Influence of surface layer slurry temperature on surface cracks and holes of ZTC4 titanium alloy by investment casting

In this work,the influences of surface layer slurry at different temperatures(10℃,14℃,18℃,22℃)on wax patterns deformation,shrinkage,slurry coating characteristics,and the surface quality of the casting were investigated by using a single factor variable method.The surface morphologies of the shell molds produced by different temperatures of the surface(first)layer slurries were observed via electron microscopy.Furthermore,the microscopic composition of these shell molds was obtained by EDS,and the osmotic effect of the slurry on the wax patterns at different temperatures was also assessed by the PZ-200 Contact Angle detector.The forming reasons for the surface cracks and holes of thick and large ZTC4 titanium alloy by investment casting were analyzed.The experimental results show that the surface of the shell molds prepared by the surface layer slurry with a low temperature exhibits noticeable damage,which is mainly due to the poor coating performance and the serious expansion and contraction of wax pattern at low temperatures.The second layer shell material(SiO_(2),Al_(2)O_(3))immerses into the crack area of the surface layer,contacts and reacts with the molten titanium to form surface cracks and holes in the castings.With the increase of the temperature of surface layer slurry,the damage to the shell surface tends to weaken,and the composition of the shell molds'surface becomes more uniform with less impurities.The results show that the surface layer slurry at 22℃is evenly coated on the surface of the wax patterns with appropriate thickness,and there is no surface shell mold rupture caused by sliding slurry after sand leaching.The surface layer slurry temperature is consistent with the wax pattern temperature and the workshop temperature,so there is no damage of the surface layer shell caused by expansion and contraction.Therefore,the shell mold prepared by the surface layer slurry at this temperature has good integrity,isolating the contact between the low inert shell material and the titanium liquid effectively,and the ZTC4 titanium alloy cylinder casting prepared by this shell mold is smooth,without cracks and holes.

Experimental study of the damage characteristics of rocks containing non-penetrating cracks under cyclic loading

The damage evolution process of non-penetrating cracks often causes some unexpected engineering disasters.Gypsum specimens containing non-penetrating crack(s)are used to study the damage evolution and characteristics under cyclic loading.The results show that under cyclic loading,the relationship between the number of non-penetrating crack(s)and the characteristic parameters(cyclic number,peak stress,peak strain,failure stress,and failure strain)of the pre-cracked specimens can be represented by a decreasing linear function.The damage evolution equation is fitted by calibrating the accumulative plastic strain for each cycle,and the damage constitutive equation is proposed by the concept of effective stress.Additionally,non-penetrating cracks are more likely to cause uneven stress distribution,damage accumulation,and local failure of specimen.The local failure can change the stress distribution and relieve the inhibition of non-penetrating crack extension and eventually cause a dramatic destruction of the specimen.Therefore,the evolution process caused by non-penetrating cracks can be regarded as one of the important reasons for inducing rockburst.These results are expected to improve the understanding of the process of spalling formation and rockburst and can be used to analyze the stability of rocks or rock structures.

Intelligent extraction of road cracks based on vehicle laser point cloud and panoramic sequence images

In light of the limited efficacy of conventional methods for identifying pavement cracks and the absence of comprehensive depth and location data in two-dimensional photographs,this study presents an intelligent strategy for extracting road cracks.This methodology involves the integration of laser point cloud data obtained from a vehicle-mounted system and a panoramic sequence of images.The study employs a vehicle-mounted LiDAR measurement system to acquire laser point cloud and panoramic sequence image data simultaneously.A convolutional neural network is utilized to extract cracks from the panoramic sequence image.The extracted sequence image is then aligned with the laser point cloud,enabling the assignment of RGB information to the vehicle-mounted three dimensional(3D)point cloud and location information to the two dimensional(2D)panoramic image.Additionally,a threshold value is set based on the crack elevation change to extract the aligned roadway point cloud.The three-dimensional data pertaining to the cracks can be acquired.The experimental findings demonstrate that the use of convolutional neural networks has yielded noteworthy outcomes in the extraction of road cracks.The utilization of point cloud and image alignment techniques enables the extraction of precise location data pertaining to road cracks.This approach exhibits superior accuracy when compared to conventional methods.Moreover,it facilitates rapid and accurate identification and localization of road cracks,thereby playing a crucial role in ensuring road maintenance and traffic safety.Consequently,this technique finds extensive application in the domains of intelligent transportation and urbanization development.The technology exhibits significant promise for use in the domains of intelligent transportation and city development.

Effect of carbon material and surfactant on ink property and resulting surface cracks of fuel-cell microporous layers

Ensuring the consistency of electrode structure in proton-exchange-membrane fuel cells is highly desired yet challenging because of wide-existing and unguided cracks in the microporous layer(MPL). The first thing is to evaluate the homogeneity of MPL with cracks quantitatively. This paper proposes the homogeneity index of a full-scale MPL with an area of 50 cm~2, which is yet to be reported in the literature to our knowledge. Besides, the effects of the carbon material and surfactant on the ink and resulting MPL structure have been studied. The ink with a high network development degree produces an MPL with low crack density, but the ink with high PDI produces an MPL with low crack homogeneity. The polarity of the surfactant and the non-polarity of polytetrafluoroethylene(PTFE) are not mutually soluble,resulting in the heterogeneous PTFE distribution. The findings of this study provide guidelines for MPL fabrication.

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.

Evaluation of the injection and plugging ability of a novel epoxy resin in cement cracks

Sustained casing pressure(SCP)is a crucial issue in the oil and gas production lifecycle.Epoxy resins,exhibiting exceptional compressive strength,ductility,and shear bonding strength,have the potential to form reliable barriers.The injectivity and sealing capacity of the epoxy resin is crucial parameters for the success of shallow remediation operations.This study aimed to develop and assess a novel solid-free resin sealant as an alternative to Portland cement for mitigating fluid leakage.The investigation evaluated the viscosity,compressive strength,and brittleness index of the epoxy resin sealant,as well as its tangential and normal shear strengths in conjunction with casing steel.The flow characteristics and sealing abilities of conventional cement and epoxy resin were comparatively analyzed in cracks.The results showed that the application of a viscosity reducer facilitated control over the curing time of the epoxy resin,ranging from 1.5 to 6 h,and reduced the initial viscosity from 865.53 to 118.71 m Pa,s.The mechanical properties of the epoxy resin initially increased with a rise in curing agent content before experiencing a minor decrease.The epoxy resin containing 30%curing agent exhibited optimal mechanical properties.After a 14-day curing period,the epoxy resin's compressive strength reached81.37 MPa,2.12 times higher than that of cement,whereas the elastic modulus of cement was 2.99 times greater than that of the epoxy resin.The brittleness index of epoxy resin is only 3.42,demonstrating high flexibility and toughness.The tangential and normal shear strengths of the epoxy resin exceeded those of cement by 3.17 and 2.82 times,respectively.In a 0.5 mm-wide crack,the injection pressure of the epoxy resin remained below 0.075 MPa,indicating superior injection and flow capabilities.Conversely,the injection pressure of cement surged dramatically to 2.61 MPa within 5 min.The breakthrough pressure of0.5 PV epoxy resin reached 7.53 MPa,decreasing the crack's permeability to 0.02 D,a mere 9.49%of the permeability observed following cement plugging.Upon sealing a 2 mm-wide crack using epoxy resin,the maximum breakthrough pressure attained 5.47 MPa,3.48 times of cement.These results suggest that epoxy resin sealant can be employed safely and effectively to seal cracks in the cement.

Effect of drying cracks on swelling and self-healing of bentonite-sand blocks used as engineered barriers for radioactive waste disposal

Experiments were conducted to evaluate the healing of drying cracks in air-dried bentonite-sand blocks after hydration and swelling in groundwater,providing justifications to simplify the protection of blocks prior to installation in a high-level radioactive waste repository.Synthetic groundwater was prepared to represent the geochemistry of Beishan groundwater,and was used to hydrate the blocks during the swelling pressure and swelling strain measurements,as Beishan is the most promising site for China's repository.Healing of the surface cracks was recorded by photography,and healing of the internal cracks was visualized by CT images and hydraulic conductivity of air-dried blocks.The results indicate that the maximum swelling pressure and swelling strain are primarily affected by the geochemistry of Beishan groundwater,but not affected by the drying cracks.The maximum swelling pressure and swelling strain of air-dried blocks are comparable to or even higher than the pressure and strain of fresh blocks.The maximum swelling pressure measured in strong(i.e.high ion strength)Beishan groundwater was 44%of the pressure measured in deionized(DI)water,and the maximum swelling strain was reduced to 23%of the strain measured in DI water.Nevertheless,the remained swelling of the blocks hydrated in strong Beishan groundwater was sufficient to heal the surface and internal drying cracks,as demonstrated by the pictures of surface cracks and CT images.The hydraulic conductivity of the air-dried block permeated with strong groundwater was comparable(3.7×higher)to the hydraulic conductivity of the fresh block,indicating the self-healing of drying cracks after hydration and swelling in groundwater.A simplified method of protecting the block with plastic wraps before installation is recommended,since the remained swelling of the block hydrated in Beishan groundwater is sufficient to heal the drying cracks.

Elimination of cracks in stainless steel casings via 3D printed sand molds with an internal topology structure

The important supporting component in a gas turbine is the casing,which has the characteristics of large size,complex structure,and thin wall.In the context of existing 3DP sand casting processes,casting crack defects are prone to occur.This leads to an increase in the scrap rate of casings,causing significant resource wastage.Additionally,the presence of cracks poses a significant safety hazard after the casings are put into service.The generation of different types of crack defects in stainless steel casings is closely related to casting stress and the high-temperature concession of the sand mold.Therefore,the types and causes of cracks in stainless steel casing products,based on their structural characteristics,were systematically analyzed.Various sand molds with different internal topology designs were printed using the 3DP technology to investigate the impact of sand mold structures on high-temperature concession.The optimal sand mold structure was used to cast casings,and the crack suppression effect was verified by analyzing its eddy current testing results.The experimental results indicate that the skeleton structure has an excellent effect on suppressing cracks in the casing.This research holds important theoretical and engineering significance in improving the quality of casing castings and reducing production costs.

Assessing the range of blasting-induced cracks in the surrounding rock of deeply buried tunnels based on the unified strength theory

Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-induced cracks often ignore the impact of the in-situ stress,especially that of the intermediate principal stress.The particle displacement−crack radius relationship was established in this paper by utilizing the blasthole cavity expansion equation,and theoretical analytical formulas of the stress−displacement relationship and the crack radius were derived with unified strength theory to accurately assess the range of cracks in deep surrounding rock under a blasting load.Parameter analysis showed that the crushing zone size was positively correlated with in-situ stress,intermediate principal stress,and detonation pressure,whereas negatively correlated with Poisson ratio and decoupling coefficient.The dilatancy angle-crushing zone size relationship exhibited nonmonotonic behavior.The relationships in the crushing zone and the fracture zone exhibited opposite trends under the influence of only in-situ stress or intermediate principal stress.As the in-situ stress increased from 0 to 70 MPa,the rate of change in the crack range and the attenuation rate of the peak vibration velocity gradually slowed.

Eddy current quantitative evaluation of high-speed railway contact wire cracks based on neural network

Purpose–The purpose of this study is to study the quantitative evaluation method of contact wire cracks by analyzing the changing law of eddy current signal characteristics under different cracks of contact wire of high-speed railway so as to provide a new way of thinking and method for the detection of contact wire injuries of high-speed railway.Design/methodology/approach–Based on the principle of eddy current detection and the specification parameters of high-speed railway contact wires in China,a finite element model for eddy current testing of contact wires was established to explore the variation patterns of crack signal characteristics in numerical simulation.A crack detection system based on eddy current detection was built,and eddy current detection voltage data was obtained for cracks of different depths and widths.By analyzing the variation law of eddy current signals,characteristic parameters were obtained and a quantitative evaluation model for crack width and depth was established based on the back propagation(BP)neural network.Findings–Numerical simulation and experimental detection of eddy current signal change rule is basically consistent,based on the law of the selected characteristics of the parameters in the BP neural network crack quantitative evaluation model also has a certain degree of effectiveness and reliability.BP neural network training results show that the classification accuracy for different widths and depths of the classification is 100 and 85.71%,respectively,and can be effectively realized on the high-speed railway contact line cracks of the quantitative evaluation classification.Originality/value–This study establishes a new type of high-speed railway contact wire crack detection and identification method,which provides a new technical means for high-speed railway contact wire injury detection.The study of eddy current characteristic law and quantitative evaluation model for different cracks in contact line has important academic value and practical significance,and it has certain guiding significance for the detection technology of contact line in high-speed railway.

Detection and Genesis Analysis of Cracks in Prestressed Box Girder of a Certain Project

This paper introduces a crack detection example of the prestressed box girder in a certain project. The morphology of the box girder cracks was surveyed and mapped. The length, width, and depth of the cracks were inspected, and the strength and reinforcement configuration of the components were tested. The test results indicate that the strength and reinforcement configuration of the inspected components meet the design requirements. The crack at the end of the top plate of the box girder is a local compressive crack at the anchorage end. The width and length of the crack on the bottom surface of the top plate are not significant, and the depth is relatively shallow. Judging from the crack morphology, this crack is identified as a temperature crack. Additionally, based on the treatment measures for cracks of different widths, the treatment measures for the cracks of the components in this project are derived, providing a reference basis for similar projects in the future.

Flexible Strain Sensors with Ultra‑High Sensitivity and Wide Range Enabled by Crack‑Modulated Electrical Pathways

This study presents a breakthrough in flexible strain sensor technology with the development of an ultrahigh sensitivity and wide-range sensor,addressing the critical challenge of reconciling sensitivity with measurement range.Inspired by the structure of bamboo slips,we introduce a novel approach that utilises liquid metal to modulate the electrical pathways within a cracked platinum fabric electrode.The resulting sensor demonstrates a gauge factor greater than 108 and a strain measurement capability exceeding 100%.The integration of patterned liquid metal enables customisable tuning of the sensor’s response,while the porous fabric structure ensures superior comfort and air permeability for the wearer.Our design not only optimises the sensor’s performance but also enhances the electrical stability that is essential for practical applications.Through systematic investigation,we reveal the intrinsic mechanisms governing the sensor’s response,offering valuable insights for the design of wearable strain sensors.The sensor’s exceptional performance across a spectrum of applications,from micro-strain to large-strain detection,highlights its potential for a wide range of real-world uses,demonstrating a significant advancement in the field of flexible electronics.

Novel Methodologies for Preventing Crack Propagation in Steel Gas Pipelines Considering the Temperature Effect

Using the software ANSYS-19.2/Explicit Dynamics,this study performedfinite-element modeling of the large-diameter steel pipeline cross-section for the Beineu-Bozoy-Shymkent gas pipeline with a non-through straight crack,strengthened by steel wire wrapping.The effects of the thread tensile force of the steel winding in the form of single rings at the crack edges and the wires with different winding diameters and pitches were also studied.The results showed that the strengthening was preferably executed at a minimum value of the thread tensile force,which was 6.4%more effective than that at its maximum value.The analysis of the influence of the winding dia-meters showed that the equivalent stresses increased by 32%from the beginning of the crack growth until the wire broke.The increment in winding diameter decelerated the disclosure of the edge crack and reduced its length by 8.2%.The analysis of the influence of the winding pitch showed that decreasing the distance between the winding turns also led to a 33.6%reduction in the length of the straight crack and a 7.9%reduction in the maximum stres-ses on the strengthened pipeline cross-section.The analysis of the temperature effect on the pipeline material,within a range from-40℃ to+50℃,resulted in a crack length change of up to 5.8%.As the temperature dropped,the crack length decreased.Within such a temperature range,the maximum stresses were observed along the cen-tral area of the crack,which were equal to 413 MPa at+50℃ and 440 MPa at-40℃.The results also showed that the presence of the steel winding in the pipeline significantly reduced the length of crack propagation up to 8.4 times,depending on the temperature effect and design parameters of prestressing.This work integrated the existing methods for crack localization along steel gas pipelines.

A 3D discrete model for soil desiccation cracking in consideration of moisture diffusion

Soil desiccation cracking is a common phenomenon on the earth surface.Numerical modeling is an effective approach to study the desiccation cracking mechanism of soil.This work develops a novel 3D moisture diffusion discrete model that is capable of dynamically assessing the effect of cracking on moisture diffusion and allowing moisture to be discontinuous on both sides of the cracks.Then,the parametric analysis of the moisture exchange coefficient in the 3D moisture diffusion discrete model is carried out for moisture diffusion in continuous media,and the selection criterion of the moisture exchange coefficient for the unbroken cohesive element is given.Subsequently,an example of moisture migration in a medium with one crack is provided to illustrate the crack hindering effect on moisture migration.Finally,combining the 3D moisture diffusion discrete model with the finite-discrete element method(FDEM),the moisture diffusion-fracture coupling model is built to study the desiccation cracking in a strip soil and the crack pattern of a rectangular soil.The evolution of crack area and volume with moisture content is quantitatively analyzed.The modeling number and average width of cracks in the strip soil show a good consistency with the experimental results,and the crack pattern of the rectangular soil matches well with the existing numerical results,validating the coupled moisture diffusion-fracture model.Additionally,the parametric study of soil desiccation cracking is performed.The developed model offers a powerful tool for exploring soil desiccation cracking.

Effect of surface crack on the bearing capacity of strip footing placed on rock mass

In hilly regions,the existence of surface cracks in rock mass induces a potential threat to structural stability.Thus,the present research aims to explore the impact of surface cracks on the loadbearing capacity of strip footing placed on the rock mass.By taking into account the various boundary constraints across the surface of crack edges,the study investigates the presence of two categories of surface cracks,namely(1)separated crack,and(2)fine crack.The lower bound limit analysis is employed in conjunction with the finite element method(LBFELA)to conduct the numerical analysis.In order to evaluate rock mass yielding,the power conic programming(PCP)method is utilized to implement the generalized Hoek-Brown(GHB)failure criterion.The stability of the strip footing is analyzed by determining the bearing capacity factor(Nσγ),which is presented in the form of design charts by varying the strength parameters of rock,including the Geological Strength Index(GSI),Hoek-Brown material parameter(mi),Disturbance factor(D),and Normalised Uniaxial Compressive Strength(σci/γB),whereγis the unit weight of rock mass,and B is the width of strip footing.The study also investigates the impact of cracks on strip footings,considering different positions of the crack(LC)and depths of the crack(DC).The results demonstrate that the influence of the fine crack is only noticeable until the LC/B ratio reaches 6.However,for the separated crack,its impact remains significant even when the LC/B ratio exceeds 16.The appearance of fine crack at the edge of the footing results in a decrease in the magnitude Nσγof up to 45%,indicating a substantial reduction in the stability of the footing.The failure patterns are presented and discussed in detail for various cases in this study to examine the effect of surface cracks on the strip footing and to address the extent of the plastic collapse.

Microstructure effect of mechanical and cracking behaviors on brittle rocks using image-based fast Fourier transform method

The internal microstructures of rock materials, including mineral heterogeneity and intrinsic microdefects, exert a significant influence on their nonlinear mechanical and cracking behaviors. It is of great significance to accurately characterize the actual microstructures and their influence on stress and damage evolution inside the rocks. In this study, an image-based fast Fourier transform (FFT) method is developed for reconstructing the actual rock microstructures by combining it with the digital image processing (DIP) technique. A series of experimental investigations were conducted to acquire information regarding the actual microstructure and the mechanical properties. Based on these experimental evidences, the processed microstructure information, in conjunction with the proposed micromechanical model, is incorporated into the numerical calculation. The proposed image-based FFT method was firstly validated through uniaxial compression tests. Subsequently, it was employed to predict and analyze the influence of microstructure on macroscopic mechanical behaviors, local stress distribution and the internal crack evolution process in brittle rocks. The distribution of feldspar is considerably more heterogeneous and scattered than that of quartz, which results in a greater propensity for the formation of cracks in feldspar. It is observed that initial cracks and new cracks, including intragranular and boundary ones, ultimately coalesce and connect as the primary through cracks, which are predominantly distributed along the boundary of the feldspar. This phenomenon is also predicted by the proposed numerical method. The results indicate that the proposed numerical method provides an effective approach for analyzing, understanding and predicting the nonlinear mechanical and cracking behaviors of brittle rocks by taking into account the actual microstructure characteristics.

Thermal Stresses and Cracks During the Growth of Large-sized Sapphire with SAPMAC Method

The finite-element method has been used to study the thermal stress distribution in large-sized sapphire crystals grown with the sapphire growth technique with micro-pulling and shoulder-expanding at cooled center （SAPMAC） method. A critical defect model has been established to explain the growth and propagation of cracks during the sapphire growing process. It is demonstrated that the stress field depends on the growth rate, the ambient temperature and the crystallizing direction. High stresses always exist near the growth interfaces, at the shoulder-expanding locations, the tailing locations and the sites where the diameters undergo sharp changes. The maximum stresses always occur at the interface of seeds and crystals. Cracks often form in the critical defect region and spread in the m-planes and a-planes under applied tensile stresses during crystal growth. The experimental results have verified that with the improved system of crystal growth and well-controlled techniques, the large-sized sapphire crystals of high quality can be grown due to absence of cracks.

Causes and control of welding cracks in electron-beam-welded superalloy GH4169 joints

Welding joint of GH4169 alloy with a good formation was obtained. No macroscopic defects occurred in the joint. The weld had mainly a dendritic structure; the base metal was a solid solution of Ni, Cr, and Fe, and the strengthening-phase particles such as Ni3Nb were dispersively distributed along the grain boundary. The average tensile strength of the joint reached 743.7 MPa, and the Vickers hardness of the weld exceeded HV 300. Because of the segregation of the low-melting compound Ni3Nb at the grain boundary of the fusion zone, liquid cracks tended to occur as a result of welding stress. The formation of liquid cracks was inhibited by adding an alloying element, Mn, to the welding bath, because Mn diffused to the fusion zone and the high-melting phase Mn2Nb formed, and thus the overall properties of the joint were improved.

New Formulation for Arbitrary Cracks Problem and Its Stress Intensity Factor of Plane Elasticity

Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.