A MODE-Ⅱ GRIFFITH CRACK IN DECAGONAL QUASICRYSTALS

By using the method of stress functions, the problem of mode-Ⅱ Griffith crack in decagonal quasicrystals was solved. First, the crack problem of two-dimensional quasi-crystals was decomposed into a plane strain state problem superposed on anti-plane state problem and secondly, by introducing stress functions, the 18 basic elasticity equations on coupling phonon-phason field of decagonal quasicrystals were reduced to a single higher- order partial differential equations. The solution of this equation under mixed boundary conditions of mode-Ⅱ Griffith crack was obtained in terms of Fourier transform and dual integral equations methods. All components of stresses and displacements can be expressed by elemental functions and the stress intensity factor and the strain energy release rate were determined.

A PENNY-SHAPED CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SOLID:MODES Ⅱ AND Ⅲ PROBLEMS

An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solution of three-dimensional piezoelasticity and the four harmonics involved are represented by one complex potential.Previous results in potential theory are then utilized to obtain the exact solution that is expressed in terms of elementary functions.Comparison is made between the current results with those published and good agreement is obtained.

In-plane shear(ModeⅡ) crack sub-critical propagation of rock at high temperature

In-plane shear crack sub-critical propagation of rock at high temperature was studied by finite element method and shear-box(i.e.compression-shear) test with newly designed electrically conductive adhesive method.Numerical and experimental results show that the normalized shear(Mode Ⅱ) stress intensity factors,K ⅡT/KT0 is decreased as the temperature increases because high temperature can improve stress distribution at crack tip and reduce the Mode Ⅱ stress intensity factor.Microscopic features of fractured surface are of little pits and secondary micro-cracks in the vicinity(1.5-4.0 mm) of the crack tip.The chevron-shape secondary cracks gradually merge in the length of about 4-5 mm and disappear along the direction of crack propagation.Stable shear crack propagation time is increased with the increasing temperature while the stable shear crack propagation rate is decreased with the increasing temperature,since high temperature can increase the shear(Mode Ⅱ) fracture toughness and prevent the crack growth.It is necessary to ensure the ligament of specimen long enough to measure the maximum unstable crack propagation rate of rock.

Effect of holes on in-plane shear(Mode Ⅱ) crack sub-critical propagation of rock

Shear-box(i.e.compression-shear) test and newly designed electrically conductive adhesive method were used to measure shear crack sub-critical propagation time and rate of sandstone specimen.Different cubic specimens with and without holes were tested to study the effect of holes on the shear crack sub-critical propagation.Numerical and experimental results show that three independent variables of hole,the interval distance S,the distance between the center of hole and the crack tip L,and hole radius R,have different contribution to the ratio of stress intensity factor of the specimen with holes to that of the specimen without hole,KⅡ/KⅡ0.Increasing S and decreasing L and R will result in the decrease of KⅡ/KⅡ0 and help crack arrest.The weight relation of the independent variables for KⅡ/KⅡ0 is S>L>R.The specimen DH3 with the largest value of S and the smallest values of L and R has the longest sub-critical crack propagation time and the smallest sub-critical crack propagation rate.Adding two suitable holes symmetrically to the original crack plane in rock specimen is considered to be a potential method for crack arrest of rock.

Interface crack problems for mode Ⅱ of double dissimilar orthotropic composite materials

The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.

General forms of elastic-plastic matching equations for mode-Ⅲ cracks near crack line

Crack line analysis is an effective way to solve elastic-plastic crack problems. Application of the method does not need the traditional small-scale yielding conditions and can obtain sufficiently accurate solutions near the crack line. To address mode- Ⅲ crack problems under the perfect elastic-plastic condition, matching procedures of the crack line analysis method axe summarized and refined to give general forms and formulation steps of plastic field, elastic-plastic boundary, and elastic-plastic matching equations near the crack line. The research unifies mode-III crack problems under different conditions into a problem of determining four integral constants with four matching equations. An example is given to verify correctness, conciseness, and generality of the procedure.

Crack initiation ahead of piled-up of dislocations emitted from a mode Ⅱ blunt crack

In situ tensile tests in a transmission electronmicroscope(TEM)show that dislocations emitted from a modelⅡcrack tipwill form a inverse piled-up group after equilibrium or a doublepiled-up group when they meet a obstruction, e.g., grain boundary orsecond phase. A microcrack can initiates in front of the piled-upgroup of dislocations. Micromechanics analysis shows thatdislocations emitted from a modelⅡblunt crack tip can form a inversepiled-up or double piled-up group, depending upon the applied stressintensity factor K_Ⅱa, lattice friction stressτ_f and the distanceof the obstruction from the crack tip L.

Crack-tip field on mode Ⅱ interface crack of double dissimilar orthotropic composite materials

Two systems of non-homogeneous linear equations with 8 unknowns are obtained.This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions.By solving the above systems of non-homogeneous linear equations,the two real stress singularity exponents can be determined when the double material parameters meet certain conditions.The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit.By substituting these parameters into the corresponding mechanics equations,theoretical solutions to the stress intensity factor,the stress field and the displacement field near the crack tip of each material can be obtained when both discriminants of the characteristic equations are less than zero.Stress and displacement near the crack tip show mixed crack characteristics without stress oscillation and crack surface overlapping.As an example,when the two orthotropic materials are the same,the stress singularity exponent,the stress intensity factor,and expressions for the stress and the displacement fields of the orthotropic single materials can be derived.

A MODE Ⅱ CRACK IN A TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS

The present study develops the fracture theory for a two-dimensional octagonal quasicrystals. The exact analytic solution of a Mode Ⅱ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate were determined, the physical sense of the results relative to phason and the difference between mechanical behaviors of the crack problem in crystal and quasicrystal were figured out. These provide important information for studying the deformation and fracture of the new solid phase.

ROUGHNESS-INDUCED SHEAR RESISTANCE OF MODE Ⅱ CRACK GROWTH

It is obtained in this paper that the fatigue threshold value of mode H was 1.9 times of that of mode Ⅰ in dual-phase steel(DPS),and the normal stress intensity factor range oJ mode Ⅱ branch crack tip was 2.2 times of that of mode Ⅰ.Above results illustrate that the resistance of mode Ⅱ crack growth was higher than that of mode Ⅰ,the former resulting from roughness-induced shear resistance,the latter,crack closure. The mode Ⅱ component can play two important roles in near-threshold fatigue crack growth:(1)increasing crack tip plasticity which accelerates the crack growth and(2)intro- ducing crack surface contact and rubbing to reduce the crack propagation rate.By means of crack closure,the quantity of shear resistance was easily solved in this paper.The friction shear stress strength factor range of mode Ⅱ,K_,is still much higher than the closure stress strength factor range of mode Ⅰ,K_(Ⅰ,cl).This illustrated that the roughness enlarged the second role and played a role of shielding crack tip from mode Ⅱ crack.

(Ⅰ+Ⅱ)MIXED MODE HYDROGEN INDUCED CRACKING

Hydrogen induced cracking(HIC)of 0.3% C,1% Cr,1% Mn,1% Si high strength steel has been studied under simple mode Ⅰ,mode Ⅱ and(Ⅰ+Ⅱ)mixed mode loading conditions.Af- ter being hydrogen-charged in IN H_2SO_4 solution,the material behaved hydrogen embrittlement in all the cases studied.The threshold K_(ⅡH)/K_(ⅡX) of HIC under mode Ⅱ load- ing was 0.27,which was nearly the same as that K(ⅠH)/K_(ⅠX)=0.29 under mode Ⅰ loading. While the thresholds of-HIC under(Ⅰ+Ⅱ)mixed mode loading were 0.36,0.41 and 0.37 cor- responding to the K_Ⅱ/K_Ⅰ ratio of 0.27,0.4 and O.81.The results show that simple mode Ⅰ or mode Ⅱ loading is more susceptible to hydrogen embrittlement than(Ⅰ+Ⅱ)mixed mode. For explaining the experimental results,the effects of triaxial stress as well as plastic deformation ahead of crack tip has been discussed.

Simultaneously measuring initiation toughness of pure mode Ⅰ and mode Ⅱ cracks subjected to impact loads

In order to simultaneously measure the initiation toughness of pure mode Ⅰ and mode Ⅱ cracks in one specimen,a large-size double-cracked concave-convex plate(DCCP)specimen configuration was proposed.Impacting tests were implemented in the drop plate impact device.Strain gauges were employed to measure impact loads and crack initiation time.The corresponding numerical model was established by using the dynamic finite difference program AUTODYN,and the experimental-numerical method and ABAQUS code were utilized to obtain the initial fracture toughness of the crack.Using experiments and numerical research,we concluded that the DCCP specimen is suitable for measuring the initial fracture toughness of pure mode Ⅰ and mode Ⅱ cracks at the same time;the dynamic initiation toughness increases with the increase of loading rate and the crack initiation time decreases with increasing loading rate;the initiation toughness of mode Ⅱ crack is 0.5 times that of mode Ⅰ crack when subjected to the same loading rate.For the pre-crack in the vicinity of the bottom of a sample,when its length increases from 20 to 100 mm,the dynamic initiation toughness of the pure mode Ⅰ crack gradually decreases,and the longer the lower crack length is,the easier the crack would initiate,but the dynamic initiation toughness of pure mode Ⅱ crack varies little.

EFFECT OF TEMPERATURE ON THE FRACTURE MODES OF BHW-35 STEEL UNDER MODE-Ⅱ LOADING

Finite element method(FEM)has been used to analyze the stress and strain fields and the stress tri-axial levels around the tip of the crack under mode-Ⅱ loading.The results show that: under mode-Ⅱ loading,the direction of the maximum tensile stress and that of the maximum tri-axial levels(R_ )exist at an angle of-75.3°from the original crack plane:the maximum shear stress and R_ =0 exist along the original crack plane. Mode-Ⅱ loading experiment using BHW-35 steel at different temperatures show that there are two kinds of fracture mode.opening mode(or tensile mode)and sliding mode(or shear mode).A de- crease in temperature causes the fracture mode to change from shear mode to tensile mode.For BHW- 35 steel,this critical temperature is about-90C.Actually.under any kind of loading mode(mode Ⅰ,mode Ⅱ,mode Ⅲ or mixed mode),there always exist several kinds of potenital fracture modes (for example,opening mode.sliding mode.tearing mode or mixed mode).The effect of temperature under mode-Ⅱ loading is actually related to the change of the elastic-plastic properties of the material.

ASYMPTOTIC ANALYSIS OF MODE Ⅱ STATIONARY GROWTH CRACK ON ELASTIC-ELASTIC POWER LAW CREEPING BIMATERIAL INTERFACE

A mechanical model was established for modeⅡinterfacial crack static growing along an elastic_elastic power law creeping bimaterial interface. For two kinds of boundary conditions on crack faces, traction free and frictional contact, asymptotic solutions of the stress and strain near tip_crack were given. Results derived indicate that the stress and strain have the same singularity, there is not the oscillatory singularity in the field; the creep power_hardening index n and the ratio of Young's module notably influence the crack_tip field in region of elastic power law creeping material and n only influences distribution of stresses and strains in region of elastic material. When n is bigger, the creeping deformation is dominant and stress fields become steady,which does not change with n. Poisson's ratio does not affect the distributing of the crack_tip field.

The crack tip fields of Mode Ⅱ stationary growth crack on bimaterial interface

A mechanical model is established for mode II interfacial crack static growing along an elastic-elastic power law creeping bimaterial interface. For frictional contact of boundary conditions on crack faces, asymptotic solutions of the stresses and strains of near tip-crack are got. It was shown that in stable creep growing phase, elastic deformation and viscous deformation are equally dominant in the near-tip field, the stress and strain have the same singularity and there is not the oscillatory singularity the field. Through numerical calculation , it is shown that the frictional coefficient η notably influence the crack-tip field.

THE EXACT SOLUTIONS OF ELASTIC－PLASTIC CRACK LINE FIELD FOR MODE Ⅱ PLANE STRESS CRACK

The near crack line field analysis method has been used to investigate into the exact elastic-plastic solutions of a mode Ⅱ crack under plane stress condition in anelastic-perfectly plastic solid. The assumptions of the usual small scale yielding theoryhave been completely. dbandoned and the correct .formulations of matching conditionsat the elastic-plastic boundary have been given. By matching the general solution of the plastic stress field (but not the special solution used to be adopted) will the exactelastic stress field (but not the crack tip K-dominant field) at the elastic-plasticboundary. near the crack line, the plastic .stresses, the length of the plastic zone and theunit normal vector of the elaslic-plastic boundary. which sufficiently precise nearthe crack line region, hare been given.

混凝土Ⅱ型断裂的FCM和断裂能

本文讨论了混凝土Ⅱ型断裂的机理,并给出了一个产生Ⅱ型断裂的充分条件.从而,提出了Ⅱ型虚拟裂纹模型(FCM).并据此用有限元计算了属于Ⅱ型的剪切断裂能和压剪断裂能.在用刚性加载架对混凝土试样测得剪切荷载-切口相对位移全曲线的基础上,获得了剪切断裂能和压剪断裂能的试验值,它与电算值相当接近.试验结果表明,混凝土Ⅱ型断裂能约为Ⅰ型断裂能的20倍.

正交异性双材料的Ⅱ型界面裂纹尖端场

通过引入含16个待定实系数和两个实应力奇异指数的应力函数,再借助边界条件,得到了两个八元非齐次线性方程组.求解该方程组,在双材料工程参数满足适当条件下,确定了两个实应力奇异指数.根据极限唯一性定理,求出了全部系数,得到了应力函数的表示式.代入相应的力学公式,推出了当特征方程组两个判别式都小于0时,每种材料的裂纹尖端应力强度因子、应力场和位移场的理论解.裂纹尖端附近的应力和位移有混合型断裂特征,但没有振荡奇异性和裂纹面相互嵌入现象.作为特例,当两种正交异性材料相同时,可以推出正交异性单材料Ⅱ型断裂的应力奇异指数、应力强度因子公式、应力场、位移场表示式.

Ⅱ型荷载下混凝土剪切断裂的测试研究

有关混凝土的断裂行为己被广泛研究,但很少是针对剪切断裂的情况.本文采用 型(四点剪切)加载,进行一系列测试,研究了混凝土单边预制裂纹(SEN)直梁剪切断裂的技术和条件.初步实现了混凝土的剪切断裂,测得混凝土的 型断裂韧度因子K C.实验结果显示,试件的几何尺寸越大,养护的龄期越长,实验效果越理想,在这两个因素中,试件尺寸的影响更明显.此外,混凝土的配合比与粗集料对测试结果也有重要影响,而细集料的影响似乎并不明显.同时,文中对实验结果进行了详细的分析,最后,得出一些具有工程实用价值的结论.

A-Ⅸ-Ⅱ压装炸药失效模式分析

为了探讨A-Ⅸ-Ⅱ压装炸药的失效模式,通过扫描电镜、工业CT分别对低装药密度、中装药密度和高装药密度A-Ⅸ-Ⅱ炸药装药在高低温循环温度应力施加下的结构稳定性进行分析研究,并讨论了裂纹和"渗油"两种结构失稳模式。研究表明A-Ⅸ-Ⅱ压装炸药的主要失效模式是药柱产生裂纹,"渗油"引起的结构失稳是否会导致装药失效还有待进一步研究。