) and one varying the frequency of heat stress exposure (heating from 4 °C to 12 °C every one, two, or three days) and examined consequences for reproductive success and metabolic responses. We found that more heat stress reduced reproductive output, but not timing of reproduction. Surprisingly, individuals sampled at different times during heat stress exposure were undifferentiable when all metabolite concentrations were analysed with redundancy analysis, however some individual metabolites did exhibit significant differences. Overall, our findings suggest that warmer temperatures in the sub-Antarctic may put this species at greater risk, especially when combined with other concurrent threats from biological invasions.

Theoretical analysis of the scattering characteristics of blasting stress waves at an arc-shaped interface crack in a deep rock mass with high in-situ stress

A mathematical model of blasting stress wave scattering at an arc-shaped interface crack is established to theoretically analyze and verify the scattering characteristics of blasting stress waves at an arc-shaped interface crack in a deep rock mass with high in-situ stress. Based on the continuum mechanics, finite deformation, and incremental stress theories and the geometric and physical characteristics of the arc-shaped interface crack, the mathematical model includes a set of the first class of singular integral equations with Hilbert kernels. The opening and dislocating displacements of the arc-shaped interface crack and the effective stress components of scattered stress waves are numerically calculated and discussed with the variation of the type, frequency, and incident angle of the blasting stress wave; the curvature radius and opening angle of the arc-shaped interface crack. The condition that the dynamic stress intensity factors and energy release rates at the upper and lower tips of the arc-shaped interface crack reach peak are also provided. It is found that when the frequency of the blasting stress wave and the curvature radius of the arc-shaped interface crack increase, the peaks of the above dynamic stress intensity factors will increase further, and the arc-shaped interface crack is more likely to expand or destabilize. Although the order of in-situ stress is much smaller than that of Young’s modulus of the deep rock mass, it increases the effective stress concentration of scattered stress waves and the opening and dislocating displacements of the arc-shaped interface crack. These findings will provide theoretical guidance for analyzing the cracking characteristics of blasting stress waves in deep rock masses with high in-situ stress.

Modeling of Mode I crack-tip dislocation nucleation in three FCC materials: Ni, Cu and Al

An accurate estimation of the critical stress intensity factor for crack tip dislocation nucleation under Mode I loading is of great importance to determine whether a material is intrinsically ductile or not. Here, shear displacements and energy change at crack tip in FCC nickel, copper and aluminum are investigated during Mode I fracture process using atomistic simulations. In light of our simulation results, a new shear resistance model is formulated by a general Fourier expansion with coefficients identified by the computed energy curve. The new model involving the step formation energy which can be regarded as a new parameter and unstable stable stacking fault energy, reduces to Rice theory if no step exists. The criterion for nucleation is developed based on the idea that crack tip behaviors are controlled by the shear resistance and the maximum point serves as an obstacle to conquer. The predictions of the critical shear displacement corresponding to maximum shear resistance position and the critical nucleation energy show good agreement with simulation results. In addition, the new model can be further utilized to study the effect of complex stress state on Mode I crack tip dislocation nucleation.

Mechanical properties and insulation damage of PMSG stator end windings with eccentricity considerations

The mechanical properties and insulation damage of stator end windings in permanent magnet synchronous generator (PMSG) are investigated by theoretical analysis, finite element analysis (FEA) and experiment verification. First, a theoretical model of the winding electromagnetic force (EF) and vibration response before and after eccentricity faults are established. Then, the stress/strain distribution of the end windings under different working conditions is analyzed. Finally, the insulation damage behavior of end windings with initial cracks is studied and characterized using the stress intensity factor (SIF). The results indicate that the winding EF and vibration responses vary under different faults. The stress/strain at the joint of the winding is the largest, and the insulation layer has the maximum stress/strain under the same section. Additionally, the SIF amplitude of the crack at the winding joint is the largest. And the SIF amplitude of the crack will increase with the increase of fault degree/crack depth/crack length. The contribution of this paper lies in the comprehensive analysis of the winding EF distribution, vibration response, stress and strain, and insulation damage before and after eccentricity. This analysis can provide valuable reference for the health monitoring of PMSG eccentricity faults and the prevention of winding insulation damage.

Modeling Interface Damage with Random Interface Strength on Asphalt Concrete Impervious Facings.

Asphalt concrete impervious facings, widely adopted as the impervious structures for rockfill dams and upper reservoirs in pumped storage power stations, typically have a multilayer structure with a thin sealing layer, a thick impervious layer, and a thick leveling bonding layer. The properties of the interfaces between these layers are crucial for the overall performance of the facings. This paper develops a model to investigate the complex interface damage behavior of the facing under static water pressure and gravity. The model considers two damage origins: one is the interface adhesion-decohesion damage, which is described by the cohesive zone model (CZM) combined with the Weibull-type random interface strength distribution, and the other is the bulk damage of each layer, described by Mazars' model. Primarily, a comparison between numerical simulation and indoor direct shear tests validates the reliability of the CZM for the asphalt concrete layer interface. Then, the damage distribution of the two interfaces is simulated, and the characteristics of the interface stress are analyzed in detail. The interface shear stresses of the ogee sections, which have different curvatures, all show an interesting oscillation between the thin sealing layer and the impervious layer, and the interface damage at this interface exhibits high heterogeneity. Furthermore, tension stress exists in the local zones of the ogee section, and the damage in this section is significantly greater than in other parts of the facings.

Longitudinal Shear of a Composite Material in Which the Binder and Inclusions are Weakened by Cohesive Cracks

Background: An elastic medium is considered that is weakened by a doubly periodic system of round holes filled with washers made of a homogeneous elastic material and has cohesive cracks, the surface of which is uniformly covered with a cylindrical non-metallic film. The binder (medium) is weakened by two doubly periodic systems of rectilinear cohesive cracks, directed parallel to the abscissa and ordinate axes, and the length of the crack and their dimensions are not the same (different). General concepts are constructed that describe a class of problems with doubly periodic stress distribution outside circular holes and cohesive cracks under longitudinal shear. The analysis of the limit equilibrium of cracks within the framework of the end zone model is performed on the basis of a nonlocal failure criterion with a force condition for the advancement of the crack tip and a deformation condition for determining the advance of the edge of the end zone of the crack. In solving the problem, the main resolving equations are obtained in the form of infinite algebraic systems and three nonlinear singular integro-differential equations. The equations obtained in each approximation were solved by the Gaussian method with the choice of the main element for different order values depending on the radius of the holes. Calculations were carried out to determine the forces in the connections of the end zones and the ultimate loads causing crack growth. Objective: In the considered problem, the problem of longitudinal slip weakened by cracks parallel to the x axis in the filling medium with two pairs of two periodic cracks weakened by 2 periodic circular holes is considered. In the problem, the boundary problem along the contour of the circular holes is determined, and at the same time, the surface problem is established for the cracks parallel to the x and y axes. The solution of the problem is sought analytically, and taking into account the boundary condition, a system of linear algebraic equations for circular holes and 3 singular integral equations for cracks is obtained. Theoretical Framework: The problem is solved analytically, as the system of linear algebraic equations obtained for circular holes and the system of linear integral equations are jointly solved, and the stress intensity factor at the end of the cracks is determined. Method: The problem was solved using "Kolosova Muskhalashvili" functions and "Collondia's method of solving singular integral equations". Results and Discussion: The main essence of the considered issue is that the stress intensity factor at the end of the cracks is determined according to Fig. 1. Research Implications: For the first time, the stress intensity factor was calculated in composite materials with two pairs of biperiodic cracks of different lengths weakened by biperiodic round holes. Originality/Value: For the first time, the stress intensity coefficient was determined in composite materials with two periodic two pairs of cohesive cracks.