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 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.

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.

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.

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.

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.

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.

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.

Microstructure,mechanical and fracture properties of friction stir welded 2195 Al-Li alloy joints

The 8 mm-thick 2195 Al-Li alloy joints were achieved by Friction Stir Welding(FSW).The microstructural evolution,temperature-dependent mechanical properties,and fracture properties were studied.The T1,δ’/β’and θ’precipitates were observed in the Base Metal(BM)and the Heat Affected Zone(HAZ).Most of the precipitates,except for re-precipitated δ’/β’phases,were dissolved in the Nugget Zone(NZ).The tensile specimens that failed at cryogenic temperatures(-196℃)had the maximum Ultimate Tensile Strength(UTS),and the fracture surface showed the inter-granular fracture characteristics.Compared to those at room temperature(25℃),the decreasing tensile properties at high temperature(180℃)were related to microstructure and strain hardening effects.The NZ presented the optimal fracture toughness,and the Crack Tip Opening Displacement(CTOD)was mutually dominated by microhardness and grain size.Analysis on Fatigue Crack Growth(FCG)rates indicates that the Thermal-Mechanically Affected Zone(TMAZ)exhibited the most superior fatigue resistance performance at stress intensity range below17 MPa.m1/2due to compressive residual stress and the crack closure effect.The fatigue fracture surfaces reveal that the crack propagation zone was characterized by the striations and secondary cracks.Also,inter-granular fracture behavior was responsible for the fastest FCG rates in the NZ.

Microstructure and mechanical properties of forged Al-7.1Zn-1.1Mg-1.6Cu-0.14Zr alloy after two-step ageing treatment at 120 and 170℃

The tensile properties, electrical conductivity, and microstructure of the forged A1-7.1Zn-1.1Mg-1.6Cu-0.14Zr alloy were investigated after a two-step ageing treatment at 120 and 170℃. The results indicate that the strength of the alloy reaches the peak value at 170~C for 1 h during the second step ageing and then decreases sharply. However, the electrical conductivity value increases continuously with the second ageing time increasing. The fracture mechanism of the alloy is intergranular fracture for 1 h and then changes to dimple transgranular fracture later, and the toughness of the alloy is improved significantly. The phases of rl＇ and 1＂1 are major precipitates in the alloy under the two-step ageing condition. Discontinuous grain boundary precipitates and precipitate-flee zones along the grain boundary are clearly observed.

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.

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.

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.

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.