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

IntroductionTherearesomeinterfacesinpracticeengineering ,forinstance ,thereareinterfacesbetweenmud_rocklayerwhichhascreepingcharacterindeformationandelasticrocklayer.Oneimportantreasonforthefailureofcasingofoilandwaterwellsisthecreepandglidingofmud_rockalongelasticrocksurface[1].ResearchesofproblemofModeⅡstationarygrowthcrackonelastic_elasticpowerlawcreepingbimaterialinterfacehaveboththeoreticalandengineeringsignificance .Theproblemofinterfacecrackbetweentwoelasticmaterialhadbeenfirstlystudi…     

ASYMPTOTIC ANALYSIS OF MODE Ⅱ STATIONARY GROWTHCRACK ON ELASTIC-ELASTIC POWER LAWCREEPING BIMATERIAL INTERFACE

A mechanical model was established for mode Ⅱ interfacial crack static growingalong an elastic-elastic power law creeping bimaterial interface. For two kinds of boundaryconditions on crack faces, traction free and frictional contact, asymptotic solutions of thestress and strain near tip-crack were given. Results derived indicate that the stress andstrain have the same singularity, there is not the oscillatory singularity in the field; thecreep 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 ofstresses and strains in region of elastic material. When n is bigger, the creepingdeformation 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.     

ASYMPTOTIC ANALYSIS OF PLANE-STRAIN MODE I STEADY-STATE CRACK GROWTH IN TRANSFORMATION TOUGHENINGCERAMICS(Ⅱ)

I.IntroductionThemechanismoffracturetoughnessenhancementinceramicshasbeenwidelystudiedsincetheearlyl98Os.ThepioneeringconstitutivemodeldevelopedbyBudianskyetal.ll1includestheeffectofplasticdiIation,butneglectsthetransformation-inducedshearstrain.Andtheirc…     

ASYMPTOTIC ANALYSIS OF PLANE-STRAIN MODE I STEADY-STATE CRACK GROWTH IN TRANSFORMATION TOUGHENING CERAMICS(Ⅱ)

Based on a constitutive law which includes the shear components of transformation plasticity, the asymptotic solutions to near-tip fields of plane-strain mode I steadity propagating cracks in transformed ceramics are obtained for the case of linear isotropic hardening. The stress singularity, the distributions of stresses and velocities at the crack tip are determined for various material parameters. The factors influencing the near-tip fields are discussed in detail.Project supported by the National Natural Science Foundation of China     

DYNAMIC PROPAGATION PROBLEM ON DUGDALE MODEL OF MODE Ⅲ INTERFACE CRACK

By the theory of complex functions, the dynamic propagation problem on Dugdale model of mode Ⅲ interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are obtained by the methods of self-similar functions. The problems dealt with can be easily transformed into Riemann-Hilbert problems and their closed solutions are attained rather simply by this approach. After those solutions were utilized by superposition theorem, the solutions of arbitrarily complex problems could be obtained.     

INTERACTION OF A DISLOCATION DIPOLE WITH A MODE III INTERFACE CRACK

Interaction between a screw dislocation dipole and a mode III interface crack is investigated. By using the complex variable method, the closed form solutions for complex potentials are obtained when a screw dislocation dipole lies inside a medium. The stress fields and the stress intensity factors at the tip of the interface crack produced by the screw dislocation dipole are given. The influence of the orientation, the dipole arm and the location of the screw dislocation dipole as well as the material mismatch on the stress intensity factors is discussed. The image force and the image torque acting on the screw dislocation dipole center are also calculated. The mechanical equilibrium position of the screw dislocation dipole is examined for various material property combinations and crack geometries. The results indicate that the shielding or anti-shielding effect on the stress intensity factor increases abruptly when the dislocation dipole approaches the tip of the crack. Additionally, the disturbation of the interface crack on the motion of the dislocation dipole is also significant.     

INTERACTION OF A DISLOCATION DIPOLE WITH A MODE Ⅲ INTERFACE CRACK

Interaction between a screw dislocation dipole and a mode Ⅲ interface crack is investigated. By using the complex variable method, the closed form solutions for complex potentials are obtained when a screw dislocation dipole lies inside a medium. The stress fields and the stress intensity factors at the tip of the interface crack produced by the screw dislocation dipole are given. The influence of the orientation, the dipole arm and the location of the screw dislocation dipole as well as the material mismatch on the stress intensity factors is discussed. zThe image force and the image torque acting on the screw dislocation dipole center are also calculated. The mechanical equilibrium position of the screw dislocation dipole is examined for various material property combinations and crack geometries. The results indicate that the shielding or anti-shielding effect on the stress intensity factor increases abruptly when the dislocation dipole approaches the tip of the crack. Additionally, the disturbation of the interface crack on the motion of the dislocation dipole is also significant.     

A CATASTROPHE ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

This paper presents an attempt at the application of catastrophe theory to the stabilityanalysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions ofJ-integral in the completely yielding state for the ideal plastic material, the critical condition of losingstability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory.The process of the crack growth from geometrical sense is described.     

MICROMECHANICS ANALYSIS ON EVOLUTION OF CRACK IN VISCOELASTIC MATERIALS

ＩｎｔｒｏｄｕｃｔｉｏｎＡｓｓｈｏｗｎｂｙＺＨＡＮＧａｎｄＸＩＯＮＧ ( 1 997) [1],ｕｎｄｅｒｃｏｎｓｔａｎｔｌｏａｄｉｎｇｔｈｅｃｒａｃｋｉｎｖｉｓｃｏｅｌａｓｔｉｃｍａｔｅｒｉａｌｓｈａｓａｎｉｎｃｕｂａｔｉｏｎｔｉｍｅ ,ｗｉｔｈｉｎｉｔｔｈｅｃｒａｃｋｏｐｅｎｉｎｇｄｉｓｐｌａｃｅｍｅｎｔ (ＣＯＤ)ｉｓｃｈａｎｇｉｎｇｌａｒｇｅｒｗｉｔｈｔｉｍｅ,ｗｈｉｌｅｔｈｅｃｒａｃｋｌｅｎｇｔｈｋｅｅｐｓｃｏｎｓｔａｎｔ.Ｉｎｖｅｓｔｉｇａｔｉｏｎｏｎｔｈｅｇｒａｄｕａｌｏｐｅｎｉｎｇｏｆｔｈｅｃｒａｃ…     

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

ＴＨＥＥＸＡＣＴＳＯＬＵＴＩＯＮＳＯＦＥＬＡＳＴＩＣ－ＰＬＡＳＴＩＣＣＲＡＣＫＬＩＮＥＦＩＥＬＤＦＯＲＭＯＤＥＩＩＰＬＡＮＥＳＴＲＥＳＳＣＲＡＣＫＹｉＺｈｉｊｉａｎ（易志坚）ＷａｎｇＳｈｉｊｉｅ（王士杰）ＷａｎｇＸｉａｎｇｊｉａｎ（王向坚）（Ｒｅｃｅ...     

ON THE PLANE PIEZOELECTRIC PROBLEM OF A LOADED CRACK TERMINATING AT A MATERIAL INTERFACE

The plane problem of a crack terminating at the interface of a bimaterial piezoelectric,and loaded on its faces, is treated. The emphasis is placed on how to transform this problem into anon-homogeneous Hilbert problem. To make the derivation tractable, the concept of the axial conju-gate is introduced and related to the complex conjugate. The angle between the crack line and the inter-face may be arbitrary. Numerical results are given to illustrate the stress singularity at crack tip.     

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

ＴＨＥＥＸＡＣＴＳＯＬＵＴＩＯＮＳＯＦＥＬＡＳＴＩＣ－ＰＬＡＳＴＩＣＣＲＡＣＫＬＩＮＥＦＩＥＬＤＦＯＲＭＯＤＥⅡＰＬＡＮＥＳＴＲＥＳＳＣＲＡＣＫＹｉＺｈｉｊｉａｎ（易志坚）ＷａｎｇＳｈｉｊｉｅ（王士杰）ＷａｎｇＸｉａｎｇｊｉａｎ（王向坚）（Ｒｅｃｅｉ...     

A DISCUSSION ABOUT THE EFFECTIVENESS ON USING A VARIATE-TRANSFORMATION TO FIND OUT SOLUTIONS OF MODE Ⅲ CRACK PROBLEMS IN POWER HARDENING MEDIA

By the use of the transformations of physical plane to strain plane and physical planeto stress plane,an analytic expression of the asymptotic solution near a modeⅢcrack tipin a power hardening medium can be obtained.In this paper the effectiveness of thetransformation is discussed.Analytical results show that the transformation is effectiveexcept for a special limit case of power hardening media—the ideal plastic materials.     

DISCUSSIONS ON“AN ASYMPTOTIC ELASTIC PLASTIC ANALYSIS IN PLANE STRAIN DEFORMATION NEAR A CRACK TIP”

I.In his paper,prof.D.W.Hsueh derived the following functionf(θ)=-[(1 2n)/(1 n)~2-k_1~2]A_1/k_1θ-[(1 2n)/(1 n)~2-k_2~2]A_2/k_2-cosk_2θ(1)In calculation of coefficients A_1,A_2 a mistake occurred.Making use of f′(π)=0 andf(0)=0,     

AN INVESTIGATION ON ASYMPTOTIC NEAR-TIP FIELDS OF DYNAMIC CRACK IN AN ELASTIC-PERFECTLY PLASTIC COMPRESSIBLE MATERIAL

The stress and deformation fields near the tip of a mode-I dynamic crack steadilypropagating in an elastic-perfectly plastic compressible material are considered under plane strain condi-tions. Within the framework of infinitesimal displacement gradient theory, the material is character-ized by the Von Mises yield criterion and the associated J_2 flow theory of plasticity. Through rigorousmathematical analysis, this paper eliminates the possibilities of elastic unloading and continuousasymptotic fields with singular deformation, and then constructs a fully continuous and boundedasymptotic stress and strain field. It is found that in this solution there exists a parameter (?)_0 whichcannot be determined by asymptotic analysis but may characterize the effect of the far field. Lastly thevariations of continuous stresses, velocities and strains around the crack tip are given numerically fordifferent values of (?)_0.     

POWER LAW DISTRIBUTION AND SELF-ORGANIZED CRITICALITY OF DISPERSED PARTICLES

Research on particulate characteristics has been an important frontier in physics and chemistry during the past decades. It has however been mostly focused on granular materials with short-range interactions. In this work, it was found that the power law of particle size distribution applied to the long-range interacting system of floating dust in air, from which we deduced that self-organized criticality might hold for floating dust just as granular materials with short-range interactions. This feature may reveal underlying kinetic mechanisms, important in dispersed particle systems. In industry, power law of size distribution of dispersed particles can be used to investigate the change of dust size, and the power law parameter could be taken as an important index for dust separation.     

ANALYSIS OF SURFACE CRACK ON FORWARD EXTRUDING BAR DURING AXISYMMETRIC CUP-BAR COMBINED EXTRUSION PROCESS

In this paper,the kinematically admissible velocity field with surface crack on forwardextruding bar is put forward during the axisymmetric cup-bar combined extrusion process,in accordance with the results of model experiments.On the basis of velocity field,the necessary condition for surface crack formation onthe forward extruding bar is derived,with the help of upper bound theorem and theminimum energy principle.Meanwhile,the relationships between surface crack formationand combination of reduction in area for the part of forward and backward extursions(εb,εf),relative residual thickness of billet(T/R_0),frictional factor(m)or relativeland length of ram and chamber(l_b/R_0,l_f/R_0)are calculated during the extrusion process.Therefore,whether the surface crack on forward exturding bar occurs can be predictedbefore extruding the lower-plasticity metals for axisymmetric cup-bar combined extrusionprocess.The analytical results agree very well with experimental results of aluminium alloyLY12 (ASTM2024)an     

ASYMPTOTIC ANALYSIS OF A CLASS OF NONLINEAR OSCILLATION EQUATION IN ELECTRICAL ENGINEERING

ＡＳＹＭＰＴＯＴＩＣＡＮＡＬＹＳＩＳＯＦＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＯＳＣＩＬＬＡＴＩＯＮＥＱＵＡＴＩＯＮＩＮＥＬＥＣＴＲＩＣＡＬＥＮＧＩＮＥＥＲＩＮＧＣｈｅｎｇＹｏｕ－ｌｉａｎｇ（程友良）（ＤｅｐａｒｔｍｅｎｔｏｆＦｕｎｄａｍｅｎｔａｌＣｏｕ...     

ANALYSIS ON IMPACT RESPONSES OF UNRESTRAINED PLANAR FRAME STRUCTURE(Ⅱ)—NUMERICAL EXAMPLE ANALYSIS

By using the formula derived in Part （ Ⅰ ）, the instant response of an unrestrained planar frame structure subjected to the impact of a moving rigid-body are evaluated and analysed. The impact force-time history between the structure and the moving rigid-body, shear force and bending moment distribution along the beams, axial force distribution along the bars were calculated. The wave propagation phenomena of the longitudinal wave in the bars, the flexural and shear waves in the beams were also analysed. The numerical results show that the time duration of impact force is controlled by the flexural wave and the longitudinal wave ; the shear effect in beams should not be neglected in the impact response analysis of structures.