Coplanar Cracks Research Articles

Research on the propagation characteristics of multiple cracks in steel bridge joints

This study explores the morphological changes and interaction mechanisms of multiple crack propagations in steel bridge joints. Fatigue testing was conducted to determine the locations at which multiple cracks initiated and to obtain fatigue fracture surfaces with easily discernible crack propagation traces. Based on the theory of fracture mechanics, the propagation behavior of coplanar and out-of-plane cracks in joints was simulated using ABAQUS and FRANC3D joint simulation technology. The characteristics of the morphological changes were analyzed, and the interaction mechanism between different crack spacings was investigated to quantitatively characterize the relative positions at which cracks were enhanced or suppressed. The results showed that coplanar cracks exhibited different morphological trends and propagation rates in different stages of propagation. The shape of the crack front continuously changed, and the merging point that appeared during fusion rapidly expanded and evolved into a semi-elliptical crack. The fatigue life was more sensitive to the relative position of multiple cracks. In particular, the fusion of coplanar cracks significantly reduced the fatigue life, and the mutual suppression effect between heterogeneous cracks increased the fatigue life. When the ratio of coplanar crack spacing to crack length (s/2c) was less than 0.2, the crack fusion process significantly accelerated. In addition, when the a2/a1 ratio of the crack propagation depth dropped below 0.5, the suppression effect was significant. Finally, by determining the spacing between multiple cracks, the method established this study can provide a reference for the design of fatigue resistance and joint optimization.

Mastering the art: Proficient finite element implementation and robust evaluation of a strain-hardening porous ductile material crack growth prediction model at finite strain

Accurate prediction of crack extension is crucial for ensuring the structural integrity of metal components exposed to diverse loads. While the Gurson model and its extensions are widely accepted for delineating ductile fracture stages, especially in porous materials with a rigid-perfectly plastic matrix, their efficacy diminishes in the presence of strain-hardening matrices. To address this limitation, our study introduces a robust numerical implementation and assessment of Perrin's model. In contrast to Gurson's approach, Perrin's model incorporates two distinct strain-hardening parameters derived from an intricate analysis of a strain-hardening hollow sphere subjected to axisymmetric loading.Moving beyond theoretical discussions, this paper actively engages in the rigorous evaluation of Perrin's model under various scenarios, encompassing isotropic, kinematic, and mixed isotropic-kinematic hardening conditions. The model's effectiveness is convincingly demonstrated through meticulous comparisons between numerical simulations and real-world experimental observations conducted on pre-cracked specimens.Facing challenges related to achieving global elastic-plastic convergence in large-scale simulations, our research introduces a sophisticated approach. Leveraging stiffness tangent moduli ensure the maintenance of quadratic convergence in global Newton method iterations. This not only enhances the reliability of our simulations but also underscores the practical applicability of our findings.The study also focuses on the necking and crack propagation of a cylindrical specimen through meticulous computational modeling. Our mesh captures intricate details and addresses stress gradients, revealing coplanar crack propagation contrary to prior beliefs. The confirmation of the cup-cone fracture effect challenges previous interpretations, emphasizing the critical role of void nucleation. This reinforces the credibility and applicability of our approach in advancing the understanding of material fracture behavior.In summary, this study significantly contributes to existing knowledge in fracture prediction models, offering a robust framework for predicting ductile fracture under substantial deformations. The presented findings pave the way for advancements in structural engineering, providing invaluable insights for optimizing the performance and resilience of metal structures in real-world applications.

Three-dimensional numerical simulation of dynamic strength and failure mode of a rock mass with cross joints

To study the dynamic mechanical properties and failure characteristics of intersecting jointed rock masses with different joint distributions under confining pressure, considering the cross angle α and joint persistence ratio η, a numerical model of the biaxial Hopkinson bar test system was established using the finite element method–discrete-element model coupling method. The validity of the model was verified by comparing and analyzing it in conjunction with laboratory test results. Dynamics-static combined impact tests were conducted on specimens under various conditions to investigate the strength characteristics and patterns of crack initiation and expansion. The study revealed the predominant factors influencing intersecting joints with different angles and penetrations under impact loading. The results show that the peak stress of the specimens decreases first and then increases with the increase of the cross angle. When α < 60°, regardless of the value of η, the dynamic stress of the specimens is controlled by the main joint. When α ≥ 60°, the peak stress borne by the specimens decreases with increasing η. When α < 60°, the initiation and propagation of cracks in the cross-jointed specimens are mainly controlled by the main joint, and the final failure surface of the specimens is composed of the main joint and wing cracks. When α ≥ 60° or η ≥ 0.67, the secondary joint guides the expansion of the wing cracks, and multiple failure surfaces composed of main and secondary joints, wing cracks, and co-planar cracks are formed. Increasing lateral confinement significantly increases the dynamic peak stress able to be borne by the specimens. Under triaxial conditions, the degree of failure of the intersecting jointed specimens is much lower than that under uniaxial and biaxial conditions.

Experimental Study on Mechanical Characteristics of Prefabricated Fractured Sandstone Samples under Uniaxial Cyclic Compression

The loading-unloading physical and mechanical characteristics of fractured coal-bearing strata are greatly affected by fracture occurrence. In order to study the physical and mechanical response characteristics of fractured rock under cyclic compression, this paper takes prefabricated fractured sandstone samples with different dip angles as the object, and uses uniaxial cyclic loading and unloading test to study the influence of crack dip angle on sample strength, failure mode and crack propagation law. The results show that with the increase of crack inclination angle, the cyclic loading and unloading peak strength and elastic modulus of the sample increase significantly, and the peak strain decreases first and then increases. During the cyclic loading process, the area of the hysteresis loop gradually decreases, the slope gradually increases, the energy con-sumed by the hysteresis loop gradually decreases, the cumulative plastic deformation increases, and the curve shape presents a “concave” type; when it is 15 ° and 30 °, the cracks at the crack tip are wing cracks. When it is 45 °, the cracks at the crack tip are secondary inclined cracks and wing cracks. When it is 60 °, 75 ° and 90 °, the cracks at the crack tip are secondary coplanar cracks and wing cracks. With the increase of fracture dip angle, the number of cycles and peak strength at failure are increasing.

Size effects in the toughening of brittle materials by heterogeneities: A non-linear analysis of front deformations

Traditional computational approaches in simulating crack propagation in perfectly brittle materials rely on the estimate of stress intensity factors along the rupture front. This proves highly challenging in 3D when the crack geometry departs from very specific cases for which analytical solutions are available, like e.g. the penny-shaped crack geometry. Here, we extend the first-order theory of Gao and Rice (1987b), and predict the distribution of the mode I stress intensity factor KI along the front of a tensile coplanar crack that is slightly perturbed from a reference penny-shaped configuration, up to second order in the perturbation amplitude. Our theory is validated against analytical solutions available for embedded elliptical cracks, and its range of validity is further assessed using numerical simulations performed on cosine front perturbations of varying mode and amplitude. It is then used to develop a homogenization framework for the toughness of weakly disordered media. The effective toughness and its fluctuations are bridged quantitatively to the intensity of the toughness fluctuations and their spatial structure. Our theoretical predictions are compared to the results of ∼1 million simulations of crack propagation building on our second-order theory and Fast Fourier Transforms. We show that the impact of toughness heterogeneities is size-dependent, as they generally weaken the material when the crack size is lower or comparable to the typical heterogeneity size, but reinforces it otherwise. It results in an apparent R-curve behavior of the brittle composite at the macroscale.

Dynamic properties and failure mechanism of granite with non-persistent joints subjected to impact load

A Split-Hopkinson pressure bar was used to carry out a series of impact tests on prefabricated granite specimens containing joints with different inclination angles and at different joint persistency values. The results were used to determine the degradation effect of the non-persistent joints on the specimens and investigate the failure mechanism of the granite subjected to impact load. The effect of varying the length and inclination angle of the joint on the dynamic characteristics of the granite was systematically analyzed based on a consideration of the specimens’ dynamic mechanical properties. A continuum-discrete coupled model was subsequently established based on the results of the laboratory tests and used to investigate the failure mechanism and crack propagation behavior occurring on a microscopic scale. The results show that the geometric parameters of the joints and the loading rate have a significant effect on the dynamic response of the granite. Moreover, there is a good power function relationship between the dynamic increase factor and loading rate of the prefabricated jointed rock specimen when the loading rate is low to medium. As the inclination angle of the joint increases, the failure mode of the specimen transitions from tensile splitting failure → mixed tensile–shear failure → main shear failure → micro-damage failure. As the penetration of the joint increases, the failure mode of the specimen evolves from micro-damage failure → tensile splitting failure → mixed tensile–shear failure. When subjected to uniaxial impact loading, the main cracks in the jointed rock specimen are usually wing cracks and coplanar cracks. Anti-wing cracks are not generated by themselves but appear alongside other cracks as a supplementary means of achieving stress release. The present results offer a sound basis for evaluating the stability of jointed rock mass under the dynamical loading.

Coalescence of Two Coplanar Internal Penny-Shaped Cracks in Brittle Solid under Uniaxial Tension Based on 3D-ILC

Crack coalescence is an important topic in the research of brittle fracture mechanics. Most of the previous studies have focused on surface or penetrating cracks, while few experimental studies have been performed on internal cracks coalescence. This study fills in the missing data. First, the 3D internal laser-engraved crack (3D-ILC) method was introduced to make internal cracks in glass without causing any damage to the surfaces of the glass. Next, uniaxial tensile tests were performed on the samples with two coplanar internal penny-shaped cracks. A new grid reconstruction algorithm is also proposed to simulate the coalescence and the growth path of two coplanar internal cracks. The crack coalescence process and fracture characteristics were analyzed in detail. The results indicate that the fracture in the test is static fracture, while the fracture is Mode I, based on the characteristics of the fracture morphology. In addition, the Wallner lines were observed after the coalescence of cracks, which were overall elliptical in shape. Before coalescence, the stress intensity factor I (KI) at the center was higher than that at the outside, indicating the attraction of the twin cracks. Then, after coalescence, the KI increased significantly at that coalescence site, which indicated that the new crack had rapidly become “elliptical” in shape following the coalescence. The normalized KII/|KImax| and KIII/|KImax| of the coplanar cracks were approximately equal to 0 in the simulation, and it was confirmed that the fracture in the test was Mode I.

An extended Bueckner–Rice theory for arbitrary geometric perturbations of cracks

The aim of this paper is to define a new, simple and efficient method of solution of elasticity problems for 3D bodies containing cracks slightly perturbed out of their original plane or surface. This method extends that proposed by Rice (1985, 1989), from a re-formulation of Bueckner (1987)’s 3D weight function theory, for the treatment of coplanar crack perturbations. First, a general formula is derived for the variation of total energy of a cracked elastic body, resulting from some small but otherwise arbitrary geometric perturbation of the embedded crack(s). This formula, which involves integrals over both the front and the surface of the crack, is derived from an expression of deLorenzi (1982) and Destuynder et al. (1983) in the form of a volumic integral, originally limited to purely tangential crack perturbations but duly extended here to arbitrary perturbations having both tangential and normal components. It is then used to derive a general expression of the variation of displacement arising from a general perturbation of the crack(s), anywhere in the cracked body. The reasoning here basically follows the same lines as in the works of Rice (1985, 1989), but for the presence of an additional normal component of the crack perturbation. The possible use of the formalism developed to treat problems of out-of-plane, or out-of-surface perturbations of cracks is finally briefly evoked; the straightforwardness of the new method proposed is hoped to permit future applications to non-coplanar crack problems too complex to be accessible by more conventional methods.

Influence of the Preexisting Fracture Network on the Mechanical Properties of Rock Mass and the Secondary Crack Propagation

Preexisting fracture network (PFN) is ubiquitous in natural rock mass and is one of the key factors affecting the mechanical properties of rock mass. This research employed a combined approach of theoretical analysis and finite element numerical simulation to investigate the mechanical behavior of PFN-containing rock mass. Based on the sliding crack model and fracture mechanics theory, the initiation mechanism of closed and open cracks driven by compressive and shear stress was theoretically analyzed. Rock mass models with different inclination angles (β) of PFN were built in Fast Lagrangian Analysis of Continua in 3 Dimensions. The complete stress–strain curves of rock mass and the secondary crack propagation were obtained. Results indicated that the increase of β reduced the strength and elastic modulus of rock mass. When β is less than 45°, this influence is more prominent. Based on the load-bearing capacity of PFN-containing rock mass, the stress–strain curves can be classified into two types: type I curve has multipeak and is strain-softening in the postpeak stage when β is 15°, 30°, 45°, 60°, and 90°; type II curve is unimodal and with brittle failure when β is 60° and 75°. Secondary crack propagation can be classified into four main types: type I is the coplanar crack, type II is the wing crack around PFN, type III is the near-field wing crack, and type IV is the macroscopic shear crack.

Quasi-static crack front deformations in cohesive materials

When a crack interacts with material heterogeneities, its front distorts and adopts complex tortuous configurations that are reminiscent of the energy barriers encountered during crack propagation. As such, the study of crack front deformations is key to rationalize the effective failure properties of micro-structured solids and interfaces. Yet, the impact of a localized dissipation in a finite region behind the crack front, called the process zone, has often been overlooked. In this work, we derive the equation ruling 3D coplanar crack propagation in heterogeneous cohesive materials where the opening of the crack is resisted by some traction in its wake. We show that the presence of a process zone results in two competing effects on the deformation of crack fronts: (i) it makes the front more compliant to small-wavelength perturbations, and (ii) it smooths out local fluctuations of strength and process zone size, from which emerge heterogeneities of fracture energy. Their respective influence on front deformations is shown to strongly impact the stability of perturbed crack fronts, as well as their stationary shapes when interacting with arrays of tough obstacles. Overall, our theory provides a unified framework to predict the variety of front profiles observed in experiments, even when the small-scale yielding hypothesis of linear elastic fracture mechanics breaks down.

Stress–strain and acoustic emission characteristics of cement-based materials used to simulate soft rock with fractures

Instability failure in rock mass engineering is closely related to expansion of joint fissures. In this study, uniaxial compression tests and acoustic emission (AE) measurements were carried out simultaneously on specimens of soft rock-like material with different fracture angles and connectivity values to better understand their influence on the deformation and failure of the material. The stress–strain curve and AE signal of fractured soft rock-like material are similar to those of intact soft rock-like; specifically, they exhibit a compaction, elastic deformation, stable fracture development, and unstable fracture development. The main differences between fractured and intact material occur during post-peak failure stage. Under the combined influence of fracture angle and connectivity, the uniaxial compressive strength of fractured soft rock-like material (f_{cu}^{^{prime}}) is lower than that of the intact soft rock-like material (fcu), and can be described by the relationship f_{cu}^{^{prime}} = f_{cu} cdot alpha, where alpha is the strength reduction coefficient, fitted as alpha = 0.8228 + 0.00411x - 0.00789y. In this equation, x is the fracture angle (^circ) and y is the fracture connectivity (%). Under uniaxial compression, the main types of secondary cracks were wing cracks and secondary coplanar cracks. The specimen with a fracture angle of 30° mainly underwent tensile failure under loading, whereas those with fracture angles of 45° and 60°mainly experienced shear failure under high-connectivity conditions (45%).

Elastic surface crack interaction and its engineering critical assessment within the framework of fitness-for-service standards

In real industrial conditions, it’s common to witness the interaction of multiple cracks such that their stress fields and crack driving forces are disturbed. For coplanar cracks, a greater hazard is expected because of the amplification phenomenon. FFS standards deal with this by proposing interaction rules and idealizing a single bonding flaw for the FAD methodology to be used. The goal of this paper is to analyze the effectiveness of this standards methodology considering twin surface semielliptical cracks on a plate under mode I loading on the interaction range using FE analyses. Results confirm that the amplification phenomena due to the interaction are higher on the interacting crack tip and progressively higher as the coplanar horizontal distance decreases. The loss of constraint was observed to decrease as the coplanar horizontal distance decreased, but little change was observed regarding its parametric angular position. A higher amplification was found at the coplanar horizontal distance on which crack interaction is to be considered meaningful, which indicates inconsistency regarding the interaction criteria used on FFS standards. To conclude, the engineering critical assessment of the bonding flaw proved to be over-conservative as the remaining operational life was observed on the assessment of the interacting flaws.

RESEARCH OF ACOUSTIC EMISSIONS FROM THE SYSTEM OF COMPLANARY CRACKS

The dynamic problem of the displacement field in an elastic half-space caused by the time-steady displacement of the surfaces of the system of disc-shaped coplanar cracks is solved. The solutions are obtained by the method of boundary integral equations. The dependences of elastic displacements on the surface of the half-space on the wave number, the number of defects and the depths of their occurrence are constructed.

Numerical Simulation of Cracks in Automotive Coatings Under Mechanical and Thermal Loading Using Element Free Galerkin Method

ABSTRACT The work presented in this paper aims to delve into the applications of Element Free Galerkin Method (EFGM) which is a type of Meshless Method (MM) to the area of Automobile Engineering. EFGM is implemented to detect a change in the material property at the interface of the coating along with the identification of crack. Simulation of centre crack in coatings has been reported for the first time using EFGM. Simulations with change in crack inclination angle, change in crack length are reported. Multiple cracks are reported in the form of collinear cracks, coplanar cracks and the effect of their presence on primary crack has been discussed. This work involves the study which leads to understanding the effect of temperature on the stress fields of the cracks present in coatings. Variations of the temperature field parallel to crack and perpendicular crack shows enticing results. The effect of variation in materials properties of coating and substrate is discussed. The work reveals the nature of crack severity in automobile coatings. Various conditions depicted in this work enhance the understanding of researches in comprehending the effect of thermal load in coated materials.

Dispersion of Longitudinal Waves by Four Coplanar Mode-I Cracks in an Infinite Elastic Medium

Dispersion of Longitudinal Waves by Four Coplanar Mode-I Cracks in an Infinite Elastic Medium

Investigation on the Fracturing Permeability Characteristics of Cracked Specimens and the Formation Mechanism of Inrush Channel from Floor

To study the fracture characteristics and the permeability change law of the cracked specimens during the complete stress-strain process, a mechanical model was constructed, from which different types of crack initiation angles were obtained. The crack inclination angles under uniaxial compression, confining compression, and confining tension, and the influence of confining pressure and pore water pressure on the crack propagation and permeability of rock mass were investigated and simulated with RFPA-Flow software using prefabricated crack models with crack initiation angles of 30°, 45°, and 60°. Furthermore, the formation mechanism of inrush channel from floor was qualitatively analyzed. The results indicated that the theoretical initiation angles of wing cracks, secondary coplanar cracks, and secondary inclined antiwing cracks were found to be 70.53°, 0°, and 123.8°, which were consistent with the simulation results. The crack propagation was mainly concentrated at the postpeak stage of the complete stress-strain curve, causing the peak of seepage velocity to lag behind the stress peak. For the case with a constant confining pressure, the rate of crack initiation and propagation to final failure was positively correlated with the internal pore pressure. For the case with a constant water pressure, the speed of crack initiation and propagation to final failure decreased first and then increased as the confining pressure increased. In addition, the longitudinal propagation of wing cracks and the increase in permeability were prone to occur in the low confining pressure zone, which induced the formation of water inrush channels. The research result provides an improved understanding for predicting and preventing water inrush disasters.

Attenuation and dispersion of P-waves in fluid-saturated porous rocks with a distribution of coplanar cracks — Scattering approach

Wave-induced fluid flow (WIFF) between cracks and micropores is one of the major mechanisms causing attenuation and dispersion within seismic frequency ranges. Previous non-interaction-approximation (NIA) models often assume that the distribution of cracks is dilute, neglecting the influences of interacting cracks on dispersion and attenuation. To overcome this restriction, we have investigated the interaction between coplanar cracks and their influences on seismic dispersion and attenuation. First, a scattering problem for a longitudinal (P) wave normally impinging on a plane with equally distributed coplanar cracks in a porous medium is solved using an integral transform approach. Then, based on the solution, an effective wavenumber is derived for P-wave propagation in a porous material with coplanar cracks. It is found that the magnitude of dispersion and attenuation can significantly increase when the spacing between adjacent cracks decreases even if the crack density is unchanged. Moreover, frequency-dependent asymptotic behavior of inverse quality factor is also different from that of the NIA models at frequencies lower than the WIFF relaxation frequency. Specifically, the inverse quality factor scales with the square root of the frequency at low frequencies. When the spacing between adjacent cracks is large, an additional frequency-dependent scale occurs at relatively higher frequencies (but still lower than the WIFF relaxation frequency) with inverse quality factor scales with the first power of frequency. When the spacing becomes much larger so that the interaction between the adjacent cracks is negligible, the present model exactly reduces to an NIA model for the distribution of aligned slit cracks and the first power scale can maintain attenuation within low frequencies.

Constraint-based failure assessment for pipelines with coplanar circumferential cracks under biaxial loading

The presence of coplanar or multiple cracks emerges as a common problem in many engineering structures, e.g., at the toe of circumferential welds of pipelines subjected to cyclic actions and in other piping systems for the nuclear power plants. The failure assessment diagram provides a convenient means to examine the competing failure between the fracture failure and plastic collapse failure, often for structural components with a single crack. The existing failure assessment diagram relies on the leading term characterizing the near-tip stress solutions, and ignores the geometry or plasticity-induced constraint variations. This paper aims to integrate the crack interaction effect between two coplanar cracks, measured by a constraint-based crack interaction factor, into the option 3 failure assessment curve in the engineering standard. This study examines three types of circumferential coplanar cracks in a pipe: two coplanar embedded cracks; two coplanar surface cracks; and a surface crack interacting with an embedded crack. Using a modified J solution based on a proposed crack interaction factor, this investigation quantifies the plasticity-driven increase in the near-tip opening stress for coplanar cracks. The stress field estimated based on this modified J solution agrees closely with the numerically computed stress field near the coplanar crack tips at large deformation levels. This work subsequently integrates the modified J solution into the failure assessment diagram. The failure assessment diagram based on the equivalent crack size recommended in BS7910 appears to be un-conservative for a number of coplanar cracks considered in this study.

Hydrogen assisted fatigue life of Cr–Mo steel pressure vessel with coplanar cracks based on fatigue crack growth analysis

Fatigue life of 4130X steel hydrogen storage vessel with coplanar cracks for hydrogen refueling station was analyzed in this paper. Subcritical cracking threshold (KIH) in 45 MPa hydrogen and fracture toughness (KIC) of 4130X were measured by sampling on a manufactured vessel. Based on the test results, fatigue growth behavior of coplanar cracks was analyzed using the numerical simulation method, and the fatigue lives of the vessel with coplanar cracks were calculated. Furthermore, the re-characterisation methods which were used to simplify the coplanar cracks in different standards were compared. Results indicate that the fracture toughness of 4130X can be reduced by 73.7% in 45 MPa hydrogen compared with that in air. Because of the deterioration of material mechanical properties, the fatigue life of the vessel with coplanar cracks under hydrogen pressure cyclic loading can be reduced by more than 90% compared with that under hydraulic pressure cyclic loading, which is similar to the case of one single crack. The smaller the critical distance of the coalescence criterion, the greater the fatigue life determined by the re-characterisation methods. The fatigue life calculated according to the coalescence criterion in BS 7910 or ASME BPVC. XI is closer to that determined by the numerical simulation method.

Experimental observation and numerical investigation on propagation and coalescence process of multiple flaws in rock-like materials subjected to hydraulic pressure and far-field stress

In this paper, a newly developed rock-like material (cement mortar) was proposed. Multiple flaws (including horizontal and inclined flaws) were prefabricated in the testing specimens, and a number of specimens subjected to hydraulic pressure and far-field stress were performed to study the crack propagation and coalescence process. Experimental results show as following. (1) Under uniaxial compressive condition, the propagation path and direction of preexisting flaws change obviously after the inclined flaws meet the horizontal flaws during the propagation process, and the phenomenon of ‘displacement jumping’ appears. (2) Under biaxial compressive condition, the increase of lateral pressure suppresses the initiation of cracks and secondary cracks at the ends of the inclined flaws. Under the condition of high lateral pressure, these inclined flaws would not propagate through the horizontal flaws and the failure mode changes from splitting to shear failure. The shielding effect of horizontal flaws on stress transfer is gradually increased. (3) Under the combined action of internal water pressure and far-field stress, with the increase of internal water pressure, the maximum principal stress distribution at the tip of wing crack in uniaxial compression gradually decreases, and the initiation stress, initiation angle and peak strength are also gradually reduced. The crack propagation and coalescence laws obtained by numerical simulation based on Continuum-based Discrete Element Method (CDEM) are basically in good agreement with the experimental results. The numerical analysis of the inclined flaws with different internal water pressures penetrating through the horizontal flaws without water pressure is also carried out. With the increase of internal water pressure, the inclined flaws firstly initiates the coplanar crack and then generates the wing crack. When the wing crack propagates though the horizontal flaw, the propagation path also changes. Under the combined action of internal water pressure and far-field stress, the lateral pressure also suppresses the initiation of the wing crack. The increase of internal water pressure weakens the restraint effect of lateral pressure on wing cracks.