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 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 GROWTH CRACK ON ELASTIC-ELASTIC POWER LAW CREEPING BIMATERIAL INTERFACE

A mechanical model was established for mode Ⅱ interfacial 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 cracktip 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.     

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     

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

ＥＸＡＣＴＳＯＬＵＴＩＯＮＳＯＦＮＥＡＲＣＲＡＣＫＬＩＮＥＦＩＥＬＤＳＦＯＲＭＯＤＥＩＣＲＡＣＫＵＮＤＥＲＰＬＡＮＥＳＴＲＥＳＳＣＯＮＤＩＴＩＯＮＩＮＡＮＥＬＡＳＴＩＣ－ＰＥＲＦＥＣＴＬＹＰＬＡＳＴＩＣＳＯＬＩＤＥＸＡＣＴＳＯＬＵＴＩＯＮＳＯＦＮＥＡ...     

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...     

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...     

ASYMPTOTIC DYNAMIC SOLUTION TO THE MODE Ⅰ PROPAGATING CRACK-TIP FIELD IN ELASTIC-VISCOPLASTIC MATERIAL

IntroductionItiswell_knownthatinfracturetheory ,itisveryimportanttodeterminethestressandstrainfieldsnearacrack_tip .Byintroducingastressintensityfactor,wecanidentifycompletelythefeatureofcrack_tipfieldforthelinearelasticmaterials.However,itbecomesmuchmorecomplicatedtodeterminethecrack_tipfieldsfornonlinearmaterials,forthefieldsareverysensitivetothematerialbehaviorandcrackstate.Asfarastheauthorknows,theearlieststudyonthegrowingcrack_tipfieldsinplasticmaterialwasgivenbyChitaleyandMcClintock[1]…     

ON THE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF CERTAIN FIFTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS

The sufficient conditions are given for all solutions of certain non- autonomous differential equation to be uniformly bounded and convergence to zero as t →∞ ?. The result given includes and improves that result obtained by Abou-El-Ela & Sadek .     

ASYMPTOTIC DYNAMIC SOLUTION TO THE MODE Ⅰ PROPAGATING CRACK-TIP FIELD IN ELASTIC-VISCOPLASTIC MATERIAL

A new elastic-viscoplastic mode was proposed to analyze the stress and strain fields surrounding the tip of a propagating mode Ⅰ cracks. A proper displacement pattern was suggested and asymptotic equations were derived, and numerical solutions were illustrated. The analysis and calculation show that the crack-tip field is of logarithmic singularity for smaller viscosity, however no solution exists for large viscosity. By a careful analysis and comparison, it is found that the present results retain all merits of those given by Gao Yu-chen, while removing existing problems.     

ASYMPTOTIC NON-STABILITY AND BLOW-UP AT BOUNDARY FOR SOLUTIONS OF A FILTRATION EQUATION

For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.     

THE ASYMPTOTIC SOLUTIONS OF AXISYMMETRICAL PROBLEMS FOR THE CYLINDRICAL SHELLS WITH VARYING WALL THICKNESS

In this paper,the uniformly valid asymptotic solutions of axisymmetrical problems forthe cylindrical shells with varying wall thickness are given.     

SERIES PERTURBATIONS APPROXIMATE SOLUTIONS TO N-S EQUATIONS AND MODIFICATION TO ASYMPTOTIC EXPANSION MATCHED METHOD

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅａｓｙｍｐｔｏｔｉｃｅｘｐａｎｓｉｏｎｍａｔｃｈｅｄｍｅｔｈｏｄｗａｓｄｅｖｅｌｏｐｅｄｏｎｔｈｅｂａｓｉｓｏｆＰｌａｎｄｔｌ’ｓＢｏｕｎｄａｒｙＬａｙｅｒｓＴｈｅｏｒｙ[1- 3].Ｉｎ 1 960’ｓｌａｔｅｒ,ｔｈｅｖａｌｉｄｍａｔｃｈｅｄｐｒｉｎｃｉｐｌｅｓｗｅｒｅａｄｖａｎｃｅｄｂｙＶａｎＤｙｋｅａｎｄＫａｐｌｕｎ[4 ,5 ],ｒｅｓｐｅｃｔｉｖｅｌｙ .Ｂｕｔｔｈｅａｐｐｌｉｃａｂｌｅｒａｎｇｅｏｆｔｈｅｍｅｔｈｏｄｗａｓｒｅｓｔｒｉｃｔｅｄｂｙｔｈｅｄｉｆｆｉｃｕｌｔｙｔｈ…     

A MODE Ⅱ CRACK IN A TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｄｉｓｃｏｖｅｒｙｏｆｑｕａｓｉｃｒｙｓｔａｌａｒｏｕｎｄ 1 984 [1,2 ,3]ｉｓｓｉｇｎｉｆｉｃａｎｔｂｒｅａｋｔｈｒｏｕｇｈｆｏｒｃｏｎｄｅｎｓｅｄｍａｔｔｅｒｐｈｙｓｉｃｓｉｎｒｅｃｅｎｔｙｅａｒｓ.Ｔｈｅｑｕａｓｉｐｅｒｉｏｄｉｃｓｙｍｍｅｔｒｙｏｆｓｏｌｉｄｐｒｅｓｅｎｔｓｇｒｅａｔｔｈｅｏｒｅｔｉｃａｌｓｉｇｎｉｆｉｃａｎｃｅ .Ｎｕｍｅｒｏｕｓｑｕａｓｉｃｒｙｓｔａｌｌｉｎｅｍａｔｅｒｉａｌｓｗｉｔｈｓｔａｂｌｅｐｒｏｐｅｒｔｙｗｅｒｅｐｒｏｄｕｃｅｄ ,ｔｈｉ…     

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.     

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,     

POLYNOMIAL SOLUTIONS TO PIEZOELECTRIC BEAMS (Ⅱ)——ANALYTICAL SOLUTIONS TO TYPICAL PROBLEMS

IntroductionThis paper is a continuation of Ref.[1],in which a series of orthotropic piezoelectricplane problems was solved and the corresponding exact solutions were obtained with the trial-and-error method,on the basis of the general solution expressed …     

GENERAL FORM OF MATCHING EQUATION OF ELASTIC-PLASTIC FIELD NEAR CRACK LINE FOR MODEⅠCRACK UNDER PLANE STRESS CONDITION

ＩｎｔｒｏｄｕｃｔｉｏｎＣｒａｃｋ＿ｌｉｎｅａｎａｌｙｓｉｓｍｅｔｈｏｄｗａｓｏｒｉｇｉｎａｌｌｙｐｒｏｐｏｓｅｄｂｙＡｃｈｅｎｂａｃｈａｎｄＬｉ[1]ａｎｄｗａｓｆｕｒｔｈｅｒｓｔｕｄｉｅｄｂｙＧＵＯａｎｄＬＩ[2 ].Ｈｏｗｅｖｅｒ,ｔｈｅｅａｒｌｉｅｒｃｒａｃｋｌｉｎｅｆｉｅｌｄａｎａｌｙｓｉｓｍｅｔｈｏｄｓｏｌｖｅｓｔｈｅｐｒｏｂｌｅｍｂｙｍａｔｃｈｉｎｇａｓｐｅｃｉｆｉｃｓｏｌｕｔｉｏｎｏｆｐｌａｓｔｉｃｆｉｅｌｄｎｅａｒｃｒａｃｋｌｉｎｅｗｉｔｈｅｌａｓｔｉｃｓｉｎｇｕｌａｒＫｆｉｅｌｄｎｅ…