EXPERIMENTAL AND THEORETICAL STUDY OF STATIC-DYNAMIC MIXED MODE BRITTLE FRACTURE OF ROCK

A new criterion of static dynamic state mixed mode brittle fracture initiation in rock is suggested, i.e. the distortion strain energy criterion.When t →∞, the static state distortion strain energy criteria and the formula for determiming static state fracture angle are obtained. The new static state criterion, suggested by authors, is in good agreement with the author′s experimental results. In addition, the relative accuracy of three current fracture theories and the new criterion in predicting static state mixed mode initiation fracture loading and fracture angle in rock have been evaluated experimentally.

MECHANISM ANALYSIS OF THICKNESS EFFECT ON MIXED MODE Ⅰ/Ⅱ FRACTURE OF LC4-CS ALUMINUM ALLOY

Mixed mode Ⅰ/Ⅱ fracture erperiments of LC4-CS aluminum alloy were conductedby using tension--shear specimens with thicknesses of 2, 4, 8 and 14mm. Fracturemechanisms of thickness effect on mixed mode Ⅰ/Ⅱ fracture were first examined fromfracture surface morphology to correlate with the macroscopic fracture behavior andstress state. It is found that specimen thickness has a strong influence on mixed modefracture. As thickness varies from thin to thick the macroscopic fracture surfacesappear the characteristics of plane stress state (2mm, 4mm--thick specimen), three--dimensional stress state (8mm--thick specimens), and plane strain state (14mm--thickspecimens), respectively. The specimens of all kinds of thicknesses are typical of ten-sile type failure under mode Ⅰ loading condition and shear type failure under mode Ⅱloading condition. Two distinct features coexist on the fracture surfaces under mixedmode loading conditions, and the corresponding proportion varies with loading mix-ity. Void--growth processes are the failure mechanism in both predominately tensile-and shears--type fractures. The size and depth of dimples on the fracture surface varygreatly with thickness. Therefore, it is extraordinary necessary to take into accountthe thickness effect when a mixed mode fracture criterion is being established.

Multiscale Hybrid-Mixed Finite Element Method for Flow Simulation in Fractured Porous Media

The multiscale hybrid-mixed(MHM)method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with fractures.The two-dimensional fluid flow in the reservoir and the one-dimensional flow in the discrete fractures are approximated using mixed finite elements.The coupling of the two-dimensional matrix flow with the one-dimensional fracture flow is enforced using the pressure of the one-dimensional flow as a Lagrange multiplier to express the conservation of fluid transfer between the fracture flow and the divergence of the one-dimensional fracture flux.A zero-dimensional pressure(point element)is used to express conservation of mass where fractures intersect.The issuing simulation is then reduced using the MHM method leading to accurate results with a very reduced number of global equations.A general system was developed where fracture geometries and conductivities are specified in an input file and meshes are generated using the public domain mesh generator GMsh.Several test cases illustrate the effectiveness of the proposed approach by comparing the multiscale results with direct simulations.

A MIXED MODE FRACTURE CRITERION BASED ON THE MAXIMUM TANGENTIAL STRESS IN BRITTLE INCLUSION

A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture criterion, including the fracture direction and the critical load, was established based on the maximum tangential stress in the inclusion for brittle inclusioninduced fracture materials. The proposed fracture criterion is a function of the inclusion fracture stress, its size and volume fraction, as well as the elastic constants of the inclusion and the matrix material. The present criterion will reduce to the conventional one as the inclusion having the same elastic behavior as the matrix material. The proposed solutions are in good agreement with detailed finite element analysis and measurement.

INFLUENCES OF HEAT-TREATING PROCESS ON DUCTILE FRACTURE MECHANISM UNDER MIXED MODE LOADINGS

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Computational Fracture Analysis of an AFM-Specimen under Mixed Mode Loading Conditions

Fracture processes in ship-building structures are in many cases of a 3-D character. A finite element （FE） model of an all fracture mode （AFM） specimen was built for the study of 3-D mixed mode crack fracture behavior including modes Ⅰ,Ⅱ, and Ⅲ. The stress intensity factors （SIFs） were calculated by the modified virtual crack closure integral （MVCCI） method, and the crack initiation angle assessment was based on a recently developed 3-D fracture criterion--the Richard criterion. It was shown that the FE model of the AFM-specimen is applicable for investigations under general mixed mode loading conditions, and the computational results of crack initiation angles are in agreement with some available experimental findings. Thus, the applicability of the FE model of the AFM-specimen for mixed mode loading conditions and the validity of the Richard criterion can be demonstrated.

Experiment on Mode Ⅰ/Ⅱ Mixed Interfacial Fracture Characterization of Foam Core Sandwich Materials at Elevated Temperatures

Foam-cored sandwich materials have been widely used in the civil engineering due to their advantages such as lightweight,high strength,and excellent anti-corrosion ability. However,the interfacial bonding strength of foamcored sandwich materials is weakened at elevated temperatures. In practice,the effect of high temperature cannot be ignored,because the composites and foams are sensitive to the change of temperature in the environment. In this study,a series of single-leg bending beams were tested at different temperatures to evaluate the influences of high temperatures on Mode Ⅰ/Ⅱ mixed interfacial fracture of foam core sandwich materials. The temperature was from29 ℃ to 90 ℃,covered the glass transition temperature of composites and foam core,respectively. The Mode Ⅰ/Ⅱ mixed interfacial crack prorogation and its corresponding interfacial strain energy release rate were summarized.

DYNAMIC MIXED MODE FRACTURE INITIATION IN ROCK^+

In this paper, a distortion dynamic strain energy density factor criterion for dynamic mixed-mode fracture initiation in rock is suggested.The results of the investigation on 14 three-point bending (TPB) and four-point bending(FPB) rock specimens tested u

MODE II AND MIXED MODE I-II ROCK FRACTURE RESEARCH

of PhD thesis For the mode I rock fracture toughness measurement,three standard methods have been recommended by the ISRM,but there has not been a standard method for the determination of mode II and mixed mode I-II rock fracture toughness. However mode II and mixed mode I-II fracturing of rock structures is more commonly observed than mode I in various geological and structural engineering settings. So it is of great important to thoroughly research these rock fracture problems and establish a standard method for determining the mode II or mixed mode I-II fracture toughness for rock materials. Based on the progress made for mode I rock fracture research,the cracked chevron notched Brazilian disk (CCNBD) specimen was also introduced for mode II and mixed mode I-II rock fracture toughness measurement. When the crack is orientated at an angle with respect to the diametrical loading,the crack of the CCNBD specimen is exposed to the mode II or mixed mode I-II stress distribution conditions. The solutions for stress intensity factors in the vicinity of the crack tip have been evaluated by the stepwise superimposition technique. In order to make sure that the theoretical analysis is correct,numerical calculation method has been employed to calibrate the theoretical results. It has been proved that the theoretical results yielded by the dislocation method are correct and reliable. According to the characteristic that the propagation of the crack in the CCNBD specimen is in its own plane and application of the energy superposition principle,the stress intensity factor of the mixed mode I-II has been defined in dimensionless terms as 212II2Imix])()[(***+=YYY. It was found that the curve of *mixY was concave. There exists a lowest point which corresponds to the maximum external load and indicates the crack has reached its critical state. Since the values of ***IIImix and YYY, are only dependent on the specimen geometry (qaaa and 10B,,),the critical values of ***IIImix and YYY, can be to known as long as the CCNBD specimen is prepared ready. It is only necessary to record the maximum load during the fracture tests. The fracture locus is very useful to know whether the crack in a rock structure has reached its critical condition. According to the amount of practical fracture testing data obtained,the rock fracturing locus was found to be 123IICII23ICI=+KKKK and the S-critical criterion was found to be more suitable for rock mixed mode I-II fracturing assessment.

Tensile and tear-type fracture toughness of gypsum material:Direct and indirect testing methods

In this context,four specimens,i.e.(i)circumferentially notched cylindrical torsion(CNCT),(ii)circum-ferentially notched cylindrical direct tension(CNCDT),(iii)edge notch disc bend(ENDB)and(iv)three-point bend beam(3PBB),were utilized to measure the modesⅠandⅢfracture toughness values of gypsum.While the CNCT specimen provides pure modeⅢloading in a direct manner,this pure mode condition is indirectly produced by the ENDB specimen.The ENDB specimen provided lower KⅢc and a non-coplanar(i.e.twisted)fracture surface compared with the CNCT specimen,which showed a planar modeⅢfracture surface.The ENDB specimen is also employed for conducting pure modeⅠ(with different crack depths)and mixed modeⅠ/Ⅲtests.KIc value was independent of the notch depth,and it was consistent with the RILEM and ASTM standard methods.But the modeⅢfracture results were highly sensitive to the notch depth.While the fracture resistance against modeⅢwas significantly lower than that of modeⅠ,the greater work of fracture under modeⅢwas noticeable.

Three-dimensional analysis of spreading and mixing of miscible compound in heterogeneous variable-aperture fracture

As mass transport mechanisms,the spreading and mixing(dilution) processes of miscible contaminated compounds are fundamental to understanding reactive transport behaviors and transverse dispersion.In this study,the spreading and dilution processes of a miscible contaminated compound in a three-dimensional self-affine rough fracture were simulated with the coupled lattice Boltzmann method(LBM).Moment analysis and the Shannon entropy(dilution index) were employed to analyze the spreading and mixing processes,respectively.The corresponding results showed that the spreading process was anisotropic due to the heterogeneous aperture distribution.A compound was transported faster in a large aperture region than in a small aperture region due to the occurrence of preferential flow.Both the spreading and mixing processes were highly dependent on the fluid flow velocity and molecular diffusion.The calculated results of the dilution index showed that increasing the fluid flow velocity and molecular diffusion coefficient led to a higher increasing rate of the dilution index.

Effect of Heat Treatment on Delayed Fracture Resistance of High Strength Steel 30CrMnSi2NiNb

The steel specimens of nominal composition 0.3C-1.0Cr-1.0Mn-2.0Si-1.0Ni-0.04 Nb were quenched and tempered or isothermally quenched from various temperatures.It is found that the steel quenched and tempered with a tensile strength of 1 500-1 600 MPa has a KISCC（critical stress intensity factor） value below 15.0 MPa · m1/2.The steel isothermally quenched with a tensile strength of 1 350-1 750 MPa has a KISCC value about 20.0 MPa·m1/2.In addition,with increase of isothermal quenching temperature,the tensile strength decreases greatly and KISCC value does not pronouncedly change.The microstructure of isothermally quenched specimens is composed of bainite and retained austenite.The delayed fracture resistance is dependent on the stability of austenite,which is in turn related to the retained austenite volume fraction and carbon content in austenite.

A MIXED ELECTRIC BOUNDARY VALUE PROBLEM FOR AN ANTI-PLANE PIEZOELECTRIC CRACK

The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation.The crack face is partly conductive and partly impermeable.The results show that the stress intensity factor is identical with the mode Ⅲ stress intensity factor independent of the conducting length.But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and are singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.

CRACK TIP STRUCTURE AND DUCTILE-BRITTLE TRANSITION IN BULK SINGLE CRYSTALS

Based on the crack tip structure a new model of ductile -brittle transition was proposed. Using this new model we calculated the dependence of the transition temperature-strain rate over a wide range of strain rate. Finally the significance of this new model is discussed in detail.

Toughness and Fracture Mechanism of Carbon Fiber Reinforced Epoxy Composites

The fracture toughness of carbon fiber reinforced epoxy composite(CFRP)was investigated through mode I and mode II shaped fracture system in this paper.A novel polyimide with trifluoromethyl groups and grafted nanosilica were used to modify epoxy resin.Effect of modified resin and unmodified resin on fracture toughness of CFRP was compared and discussed.Lay-up angles and thicknesses effects on fracture toughness of composites were also investigated.The fracture toughness of CFRP was obtained through double cantilever beam(DCB)and end notched flexure(ENF)tests.The results showed that the composites prepared by modified resin exhibited high fracture toughness compared with unmodified composites.The fracture toughness value of mode I increased from 1.83 kJ/m2 to 4.55 kJ/m2.The fracture toughness value of mode II increased from 2.30 kJ/m2 to 6.47 kJ/m2.

Development of X-FEM methodology and study on mixed-mode crack propagation

The extended finite element method（X-FEM） is a novel numerical methodology with a great potential for using in multi-scale computation and multi-phase coupling problems. The algorithm is discussed and a program is developed based on X-FEM for simulating mixed-mode crack propagation. The maximum circumferential stress criterion and interaction integral are deduced. Some numerical results are compared with the experimental data to prove the capability and efficiency of the algorithm and the program. Numerical analyses of sub-interfacial crack growth in bi-materials give a clear description of the effiect on fracture made by interface and loading condition.

Microscopic characteristics of different fracture modes of brittle rock

Three types of rock specimens, three-point bending specimen, anti-symmetric four-point bending specimen and direct shearing specimen, were used to achieve Mode I, Mode II and mixed mode I–II fracture, respectively. Microscopic characteristics of the three fracture modes of brittle rock were studied by SEM technique in order to analyze fracture behaviors and better understand fracture mechanisms of different fracture modes of brittle rock. Test results show that the microscopic characteristics of different fracture modes correspond to different fracture mechanisms. The surface of Mode I fracture has a great number of sparse and steep slip-steps with few tearing ridges and shows strong brittleness. In the surface of Mode II fracture there exist many tearing ridges and densely distributed parallel slip-steps and it is attributed to the action of shear stress. The co-action of tensile and shear stresses results in brittle cleavage planes mixed with streamline patterns and tearing ridges in the surface of mixed mode I–II fracture. The measured Mode II fracture toughness K II C and mixed mode I–II fracture toughness K mC are larger than Mode I fracture toughness K I C · K II C is about 3.5 times K I C, and KmC is about 1.2 times K I C.

EFFECT OF LOADING RATE AND TEMPERATURE ON DUCTILE-BRITTLE TRANSITION OF A CARBON STEEL

The dynamic fracture toughness of a mild steel has been studied at different loading rates and temperatures.The material exhibits a transition from tough to brittle fracture with the chang- ing loading rate alone.Analysis of the fracture process by the theory of thermal activation suggests that the fracture activation energy approximates to the bond energy of the{100}of a unit cell.The toughness can be resolved into two parts,J-(fd)=J_a+J_l,where J_a is the athermal part,being independent on temperature and loading rate,while J_l=(K/K_o)^(1/n)exp(Q_f/nkT),which controls the fracture process is temperature and load- ing rate dependent.The transition of fracture mechanism caused by both temperature and loading rate is associated with the thermal movement of atoms.

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

气水两相下降流中泡状流与段塞流转换边界研究

针对塔河油田气水混注驱替“阁楼油”过程中泡状流与段塞流转换边界不清的问题,利用数值模拟方法对气水两相下降流中泡状流与段塞流进行了模拟分析。结果表明:在气相表观流速为0.01~1.00 m/s、液相表观流速为0.03~2.00 m/s、管径为76 mm的模拟条件下,管道中主要为泡状流和段塞流;与模拟结果相比,Barnea、Kokal、薛玉卿模型预测的转换边界偏小,Bhagwat和Yijun模型预测的转换边界偏大;随着气相表观流速增加,泡状流向段塞流转换时所需液量逐渐增大;在低液量条件下,越靠近管道中心,气泡数量越多,空隙率越大;随液量增加,单个小气泡体积减小,气泡在整个管道横截面上分布越均匀。基于漂移模型,考虑气泡群滑脱速度,建立了新的泡状流与段塞流转换边界模型,216组文献数据验证结果显示,新模型准确率为95.37%,准确度较高。建立的泡状流—段塞流转换边界模型,不仅可提高井筒压力、温度模型的计算精度,同时对塔河油田现场注入井井口参数优化、注入设备优选和提高“阁楼油”驱替效率有很好的理论指导意义。