Crack Tip Stress Field Research Articles

Effects of multiple reflected P waves on crack-tip stress and crack propagation in directional fracturing blasting

Directional fracturing blasting is effective for rock engineering, but it is inevitably disturbed by multiple reflected waves from different directions in natural rock mass due to discontinuous boundaries. Reflected waves affect both crack-tip stress and crack propagation, hence affect the results of directional fracturing blasting. In this paper, with the aid of high-speed photography, an optical caustics method is used to study effects of multiple reflected P waves on a directional blast-induced crack in a polymethyl methacrylate (PMMA) plate, specifically on crack path, crack fracturing mode, crack-tip stress and crack velocity. Crack-tip stress field is indicated by the shape of caustics pattern. Before the loading of reflected P waves, the mode I directional crack driven by blast-induced gases propagates in a straight path; crack-tip stress field is K-dominated, and crack-tip caustics pattern is consistent with classical caustics theory. On the contrary, under the loading of reflected P waves, the directional crack changes to be mixed-mode I + II and propagates in a curved path; Crack-tip stress field is non-K-dominated due to transient stress superposition of reflected P waves, and crack-tip caustics pattern is consistent with modified caustics theory. Transient stress superposition is not obvious for reflected P waves with a longer reflection distance. The tension loading of reflected P waves plays a more important role than the compression loading, which increases crack-tip stress intensity factors and crack velocity. This study provides a comprehensive understanding of effects of multiple reflected P waves from different directions on directional fracturing blasting.

Crack Growth Analytical Model Considering the Crack Growth Resistance Parameter Due to the Unloading Process

Crack growth analysis is essential for probabilistic damage tolerance assessment of aeroengine life-limited parts. Traditional crack growth models directly establish the stress ratio–crack growth rate or crack opening stress relationship and focus less on changes in the crack tip stress field and its influence, so the resolution and accuracy of maneuvering flight load spectral analysis are limited. To improve the accuracy and convenience of analysis, a parameter considering the effect of unloading amount on crack propagation resistance is proposed, and the corresponding analytical model is established. The corresponding process for acquiring the model parameters through the constant amplitude test data of a Ti-6AL-4V compact tension specimen is presented. Six kinds of flight load spectra with inserted load pairs with different stress ratios and repetition times are tested to verify the accuracy of the proposed model. All the deviations between the proposed model and test life results are less than 10%, which demonstrates the superiority of the proposed model over the crack closure and Walker-based models in addressing relevant loading spectra. The proposed analytical model provides new insights for the safety of aeroengine life-limited parts.

Mixed-mode crack-tip stress intensity factors measurements by caustics method: A comparison between low and high loading rate conditions

Mixed-mode crack-tip stress field is different in low and high loading rate conditions, resulting in different mixed-mode stress intensity factors (SIFs) measurements. How to correctly measure mixed-mode SIFs in different loading rate conditions is of critical importance. To this end, mixed-mode SIFs are measured and compared by optical caustics method with high-speed photography, specifically by the interpretation of crack-tip optical image, i.e., caustics pattern which reflects crack-tip stress field. Different mixed-mode caustics patterns in shape are observed in drop weight and blast loading conditions, indicating that corresponding crack-tip stress field and mixed-mode SIFs measurements are different. Under drop weight loading, mixed-mode caustics patterns are consistent with the classical caustics interpretation for SIFs measurements, while those under reflected P wave loading in blasts are not consistent. Therefore, a modified mixed-mode caustics interpretation is proposed and verified to be available for SIFs measurements in blast loading condition. Finally, underlying reasons for different mixed-mode SIFs measurements in low and high loading rate conditions are discussed, and it is concluded that in low loading rate condition, a longer loading time results in crack-tip K-dominated stress field which is suitable for the classical caustics interpretation, while in high loading rate condition, the loading time is too short to form K-dominated stress field in the crack tip, hence a modified caustics interpretation is necessary. This paper benefits correct applications of caustics method to mixed-mode SIFs measurements in different loading rate conditions.

Numerical Simulation and ANN Prediction of Crack Problems within Corrosion Defects.

Buried pipelines are widely used, so it is necessary to analyze and study their fracture characteristics. The locations of corrosion defects on the pipe are more susceptible to fracture under the influence of internal pressure generated during material transportation. In the open literature, a large number of studies have been conducted on the failure pressure or residual strength of corroded pipelines. On this basis, this study conducts a fracture analysis on buried pipelines with corrosion areas under seismic loads. The extended finite element method was used to model and analyze the buried pipeline under seismic load, and it was found that the stress value at the crack tip was maximum when the circumferential angle of the crack was near 5° in the corrosion area. The changes in the stress field at the crack tip in the corrosion zone of the pipeline under different loads were compared. Based on the BP algorithm, a neural network model that can predict the stress field at the pipe crack tip is established. The neural network is trained using numerical model data, and a prediction model with a prediction error of less than 10% is constructed. The crack tip characteristics were further studied using the BP neural network model, and it was determined that the tip stress fluctuation range is between 450 MPa and 500 MPa. The neural network model is optimized based on the GA algorithm, which solves the problem of convergence difficulties and improves the prediction accuracy. According to the prediction results, it is found that when the internal pressure increases, the corrosion depth will significantly affect the crack tip stress field. The maximum error of the optimized neural network is 5.32%. The calculation data of the optimized neural network model were compared with the calculation data of other models, and it was determined that GA-BPNN has better adaptability in this research problem.

Influence of Interaction between Microcracks and Macrocracks on Crack Propagation of Asphalt Concrete.

This paper aims to reveal the interaction relationship between microcracks and macrocracks and the influence of the interaction on the crack propagation behavior. A theoretical model of asphalt concrete was established for the interaction between microcracks with different crack densities and a macrocrack. And a meso-structure model of AC-13 dense-graded asphalt concrete was established by combining the Talyor medium method and the DEM (discrete element method). Macro and micro parameters, such as the stress-strain characteristics, crack evolution parameters, and crack tip stress field, were obtained through a semi-circular bend virtual test and used to study the characteristics of crack propagation under the interaction between microcracks and the macrocrack. The results indicate that the interaction has an effect throughout the process of asphalt concrete damage, and shows shielding and acceleration effects as the microcrack density changes. When the microcrack density is low (f3 ≤ 0.8), the crack propagation process, which is affected by the interaction effect, exhibits significant differences, and the interaction effect shows the shielding effect. When the microcrack density is high (f3 > 0.8), the fracture stage is mainly affected by the interaction effect, which shows the acceleration effect. The results provide a predictive theoretical and numerical model for low-temperature cracking of asphalt pavement, and theoretical support for the design, maintenance, and upkeep of long-life pavement.

Crack-tip plastic zone and initiation mechanism of rock based on Eshelby stress

The crack initiation and propagation mechanism of rock is significantly related to characteristics of the crack-tip plastic zone due to energy dissipation. In this paper, conservation integral and configurational stress/force is derived by the Noether’s method. The crack-tip configurational stress field is then deduced and analyzed. Additionally, the Drucker–Prager yield criterion of configurational stress is derived and it is used to predict the crack-tip plastic zone of rock. The fracture criteria of rock are also developed based on the critical area and minimum polar radius of the crack-tip plastic zone. Subsequently, the effects of bedding dip angles and porosity on rock mixed mode fracture are investigated, and the fracture resistance of rock is assessed using the resistivity and wave velocity. It is shown that the configurational force as the crack driving force is induced by the invariant transformation of an action integral with respect to translation of a defect. It is also found that the crack-tip plastic zone assessed by Drucker–Prager yield criterion of Cauchy stress is discontinuous at the crack surface while that predicted by yield criterion of configurational stress is continuous. The present fracture criteria take into account the internal friction angle, and the predicted initiation angles and fracture loads are in good agreement with those determined by the maximum tensile stress (MTS) fracture criterion and experiments. The fracture loading envelope decreases with the porosity, bedding dip angles and resistivities of rock, but increases with wave velocity.

Analysis of crack-tip stress field in unidirectional fiber-reinforced composites based on 3D micromechanical model

Accurately clarifying the influence of cracks on the mechanical behaviors of unidirectional fiber-reinforced composites (UD FRCs) is of great significance for the structural integrity evaluation of UD FRCs with defects. Although several experiments and numerical analyses have explored the impact of cracks on stress field, satisfactory quantitative characterizations of crack size, a/W and location, Δ, fiber content, Vf have not yet been obtained. In this paper, the accurate and detailed microscopic models containing crack were first established and thoroughly validated. Then, a parametric study was conducted using three-dimensional micromechanical analysis to investigate how the crack size and location, fiber content affect the von Mises, stress triaxiality, Lode angle and J-integral of UD FRCs. Results showed that homogeneous models, whether isotropic or anisotropic, cannot accurately describe the mechanical behavior of cracked UD FRCs. The von Mises stress and J-integral are greatly influenced by the crack and fiber content, while stress triaxiality and Lode angle are not sensitive to changes in these factors. Further, the von Mises and J-integral increase with the decrease of Vf and the increase of a/W, but show a more complex trend in the variation of Δ. These findings will help clarify the failure mechanism of cracked UD FRCs and can be used for reliability evaluation.

Unified theoretical solutions for describing the crack-tip stress fields of mode-II cracked specimens under the fully plastic condition

Potential novel singular solutions to the crack-tip stress fields beyond the asymptotic solution frame are discussed in this study. It is believed that one of them is not only suitable for the crack-tip stress fields of mode-I cracked specimens but also for those of mode-II cracked specimens. The crack-tip stress fields of mode-II cracked specimens are investigated based on the singular solution and the stress factor of mode-II cracked specimen derived from energy density equivalence principle. Further, special functions for describing the coefficients of normalized stress distributions of mode-II cracked specimens are proposed. The method to determine the parameters in the theoretical solutions are introduced. To give an example, one set of parameters for compact shear specimen under plane-strain conditions are determined by the finite element analysis of a few typical materials and geometries conditions. Finally, comparisons of radial and circumferential stress distributions and contour lines of equivalent stress are completed for the compact shear specimens and Arcan-shaped shear specimens of power-law plastic materials under plane-strain and plane-stress conditions. And the results show that the applicability and reliability of the proposed unified theoretical solutions are verified.

Diagnosis of Mechanoluminescent Crack Based on Double Deep Learning in Al 7075

The phenomenon of mechanoluminescence (ML) refers to the emission of light induced by mechanical stimulation applied to mechano-optical materials for example SrAl<sub>2</sub>O<sub>3</sub>:Eu,Dy (SAO). Numerous technologies on the basis of ML have been presented to visualize the stress or strain in various structures for the applications including structural health monitoring. As a result, extensive attention has been devoted to the design, synthesis, characteristics, optimizations, and applications of ML materials. However, challenges still remain in the standardization of ML measurement and evaluation, thereby commercially viable ML applications are currently unavailable. To overcome these difficulties, present study proposes ML measurement and evaluation techniques employing the ML fracture mechanics, finite element method, and dual deep learnings. For the effective normalization of visualized ML images under fixed initial ML intensity condition, continuous UV irradiation above the critical ML power density has been subjected to tensile and compact tension (CT) specimens. Therefore, Plastic Stress Intensity Factor (SIF) as well as crack tip stress field have been extracted successfully from normalized ML images based on ML fracture mechanics. To complement and verify the ML analysis, numerical FEM simulation and analytical ASTM calculation have been also provided. Finally, a double deep learning consists of Generative Adversarial Networks (GAN) and Convolutional Neural Networks (CNN) has been trained and tested for the standard evaluation of in-situ ML images.

Numerical Investigation of Thermoelastic Crack Interactions in Various Materials using a Novel Enrichment Approach

Crack interaction studies play a crucial role in understanding and predicting the fracture behaviour of various engineering components subjected to thermomechanical loads. The present work investigates the interaction effect of multiple cracks in different types of material subjected to thermoelastic loadings using Element free Galerkin method (EFGM). These materials include isotropic material, orthotropic material, functionally graded material, and layered material. These all materials are subjected to thermoelastic loads in presence of multiple cracks to investigate the effect of crack interactions. A novel modified Intrinsic enrichment has been proposed to precisely capture the interaction effect and stress fields in the presence of multiple cracks. The proposed algorithm has been tested for a benchmark problem and it produced better stress fields in comparison to the conventional EFGM procedure. Stress intensity factors corresponding to variations in crack parameters have been evaluated concerning with the primary crack. Results reveal that presence of multiple cracks alters the crack tip stress fields owing to the interaction effect i.e shielding or amplification. Additionally, parameters such as crack length, crack orientation, distance between cracks, and domain properties greatly influence the stress intensity factor of the primary crack. These parameters exhibit varying behaviour under distinct circumstances, and their effects have been thoroughly analysed. Current work provides valuable insights into the effects of crack interactions in different media under thermoelastic loadings, thereby ensuring the structural integrity and durability of these materials for practical applications.

Study on low temperature crack resistance of warm-mixed recycled SBS modified asphalt mixtures

In view of the cold winter in northern China and the large temperature difference between day and night, the asphalt pavement has been in low temperature service for a long time, in addition to experiencing the aging effect of water and salt erosion, jointly leading to a particularly serious pavement cracking phenomenon. Therefore, a quantity of Reclaimed Asphalt Pavement (RAP) is produced for the repair and renovation of old roads. Faced with the problems of inadequate reuse rate of RAP and high energy consumption of thermal regeneration, it is of great practical significance to explore the technology of warm mix regeneration. In order to study the adaptability of recycled SBS modified asphalt mixtures to low temperature after complex environmental erosion (long-term aging, water freeze-thaw cycle, and salt freeze-thaw cycle), two mixing methods, including hot mixing and warm mixing, were selected, and a Semi-Circular Bending Test was performed. SCB and Digital Image Correlation (DIC) techniques were used to evaluate the low temperature properties of recycled asphalt mixtures by fracture toughness, fracture energy and horizontal strain density damage. Combined with an Atomic Force Microscope (AFM) test, the microscopic analysis of recycled asphalt was carried out to verify the mechanism of low temperature cracking. The results showed that the low temperature cracking resistance of the reclaimed asphalt mixtures with warm mix was slightly worse than that with hot mix. The overall low temperature cracking resistance of the reclaimed SBS modified asphalt mixtures decreased with the increase in RAP content. The low temperature performance of the warm-mixed reclaimed asphalt mixtures deteriorated greatly when the RAP content was 80 %. The influencing factors of environmental conditions on the low temperature cracking resistance of the warm-mixed recycled SBS modified asphalt mixtures were listed as below: long-term aging > salt freeze-thaw cycle > water freeze-thaw cycle. The influence of salt on the stress field of crack tip and the microstructure of recycled asphalt after freeze-thaw was greater than that of water erosion. The changes of the microscopic adhesion were in good agreement with the macroscopic test results, which could be employed as the index evaluating the low temperature crack resistance of the warm-mixed SBS modified asphalt mixtures. The addition of warm mixing agent would play a positive role in the low temperature crack resistance of recycled asphalt mixtures with a RAP content of less than 60 % to a certain extent, so warm-mixed recycled asphalt mixtures were more suitable for the application in northern areas.

Constraint loss correction: Enhancing transferability of fracture toughness of Eurofer97 compact tension specimens between specimen sizes

This paper proposes and implements a constraint loss correction as a supplement to the ASTM correction factor for the master curve method (ASTM-E1921) for Eurofer97 reduced activation steel in order to enhance the transferability of results between compact tension (CT) specimen sizes. To facilitate the acquisition and scalability of reliable fracture toughness data from one specimen size to another and to apply the Master-Curve method with confidence when using small specimens, the difference in the structure of the crack tip stress field between large and small specimens was modeled. The stress intensity factors and critical volumes/stresses of two specimen sizes (1 T and 0.18 T) were calculated with 3D finite element simulations run over a large displacement range and at a temperature range of −120 to −80 °C and the results were compared with real data from a database of toughness tests of Eurofer97 steel. The K values from a miniaturized specimen without or with ASTM correction and with the proposed combined correction with constraint loss factor (which is variable over the entire loading range) were compared with simulated CT-1 T stress intensity values. It was found that this new correction factor was accurate up to a target toughness of 200 MPa.m1/2, which represents a major improvement on the current state of the art.

Numerical Investigation on Crack Propagation of Three-Dimensional Pipeline Under Seismic Wave Loading

Cracks in transport pipelines significantly impact their structural safety, making pipeline fracture damage a major concern. While experimental tests can study crack growth, their setup and costs are substantial. To address this, our work involves parametric analyses to investigate the effects of initial crack length, load types and sizes, and pipe wall thickness on the crack tip stress field. The finite element model is established according to the actual operation, and the crack defects of the pipe are established by the extended finite element method (XFEM). The crack tip variation is studied by extracting the von Mises stress and strain at the crack tip. When the crack propagates, the stress field at the crack tip will fluctuate in a certain range. The relationship between stress field fluctuation and crack propagation was studied by changing the XFEM crack growth for comparative analysis. Utilizing 429 numerical results obtained from a parametric numerical model implemented with Python and Abaqus, we establish a back propagation (BP) neural network prediction model to forecast the stress field at the crack tip. The relative errors between the numerical results and the predictions by our model remain below 5%. In conclusion, our proposed approach for analyzing pipeline fracture under multiple loads proves valuable for pipeline safety assessment, and it offers useful insights for evaluating the suitability of transportation pipelines.

An experimental analysis of crack terminating perpendicular to the bimaterial interface under varying mode mixities

SIFs for crack terminating perpendicular to the interface of a bimaterial subjected to varying mode mixities are evaluated with a novel bimaterial specimen using the experimental technique of photoelasticity. A simple form of multiparameter equation defining the stress field for the crack terminating at the interface at an arbitrary angle along with the details on interfacial SIF and combined SIF for a bimaterial problem are brought out. The stress field equation is incorporated in an in-house developed PSIF software as a separate problem module for the determination of crack tip stress field parameters using a non-linear least squares methodology. A compact bimaterial Brazilian disc specimen with crack in one of the material sides terminating perpendicular to the interface and at an arbitrary angle to the point of loading, is considered for the study. SIFs of two such specimens, a polymer–polymer pair, and a metal-polymer pair with two different bimaterial constants are determined. The normalized SIF values are evaluated as a function of crack orientation angles. The SIF values for the metal-polymer pair were found to be higher compared to the polymer–polymer interface. The peak values of SIFs are observed at a crack orientation angle of 30°. At orientation angles close to 0° and 90°, the SIF values were less pronounced.

Photoelastic analysis of crack terminating at an arbitrary angle to the bimaterial interface under four point bending

A bimaterial strip made of Aluminum-Epoxy pair with crack terminating at an arbitrary angle to the interface subjected to bending is studied using photoelasticity technique. When the crack terminates at an arbitrary angle to the interface, the stress singularity depends on the bimaterial elastic constants as well as the geometry of the crack. The shape of the photoelastic fringe patterns observed at the crack tip terminating at the interface varied based on the crack inclination angle. Complex crack tip stress field equation for crack terminating at an arbitrary angle to the interface along with an over deterministic non-linear least squares method incorporated in an in-house developed PSIF software is used for the evaluation of SIFs. The effect of the crack inclination angle on the SIF values is brought out. Mode-I and Mode-II SIFs, interfacial SIF, combined SIF, and phase angle are evaluated for the bimaterial pair considered. The corresponding normalized SIF values are calculated. It is observed that the SIF values increase with the crack inclination angle. Cracks at angles greater than 45° have significant SIF values, with highest SIF values occurring for 90° crack.

Criteria for determining the fatigue limit of Ni-based superalloy 718, considering the competition between opening- and shear-mode fatigue crack-growth

The mechanism that determines the fatigue limit associated with small-crack arrest in Ni-based superalloy 718 remains under debate. In order to comprehensively assess the alloy’s fatigue limit in relation to the growth threshold of a small fatigue crack, (i) a ΔKI-decreasing fatigue crack-growth test, (ii) torsional fatigue tests and (iii) tension-compression fatigue tests were conducted under fully-reversed loading conditions. In addition, elastic, crack-tip stress fields were analyzed for cracks under various loading conditions. Based on the results, a novel strategy for evaluating the alloy’s fatigue limit is proposed after consideration of two crack-arresting modes (i.e., opening and shear modes).

Theoretical solutions for 2D mode-I crack-tip stress fields in power-law plastic materials based on the stress factor derived from the developed median-energy–density equivalence method

This study presents the energy density equivalence equation, demonstrating that the strain energy density of an arbitrary representative volume element (RVE) under a complex stress state equals to that under a uniaxial stress state when volume change is neglected. Based on the developed median-energy–density equivalence method, the analytical solution for equivalent stress of the RVE at the energy density equivalence point in power-law plastic materials is derived in a new method and the concept of stress factor is proposed. Additionally, novel special functions are introduced to accurately describe the angular distributions of stresses in this study. By combining the stress factor, integral theoretical solutions for mode-I crack tip stress fields in power-law plastic materials under finite plane conditions are proposed. Finally, parameterized studies are conducted on bending and tension specimens under plane-strain and plane-stress conditions. The results of stress distributions and contour lines predicted by the integral theoretical solutions are compared with the finite element analysis and HRR solutions for five mode-I plane specimens, providing verification of the solutions’ applicability.

The coupling effects of strain gradient and damage on Mode I crack tip stress fields

The cleavage fracture of metallic materials is determined by the crack tip stress field depending on plastic strain gradient and microstructural damage. The synergistic effects of strain gradient and damage on the stress fields near a Mode I crack tip in metallic materials are investigated using a modified conventional theory of mechanism-based strain gradient plasticity (CMSG). Besides preserving the essence of classical CMSG, a stress-dependent damage variable is introduced to characterize the effect of microstructural damage on the material's intrinsic length, elastic modulus and plastic yielding criterion. Based on the present theoretical model, it is found that the strain gradient and microstructural damage effects both are prominent in a small region near the Mode I crack tip, at which the damage evolution is determined by the strain gradient. Although the crack tip stress field with strain gradient and damage effects is lower than the existing ones influenced only by strain gradient, it is still significantly higher compared with the yielding strength of the material so that the cleavage fracture at the crack tip can be well explained. The damage-induced stress level reduction indicates that the stress concentration at the crack tip can be alleviated to inhibit the crack propagation. As a result, when the damage effect is considered, not only a larger external load is required to induce crack propagation but also the plastic region in front of the crack tip is enlarged, consequently leading to increases of fracture strength and energy dissipation in the material. The present research provides a more precise prediction of the crack tip stress distribution in metallic materials, which is helpful for better understanding the microscopic mechanism of the cleavage fracture phenomenon.

An efficient meshfree framework for simulation of crack tip stress fields in two-dimensional graded media subjected to thermoelastic loads

In the present work a novel framework of algorithm has been proposed for enhancing the versatility of the element-free Galerkin method for modeling of fracture in graded media subjected to thermoelastic loadings. The proposed work restructures the conventional element free Galerkin method (EFGM) at multiple level through generic MATLAB algorithms thereby developing an efficient and robust method for simulating crack tip stress fields in graded material subjected to thermoelastic loads. The proposed algorithm utilizes varying nodal density criterion in conjunction with optimum Gaussian quadrature around these nodes for numerical integration of the governing equations. The proposed algorithm also incorporates blended approximation which is effective for simulating crack tip stress fields in both convex and non-convex problem domains. Nonequilibrium formulation has been selected for evaluating stress intensity factors (SIFs) for the fracture problems in graded media. A few problems of cracked domain subjected to thermoelastic loads have been modeled and simulated to illustrate the effectiveness of proposed framework of algorithms. Further, three component level problems having non-convex domains have also been discussed to establish the robustness and modeling capabilities of the proposed work. A good agreement between the simulated results and reference data demonstrates the algorithm’s competence and robustness for modeling thermoelastic fracture in graded materials. The proposed methodology improves the computational efficiency and flexibility of the element-free Galerkin method for modeling thermoelastic fracture in graded media. Moreover, enhancement of computing speed with the proposed methodology adds to its modeling potential.

Modified Model of Crack Tip Stress Field Considering Dislocation Slip Accumulation and Crack Tip Blunting

This study uses the digital image correlation technique to measure the crack tip displacement field at various crack lengths in U71MnG rail steel, and the interpolated continuous displacement field was obtained by fitting with a back propagation (BP) neural network. The slip and stacking of dislocations affect crack initiation and growth, leading to changes in the crack tip field and the fatigue characteristics of crack growth. The Christopher-James-Patterson (CJP) model describes the elastic stress field around a growing fatigue crack that experiences plasticity-induced shielding. In the present work, this model is modified by including the effect of the dislocation field on the plastic zone of the crack tip and hence on the elastic field by introducing a plastic flow factor ρ, which represents the amount of blunting of the crack tip. The Levenberg-Marquardt (L-M) nonlinear least squares method was used to solve for the stress intensity factors. To verify the accuracy of this modified CJP model, the theoretical and experimental plastic zone errors before and after modification were compared, and the variation trends of the stress intensity factors and the plastic flow factor ρ were analysed. The results show that the CJP model, with the introduction of ρ, exhibits a good blunting trend. In the low plasticity state, the modified model can accurately describe the experimental plastic zone, and the modified stress intensity factors are more accurate, which proves the effectiveness of dislocation correction. This plastic flow correction provides a more accurate crack tip field model and improves the CJP crack growth relationship.