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.

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.

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.

Influence of gas transport mechanisms on the productivity of multi-stage fractured horizontal wells in shale gas reservoirs

In order to investigate the influence on shale gas well productivity caused by gas transport in nanometer- size pores, a mathematical model of multi-stage fractured horizontal wells in shale gas reservoirs is built, which considers the influence of viscous flow, Knudsen diffusion, surface diffusion, and adsorption layer thickness. A dis- crete-fracture model is used to simplify the fracture mod- cling, and a finite element method is applied to solve the model. The numerical simulation results indicate that with a decrease in the intrinsic matrix permeability, Knudsen diffusion and surface diffusion contributions to production become large and cannot be ignored. The existence of an adsorption layer on the nanopore surfaces reduces the effective pore radius and the effective porosity, resulting in low production from fractured horizontal wells. With a decrease in the pore radius, considering the adsorption layer, the production reduction rate increases. When the pore radius is less than 10 nm, because of the combined impacts of Knudsen diffusion, surface diffusion, and adsorption layers, the production of multi-stage fractured horizontal wells increases with a decrease in the pore pressure. When the pore pressure is lower than 30 MPa, the rate of production increase becomes larger with a decrease in pore pressure.

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.

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.

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.

Bending properties and fracture mechanism of C/C composites with high density preform

C/C composites with banded structure pyrocarbon were fabricated by fast chemical vapor infiltration（CVI）,with C3H6 as carbon source,N2 as carrier gas,and three-dimensional（3D） 12K PAN-based carbon fabric with high density of 0.94 g/cm3 as preform.Experimental results indicated that the fracture characteristics of C/C composites were closely related to the frequency of high-temperature treatment（HTT） at the break of CVI process.According to the load？displacement curves,C/C composites showed a pseudoplastic fracture after twice of HTT.After three times of HTT,load？displacement curves tended to be stable with a decreasing bending strength at 177.5 MPa.Delamination failure and intrastratal fiber fracture were observed at the cross-section of C/C composites by scanning electronic microscope.Because the content of pyrocarbon and fibers has a different distribution in layers,the C/C composites show different fracture characteristics at various regions,which leads to good toughness and bending strength.

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.

General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics

Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is investigated systematically. The gov- erning equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the opera- tor method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form so- lutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.

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.

Fracture of two three-dimensional parallel internal cracks in brittle solid under ultrasonic fracturing

Similar to hydraulic fracturing(HF), the coalescence and fracture of cracks are induced within a rock under the action of an ultrasonic field, known as ultrasonic fracturing(UF). Investigating UF is important in both hard rock drilling and oil and gas recovery. A three-dimensional internal laser-engraved crack(3D-ILC) method was introduced to prefabricate two parallel internal cracks within the samples without any damage to the surface. The samples were subjected to UF. The mechanism of UF was elucidated by analyzing the characteristics of fracture surfaces. The crack propagation path under different ultrasonic parameters was obtained by numerical simulation based on the Paris fatigue model and compared to the experimental results of UF. The results show that the 3D-ILC method is a powerful tool for UF research.Under the action of an ultrasonic field, the fracture surface shows the characteristics of beach marks and contains powder locally, indicating that the UF mechanism includes high-cycle fatigue fracture, shear and friction, and temperature load. The two internal cracks become close under UF. The numerical result obtained by the Paris fatigue model also shows the attraction of the two cracks, consistent with the test results. The 3D-ILC method provides a new tool for the experimental study of UF. Compared to the conventional numerical methods based on the analysis of stress-strain and plastic zone, numerical simulation can be a good alternative method to obtain the crack path under UF.

Study on orientation fracture blasting with shaped charge in rock

On the basis of the theories of mechanics of explosive and rock fracture mechanics, the mechanism of crack initiation and its expansion of directional fracture controlled blasting with shaped charges in rock were studied, then the blasting parameters were designed and tested by a model test in laboratory and field experiment. The experimental and test results showed that the energy from blasting is directionally concentrated for the cumulative action. The directional expansion of cracks is satisfactory, the results of the model test and field test suggested that the orientation fracture blasting with shaped charge is a good means of excavating tunnels or cutting rock.

Research progress on permeability improvement mechanisms and technologies of coalbed deep-hole cumulative blasting

Coalbed gas extraction is an important means of exploiting and utilizing gas resources,as well as a means of preventing coal mine disasters.In view of the low gas extraction rate from coalbeds with high gas content and low permeability,a method of improving permeability through deep-hole cumulative blasting is applied to develop initial directional fractures using a jet flow.Under the action of the blasting stress wave and detonation gas wedge,the fractures extend over a large range within the coal,thereby improving coalbed permeability.This study focuses on the criteria of cumulative blasting-induced coalbed fracturing based on a literature review of the penetration effect of cumulative blasting.On this basis,we summarize the coal fracturing zone,crack extension process,and the key technologies of charging and hole sealing for cumulative blasting.In addition,the latest research progress in the optimization of field test drilling and blasting parameters for cumulative blasting is introduced.Research findings indicate that the permeability improvement mechanism of cumulative blasting could be further enhanced,and the technology and technical equipment are in urgent need of improvement.Finally,development trends in the cumulative blasting permeability improvement technique are identified.

Fracture mechanics model of fully mechanized top coal caving of shallow coal seams and its application

Based on break characteristics of roofs in fully mechanized top-coal mining of thick shallow coal seams, a fracture mechanics model was built, and the criterion of crack propagation in the main roof was derived using the fracture mechanics theory. The relationships between the fracture length of the roof and the working resistance of the supports were discovered, and the correlations between the load on the overlying strata and the ratio of the crack's length to the thickness of the roof were obtained. Using a working face of Jindi Coal Mine, Xing county Shanxi province as an example, the relationships between the fracture length of the roof and the working resistance of the supports were analysed in detail. The results give a design basis in hydraulic top coal caving supports, which could provide useful references in the practical application. On-site experiment proves that the periodic weighting step interval of the caving face is 15–16 m, which is basically consistent with the theoretical analysis results, and indicates that the mechanized caving hydraulic support is capable of meeting the support requirements in the mining of a super-thick but shallowly buried coal seam.

Peridynamic Modeling and Simulation of Fracture Process in Fiber-Reinforced Concrete

In this study,a peridynamic fiber-reinforced concrete model is developed based on the bond-based peridynamic model with rotation effect(BBPDR).The fibers are modelled by a semi-discrete method and distributed with random locations and angles in the concrete specimen,since the fiber content is low,and its scale is smaller than the concrete matrix.The interactions between fibers and concrete matrix are investigated by the improvement of the bond’s strength and stiffness.Also,the frictional effect between the fibers and the concrete matrix is considered,which is divided into static friction and slip friction.To validate the proposed model,several examples are simulated,including the tensile test and the three-point bending beam test.And the numerical results of the proposed model are compared with the experiments and other numerical models.The comparisons show that the proposed model is capable of simulating the fracture behavior of the fiber-reinforced concrete.After adding the fibers,the tensile strength,bending strength,and toughness of the fiber-reinforced concrete specimens are improved.Besides,the fibers distribution has an impact on the crack path,especially in the three-point bending beam test.

Numerical simulation on effect of heterogeneity on modeΙfracture characteristics of rock

Rock is more sensitive to tensile loading than compressive loading,since the tensile strength of rock is much lower than compressive strength.The fracture characteristics of rock in the tensile state are of great significance to the understanding of rock failure mechanisms.To this end,we have conducted numerical simulation researches on modeⅠcracking process of rock with varying homogeneity,using the Realistic Failure Process Analysis program.With the increase of homogeneity,cracks are concentrating to the ligament area with a decreasing number of crack bifurcations,and the main crack path is becoming smooth.Crack behaviors and mechanical properties are influenced significantly when the homogeneity index is in the range of 1.5 to 5.When the homogeneity index is greater than 30,they are not affected by rock homogeneity and the rock can be considered as essentially homogeneous.It is considered that the global and local strengths are affected by the distribution of rock mechanical properties at mesoscale,which influence the crack behaviors and mechanical characteristics.

Fracture mechanics analysis on Smart-Cut~ technology.Part 1:Effects of stiffening wafer and defect interaction

In the present paper, continuum fracture mechanics is used to analyze the Smart-Cut process, a recently established ion cut technology which enables highly efficient fabrication of various silicon-on-insulator （SOI） wafers of high uniformity in thickness. Using integral transform and Cauchy singular integral equation methods, the mode-I and mode-II stress intensity factors, energy release rate, and crack opening displacements are derived in order to examine several important fracture mechanisms involved in the Smart-Cut process. The effects of defect interaction and stiffening wafer on defect growth are investigated. The numerical results indi- cate that a stiffener/handle wafer can effectively prevent the donor wafer from blistering and exfoliation, but it slows down the defect growth by decreasing the magnitudes of SIF＇s. Defect interaction also plays an important role in the splitting process of SOI wafers, but its contribution depends strongly on the size, interval and internal pressure of defects. Finally, an analytical formula is derived to estimate the implantation dose required for splitting a SOI wafer.