Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough ...Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.展开更多
Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilt...Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.展开更多
The quantitative determination and evaluation of rock brittleness are crucial for the estimation of excavation efficiency and the improvement of hydraulic fracturing efficiency.Therefore,a“three-stage”triaxial loadi...The quantitative determination and evaluation of rock brittleness are crucial for the estimation of excavation efficiency and the improvement of hydraulic fracturing efficiency.Therefore,a“three-stage”triaxial loading and unloading stress path is designed and proposed.Subsequently,six brittleness indices are selected.In addition,the evolution characteristics of the six brittleness indices selected are characterized based on the bedding effect and the effect of confining pressure.Then,the entropy weight method(EWM)is introduced to assign weight to the six brittleness indices,and the comprehensive brittleness index Bcis defined and evaluated.Next,the new brittleness classification standard is determined,and the brittleness differences between the two stress paths are quantified.Finally,compared with the previous evaluation methods,the rationality of the proposed comprehensive brittleness index Bcis also verified.These results indicate that the proposed brittleness index Bccan reflect the brittle characteristics of deep bedded sandstone from the perspective of the whole life-cycle evolution process.Accordingly,the method proposed seems to offer reliable evaluations of the brittleness of deep bedded sandstone in deep engineering practices,although further validation is necessary.展开更多
The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling.An improved staggered algorithm with energy and damage iterative tolerance convergence cri...The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling.An improved staggered algorithm with energy and damage iterative tolerance convergence criteria is developed based on the residuals of displacement and phase-field.The improved staggered solution scheme is implemented in the commercial software ABAQUS with user-defined element subroutines.The layered system of finite elements is utilized to solve the coupled elastic displacement and phase-field fracture problem.A one-element benchmark test compared with the analytical solution was conducted to validate the feasibility and accuracy of the developed method.Our study shows that the result calculated with the developed method does not depend on the selected size of loading increments.The results of several numerical experiments show that the improved staggered algorithm is efficient for solving the more complex brittle fracture problems.展开更多
Because plant mechanical strength influences plant growth and development,the regulatory mechanisms underlying cell-wall synthesis deserve investigation.Rice mutants are useful for such research.We have identified a n...Because plant mechanical strength influences plant growth and development,the regulatory mechanisms underlying cell-wall synthesis deserve investigation.Rice mutants are useful for such research.We have identified a novel brittle culm 25(bc25)mutant with reduced growth and partial sterility.BC25 encodes an UDP-glucuronic acid decarboxylase involved in cellulose synthesis and belongs to the UXS family.A single-nucleotide mutation in BC25 accounts for its altered cell morphology and cellwall composition.Transmission electron microscopy analysis showed that the thickness of the secondary cell wall was reduced in bc25.Monosaccharide analysis revealed significant increases in content of rhamnose and arabinose but not of other monosaccharides,indicating that BC25 was involved in xylose synthesis with some level of functional redundancy.Enzymatic assays suggested that BC25 functions with high activity to interconvert UDP-glucuronic acid(UDP-Glc A)and UDP-xylose.GUS staining showed that BC25 was ubiquitously expressed with higher expression in culm,root and sheath,in agreement with that shown by quantitative real-time(q RT)-PCR.RNA-seq further suggested that BC25 is involved in sugar metabolism.We conclude that BC25 strongly influences rice cell wall formation.展开更多
Locked segments are recognized as a critical role that controls the stability of rock slopes but remain an unclear and challenging problem with respect to their role incorporated into the failure mechanism.In order to...Locked segments are recognized as a critical role that controls the stability of rock slopes but remain an unclear and challenging problem with respect to their role incorporated into the failure mechanism.In order to study the effect of the locked segments on the initial failure process of rockslides,thirty-six groups of locked segment specimens with three different lithologies were prepared,direct shear tests were carried out to obtain the accelerations caused by brittle failure of the locked segment specimens.Experiment results showed that the maximum accelerations caused by the brittle failure of locked segment specimens was 2.91 g in the horizontal direction,and 3.18 g in the vertical direction.We took the Wangjiayan rockslide in 2008 Wenchuan earthquake as an example,the critical balance condition of the sliding mass under combined effect of gravity and accelerations induced by brittle failure of locked segment was analyzed,which indicated that the initial failure process of the Wangjiayan rockslides was notably influenced by the existence of the locked segment.The departure acceleration and direction of the Wangjiayan rockslide were proposed.The study results can provide a new insight into the understanding of the initial failure mechanism of rockslides with locked segments.展开更多
The Mg_(17)Al_(12)-phase,which is common and important in Mg-Al alloy,has long been regarded as a brittle phase in experiments but theoretical calculations report controversial results.To unravel why theoretical calcu...The Mg_(17)Al_(12)-phase,which is common and important in Mg-Al alloy,has long been regarded as a brittle phase in experiments but theoretical calculations report controversial results.To unravel why theoretical calculations report controversial results and determine whether Mg_(17)Al_(12)is brittle or ductile,density functional theory calculations on atomic level are performed to investigate mechanic properties of Mg_(17)Al_(12)without containing alloying elements and without taking the size effect.The results showed that the parameter k-point played critical role in the DFT-based elastic calculations.The convergent G/B ratio of Mg_(17)Al_(12)was about 0.52,suggesting that the Mg_(17)Al_(12)-phase was theoretically ductile although its ductility was poor.The chemical bonding in Mg_(17)Al_(12)was the mixture of metallic Mg-Mg bond and covalent Al-Al bond.The advantage of metallic bonding over covalent bonding provided a possible explanation for the ductility of Mg_(17)Al_(12).Possible reasons for the brittleness of Mg_(17)Al_(12)in experiments are also discussed.展开更多
Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high c...Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.展开更多
Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engin...Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure.However,the crack initiation and propagation in brittle materials under composite loading remain unknown so far.In this study,a three-dimensional internal laser-engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces.The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear.The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack,which is a mixed-ModeⅠ–Ⅱ–Ⅲfracture;in contrast,ModeⅠfracture is present in the specimen with a vertical internal crack.The fractography characteristics of ModeⅢfracture display a lance-like pattern.The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure.The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.展开更多
Brittleness and ductility of shale are closely related to shale gas exploration and production. How to predict brittleness and ductility of shale is one of the key issues in the study of shale gas preservation and hyd...Brittleness and ductility of shale are closely related to shale gas exploration and production. How to predict brittleness and ductility of shale is one of the key issues in the study of shale gas preservation and hydraulic fracturing treatments. The magnitude of shale brittleness was often determined by brittle mineral content(for example, quartz and feldspars) in shale gas exploration.However, the shale brittleness is also controlled by burial depth. Shale brittle/ductile properties such as brittle, semibrittle and ductile can mutually transform with burial depth variation. We established a work flow of determining the burial depth interval of brittle–ductile transition zone for a given shale. Two boundaries were employed to divide the burial depth interval of shale brittle/ductile properties. One is the bottom boundary of the brittle zone(BZ), and the other is the top boundary of the ductile zone(DZ). The brittle–ductile transition zone(BDTZ) is between them.The bottom boundary of BZ was determined by the overconsolidation ratio(OCR) threshold value combined with pre-consolidation stress which the shale experienced over geological time. The top boundary of DZ was determined based on the critical confining pressure of brittle–ductile transition. The OCR threshold value and the critical confining pressure were obtained from uniaxial strain andtriaxial compression tests. The BZ, DZ and BDTZ of the Lower Silurian Longmaxi shale in some representative shale gas exploration wells in eastern Sichuan and western Hubei areas were determined according to the above work flow. The results show that the BZ varies with the maximum burial depth and the DZ varies with the density of the overlying rocks except for the critical confining pressure.Moreover, the BDTZ determined by the above work flow is probably the best burial depth interval for marine shale gas exploration and production in Southern China. Shale located in the BDTZ is semi-brittle and is not prone to be severely naturally fractured but likely to respond well to hydraulic fracturing. The depth interval of BDTZ determined by our work flow could be a valuable parameter of shale gas estimation in geology and engineering.展开更多
In the present paper, a micromechanically based damage model formicrocrack-weakened solids is developed. The concept of the domain of microcrackgrowth (DMG) is defined and used to describe the damage state and the ani...In the present paper, a micromechanically based damage model formicrocrack-weakened solids is developed. The concept of the domain of microcrackgrowth (DMG) is defined and used to describe the damage state and the anisotropicproperties of brittle materials. After choosing an appropriate fracture criterion ofmicrocrack, we obtain the analytical expression of DMG under a monotonically in-creasing proportional plane stress. Under a complex loading path, the evolutionequation of DMG and the overall effective compliance tensor of damaged materialsare given.展开更多
Heterogeneity is an inherent component of rock and may be present in different forms including mineral heterogeneity,geometrical heterogeneity,weak grain boundaries and micro-defects.Microcracks are usually observed i...Heterogeneity is an inherent component of rock and may be present in different forms including mineral heterogeneity,geometrical heterogeneity,weak grain boundaries and micro-defects.Microcracks are usually observed in crystalline rocks in two forms:natural and stress-induced;the amount of stressinduced microcracking increases with depth and in-situ stress.Laboratory results indicate that the physical properties of rocks such as strength,deformability,P-wave velocity and permeability are influenced by increase in miciocrack intensity.In this study,the finite-discrete element method(FDEM)is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks using the proposed micro discrete fracture network(μDFN) approach.The characteristics of the microcracks required to create μDFN models are obtained through image analyses of thin sections of Lac du Bonnet granite adopted from published literature.A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-μDFN models indicate that micro-heterogeneity has a profound influence on both the mechanical behavior and resultant fracture pattern.An increase in the microcrack intensity leads to a reduction in the strength of the sample and changes the character of the rock strength envelope.Spalling and axial splitting dominate the failure mode at low confinement while shear failure is the dominant failure mode at high confinement.Numerical results from simulated compression tests show that microcracking reduces the cohesive component of strength alone,and the frictional strength component remains unaffected.Results from simulated Brazilian tests show that the tensile strength is influenced by the presence of microcracks,with a reduction in tensile strength as microcrack intensity increases.The importance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and its effects on the mechanisms leading to spalling damage near an underground opening are also discussed.展开更多
It is known that in B (un)doped Ni 3Al polycrystals, the dependence of yield strength on grain size follows the Hall Petch relationship: σ y= σ 0+ K y d -1/2 , and the slope K y can be reduced by B doping owing to t...It is known that in B (un)doped Ni 3Al polycrystals, the dependence of yield strength on grain size follows the Hall Petch relationship: σ y= σ 0+ K y d -1/2 , and the slope K y can be reduced by B doping owing to the lowering of grain boundary resistance to slip transmission. If the intergranular cracking in polycrystalline Ni 3Al occurs from the microcavity along the grain boundaries, the effective external tensile stress for the propagation of the crack like microcavity along the grain boundaries can be deduced as: σ f= σ i+ K u d -1/2 , where K u reflects the effects of such factors as environment, strain rate, boron doping and the orientation of the grain boundary on the trend of intergranular cracking. For loaded polycrystalline Ni 3Al, it should be competitive between the intergranular cracking and slip transmission across the grain boundary. Therefore, comparing the varieties of both σ y and σ f with grain size, the dependence of ductile brittle transition on grain size, and the effects of the above factors on ductile brittle transition can be expected. The model also predicts that there exists a critical grain size for the ductile brittle transition of polycrystalline Ni 3Al alloys, and B doping can increase the critical grain size due to the reduction of the slope K y and the increase of K u. The reported experimental results verified the above model.展开更多
Transparent brittle materials such as glass and sapphire are widely concerned and applied in consumer electronics, optoelectronic devices, etc. due to their excellent physical and chemical stability and good transpare...Transparent brittle materials such as glass and sapphire are widely concerned and applied in consumer electronics, optoelectronic devices, etc. due to their excellent physical and chemical stability and good transparency. Growing research attention has been paid to developing novel methods for high-precision and high-quality machining of transparent brittle materials in the past few decades. Among the various techniques, laser machining has been proved to be an effective and flexible way to process all kinds of transparent brittle materials. In this review, a series of laser machining methods, e.g. laser full cutting, laser scribing, laser stealth dicing, laser filament, laser induced backside dry etching (LIBDE), and laser induced backside wet etching (LIBWE) are summarized. Additionally, applications of these techniques in micromachining, drilling and cutting, and patterning are introduced in detail. Current challenges and future prospects in this field are also discussed.展开更多
In order to improve the machining efficiency of ultrasonic milling,the easiest and most effective approach was started with the improvement of tool design.The main objective of this research was to utilize rotary ultr...In order to improve the machining efficiency of ultrasonic milling,the easiest and most effective approach was started with the improvement of tool design.The main objective of this research was to utilize rotary ultrasonic machining (RUM's) effectiveness in removing brittle materials to extend the applications of this independent,innovative manufacturing method (self-driving rotary ultrasonic machining),and to experimentally investigate its milling application on brittle materials.The designed tool was used in the conjunction with previously established RUM machine tools,and glass was selected as workpiece for experiments.The interrelationship between feed rate and depth of cut was discussed.By measuring the surface roughness of workpiece,the overall efficacy of utilizing RUM for milling was evaluated and presented.Ultrasonic assisted milling results in the reduction of milling resistance,which leads to a greater process rate.展开更多
Brittleness is an important parameter controlling the mechanical behavior and failure characteristics of rocks under loading and unloading conditions,such as fracability,cutability,drillability and rockburst proneness...Brittleness is an important parameter controlling the mechanical behavior and failure characteristics of rocks under loading and unloading conditions,such as fracability,cutability,drillability and rockburst proneness.As such,it is of high practical value to correctly evaluate rock brittleness.However,the definition and measurement method of rock brittleness have been very diverse and not yet been standardized.In this paper,the definitions of rock brittleness are firstly reviewed,and several representative definitions of rock brittleness are identified and briefly discussed.The development and role of rock brittleness in different fields of rock engineering are also studied.Eighty brittleness indices publicly available in rock mechanics literature are compiled,and the measurement method,applicability and limitations of some indices are discussed.The results show that(1)the large number of brittleness indices and brittleness definitions is attributed to the different foci on the rock behavior when it breaks;(2)indices developed in one field usually are not directly applicable to other fields;and(3)the term“brittleness”is sometimes misused,and many empirically-obtained brittleness indices,which lack theoretical basis,fail to truly reflect rock brittleness.On the basis of this review,three measurement methods are identified,i.e.(1)elastic deformation before fracture,(2)shape of post-peak stressestrain curves,and(3)methods based on fracture mechanics theory,which have the potential to be further refined and unified to become the standard measurement methods of rock brittleness.It is highly beneficial for the rock mechanics community to develop a robust definition of rock brittleness.This study will undoubtedly provide a comprehensive timely reference for selecting an appropriate brittleness index for their applications,and will also pave the way for the development of a standard definition and measurement method of rock brittleness in the long term.展开更多
Rockburst is a typical rock failure which frequently threatens both human life and construction equipment during highly stressed underground excavation.Rock lithology is a control factor of rockburst.In this paper,roc...Rockburst is a typical rock failure which frequently threatens both human life and construction equipment during highly stressed underground excavation.Rock lithology is a control factor of rockburst.In this paper,rockburst tests were conducted on rectangular prismatic specimens of six types of intact hard brittle rocks,i.e.granodiorite,granite,marble,basalt,sandstone and limestone,under one-free-face true triaxial loading conditions.With the use of high-speed cameras,an acoustic emission(AE)system and a scanning electron microscope(SEM),rockburst of different rocks was investigated.The results show that the strainbursts of granodiorite,granite and marble were accompanied by tensile splitting near the free face,and consequently were relatively strong with a large amount of fragment ejection and kinetic energy release.For basalt,sandstone and limestone,failure was primarily dominated by shear rupture.The strainbursts of basalt and sandstone were relatively small with minor fragment ejection and kinetic energy release;while no burst failure occurred on limestone due to its relatively low peak strength.Rock strength,fracturing and fragmentation characteristics,and failure modes of different rocks can significantly affect rockburst proneness and magnitude.The AE evolution coupled with SEM analysis reveals that the differences in the inhe rent microstructures and fracture evolution under loading are the primary factors accounting for different rockbursts in various rock types.展开更多
The brittleness prediction of shale formations is of interest to researchers nowadays.Conventional methods of brittleness prediction are usually based on isotropic models while shale is anisotropic.In order to obtain ...The brittleness prediction of shale formations is of interest to researchers nowadays.Conventional methods of brittleness prediction are usually based on isotropic models while shale is anisotropic.In order to obtain a better prediction of shale brittleness,our study firstly proposed a novel brittleness index equation based on the Voigt–Reuss–Hill average,which combines two classical isotropic methods.The proposed method introduces upper and lower brittleness bounds,which take the uncertainty of brittleness prediction into consideration.In addition,this method can give us acceptable predictions by using limited input values.Secondly,an anisotropic rock physics model was constructed.Two parameters were introduced into our model,which can be used to simulate the lamination of clay minerals and the dip angle of formation.In addition,rock physics templates have been built to analyze the sensitivity of brittleness parameters.Finally,the effects of kerogen,pore structure,clay lamination and shale formation dip have been investigated in terms of anisotropy.The prediction shows that the vertical/horizontal Young’s modulus is always below one while the vertical/horizontal Poisson’s ratio(PR)can be either greater or less than 1.Our study finds different degrees of shale lamination may be the explanation for the random distribution of Vani(the ratio of vertical PR to horizontal PR).展开更多
Rockburst, an unstable failure of brittle rocks, has been greatly concerned in rock mechanics and rock engineering for more than 100 years. The current understanding on the mechanical mechanism of rockburst is based o...Rockburst, an unstable failure of brittle rocks, has been greatly concerned in rock mechanics and rock engineering for more than 100 years. The current understanding on the mechanical mechanism of rockburst is based on the Coulomb theory, i.e. compressive-shear failure theory. This paper illustrates a series of tensile and tensile-shear fracture phenomena of rockburst, and proposes a methodology for the analysis of fracture mode and its energy dissipation process based on Griffith theory. It is believed that: (1) the fracture modes of rockburst should include compressive-shear, tensile-shear and pure tensile failures; (2) the rupture angle of rock mass decreases with the occurrence of tensile stress; (3) the proportion of kinetic energy in the released strain energy from a rockburst may be much larger than that transferred into surface energy; and (4) the understanding on the tensile and tensile-shear failure modes of rockburst may change the basic thinking of rockburst control, i.e. from keeping the reduction in initial compressive stress σ3 to restricting the creation of secondary tensile stress.展开更多
In view of fine cracks occurred on the surface of BNbRE continuous casting slabs for heavy rail in the practical production, the effect of two factors, i.e. deformation temperature, deformation velocity, on thermo pla...In view of fine cracks occurred on the surface of BNbRE continuous casting slabs for heavy rail in the practical production, the effect of two factors, i.e. deformation temperature, deformation velocity, on thermo plasticity of BNbRE steel at the third brittle zone was quantitatively investigated on GLEEBLE-1500D thermal-mechanical simulator after measuring the RA-T curve of BNbRE steel. The results provide experimental data for optimizing the technology of continuous casting secondary cooling zone and avoiding the occurrence of fine surface cracks.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.42372310).
文摘Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.
基金Project supported by the National Natural Science Foundation of China(Nos.12072297 and12202370)the Natural Science Foundation of Sichuan Province of China(No.24NSFSC4777)。
文摘Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.
基金supported by the National Natural Science Foundation of China(Nos.52034009 and 51974319)the Yue Qi Distinguished Scholar Project(No.2020JCB01)。
文摘The quantitative determination and evaluation of rock brittleness are crucial for the estimation of excavation efficiency and the improvement of hydraulic fracturing efficiency.Therefore,a“three-stage”triaxial loading and unloading stress path is designed and proposed.Subsequently,six brittleness indices are selected.In addition,the evolution characteristics of the six brittleness indices selected are characterized based on the bedding effect and the effect of confining pressure.Then,the entropy weight method(EWM)is introduced to assign weight to the six brittleness indices,and the comprehensive brittleness index Bcis defined and evaluated.Next,the new brittleness classification standard is determined,and the brittleness differences between the two stress paths are quantified.Finally,compared with the previous evaluation methods,the rationality of the proposed comprehensive brittleness index Bcis also verified.These results indicate that the proposed brittleness index Bccan reflect the brittle characteristics of deep bedded sandstone from the perspective of the whole life-cycle evolution process.Accordingly,the method proposed seems to offer reliable evaluations of the brittleness of deep bedded sandstone in deep engineering practices,although further validation is necessary.
基金supports by the National Key R&D Program of China(No.2018YFD1100401)the National Natural Science Foundation of China(No.51578142)+1 种基金the Fundamental Research Funds for the Central Universities(No.LEM21A03)Jiangsu Key Laboratory of Engineering Mechanics(Southeast University)are gratefully acknowledged.
文摘The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling.An improved staggered algorithm with energy and damage iterative tolerance convergence criteria is developed based on the residuals of displacement and phase-field.The improved staggered solution scheme is implemented in the commercial software ABAQUS with user-defined element subroutines.The layered system of finite elements is utilized to solve the coupled elastic displacement and phase-field fracture problem.A one-element benchmark test compared with the analytical solution was conducted to validate the feasibility and accuracy of the developed method.Our study shows that the result calculated with the developed method does not depend on the selected size of loading increments.The results of several numerical experiments show that the improved staggered algorithm is efficient for solving the more complex brittle fracture problems.
基金supported by the Key Research and Development Program of Zhejiang Province(2021C02056,2021C02063-6)the National Key Research and Development Program of China(2021YFD1200503)+1 种基金the Fundamental Research Funds for Central Public Welfare Research Institutes of China National Rice Research Institute(CPSIBRF-CNRRI-202101)Chinese Academy of Agricultural Sciences(CAAS-ASTIP-201X-CNRRI)。
文摘Because plant mechanical strength influences plant growth and development,the regulatory mechanisms underlying cell-wall synthesis deserve investigation.Rice mutants are useful for such research.We have identified a novel brittle culm 25(bc25)mutant with reduced growth and partial sterility.BC25 encodes an UDP-glucuronic acid decarboxylase involved in cellulose synthesis and belongs to the UXS family.A single-nucleotide mutation in BC25 accounts for its altered cell morphology and cellwall composition.Transmission electron microscopy analysis showed that the thickness of the secondary cell wall was reduced in bc25.Monosaccharide analysis revealed significant increases in content of rhamnose and arabinose but not of other monosaccharides,indicating that BC25 was involved in xylose synthesis with some level of functional redundancy.Enzymatic assays suggested that BC25 functions with high activity to interconvert UDP-glucuronic acid(UDP-Glc A)and UDP-xylose.GUS staining showed that BC25 was ubiquitously expressed with higher expression in culm,root and sheath,in agreement with that shown by quantitative real-time(q RT)-PCR.RNA-seq further suggested that BC25 is involved in sugar metabolism.We conclude that BC25 strongly influences rice cell wall formation.
基金supported by the National Natural Science Foundation of China (Grant No. 41672295)
文摘Locked segments are recognized as a critical role that controls the stability of rock slopes but remain an unclear and challenging problem with respect to their role incorporated into the failure mechanism.In order to study the effect of the locked segments on the initial failure process of rockslides,thirty-six groups of locked segment specimens with three different lithologies were prepared,direct shear tests were carried out to obtain the accelerations caused by brittle failure of the locked segment specimens.Experiment results showed that the maximum accelerations caused by the brittle failure of locked segment specimens was 2.91 g in the horizontal direction,and 3.18 g in the vertical direction.We took the Wangjiayan rockslide in 2008 Wenchuan earthquake as an example,the critical balance condition of the sliding mass under combined effect of gravity and accelerations induced by brittle failure of locked segment was analyzed,which indicated that the initial failure process of the Wangjiayan rockslides was notably influenced by the existence of the locked segment.The departure acceleration and direction of the Wangjiayan rockslide were proposed.The study results can provide a new insight into the understanding of the initial failure mechanism of rockslides with locked segments.
基金supported by National Natural Science Foundation of China(Grant No.51878246,51975183)
文摘The Mg_(17)Al_(12)-phase,which is common and important in Mg-Al alloy,has long been regarded as a brittle phase in experiments but theoretical calculations report controversial results.To unravel why theoretical calculations report controversial results and determine whether Mg_(17)Al_(12)is brittle or ductile,density functional theory calculations on atomic level are performed to investigate mechanic properties of Mg_(17)Al_(12)without containing alloying elements and without taking the size effect.The results showed that the parameter k-point played critical role in the DFT-based elastic calculations.The convergent G/B ratio of Mg_(17)Al_(12)was about 0.52,suggesting that the Mg_(17)Al_(12)-phase was theoretically ductile although its ductility was poor.The chemical bonding in Mg_(17)Al_(12)was the mixture of metallic Mg-Mg bond and covalent Al-Al bond.The advantage of metallic bonding over covalent bonding provided a possible explanation for the ductility of Mg_(17)Al_(12).Possible reasons for the brittleness of Mg_(17)Al_(12)in experiments are also discussed.
基金supports by National Natural Science Foundation of China(Grant Nos.51874351 and 52078495)Excellent Postdoctoral Innovative Talents Project of Hunan Province,China(Grant No.2020RC2001).
文摘Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.
基金National Natural Science Foundation of China,Grant/Award Numbers:51409170,51739008。
文摘Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure.However,the crack initiation and propagation in brittle materials under composite loading remain unknown so far.In this study,a three-dimensional internal laser-engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces.The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear.The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack,which is a mixed-ModeⅠ–Ⅱ–Ⅲfracture;in contrast,ModeⅠfracture is present in the specimen with a vertical internal crack.The fractography characteristics of ModeⅢfracture display a lance-like pattern.The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure.The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.
基金financially supported by the National Science&Technology Special Project(Grant No.2016ZX05061001)
文摘Brittleness and ductility of shale are closely related to shale gas exploration and production. How to predict brittleness and ductility of shale is one of the key issues in the study of shale gas preservation and hydraulic fracturing treatments. The magnitude of shale brittleness was often determined by brittle mineral content(for example, quartz and feldspars) in shale gas exploration.However, the shale brittleness is also controlled by burial depth. Shale brittle/ductile properties such as brittle, semibrittle and ductile can mutually transform with burial depth variation. We established a work flow of determining the burial depth interval of brittle–ductile transition zone for a given shale. Two boundaries were employed to divide the burial depth interval of shale brittle/ductile properties. One is the bottom boundary of the brittle zone(BZ), and the other is the top boundary of the ductile zone(DZ). The brittle–ductile transition zone(BDTZ) is between them.The bottom boundary of BZ was determined by the overconsolidation ratio(OCR) threshold value combined with pre-consolidation stress which the shale experienced over geological time. The top boundary of DZ was determined based on the critical confining pressure of brittle–ductile transition. The OCR threshold value and the critical confining pressure were obtained from uniaxial strain andtriaxial compression tests. The BZ, DZ and BDTZ of the Lower Silurian Longmaxi shale in some representative shale gas exploration wells in eastern Sichuan and western Hubei areas were determined according to the above work flow. The results show that the BZ varies with the maximum burial depth and the DZ varies with the density of the overlying rocks except for the critical confining pressure.Moreover, the BDTZ determined by the above work flow is probably the best burial depth interval for marine shale gas exploration and production in Southern China. Shale located in the BDTZ is semi-brittle and is not prone to be severely naturally fractured but likely to respond well to hydraulic fracturing. The depth interval of BDTZ determined by our work flow could be a valuable parameter of shale gas estimation in geology and engineering.
基金The project supported by National Natural Science Foundation of China
文摘In the present paper, a micromechanically based damage model formicrocrack-weakened solids is developed. The concept of the domain of microcrackgrowth (DMG) is defined and used to describe the damage state and the anisotropicproperties of brittle materials. After choosing an appropriate fracture criterion ofmicrocrack, we obtain the analytical expression of DMG under a monotonically in-creasing proportional plane stress. Under a complex loading path, the evolutionequation of DMG and the overall effective compliance tensor of damaged materialsare given.
文摘Heterogeneity is an inherent component of rock and may be present in different forms including mineral heterogeneity,geometrical heterogeneity,weak grain boundaries and micro-defects.Microcracks are usually observed in crystalline rocks in two forms:natural and stress-induced;the amount of stressinduced microcracking increases with depth and in-situ stress.Laboratory results indicate that the physical properties of rocks such as strength,deformability,P-wave velocity and permeability are influenced by increase in miciocrack intensity.In this study,the finite-discrete element method(FDEM)is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks using the proposed micro discrete fracture network(μDFN) approach.The characteristics of the microcracks required to create μDFN models are obtained through image analyses of thin sections of Lac du Bonnet granite adopted from published literature.A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-μDFN models indicate that micro-heterogeneity has a profound influence on both the mechanical behavior and resultant fracture pattern.An increase in the microcrack intensity leads to a reduction in the strength of the sample and changes the character of the rock strength envelope.Spalling and axial splitting dominate the failure mode at low confinement while shear failure is the dominant failure mode at high confinement.Numerical results from simulated compression tests show that microcracking reduces the cohesive component of strength alone,and the frictional strength component remains unaffected.Results from simulated Brazilian tests show that the tensile strength is influenced by the presence of microcracks,with a reduction in tensile strength as microcrack intensity increases.The importance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and its effects on the mechanisms leading to spalling damage near an underground opening are also discussed.
文摘It is known that in B (un)doped Ni 3Al polycrystals, the dependence of yield strength on grain size follows the Hall Petch relationship: σ y= σ 0+ K y d -1/2 , and the slope K y can be reduced by B doping owing to the lowering of grain boundary resistance to slip transmission. If the intergranular cracking in polycrystalline Ni 3Al occurs from the microcavity along the grain boundaries, the effective external tensile stress for the propagation of the crack like microcavity along the grain boundaries can be deduced as: σ f= σ i+ K u d -1/2 , where K u reflects the effects of such factors as environment, strain rate, boron doping and the orientation of the grain boundary on the trend of intergranular cracking. For loaded polycrystalline Ni 3Al, it should be competitive between the intergranular cracking and slip transmission across the grain boundary. Therefore, comparing the varieties of both σ y and σ f with grain size, the dependence of ductile brittle transition on grain size, and the effects of the above factors on ductile brittle transition can be expected. The model also predicts that there exists a critical grain size for the ductile brittle transition of polycrystalline Ni 3Al alloys, and B doping can increase the critical grain size due to the reduction of the slope K y and the increase of K u. The reported experimental results verified the above model.
基金National Natural Science Foundation of China (51575114 and 51805093)National Key R&D Program of China (2018YFB1107700)Guangzhou Science and Technology Project (201607010156).
文摘Transparent brittle materials such as glass and sapphire are widely concerned and applied in consumer electronics, optoelectronic devices, etc. due to their excellent physical and chemical stability and good transparency. Growing research attention has been paid to developing novel methods for high-precision and high-quality machining of transparent brittle materials in the past few decades. Among the various techniques, laser machining has been proved to be an effective and flexible way to process all kinds of transparent brittle materials. In this review, a series of laser machining methods, e.g. laser full cutting, laser scribing, laser stealth dicing, laser filament, laser induced backside dry etching (LIBDE), and laser induced backside wet etching (LIBWE) are summarized. Additionally, applications of these techniques in micromachining, drilling and cutting, and patterning are introduced in detail. Current challenges and future prospects in this field are also discussed.
基金Project(NSC-94-2622-E-027-036-CC3)supported by National Science Council
文摘In order to improve the machining efficiency of ultrasonic milling,the easiest and most effective approach was started with the improvement of tool design.The main objective of this research was to utilize rotary ultrasonic machining (RUM's) effectiveness in removing brittle materials to extend the applications of this independent,innovative manufacturing method (self-driving rotary ultrasonic machining),and to experimentally investigate its milling application on brittle materials.The designed tool was used in the conjunction with previously established RUM machine tools,and glass was selected as workpiece for experiments.The interrelationship between feed rate and depth of cut was discussed.By measuring the surface roughness of workpiece,the overall efficacy of utilizing RUM for milling was evaluated and presented.Ultrasonic assisted milling results in the reduction of milling resistance,which leads to a greater process rate.
基金We gratefully acknowledge financial support from the National Natural Science Foundation of China(Grant Nos.51879135 and 41877217)The work in this paper was also supported by the Hong Kong Scholars Program(Grant No.XJ2017043).
文摘Brittleness is an important parameter controlling the mechanical behavior and failure characteristics of rocks under loading and unloading conditions,such as fracability,cutability,drillability and rockburst proneness.As such,it is of high practical value to correctly evaluate rock brittleness.However,the definition and measurement method of rock brittleness have been very diverse and not yet been standardized.In this paper,the definitions of rock brittleness are firstly reviewed,and several representative definitions of rock brittleness are identified and briefly discussed.The development and role of rock brittleness in different fields of rock engineering are also studied.Eighty brittleness indices publicly available in rock mechanics literature are compiled,and the measurement method,applicability and limitations of some indices are discussed.The results show that(1)the large number of brittleness indices and brittleness definitions is attributed to the different foci on the rock behavior when it breaks;(2)indices developed in one field usually are not directly applicable to other fields;and(3)the term“brittleness”is sometimes misused,and many empirically-obtained brittleness indices,which lack theoretical basis,fail to truly reflect rock brittleness.On the basis of this review,three measurement methods are identified,i.e.(1)elastic deformation before fracture,(2)shape of post-peak stressestrain curves,and(3)methods based on fracture mechanics theory,which have the potential to be further refined and unified to become the standard measurement methods of rock brittleness.It is highly beneficial for the rock mechanics community to develop a robust definition of rock brittleness.This study will undoubtedly provide a comprehensive timely reference for selecting an appropriate brittleness index for their applications,and will also pave the way for the development of a standard definition and measurement method of rock brittleness in the long term.
基金the financial support from the National Natural Science Foundation of China under Grant No.51869003supported by the Opening Fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection(Chengdu University of Technology)under Grant No.SKLGP2017K022Study Abroad Program for Excellent PhD Students of Guangxi University。
文摘Rockburst is a typical rock failure which frequently threatens both human life and construction equipment during highly stressed underground excavation.Rock lithology is a control factor of rockburst.In this paper,rockburst tests were conducted on rectangular prismatic specimens of six types of intact hard brittle rocks,i.e.granodiorite,granite,marble,basalt,sandstone and limestone,under one-free-face true triaxial loading conditions.With the use of high-speed cameras,an acoustic emission(AE)system and a scanning electron microscope(SEM),rockburst of different rocks was investigated.The results show that the strainbursts of granodiorite,granite and marble were accompanied by tensile splitting near the free face,and consequently were relatively strong with a large amount of fragment ejection and kinetic energy release.For basalt,sandstone and limestone,failure was primarily dominated by shear rupture.The strainbursts of basalt and sandstone were relatively small with minor fragment ejection and kinetic energy release;while no burst failure occurred on limestone due to its relatively low peak strength.Rock strength,fracturing and fragmentation characteristics,and failure modes of different rocks can significantly affect rockburst proneness and magnitude.The AE evolution coupled with SEM analysis reveals that the differences in the inhe rent microstructures and fracture evolution under loading are the primary factors accounting for different rockbursts in various rock types.
基金supported by National Science and Technology Major Project(Grant No.2017ZX05049002)the NSFC and Sinopec joint key project(U1663207)support from the Sinopec Key Laboratory of Seismic Elastic Wave Technology.
文摘The brittleness prediction of shale formations is of interest to researchers nowadays.Conventional methods of brittleness prediction are usually based on isotropic models while shale is anisotropic.In order to obtain a better prediction of shale brittleness,our study firstly proposed a novel brittleness index equation based on the Voigt–Reuss–Hill average,which combines two classical isotropic methods.The proposed method introduces upper and lower brittleness bounds,which take the uncertainty of brittleness prediction into consideration.In addition,this method can give us acceptable predictions by using limited input values.Secondly,an anisotropic rock physics model was constructed.Two parameters were introduced into our model,which can be used to simulate the lamination of clay minerals and the dip angle of formation.In addition,rock physics templates have been built to analyze the sensitivity of brittleness parameters.Finally,the effects of kerogen,pore structure,clay lamination and shale formation dip have been investigated in terms of anisotropy.The prediction shows that the vertical/horizontal Young’s modulus is always below one while the vertical/horizontal Poisson’s ratio(PR)can be either greater or less than 1.Our study finds different degrees of shale lamination may be the explanation for the random distribution of Vani(the ratio of vertical PR to horizontal PR).
基金Supported by the National Natural Science Foundation of China (41030749)Ministry of Railways (2009G005-A)Chinese Academy of Sciences (KZCX2-YX-109)
文摘Rockburst, an unstable failure of brittle rocks, has been greatly concerned in rock mechanics and rock engineering for more than 100 years. The current understanding on the mechanical mechanism of rockburst is based on the Coulomb theory, i.e. compressive-shear failure theory. This paper illustrates a series of tensile and tensile-shear fracture phenomena of rockburst, and proposes a methodology for the analysis of fracture mode and its energy dissipation process based on Griffith theory. It is believed that: (1) the fracture modes of rockburst should include compressive-shear, tensile-shear and pure tensile failures; (2) the rupture angle of rock mass decreases with the occurrence of tensile stress; (3) the proportion of kinetic energy in the released strain energy from a rockburst may be much larger than that transferred into surface energy; and (4) the understanding on the tensile and tensile-shear failure modes of rockburst may change the basic thinking of rockburst control, i.e. from keeping the reduction in initial compressive stress σ3 to restricting the creation of secondary tensile stress.
基金Project supported bythe Inner Mongolian Autonomous Region Educational Department (NJ050667)
文摘In view of fine cracks occurred on the surface of BNbRE continuous casting slabs for heavy rail in the practical production, the effect of two factors, i.e. deformation temperature, deformation velocity, on thermo plasticity of BNbRE steel at the third brittle zone was quantitatively investigated on GLEEBLE-1500D thermal-mechanical simulator after measuring the RA-T curve of BNbRE steel. The results provide experimental data for optimizing the technology of continuous casting secondary cooling zone and avoiding the occurrence of fine surface cracks.
