Deformation Coefficient Research Articles

Mechanical Behaviour Evaluation of Full Iron Tailings Concrete Columns under Large Eccentric Short-Term Loading

In this study, full iron tailings concrete (FITC) was created using iron tailings from a tailings pond in Qian'an, China. Iron tailings account for 86.8% of the total mass of solid raw materials in the FITC. To enable large-scale use of FITC, a comprehensive investigation of the structural behaviour of full-iron tailing-reinforced concrete (FITRC) specimens is warranted. Therefore, eight rectangular reinforced concrete (RC) columns with conventional reinforced concrete (CRC) as a control were tested to investigate the effects of section dimensions, initial eccentricities, and concrete strengths, on the structural behaviour of FITRC columns under large eccentric short-term loading. The experimental and analytical results indicated that the sectional strain of the FITRC columns satisfied the plane-section assumption under short-term loading, and the lateral deflection curve agreed well with the half-sinusoidal curve. In addition, the FITRC columns exhibited a slightly lower cracking load and lower ultimate load capacity than the CRC columns, and the crack widths were larger than those of the CRC columns. The reduction in the load capacity observed in the FITRC was within the permissible range stated in the design code, thereby satisfying the code requirements. The deformation coefficients of the FITRC and CRC columns were identical, and the cracking and ultimate loads calculated according to the current code and theories were in good agreement with the measured results.

A prediction model for suction cavitation erosion in a journal bearing

Suction damage occurred often in dynamically loaded journal bearings. A new theoretical model, including lubrication module, boundary module and prediction module, was proposed to investigate the suction damage in a journal bearing. The results showed that, a stable cavitation area with steady temperature fields formed in the film rupture region, but no suction cavitation erosion occurred in a constant load journal bearing. It was concluded that, suction cavitation erosion occurred within the region of suction cavitation, and higher dimensionless deformation coefficients stood for more muscular suction damage strength within suction cavitation regions. It was beneficial to reduce transient impact force applied to a journal bearing for resisting suction cavitation erosion, leading to an increase of a periodic pressure coefficient.

An extended peridynamic model for analyzing interfacial failure of composite materials with non-uniform discretization

This work presents an extended ordinary state-based peridynamic model and approaches to analyze the fracture behavior of composite materials considering interfacial failure. An interface force term is introduced to characterize the interaction among different compositions in composite materials, which enables naturally the non-uniform discretization to be conveniently adopted, especially where sharp interfaces exist. The calculation of force states in different compositions is independent of each other, and the use of non-uniform discretization can improve computational efficiency significantly. Further, inspired by the cohesive zone model (CZM), the deformation coefficient and degradation behavior of interface bonds are derived by using the traction-separation law, and a mixed-mode fracture criterion for interface bonds based on the bond energy density is established as well. Validation of the proposed model and approach is established through a classical rectangular plate example, and then the proposed model is employed to analyze the failure of typical composites including laminated glass and concrete. The results show good agreement with corresponding experimental observations and it indicates that the proposed extended peridynamic model can accurately and efficiently capture and describe the fracture of composite materials with sharp interfaces.

Spatio-temporal evolution and precursory indicators of rock failure processes using acoustic emission tomography

The characterization of stress and crack development plays important part in monitoring disasters. To capture the instability enlightenment from the spatio-temporal evolution of rock damage, this paper constructs the velocity field of key nodes in the rock failure process with the active and passive collaborative acoustic emission (AE) tomography method. It realizes the exploration of the micro-crack propagation law and its potential connection with the stress environment, combining the velocity field, the AE density field, and the energy field. Furthermore, from the spatial integrity and directional evolution of the velocity field, the mutation trend coefficient (MTC) and deformation coefficient (DC) of the velocity field are proposed as precursor indicators of rock instability, respectively. Results show that the anisotropy of the velocity field increases with the aggravation of rock damage, and the stress environment controls the spatial heterogeneity of the velocity field. The most important feature of spatial heterogeneity is that there are the continuous decrease and extension of low-velocity regions and the transformation from the high velocity to the low velocity. Real-time acoustic emission monitoring of the velocity field with MTC and DC can early identify rock instability precursors and principal stress direction, which provides vital pre-alarm information for geotechnical engineering.

Design and Experiment of Ultrasonic Assistant Grinding Device of Spiral Bevel Gear

The precisely ground tooth surface of the spiral bevel gear still shows the thermal crack, and its micromorphology is the cause of high-frequency noise. The ultrasonic assistant grinding (RUAG) technology has the unique advantage of solving these problems. Therefore, this paper designed the split-type rotary device in which the disc grinder and amplitude horn are core components and bolted together. A deformation coefficient was proposed to calculate the strain stress of the disc grinder. Combined with the stepped horn resonant theory, the theoretical model of a multi-step rotating body can be used to calculate the frequency and amplitude of the grinder and horn. The harmonic response simulation was adopted to verify the theoretical results. The experiment proved that the device’s frequency, node, and amplitude are reasonable. The comparison results showed that the simulated frequency and amplitude were closer to the practical one. Moreover, the difference between them increased with the dimension of the device.

Analysis and prediction of nonuniform deformation in composite strata during tunnel excavation

Due to the influence of composite strata, traditional monitoring and measurement cannot accurately reflect the nonuniform deformation and corresponding local damage to tunnels. However, the nonuniform deformation precise analysis and effective prediction of composite strata tunnels are indispensable in related projects. This analysis established a nonuniform deformation classification method and 135 groups of numerical models for a composite strata tunnel. The nonuniform deformation classification method involves four reference-defined indexes, the average deformation coefficient, variable deformation coefficient, segmental deformation coefficient, and abnormal deformation coefficient. The numerical model took the dip angle of the formation, formation proportion, in-situ stress, and pore pressure as composite strata model conditions, with four reference indexes in the nonuniform deformation classification method as the output parameters. The intelligent model of the least squares supports vector machine (PSO-LSSVM) was innovatively utilized to predict nonuniform deformation in composite strata during tunnel excavation. The prediction results of the PSO-LSSVM are consistent with actual engineering data relying on the engineering situation of Teermo Tunnel. This approach can provide targeted guidance for a composite stratum tunnel engineering evaluation system.

Synergistically enhanced flexibility, mechanical strength and microwave absorption performances of TPE-based hybrid films via thermally assisted homogeneous separation technology

With the ever-growing electromagnetic (EM) wave pollution and the rising demand of flexible absorbing materials pasted onto the surfaces of different geometric surfaces, it is urgent to develop high-efficiency EM wave absorption films with good flexibility and mechanical strength. Traditional processing methods endow the film superior features that can be adapted to targeted geometric surfaces and complex conditions, however, the durability is not satisfactory. Confronted with the tough problem, in this work, optimized thermally assisted homogeneous separation technology was proposed to fabricate the thermoplastic elastomer-based magnetic/dielectric two-phase mixed EM wave absorption films, which can achieve good flexibility, machinability, mechanical strength, as well as excellent EM wave absorption performances due to the uniform filling of elastoplastic skeletons and chain-bridge effect between chains and particles. Benefitting from these merits, the as-prepared films exhibit good flexibility and fine mechanical properties, like good deformability (300% of the deformation compared to its original length) and low elastic coefficient (323.8 Pa). Moreover, good EM wave absorption performances can also be balanced, for example, broad effective bandwidth (>14 GHz) and tunable frequency response from high frequency to low frequency. In all, this work opens up a new pathway to realize the integration of strong EM response, good flexibility, and fine mechanical properties, and the obtained films exhibit great potentials as flexible EM wave absorption materials that can be pasted on or peeled off the targeted surfaces at any time.

Deviation from the fcc structure in the vertically deposited opal layers

The discrepancy between the experimental and theoretical results of Bragg diffraction in vertically deposited opal layers occurred in the literature. They refer to diffraction extrema associated with planes other than parallel to the top surface. Analyzing the results of spectrogoniometric studies of the transmission coefficient the new “face-centered tetragonal” (“fct”) structure was proposed. Assuming that structure a satisfactory agreement of the theoretical and experimental dependencies was obtained. Based on the new structure, the diameter of nanospheres, filling factor, deformation coefficient, and thus the length of the opal unit cell edge were obtained for several samples.

Elastic deformation effect on carboxymethyl cellulose water-based (TiO2–Ti6Al4V) hybrid nanoliquid over a stretching sheet with an induced magnetic field

An analysis is carried out to study the two-dimensional stagnant point flow of titanium dioxide -titanium alloy /carboxymethyl cellulose (CMC) water-based hybrid nanoliquid over an expanding surface characterized by the induced magnetic field (IMF). Further, the consideration of thermal buoyancy and the additional nonuniform heat source is involved in the modeling. The intent of this work has significant novelty due to the elastic deformation behavior over a stretching surface. The governing mathematical equations of the problem are reduced to a set of simultaneous ordinary differential equations and are elucidated numerically by employing the Runge-Kutta-Fehlbergs fourth-and-fifth (RKF-45) order process combined with a shooting approach. This article examines the properties of change in parameters on the functions including temperature profiles, induced magnetic field, and velocity profiles of hybrid nanoliquid, shown through graphs. The impact of the Elastic deformation coefficient reduces the temperature where as magnetic field enhance the velocity profile. Magnetic parameter boosts skin friction coefficient with an increase in the buoyancy effect. Momentum profile and induced magnetic field are affected most by the Magnetic Prandtl number

Mechanical property and cutting performance of self-lubricating cermet tools with the addition of core-shell powders

To study the influence of core-shell powders on the mechanical and cutting properties of self-lubricating cermet tools, two kinds of core-shell powders (h-BN@Al2O3 and c-BN@Al2O3) were prepared by the heterogeneous nucleation method, and they were used as the additive phase of (Ti,W)C cermet tools. Compared with the addition of c-BN@Al2O3, the addition of h-BN@Al2O3 produced a residual stress field around the matrix grain due to thermal mismatch, which improved the grain interface bonding strength and inhibited the crack propagation, having a better strengthening and toughening effect on (Ti,W)C cermet. The flexural strength and fracture toughness of the cermet with 5 vol% h-BN@Al2O3 were 1465 ± 30 MPa and 9.9 ± 0.3 MPa·m1/2, which were improved by 38 %/23 % and 3.6 %/4.2 % compared with that of the cermet without core-shell powders and with 5 vol% c-BN@Al2O3, respectively. The cutting performance of the cermet tool with 5 vol% h-BN@Al2O3 was also better than that of the cermet without core-shell powders and with 5 vol% c-BN@Al2O3. When machining 40Cr hardened steel, the h-BN in the core-shell particles was gradually exposed and formed a self-lubricating coating on the tool surface, which reduced the friction coefficient, cutting force, cutting temperature, surface roughness and chip deformation coefficient. Because the tool had both self-lubricating properties and excellent mechanical properties, the wear resistance was significantly improved and the tool life was extended to >8800 m. Within the effective cutting distance, the surface roughness of the workpiece was kept at 0.91–1.37 μm. The research results showed that the core-shell powders in the matrix grain can improve the mechanical properties because of the residual stress mechanism, and the cutting performance of the tools can be improved by its self-lubricating characteristics, so this self-lubricating cermet tool is an ideal dry-cutting tool.

Effects of effective voltages, electrode types and stretching states on electrical properties and actuation characteristics of dielectric elastomer materials

In this study, the electrical properties of DE materials were systematically tested, and the effects of different effective voltages, electrode types and stretching states on permittivity, dielectric loss, conductivity, capacitance and electrical efficiency were discussed. The frequency dependence of the electric dipole in the material is revealed from the microscopic point of view. Finally, based on the structure and volume incompressibility of the DE, the actuation coefficient of the DE is proposed to characterize its deformation effect. The results show that the permittivity of the DE is very sensitive at high frequency, especially for DE materials with carbon electrode and gold-carbon electrode. At the same effective voltage and gold electrode, the permittivity decreases with the increase of equal biaxial stretching. For the same stretching area, the permittivity of equal biaxial stretching is larger than that of unequal biaxial stretching. The DE with carbon electrode has the largest dielectric loss and is easy to be destroyed in engineering application, which needs further optimization. The dielectric loss decreases with the increase of equal biaxial stretching, which is mainly due to the decrease of orientation deviation between main chain and side chain in DE material. The electric efficiency at low frequency is generally higher than that at high frequency, and the highest electric efficiency can reach 99.64%. With the increase of frequency, the actuation deformation coefficient decreases rapidly. This work will further promote the development of DE materials used in soft robot, and provide a theoretical reference for the design of actuators and sensors.

Supporting optimization of thick seam roadway with top coal based on orthogonal matrix analysis

Aiming at the problem of large deformation and difficulty in surrounding rock control of the top coal roadway in thick seam, theoretical analysis, theoretical analysis, numerical simulation, orthogonal matrix analysis and other methods were used to study the roof deformation and support parameter optimization of the top coal roadway in thick seam. Firstly, the structural model and roof mechanical model of the top coal roadway in thick seam were established, and the deformation coefficient TK was defined based on the relationship between curvature radius and bending moment, maximum bending moment and ultimate tensile strength of beam. According to the ratio of deformation rate between TK and beam to determine the roof deformation mode of top coal roadway, the discriminant conditions of roadway roof stability under two deformation conditions are obtained. Due to the characteristics of serious coal-rock fragmentation, large roof deformation, and integration of top coal and side coal. Therefore, the combined support method of “high prestressed long and short anchor cables” is proposed by double arch bearing structure control technology. Finally, based on the orthogonal matrix analysis method of supporting parameters optimization of the top coal roadway in thick seam, the analysis amount of supporting scheme is significantly reduced, the comprehensive evaluation of multi-factor and multi-supporting effect of roadway support is realized, and the optimal supporting scheme is obtained. Compared with the surrounding rock of the roadway without support, the deformation of the roof is reduced by 27.27%, the deformation of the two sides is reduced by 45.24%, and the tensile failure volume is reduced by 54.66%. The top coal roadway in thick seam has been effectively controlled, which provides guarantee for high yield and high efficiency of the mine.

Design study on small transmission ratio harmonic reducer with new profile wave generator

A harmonic reducer (HR) is widely used because of high precision, small size, light weight and a series of advantages. However, the disadvantage is that its transmission ratio is generally not less than 60. According to a market research study, more than 60% of the reducers have the transmission ratio of less than 60. This implies that the large transmission ratio restricts the HR from applications in the market demanding a small transmission ratio (20–60). In this study, a method is presented for designing the HR with the small transmission ratio as low as 20. First, by clarifying the principle of reducing the transmission ratio of the HR, a design model of two-wave HR tooth profile is deduced in detail, and a four-tooth difference HR is designed. Aiming at solving the problem that diminishing the radial deformation coefficient leads to the reduction of the engagement depth and the increase of the pressure angle of the tooth profile, a wave generator with a new profile is proposed. Then an optimization model based on the circular spline tooth profile to envelope the flexspline tooth profile is developed for achieving the twice-conjugated engagement. Based on manufacturing considerations, the theoretical tooth profile is fitted by involute based on a given numerical approximation method. Third, a finite element analysis is carried out to investigate the stress characteristics of small transmission ratio HR. Finally, a prototype with a transmission ratio of 20 is trial-produced and tested, which shows that the design methods can be applied for the small transmission ratio HR.

Influencing mechanism of fiber deformation on mesh pattern noise in inverting-image fiber-optic arrays

Inverting-image fiber-optic array (IIFOA) is an important optical element for transferring the inverted images at 180° with high resolution and contrast. Mesh pattern noise (MPN) generated at the boundary of the multi-multi fibers in IIFOA significantly deteriorates the imaging quality and detection accuracy. The unexpected deformation of the optical fibers at the boundary of multi-fiber is one of the main factors causing MPN. In this study, the brightness distribution of the optical fibers and the corresponding microstructure were characterized by high-resolution Lambert-light microscopy and scanning probe microscopy with laser scanning, respectively. The relative transmittance of the individual optical fibers located in the MPN zone was normalized and calculated, and the cross-sectional deformation coefficient (De) of optical fiber in the twisted zone was proposed. Furthermore, the relationship among De, the relative transmittance of optical fibers, and MPN of IIFOA was established. The results show that the relative transmittance of optical fibers indicates an initial decrease and a subsequent increase with the decrease of De in the MPN generated zone. When De of the optical fibers is within the range of [0.3497, 0.9225], the relative transmittance is no more than 96.74%. The aggregation and distribution of these optical fibers at the adjacent side of the multi-multi fiber boundary causes black mesh pattern noise. When De of the optical fibers is less than 0.3228, the relative transmittance is consistently higher than 3.26% of the non-deformed fibers owing to the enhanced crosstalk of the adjacent optical fibers and even the new imaging unit formed by bonding some core fibers. The aggregation and distribution of such optical fibers at the boundary causes white mesh pattern noise. When De is between 0.3228 and 0.3497, there is no MPN, but the resolution is significantly reduced. The research results provide data support and theoretical guidance for controlling defects such as MPN and transmittance inhomogeneity in IIFOA, thus enabling the improvement of the image quality of IIFOA.

Direct assessment of changes in biomechanical properties of the cornea after ReLEx SMILE and FemtoLASIK surgeries

The SMILE group comprised 23 patients (46 eyes) with spherical refraction -3.8±1.8 diopters (D), the FemtoLASIK group included 18 patients (36 eyes) with spherical refraction -3.5±1.3 D. Analysis of the biomechanical properties of the cornea was carried out using the CORVIS ST device (Oculus, Germany) before and seven days after corneal refractive surgery. In the SMILE group, with intraoperative decrease in corneal thickness of 91.43±19.43 µm, a significant increase in the following parameters was observed: deformation coefficient (DA ratio; p=0.0001), peak distance (PD; p=0.02) and inverse concave radius (ICR; p=0.003); a decrease in the stiffness parameter at first applanation (SP-A1; p=0.0001), Corvis biomechanical index (CBI; p=0.0001), intraocular pressure (IOP; p=0.001). In the FemtoLASIK group, with intraoperative decrease in corneal thickness of 75.33±32.3 µm, we observed a significant increase in DA ratio (p=0.0002), PD (p=0.04), ICR (p=0.0002), a decrease in SP-A1 (p<0.0001), IOP values (p=0.0003). In comparison with the FemtoLASIK group, the deformation amplitude DA changed significantly less in the SMILE group (p=0.04). In the FemtoLASIK group, in comparison with the SMILE group, the DA ratio (p=0.0009) and SP-A1 (p=0.0003) significantly increased. Intraoperative corneal thickness change correlates with ICR both in SMILE (R=0.52) and in FemtoLASIK (R=0.65). Corneal biomechanical properties determined with CORVIS ST in eyes with mild to moderate myopia change to a lesser extent after ReLEx SMILE compared to FemtoLASIK.

Influence of Deformation on Sound-Absorbing Performance Under Hydrostatic Pressure

The sound-absorbing rubber coating is easy to deform under hydrostatic pressure, resulting in variation in acoustic properties. For improving the accuracy of the deformation of the sound-absorbing structure under hydrostatic pressure, four hyperelastic constitutive models of Mooney-Rivlin, Neo-Hookean, Yeoh and Arruda-Boyce were selected in fitting the tensile curve of the dumbbell specimen and the compressive curve of a cylindrical specimen. The comparison in their applicability and the accuracy showed that the Yeoh model can predict the compressive properties of carbon black filled styrene-butadiene rubber. Simulation in mechanics-sound coupling was further conducted by COMSOL software and verified by the acoustic experiments, which exhibit the non-negligible effects of pressure and tubes inserted in the cavities on the deformation and sound-absorption coefficient. Hydrostatic pressure exerts the deformation and thereafter the energy dissipation in sound transfer. Inserting a rigid tube is beneficial to improve the ability of the sound-absorbing tile to resist deformation and enhance sound absorption and dissipation. The sound absorption coefficient was above 0.4 in the frequency band above 1.5kHz even under the hydrostatic pressure of 2MPa. The numerical simulation provides one methodological reference in analyzing the influences of the structural change and the operational conditions on the sound-absorbing coating.

Study of deformation structures maps in metals under tension

The paper considers the regularities of macroscopic inhomogeneity of plastic flow during uniaxial tension of flat samples of Fe-Cr-Ni 2 mm thick. Their tension axis was oriented along the rolling direction. The average grain size was 12.5 ± 3 mm. The plastic flow curves of the alloy had long stages of linear strain hardening over the entire test temperature range 180 K &lt; T &lt; 297 K. For the experimental study of plastic deformation, we used the method of accurately reconstructing the fields of displacement vectors and calculating the components of the plastic distortion tensor using speckle photography with increments of the total strain between exposures 0.001. The field of displacement vectors as a whole over the sample during loading is inhomogeneous both in the directions of the displacement vectors and in values; in some areas, the displacement vectors nonmonotonically change directions relative to the tension axis. It has been established that in the test temperature range 180 K &lt; T &lt; 297 K, plastic flow is localized at all stages of the process. The appearance of the a′-martensite phase during the deformation of the alloy under study leads to a change in the mechanical characteristics, the work hardening coefficient, and the deformation localization parameters. The maps of deformation structures are analyzed in the form of spatial distributions of the components of the plastic distortion tensor: local elongations, narrowings, shifts and rotations. The non-linear nature of the change in the coefficient of transverse deformation from the level of acting stresses is established. The general form and quantitative parameters of the evolution of the components of the plastic distortion tensor indicate the connection of this process with the self-organization of a defective subsystem in a deformable medium.

Metody obliczeń wytrzymałości zmęczeniowej części maszyn

Regardless of the operating conditions, a load acts on the parts of a machine in different directions. These loads in particular determine the required strength and resistance of parts and determine the study and selection of appropriate strength, resistance parameters for the parts. This can be determined by their impact on oilfield equipment and machine parts. Testing is done to determine the static flexibility, flow limit, tensile strength relative to flexibility, strength period limit, and plastic deformation coefficient. In some cases, when the limits of wear of machine parts are equal, elements with a larger coefficient of deformation are more convenient. These regularities should be used in those cases when it is possible to apply the methods of fracture mechanics or when there are direct experimental data on the development of fatigue cracks, which make it possible to carry out a probabilistic assessment of the durability of structural elements at the stage of crack growth and to substantiate the corresponding limitations on the service life of products. For the safety margins of machine parts, the starting points are as follows: longitudinal bending stress in the sleeve of a solid machine part made of a plastic material cannot damage the part. The length of the first crack can be taken to be equal to several millimetres, which is determined by the capabilities of the simplest means of observation, and by the fact that in some cases even a crack of such length can be critical from the point of view of a potential brittle fracture. In this regard, the fatigue resistance characteristics used in such a calculation should correspond to the point at which the first macroscopic crack appears.

Optimum boundaries for maximum load-carrying capacity in water-lubricated composite journal bearings incorporating turbulences and inertial effects based on elastohydrodynamic analysis

Abstract The application of polymer-based composite materials as bearing liner materials in eco-friendly water lubrication has received considerable attention owing to their superior tribological behaviors, corrosion resistance, and high damping characteristics, and their design flexibility can improve the bearing performances in response to the distribution of lubricant film pressure based on the regulation of elastic constants. However, the low viscosity and high density of water essentially cause thin-filmed lubrication accompanied by a low load-carrying capacity. Particularly, a high rotational speed enhancing the wedge effect induces turbulence and considerable inertial effect. Moreover, substantial elastic deformation of the composite bearing liners alters the formation of the lubricant film. In this study, we analyze a water-lubricated composite journal bearing system incorporating the turbulence, inertial effect, and elastic deformation of the bearing liner. Reynolds equation was modified considering the turbulence and inertial effect. The elastic deformation of the composite bearing liner was determined by solving the constitutive equation. The Reynolds equation and the constitutive equation were solved via the finite difference method and finite element method, respectively. In addition, the analytical relation for the elastic deformation was derived that suitably eliminated the requirement of solving the constitutive equation. With the introduction of the primary parameters, Sommerfeld number, Reynolds number, and deformation coefficient, the relation of the normalized minimum film thickness with respect to the parameters was modeled based on the Gaussian regression model. Accordingly, we proposed the new optimal maximum load-carrying capacity boundaries that narrowed down the operating region compared to conventional boundaries.

Study on the Model and Law for Radial Leakage of Drilling Fluid in Fractured Formations.

The economic loss caused by fracture leakage accounts for 90% of all leakage costs; thus, it is necessary to find the factors that affect the leakage and to study the leakage laws of fractured strata. The advantage of this article is that we introduced fracture index deformation and fracture tortuosity parameters to characterize fracture roughness and fracture characteristic parameters using the logging data analysis method. To explore the mechanism of leakage in essence, this paper, based on fluid mechanics, improves the radial leakage model by adopting the Herschel-Bulkey (H-B) flow type drilling fluid with high calculation accuracy and comprehensively considering the factors such as drilling fluid performance parameters, fracture roughness characteristic parameters, pressure difference between the wellbore and formation, and radial extension length of the drilling fluid. The advantage of the model is that it is solved in an absolutely stable backward Euler difference format. The numerical simulation is carried out by MATLAB. The simulation results revealed that the leakage rate increased as the fracture index deformation coefficient and the fracture opening increased. The leakage rate also increased as the fracture tortuosity parameters decreased and as the fracture smoothened. However, the leakage rate decreased as the drilling fluid consistency coefficient increased. Drilling fluid dynamic shear force had a minor effect on the leakage rate. The higher the pressure difference between the wellbore and the formation, the higher the leakage rate. As the drilling fluid intrusion depth increased, the leakage rate decreased until it reached 0. Two parameters were mainly controlled in order to control the degree of leakage: differential pressure and fracture static width, which has important guiding for adjusting the drilling fluid density and predicting leaks in the field. The solution method of the model in this paper has a certain reference value for the solution of other models in the future. The conclusion can provide reference for numerical simulation, laboratory test, and field application in the future.