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.

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.

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

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

Fracture propagation in sandstone and slateeLaboratory experiments, acoustic emissions and fracture mechanics

Fracturing of highly anisotropic rocks is a problem often encountered in the stimulation of unconventional hydrocarbon or geothermal reservoirs by hydraulic fracturing. Fracture propagation in isotropic material is well understood but strictly isotropic rocks are rarely found in nature. This study aims at the examination of fracture initiation and propagation processes in a highly anisotropic rock, specifically slate. We performed a series of tensile fracturing laboratory experiments under uniaxial as well as triaxial loading. Cubic specimens with edge lengths of 150 mm and a central borehole with a diameter of13 mm were prepared from Fredeburg slate. An experiment using the rather isotropic Bebertal sandstone as a rather isotropic rock was also performed for comparison. Tensile fractures were generated using the sleeve fracturing technique, in which a polymer tube placed inside the borehole is pressurized to generate tensile fractures emanating from the borehole. In the uniaxial test series, the loading was varied in order to observe the transition from strength-dominated fracture propagation at low loading magnitudes to stress-dominated fracture propagation at high loading magnitudes.

Fracture mechanics analysis on Smart-Cut~technology.Part 2:Effect of bonding flaws

In Part 2 of the paper on the Smart-Cut process, the effects of bonding flaws characterized by the size and internal pressure before and after splitting are studied by using fracture mechanics models. It is found that the bonding flaws with large size are prone to cause severe deviation of defect growth, leading to a non-transferred area of thin layer when splitting. In a practical Smart-Cut process where the internal pressure of bonding flaws is very small, large interfacial defects always promote defect growth in the splitting process. Meanwhile, increasing the internal pressure of the bonding flaws decreases the defect growth and its deviation before splitting. The mechanism of relaxation of stiffener constraint is proposed to clarify the effect of bonding flaws. Moreover, the progress of the splitting process is analyzed when bonding flaws are present. After splitting, those bonding flaws with large size and high internal pressure are vulnerable for the blistering of the thin film during high-temperature annealing.

A comparison of electromigration failure of metal lines with fracture mechanics

Atoms constructing an interconnecting metal line in a semiconductor device are transported by electron flow in high density. This phenomenon is called electromigration, which may cause the line failure. In order to characterize the electromigration failure, a comparison study is carded out with some typical phenomena treated by fracture mechanics for thin and large structures. An example of thin structures, which have been treated by fracture mechanics, is silica opti- cal fibers for communication systems. The damage growth in a metal line by electromigration is characterized in compar- ison with the crack growth in a silica optical fiber subjected to static fatigue. Also a brief comparison is made between the electromigration failure and some fracture phenomena in large structures.

Fracture Mechanics,Crack Propagation and Microhardness Studies on Flux Grown ErAlO_3 Single Crystals

Results on fracture mechanics and crack propagation have been obtained, making use of Vickers microhardness studies on two different crystallographic planes [(110) and (001)] of flux grown erbium aluminate crystals in the load ranging from 10-100 g. The variation of microhardness with load which is best explained by Hays and Kendall's law leads to the load independent values of hardness. Classification of cracks is dealt with and it is reported that the transition from Palmqvist to median types of cracks occurs at higher loads. The values of fracture toughness (K_C), and brittleness index (B_i) are calculated using median types of cracks.

Discussion on electromagnetic crack face boundary conditions for the fracture mechanics of magneto-electro-elastic materials

This paper discusses electromagnetic boundary conditions on crack faces in magneto- electroelastic materials, where piezoelectric, piezomagnetic and magnetoelectric effects are coupled. A notch of finite thickness in these materials is also addressed. Four idealized electromagnetic boundary conditions assumed for the crack-faces are separately investigated, i.e. （a） electrically and magnetically impermeable （crack-face）, （b） electrically impermeable and magnetically permeable, （c） electrically permeable and magnetically impermeable, and （d） electrically and magnetically permeable. The influence of the notch thickness on important parameters, such as the field intensity factors, the energy release rate at the notch tips and the electromagnetic fields inside the notch, are studied and the results are obtained in closed-form. Results under different idealized electromagnetic boundary conditions on the crack-face are compared, and the applicability of these idealized assumptions is discussed.

Analysis on Fracture Mechanics of Unstable Rock

Unstable rock is a kind of global geological disaster with high frequency. This paper, considering three kinds of combined loads which are gravity, fracture water pressure and seismic force, constructs a unstable rock mechanics model and it uses a fracture mechanics method to deduce the composite stress intensity factor of the type I - II. Based on the maximum circumferential stress theory, this article calculates the theo-retical fracture angle by triangle universal formula.

Fracture Mechanics on Aluminum Specimens

ASTM standards for A413 aluminum alloy specimen assays were used based on standard E399-05, with a minimum requirement of three specimens. Linear elastic fracture mechanic testing was carried out in plane strain conditions and fracture toughness of the tested aluminum, critical stress intensity factor was determined. Four specimens with the selected geometry were made, since in the pre-cracking process a non-acceptable propagation of crack may be present, i.e., the crack does not propagate in a parabolic manner. In like manner, the Type SE (B) specimen, that is, a beam subject to bending under a monotonic load, was used. Stress efforts were induced in the experiment, the load mode for such experiments is mode I, determining a temporary value of the KQ apparent stress intensity factor. When such value complies with the validity criteria of E-399 Standard, it becomes the stress intensity factor KIC of material.

RANDOMIZATION METHOD OF DETERMINISTIC EQUATION FOR PROBABILITY FRACTURE MECHANICS

In order to obtain any probability of survival for crack growth life, a randomization method of deterministic equation for probability fracture mechanics is presented. According to this method, the deterministic equation of fracture mechanics is randomized to stochastic equation, and the parameters of the stochastic equation are estimated by means of the statistics. Three new kinds of random models to gain the p d a/ d N Δ K curve and the γ p d a/ d N Δ K curve (confidence level probability of survival fatigue crack growth rate stress intensity factor range curve) are proposed by using this randomization method. And the p d a/ d N Δ K curves and the γ p d a/ d N Δ K curves determined by these three models are discussed and compared according to the treatment result of the experimental data from CT specimens. From examples, it is found that the three deterministic fatigue crack growth rate equations determined by these models are very near and in agreement with the traditional deterministic fatigue crack growth rate equation, and these models are effectively and easily used to treat fatigue crack growth rate data.

Fracture mechanics analysis in frost breakage of reservoir revetment on cold regions

Reservoir revetment in cold regions is often damaged by frost due to the joint action of low-temperatures and cryogenic environment in winter. This damage reduces or even eliminates the function ofthe reservoir revelrnent. In this paper, practical problems in engineering were analyzed for the drainage pumping station of Tuanjie Reservoir. Based on a tradifional method of analysis and calculalion, fiacture mechanics was iricorporated to provide quantitative analysis and calculation on the problem of anti-freeze damage from the viewpoint of fracture mechanics. Thus, a new idea is put forward to resolve anti-freefing ofreservoir slope proteclion in cold regions.

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.

ENRICHED GOAL-ORIENTED ERROR ESTIMATION APPLIED TO FRACTURE MECHANICS PROBLEMS SOLVED BY XFEM

Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method （XFEM）, which involves enrichment to solve a stress singularity in the crack. Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation, the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work. By comparing the reliability of the stress intensity factor calculation, the accuracy of two programs in different cases is evaluated and the source of error is discussed. A 2-dimensional XFEM example is given to illustrate the computational procedure.

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.

FRACTURE MECHANICS ANALYSIS OF THERMAL STRAINFATIGUE LIFE FOR THE SINTERING MACHINE PALLET

In recent years elastic-plastic fracture mechanics has developed rapidly and is widely used to solve various engineering problems. The application of elastic-plastic fracture mechanics on the pallet of sintering machine is approached in detail for the first time in the present study. The theoretical results were compared with the actual data determined from sintering machine pallet. Results show that good agreement was achieved between the method suggested by the author and the actual data. The basis of determining design of the sintering machine pallet in iron and steel engineering has been provided and it will result in great economic benefits.

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.

An improved form of smoothed particle hydrodynamics method for crack propagation simulation applied in rock mechanics

The simulation of crack propagation processes in rock engineering has been not only a research hot spot among scholars but also a challenge.Based on this background,a new numerical method named improved kernel of smoothed particle hydrodynamics(IKSPH)has been put forward.By improving the kernel function in the traditional smoothed particle hydrodynamics(SPH)method,the brittle fracture characteristics of the base particles are realized.The particle domain searching method(PDSM)has also been put forward to generate the arbitrary complex fissure networks.Three numerical examples are analyzed to validate the efficiency of IKSPH and PDSM,which can correctly reveal the morphology of wing crack and the laws of crack coalescence compared with previous experimental and numerical studies.Finally,a rock slope model with complex joints is numerically simulated and the progressive failure processes are exhibited,which indicates that the IKSPH method can be well applied to rock mechanics engineering.The research results showed that IKSPH method reduces the programming difficulties and avoids the traditional grid distortion,which can provide some references for the application of IKSPH to rock mechanics engineering and the understanding of rock fracture mechanisms.

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.