Numerical methods for solving singular integral equations obtained by fracture mechanical analysis of cracked wedge

The numerical solutions to the singular integral equations obtained by the fracture mechanical analyses of a cracked wedge under three different conditions are considered. The three considered conditions are:(i) a radial crack on a wedge with a nonfinite radius under the traction-traction boundary condition,(ii) a radial crack on a wedge with a finite radius under the traction-traction boundary condition, and(iii) a radial crack on a finite radius wedge under the traction-displacement boundary condition. According to the boundary conditions, the extracted singular integral equations have different forms. Numerical methods are used to solve the obtained coupled singular integral equations, where the Gauss-Legendre and the Gauss-Chebyshev polynomials are used to approximate the responses of the singular integral equations. The results are presented in figures and compared with those obtained by the analytical response. The results show that the obtained Gauss-Chebyshev polynomial response is closer to the analytical response.

Effect of heat treatment on the microstructure,mechanical properties and fracture behaviors of ultra-high-strength SiC/Al-Zn-Mg-Cu composites

A high-zinc composite,12vol%SiC/Al-13.3 Zn-3.27 Mg-1.07Cu(wt%),with an ultra-high-strength of 781 MPa was success-fully fabricated through a powder metallurgy method,followed by an extrusion process.The effects of solid-solution and aging heat treat-ments on the microstructure and mechanical properties of the composite were extensively investigated.Compared with a single-stage sol-id-solution treatment,a two-stage solid-solution treatment(470℃/1 h+480℃/1 h)exhibited a more effective solid-solution strengthen-ing owing to the higher degree of solid-solution and a more uniform microstructure.According to the aging hardness curves of the com-posite,the optimized aging parameter(100℃/22 h)was determined.Reducing the aging temperature and time resulted in finer and more uniform nanoscale precipitates but only yielded a marginal increase in tensile strength.The fractography analysis revealed that intergranu-lar cracking and interface debonding were the main fracture mechanisms in the ultra-high-strength SiC/Al-Zn-Mg-Cu composites.Weak regions,such as the SiC/Al interface containing numerous compounds and the precipitate-free zones at the high-angle grain boundaries,were identified as significant factors limiting the strength enhancement of the composite.Interfacial compounds,including MgO,MgZn2,and Cu5Zn8,reduced the interfacial bonding strength,leading to interfacial debonding.

Microdynamic mechanical properties and fracture evolution mechanism of monzogabbro with a true triaxial multilevel disturbance method

The far-field microdynamic disturbance caused by the excavation of deep mineral resources and underground engineering can induce surrounding rock damage in high-stress conditions and even lead to disasters.However,the mechanical properties and damage/fracture evolution mechanisms of deep rock induced by microdynamic disturbance under three-dimensional stress states are unclear.Therefore,a true triaxial multilevel disturbance test method is proposed,which can completely simulate natural geostress,excavation stress redistribution(such as stress unloading,concentration and rotation),and subsequently the microdynamic disturbance triggering damaged rock failure.Based on a dynamic true triaxial test platform,true triaxial microdynamic disturbance tests under different frequency and amplitudes were carried out on monzogabbro.The results show that increasing amplitude or decreasing frequency diminishes the failure strength of monzogabbro.Deformation modulus gradually decreases during disturbance failure.As frequency and amplitude increase,the degradation rate of deformation modulus decreases slightly,disturbance dissipated energy increases significantly,and disturbance deformation anisotropy strengthens obviously.A damage model has been proposed to quantitatively characterize the disturbance-induced damage evolution at different frequency and amplitude under true triaxial stress.Before disturbance failure,the micro-tensile crack mechanism is dominant,and the micro-shear crack mechanism increases significantly at failure.With the increase of amplitude and frequency,the micro-shear crack mechanism increases.When approaching disturbance failure,the acoustic emission fractal dimension changes from a stable value to local large oscillation,and finally increases sharply to a high value at failure.Finally,the disturbance-induced failure mechanism of surrounding rock in deep engineering is clearly elucidated.

3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

Macro-meso fracture evolution mechanism of hollow cylindrical granite with different hole diameters under conventional triaxial compression

In order to study and analyze the stability of engineering rock mass under non-uniform triaxial stress and obtain the evolution mechanism of the whole process of fracture,a series of conventional triaxial compression tests and three-dimensional numerical simulation tests were carried out on hollow granite specimens with different diameters.The bearing capacity of hollow cylindrical specimen is analyzed based on elasticity.The results show that:1)Under low confining pressure,the tensile strain near the hole of the hollow cylindrical specimen is obvious,and the specimen deformation near the hole is significant.At the initial stage of loading,the compressive stress and compressive strain of the specimen are widely distributed.With the progress of loading,the number of microelements subjected to tensile strain gradually increases,and even spreads throughout the specimen;2)Under conventional triaxial compression,the cracking position of hollow cylinder specimens is concentrated in the upper and lower parts,and the final fracture mode is generally compressive shear failure.The final fracture mode of complete specimen is generally tensile fracture.Under high confining pressure,the tensile cracks of the sample are concentrated in the upper and lower parts and are not connected,while the cracks of the upper and lower parts of the intact sample will expand and connect to form a fracture surface;3)In addition,the tensile crack widths of intact and hollow cylindrical specimens under low confining pressure are larger than those under high confining pressure.

A modified 3D mean strain energy density criterion for predicting shale mixed-mode Ⅰ/Ⅲ fracture toughness

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a significant role in fracture mechanics and hydraulic fracturing.The edge-notched disk bending(ENDB)specimens are employed to measure the entire range of mixed-modeⅠ/Ⅲfracture toughness of Longmaxi shale.To theoretically interpret the fracture mechanisms,this research first introduces the detailed derivations of three established fracture criteria.By distinguishing the volumetric and distortional strain energy densities,an improved three-dimensional mean strain energy density(MSED)criterion is proposed.As the critical volumetric to distortional MSED ratio decreases,the transition from tensiondominated fracture to shear-dominated fracture is observed.Our results indicate that both peak load and applied energy increase significantly with the transition from pure mode I(i.e.,tension)to pure modeⅢ(i.e.,torsion or tearing)since mode-Ⅲcracking happens in a twisted manner and mode-Ⅰcracking occurs in a coplanar manner.The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing.The average ratio of pure mode-Ⅲfracture toughness to pure mode-Ⅰfracture toughness is 0.68,indicating that the obtained mode-Ⅲfracture resistance for a tensionbased loading system is apparent rather than true.Compared to the three mainstream fracture criteria,the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-modeⅠ/Ⅲfracture toughness of distinct materials and loading methods.

A multi-mechanism numerical simulation model for CO_(2)-EOR and storage in fractured shale oil reservoirs

Under the policy background and advocacy of carbon capture,utilization,and storage(CCUS),CO_(2)-EOR has become a promising direction in the shale oil reservoir industry.The multi-scale pore structure distribution and fracture structure lead to complex multiphase flow,comprehensively considering multiple mechanisms is crucial for development and CO_(2) storage in fractured shale reservoirs.In this paper,a multi-mechanism coupled model is developed by MATLAB.Compared to the traditional Eclipse300 and MATLAB Reservoir Simulation Toolbox(MRST),this model considers the impact of pore structure on fluid phase behavior by the modified Peng—Robinson equation of state(PR-EOS),and the effect simultaneously radiate to Maxwell—Stefan(M—S)diffusion,stress sensitivity,the nano-confinement(NC)effect.Moreover,a modified embedded discrete fracture model(EDFM)is used to model the complex fractures,which optimizes connection types and half-transmissibility calculation approaches between non-neighboring connections(NNCs).The full implicit equation adopts the finite volume method(FVM)and Newton—Raphson iteration for discretization and solution.The model verification with the Eclipse300 and MRST is satisfactory.The results show that the interaction between the mechanisms significantly affects the production performance and storage characteristics.The effect of molecular diffusion may be overestimated in oil-dominated(liquid-dominated)shale reservoirs.The well spacing and injection gas rate are the most crucial factors affecting the production by sensitivity analysis.Moreover,the potential gas invasion risk is mentioned.This model provides a reliable theoretical basis for CO_(2)-EOR and sequestration in shale oil reservoirs.

Mechanical properties and fracture mechanism of as-cast MnFeCoCuNix high-entropy alloys

MnFeCoCuNix high-entropy alloys(HEAs)with different Ni contents were fabricated by vacuum induction melting.XRD and SEM−EDS were used to analyze the phase constitution and structure,and the tensile properties of the samples were determined using a universal tensile tester.The results show that the HEAs consist of a dual-phase structure,in which FCC1 phase is rich in Fe and Co,while the FCC2 phase has high contents of Cu and Mn.As Ni content increases,the segregation of Cu decreases,accompanied by the decrease of FCC2 phase.Moreover,the tensile strength of the HEAs increases first and then decreases,and the elongation increases slightly.This is attributed to the combined effect of interface strengthening and solid solution strengthening.The in-situ stretched MnFeCoCuNi0.5 alloy shows obvious neck shrinkage during the tensile fracture process.In the initial deformation stage,the slip lines show different morphologies in the dual-phase structure.However,in the later stage,the surface slip lines become longer and denser due to the redistribution of atoms and the re-separation of the dissolved phase.

Hydro-mechanical interaction effects and channelling in threedimensional fracture networks undergoing growth and nucleation

The flow properties of geomechanically generated discrete fracture networks are examined in the context of channelling.Fracture networks are generated by growing fractures in tension,modelling the low permeability rock as a linear elastic material.Fractures are modelled as discrete surfaces which grow quasi-statically within a three-dimensional(3D)volume.Fractures may have their locations specified as a simulation input,or be generated as a function of damage,quantified using the local variation in equivalent strain.The properties of the grown networks are shown to be a product of in situ stress,relative orientation of initial flaws,and competitive process of fracture interaction and growth.Fractures grow preferentially in the direction perpendicular to the direction of maximum tension and may deviate from this path due to mechanical fracture interaction.Flow is significantly channelled through a subset of the fractures in the full domain,consistent with observations of other real and simulated fractures.As the fracture networks grow,small changes in the geometry of the fractures lead to large changes in the locations and scale of primary flow channels.The flow variability and formation of channels are examined for two growing networks,one with a fixed amount of fractures,and another with nucleating fractures.The interaction between fractures is shown to modify the local stress field,and in turn the aperture of the fractures.Pathways for single-phase flow are the results of hydro-mechanical effects in fracture networks during growth.These are the results of changes to the topology of the network as well as the result of mechanical self-organisation which occurs during interaction leading to growth and intersection.

Mechanical Properties and Fracture Mechanism of a Glass Fiber Reinforced Polypropylene Composites

To study the effect of some parameters, such as, length and fraction of glass fiber (GF), and the fraction of maleic anhydride grafted polypropylene (PP-g-MAH), on the mechanical properties of glass fiber reinforced polypropylene (GF/PP) composites, tensile tests, bending tests and impact tests were conducted. Scanning electron microscope (SEM) was used to characterize the fracture mechanisms of the composites. The results show that, compared with 3 mm GF, 9 mm GF can significantly improve the strength of the composite better. Addition of PP-g-MAH, a kind of grafting agent, into the PP-30% LGF composite can result in a better mechanical properties because of the strengthening of the bonding interface between the matrix and the fiber. When the mass fraction of GF is 30% and the PP-g-MAH fraction is 6%, the mechanical properties of the composite are the best.

Mechanical Properties and Fracture Mechanism of Boron Carbide-Lanthanum Boride Composite

The properties of boron carbide-lanthanum boride composite material prepared by hot pressed sintering method was tested, and lanthanum boride as a sintering aid for boron carbide was investigated. The result shows that the hardness of boron carbide-lanthanum boride increases with the increasing content of lanthanum boride. When the content of the lanthanum boride is 6%, the hardness reaches its supreme value of 31.83 GPa, and its hardness is improved nearly 20.52% compared to monolithic boron carbide. The content of the lanthanum boride does not greatly affect flexibility strength, however, it gives much effect on fracture toughness. The curve of fracture toughness likes the form of saw-toothed wave as the content of lanthanum boride increases in the test. When the content of the lanthanum boride is 6%, the fracture toughness reaches its supreme value of 5.14 MPa·m 1/2, which is improved nearly 39.67% compared with monolithic boron carbide materials. The fracture scanning electric microscope analysis of boron carbide-lanthanum boride composite material shows that, with the increase of the content of lanthanum boride, the interior station of monolithic boron carbide is changed. The crystallite arrangement is so compact that pores disappear gradually. The main fracture way of boron carbide-lanthanum boride composite material is intercrystalline rupture, while the transcrystalline rupture is minor, which is in accordance with fracture mechanism of ceramic material. It indicates that this change of fracture mode by the addition of lanthanum boride gives rise to the improvement of the fracture toughness.

COUPLED THERMAL/MECHANICAL ANALYSIS FOR THE FRACTURE OF FUNCTIONALLY GRADED MATERIALS UNDER TRANSIENT THERMAL LOADING

A comprehensive treatment of fracture of functionally gradedmaterials (FGMs) is provided. It is assumed that the materialproperties depend only on the coordinate perpendicular to the cracksurface And vary continuously along the crack faces. By using alaminated composite plate model to simulate the ma- Terialnon-homogeneity, an algorithm for solving the system based on Laplacetransform and Fourier transform Techniques is presented. Unlikeearlier studies that considered certain assumed propertydistributions and a Single crack problem, the current investigationstudies multiple crack problem in the FGMs with arbitrarily Varyingmaterial properties. Transient thermal stresses are presented.

Multirange Fractals in Materials: Applications to Fracture and Mechanical Alloying under Ball Milling

A new model of multirange fractals is proposed to explain the experimental results observed on the fractal dimensions of the fractured surfaces in materials. A new explanation to the Williford's multifractal curve on the relationship of fractal dimension with fracture properties in materials has been given. It shows the importance of fractorizing out the effect of fractal structure from other physical causes and separating the appropriate range of scale from multirange fractals. Mechanical alloying process under ball milling as a non-equilibrium dynamical system has been also analyzed.

Effects of the Solution Treatment on Microstructural Evolution, Mechanical Properties, and Fracture Mechanism of Nickel-Based GH4099 Superalloy

Grain growth, mechanical properties, and fracture mechanism of nickel-based GH4099 superalloy are investigated using heat treatments, tensile tests, optical microscopy (OM), and scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS). The OM observation shows that the matrix grains (γ-grains) undergo an apparent growth during the solution treatment. The grain size diameter increases from 100 to 174 μm when the solution temperature rises from 1100℃ to 1160℃ for 30 min. When the holding time increases from 15 to 60 min at 1140℃, the grain size diameter increases from 140 to 176 μm, indicating that the γ-grain growth is more sensitive to temperature than time. Standard deviation, Sv, and the grain size distribution are utilized to characterize the microstructural uniformity. To predict the grain size more accurately, we develop the grain growth kinetics and find that the growth index is close to 5. The yield strength (Rp0.2), tensile strength (Rm), and ductility (Af) are also measured. It is found that the effect decreases in the order cooling rate, solution temperature, time. Rp0.2 reduces by 47% with the increase in the cooling rate from 1℃ to 8000℃/min, while both strength and ductility exhibit little changes with time. The SEM results show that the fracture surfaces have typical mixed brittle and ductile characteristics when specimens are subjected to water quenching and air cooling. However, a complete brittle fracture occurs under furnace cooling conditions. The EDS analysis indicates that the brittle γ' (Ni3Ti) phase precipitates around the γ-grain boundary during the slow cooling process, which is the main factor yielding the complete brittle fracture. Finally, the optimal solution treatment scheme for the GH4099 superalloy is proposed—a temperature of 1140℃ for 30 min followed by air cooling.

Effect of reclaimed sand additions on mechanical properties and fracture behavior of furan no-bake resin sand

In this work, the effects of reclaimed sand additions on the microstructure characteristics, mechanical properties and fracture behavior of furan no-bake resin sand have been investigated systematically within the temperature range from 25 to 600 oC. The addition of 20%-100% reclaimed sand showed dramatic strength deterioration effect at the same temperature, which is associated with the formation of bonding bridges. Both the ultimate tensile strength(UTS) and compressive strength(CS) of the moulding sand initially increase with the increase of temperature, and then sharply decrease with the further increase of temperature, which is attributed to the thermal decomposition of furan resin. The addition amount of reclaimed sand has a remarkable effect on the room temperature fracture mode, i.e., with the addition of 0-20% reclaimed sand, the fracture mode was mainly cohesive fracture; the fracture mode converts to be mixture fracture mode as the addition of reclaimed sand increases to 35%-70%; further increasing the addition to 100% results in the fracture mode of typical adhesive fracture. The fracture surface of the bonding bridge changes from a semblance of cotton or holes to smooth with the increase of test temperature.

A generalized nonlinear three-dimensional failure criterion based on fracture mechanics

Based on fracture mechanics theory and wing crack model,a three-dimensional strength criterion for hard rock was developed in detail in this paper.Although the basic expression is derived from initiation and propagation of a single crack,it can be extended to microcrack cluster so as to reflect the macroscopic failure characteristic.Besides,it can be derived as HoekeBrown criterion when the intermediate principal stress σ_(2) is equal to the minimum principal stress σ_(3)(Zuo et al.,2015).In addition,the opening direction of the microcrack cluster decreases with the increase of the intermediate principal stress coefficient,which could be described by an empirical function and verified by 10 kinds of hard rocks.Rock strength is influenced by the coupled effect of stress level and the opening direction of the microcrack clusters related to the stress level.As the effects of these two factors on the strength are opposite,the intermediate principal stress effect is induced.

Size effects on the tensile strength and fracture toughness of granitic rock in different tests

This study investigates the tensile failure mechanisms in granitic rock samples at different scales by means of different types of tests.To do that,we have selected a granitic rock type and obtained samples of different sizes with the diameter ranging from 30 mm to 84 mm.The samples have been subjected to direct tensile strength(DTS)tests,indirect Brazilian tensile strength(BTS)tests and to two fracture toughness testing approaches.Whereas DTS and fracture toughness were found to consistently grow with sample size,this trend was not clearly identified for BTS,where after an initial grow,a plateau of results was observed.This is a rather complete database of tensile related properties of a single rock type.Even if similar databases are rare,the obtained trends are generally consistent with previous scatter and partial experimental programs.However,different observations apply to different types of rocks and experimental approaches.The differences in variability and mean values of the measured parameters at different scales are critically analysed based on the heterogeneity,granular structure and fracture mechanics approaches.Some potential relations between parameters are revised and an indication is given on potential sample sizes for obtaining reliable results.Extending this database with different types of rocks is thought to be convenient to advance towards a better understanding of the tensile strength of rock materials.

Relationship between fracture spacing and bed thickness in sedimentary rocks:Approach by means of Michaelis-Menten equation

Fractures occur in nearly all rocks at the Earth’s surface and exert essential control on the mechanical strengths of rock masses and permeability.The fractures strongly impact the stability of geological or man-made structures and flow of water and hydrocarbons,CO_(2) and storing waste.For this,the dependence of opening mode fracture spacing(s)on bed thickness(t)in sedimentary basins(reservoirs)is studied in this context.This paper shows that the MichaeliseMenten equation can provide an algebraic expression for the nonlinear s-t relationship.The two parameters have clear geological meanings:a is the maximum fracture spacing which can no longer increase with increasing t,and b is the characteristic bed thickness when s=0.5a.The tensile fracture strength(C)of the brittle beds during the formation of tensile fractures can be estimated from the two parameters.For sandstones of 16 areas reported in the literature,C ranges from 2.7 MPa to 15.7 MPa with a mean value of 8 MPa,which lies reasonably within the range of tensile strengths determined experimentally.This field-based approach by means of MichaeliseMenten equation provides a new method for estimating the tensile fracture strength of rock layers under natural conditions.

Fracture Mechanics and Its Application in the Fatigue Behavior of Reinforced Welded Hand-Holes in Aluminum Light Poles

Predicting fatigue life of a given specimen using analytical methods can sometimes be challenging. An approach worth considering for this prediction involves employing fracture mechanics. Fracture mechanics can complement both laboratory experiments and finite element analysis (FEA) in estimating fatigue life of a given specimen, if relevant. In the case of aluminum light poles containing a welded hand-hole, the fatigue life has not yet been thoroughly predicted. The University of Akron has conducted a comprehensive fatigue study on aluminum light poles through various means, albeit without of predicting of said fatigue life of the specimens. AFGROW (Air Force Growth) can be used as a fracture mechanics software to predict fatigue life. ABAQUS was used (for FEA) in conjunction with the AFGROW analysis. The purpose of this study was to ultimately predict the life of the specimens tested in the lab and was achieved with various models including hollow tube and plate models. The plate model process was ultimately found to be the best method for this prediction, yielding results that mimicked the data from the laboratory. Further application for this form of fracture mechanics analysis is still yet to be determined, but for the sake of aluminum light poles, it is possible to predict the fatigue life and utilize said prediction in the field.