THE PRECISE AND NEW ANALYSIS FOR A MODE Ⅲ GROWING CRACK IN AN ELASTIC-PERFECTLY PLASTIC SOLID

The near crack line field analysis method has been used to investigate into ModeⅢ quasistatically propagating crack in an elastic-perfectly plastic material.Thesignificance of this paper is that the usual small scale yielding theory has been brokenthrough.By obtaining the general solutions of the stresses and the displacement rate ofthe near crack line plastic region,and by matching the general solutions with theprecise elastic fields(not the usual elastic K-dominant fields)at the elastic-plasticboundary,the precise and new solutions of the stress and deformation fields,the sizeof the plastic region and the unit normal vector of the elastic-plastic boundary havebeen obtained near the crack line.The solutions of this paper are sufficiently precisenear the crack line region because the roughly qualitative assumptions of the smallscale yielding theory have not been used and no other roughly qualitative assumptionshave been taken,either.The analysis of this paper shows that the assumingly“steady-state cas     

THE MEASUREMENT OF PLASTIC DEFORMATION AND CRACK GROWTH IN CRACKED SPECIMENS BY SAM

In this paper,scanning acoustic microscope(SAM) was used to obtainsome characteristic photographs which explain the mesoscopic information of severalcracked specimens.New results on subsurface information of steel,nickel andaluminium were presented.Plastic deformation and crack initiation were observed andanalysed.The length of crack propagation was measured.SAM is particularly suited tothe study of many mesoscopic phenomena in material science because it can imagemesoscopic subsurface feature without sectioning.It is revealed that SAM has a brightfuture in the field of mesomechanics.     

THE CREEPING MOTION IN THE ENTRY REGION OF A SEMI-INFINITE CIRCULAR CYLINDRICAL TUBE

In 1969,Lew and Fung[1]considered the inlet flow into a se-mi-infinite circular cylinder at low Reynolds number.Dagan etal.[2]in1982 obtained a series solution for the creeping motionthrough a pore of finite length directly.The numerical resultsobtained in[1]also describe the entrance flow in a tube of afinite length as the Fourier integrals in the general solutions arereplaced by Fourier series.In the present paper,the Fourier in-tegralss are evaluated numerically and the velocity,pressure dis-tribution and the stream function in the entry region of a semi-infinite circular cylindrical tube is close to the factor1.3 sug-gested by Lew and Fung[1].The collocation technique applied inthe present paper is shown to converge rapidly and it should beuseful in other similar problems.     

THE FULLY PLASTIC J-INTEGRAL OF CORNER CRACKS AT A HOLE IN A PLATE

The line-spring model of surface cracks is applied to the fully plastic analysis of cornercracks at a hole in a plate.The generalized fully plastic constitutive relations and the fully plastic J-in-tegral,as well as its coefficients in polynomial expressions are given.The model obtained is incorpo-rated into a finite element program.The corner cracks at a hole in a plate subjected pure tensions arecalculated by the present model.The fully plastic J-integral is then estimated.The results obtainedshow that the line-spring model is effective for the analysis of corner cracks.The influence of thecrack depth and the hardening exponent on the fully plastic J-integral is also discussed.     

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.     

THE EXACT SOLUTIONS OF VON MISES YIELDING CRITERION FOR IDEALLY PLASTIC BODY UNDER UNIFORM PRESSURE IN CASE OF PLANE STRAIN

This problem is solved by dividing the quadratic yielding cri-terion into two linear partial differential equations.With thehelp of Cauchy’s integral.these two linear equations can be easilysolved.An example is given to show the calculation of the stresscomponents in the plastic domain and the determination of equationof the boundary line between the plastic and elastic domains.     

ANALYSIS OF THE DYNAMIC BEHAVIOR OF A GRIFFITH PERMEABLE CRACK IN PIEZOELECTRIC MATERIALS WITH THE NON-LOCAL THEORY

The dynamic behavior ofa Griffith permeable crack under harmonic anti-plane shearwaves in the piezoelectric materials is investigated by use of the non-local theory.To overcome themathematical difficulties,a one-dimensional non-local kernel is used instead of a two-dimensionalone for the anti-plane dynamic problem to obtain the stress and the electric displacement near thecrack tips.By means of Fourier transform,the problem can be solved with a pair of dual integralequations that the unknown variable is the jump of the displacement across the crack surfaces.These equations are solved with the Schmidt method and numerical examples are provided.Con-trary to the previous results,it is found that no stress and electric displacement singularities arepresent at the crack tip.The finite hoop stress and the electric displacement depend on the cracklength,the lattice parameter of the materials and the circle frequency of the incident waves.Thisenables us to employ the maximum stress hypothesis to deal with fracture problems in a naturalway.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(II)—THE ANALYSES OF THE STRESS STRUCTURE

Based on [1], the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper. The characteristics of the stress structure in the smooth region have been found that the variable z can separated out; the stresses in the midsection can be obtained by the plane strain FEM results or HRR structure modified by the stress triaxiality. The effects of load level and thickness on the stress structure can be reflected by the distribution of CTOD along the thickness direction. The obtained expressions of the stresses are very simple and visualized. The analyses of the stress structure in the shear lip show that the stresses can be obtained by different methods of interpolation to a certain precise degree. A new degree parameter of the plane strain state has been put forward and studied. The parameter can reflect relatively well the variation of the kind and thickness of the specimen as well as the load level. The fracture parameter has also been investigated to be sure that it can be obtained by modified CTOD with the stress triaxiality.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE Ⅰ CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅱ)—THE ANALYSES OF THE STRESS STRUCTURE

Based on[1],the stress structures of the smooth region and shear lip of thespecimens have been investigated in the paper.The characteristics of the stress structure inthe smooth region have been found that the variable z can separated out;the stressesin the midsection can be obtained by the plane strain FEM results or HRR structuremodified by the stress triaxiality.The effects of load level and thickness on the stressstructure can be reflected by the distribution of CTOD along the thickness direction.The obtained expressions of the stresses are very simple and visualized.The analysesof the stress structure in the shear lip show that the stresses can be obtained bydifferent methods of interpolation to a certain precise degree.A new degree parameter of the plane strain state has been put forward andstudied.The parameter can reflect relatively well the variation of the kind andthickness of the specimen as well as the load level.The fracture parameter has alsobeen investigated to be sure that it can be obta     

THE COUPLE MOTION BETWEEN VESSEL WALL AN DBLOOD IN THE ENTRANCE REGION OF A TAPERED VESSEL

ＴＨＥＣＯＵＰＬＥＭＯＴＩＯＮＢＥＴＷＥＥＮＶＥＳＳＥＬＷＡＬＬＡＮＤＢＬＯＯＤＩＮＴＨＥＥＮＴＲＡＮＣＥＲＥＧＩＯＮＯＦＡＴＡＰＥＲＥＤＶＥＳＳＥＬＣｅｎＲｅｎ－ｊｉｎｇ（岑人经）ＱｉｎＣｈａｎ（秦婵）ＴａｎＺｈｅ－ｄｏｎｇ（谭哲东）（ＳｏｕｔｈＣ...     

THE BOUNDARY INTEGRAL-VARIATIONAL THEOREMS OF AN ARBITRARY ELEMENT IN THE SOLID—COMPUTE THE ENERGY RELEASE RATE OF AN ARBITRARY CRACK EXTENSION

Based on the solid mechanics of the discrete form and its variational principles proposed by Niu^[1–2], this paper puts forward four kinds of boundary integral-variational theorems of an arbitrary element. In the course of the fracture analysis, they can be used to compute the energy release rate along the normal direction of the crack boundary. When there is a hole in the solid, and whether there are given surface forces on the hole boundary or not they can be used to compute the variation of the energy along the normal direction of the hole boundary. In the course of the discrete analysis, they can be used to establish the discrete equations, so that the values of the unknown functions are solved. At the same time, from this paper we know that the J-integral proposed by Rice^[3] represents an integral to be independent of a path imperfectly.     

THE BOUNDARY INTEGRAL-VARIATIONAL THEOREMS OF AN ARBITRARY ELEMENT IN THE SOLID—COMPUTE THE ENERGY RELEASE RATE OF AN ARBITRARY CRACK EXTENSION

Based on the solid mechanics of the discrete form and its variational principles proposed by Niu, this paper puts forward four kinds of boundary integral-variational theorems of an arbitrarg element.In the course of the fracture analysis, they can be used to compute the energy release rate along the normal direction of the crack boundary. When there is a hole in the solid, and whether there are given surface forces on the hole boundary or not they can be used to compute the variation of the energy along the normal direction of the hole boundary. In the course of the discrete analysis, they can be used to establish the discrete equations, so that the values of the unknown functions are solved. At the same time, from this paper we know that the J-integral proposed by Rice represents an integral to be independent of a path imperfectly.     

ON THE LAW OF ENERGY CONSERVATION IN THE CLASSICAL ELECTRODYNAMICS OF DEFORMABLE MEDIA——A GENERALIZATION OF THE POYNTING THEOREM

This paper establishes the generalized Poynting theorem for the electrodynamics of deformable media with a view to shedding some light on the detailed mechanism of energy transfer between the electromagnetic field and the deformable media. Global field equations are chosen as the starting point and specialized forms of the theorem are derived based on the special postulates for the electromagnetic body force.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)—THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper, three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip. of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program. The results reveal that the constraints along the thickness direction are obviously separated into two parts: the keeping similar high constraint field (Z₁) and rapid reducing constraints one (Z₂). The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively. So the three dimensional stress structure of Mode I specimens can be derived through discussing the two fields respectively. The distribution of the Crack Tip Opening Displacement (CTOD) along the thickness direction and the three dimensional distribution of the void growth ratio (V_g) near the crack tip are also obtained. The two fracture parameters are in similar trends along the thickness direction, and both of them can reflect the effect of thickness and that of the loading level to a certain degree.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)—THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper,three dimensional analyses of some general constraintparameters and fracture parameters near the crack tip of Mode I CT specimens in twodifferent thicknesses are carried out by employing ADINA program.The results revealthat the constraints along the thickness direction are obviously separated into twoparts:the keeping similar high constraint field(Z_1)and rapid reducing constraintsone(Z_2).The two fields are experimentally confiremed to correspond to the smoothregion and the shear lip on the fracture face respectively.So the three dimensionalstress structure of Mode I specimens can be derived through discussing the two fieldsrespectively.The distribution of the Crack Tip Opening Displacement(CTOD)alongthe thickness direction and the three dimensional distribution of the void growth ratio(V_9 )near the crack tip are also obtained.The two fracture parameters are in similartrends along the thickness direction,and both of them can reflect the effect ofthickness and that of the loading l     

POST-BUCKLING AND IMPERFECTION SENSITIVITY OF A COLUMN WITH AN EQUILATERAL TRIANGULAR CROSS-SECTION IN THE PLASTIC RANGE

The asymmetric initial post-buckling corresponding to the lowest bifurcation load andthe imperfection sensitivity are analysed in detail for a compressed simply supported column with anequilateral triangular cross-section in the plastic range.The effect of elastic unloading is taken into ac-count in the analysis.The asymptotic relations,including high order terms,among the load,the am-plitude of imperfection and the amplitude of the bifurcation mode are realized.The results show thatthe maximum supported load is very sensitive to imperfection.     

VARIATIONAL PRINCIPLE OF HYBRID ENERGY AND THE FUNDAMENTALS OF 3-D LAMINATE THEORY—A NEW APPROACH FOR THE ANALYSIS OF INTERLAMINAR STRESSES IN COMPOSITE LAMINATES

This paper discusses the discuntinuity of stresses and strains at interlaminar surfaces of the eomposne laminate and presents a 3-D laminate theory for composite materials. This paper also presents a new type of clastic energy based on the globally continuous variables in laminates, different from the traditional potemial energy and complementary energy. Then. a variational principle corresponding to the 3-D laminate theory is developed. The theory and the principle could be a basis of verifying the 2-D lamimte theory and deterplining the interlaminar stresses mear the free edges.     

NEW THEORY FOR EQUATIONS OF NON-FUCHSIAN TYPE——REPRESENTATION THEOREM OF TREE SERIES SOLUTION (Ⅱ)

Our main result consists in proving the representation theorem. Irregular integral is a new type of analytic function, represented by a compound Taylor-Fourier tree series, in which each coefficient of the Fourier series is a Taylor series, while the Taylor coefficients are tree series in terms of equations parameters, higher order correction terms to each coefficient having tree structure with inexhaustible proliferation. The solution obtained is proved to be convergent absolutely and uniformly in the region defined by coefficient functions of the original equation, provided the structure parameter is less than unity. Direct substitution shows that our tree series solution satisfies the equation explicity generation by generation. As compared with classical theory our method not only furnishes explicit expression of irregular integral, leading to the solution of Poincaré problem, but also provides possibility of extending the scope of investigation for analytic theory to equations with various kinds o     

NEW THEORY FOR EQUATIONS OF NON-FUCHSIAN TYPE——REPRESENTATION THEOREM OF TREE SERIES SOLUTION (Ⅱ)

Our main result consists in proving the representation theorem. Irregular integral is a new type of analytic function, represented by a compound Taylor-Fourier tree series, in which each coefficient of the Fourier series is a Taylor series, while the Taylor coefficients are tree series in terms of equations parameters, higher order correction terms to each coefficient having tree structure with inexhaustible proliferation.The solution obtained is proved to be convergent absolutely and uniformly in the region defined by coefficient functions of the original equation, provided the structure parameter is less than unity. Direct substitution shows that our tree series solution satisfies the equation explicity generation by generation.As compared with classical theory our method not only furnishes explicit expression of irregular integral, leading to the solution of Poincare problem, but also provides possibility of extending the scope of investigation for analytic theory to equations with various kinds of singularities in a unifying way.Exact explicit analytic expression for irregular integrals can be obtained by means of correspondence principle.It is not difficult to prove the convergence of the tree series solution obtained. Direct substitution shows it satisfies the equation.The tree series is automorphic, which agrees completely with Poincaré’s conjecture.     

THE DIMENSION OF SPLINE SPACE S_3~1(△) ON A TYPE OF TRIANGULATION

ＩｎｔｒｏｄｕｃｔｉｏｎＷｈｅｔｈｅｒｔｈｅｄｉｍｅｎｓｉｏｎｏｆｓｐｌｉｎｅｓｐａｃｅＳ13(△ )ｄｅｐｅｎｄｓｏｎｔｈｅｇｅｏｍｅｔｒｉｃａｌｃｈａｒａｃｔｅｒｏｆｔｒｉａｎｇｕｌａｔｉｏｎｈａｓｎｏｔｂｅｅｎｓｏｌｖｅｄ[1].Ｉｎｐａｐｅｒ [2 ] ,ｔｈｅｓｔｒａｔｉｆｉｅｄｔｒｉａｎｇｕｌａｔｉｏｎｏｎｗｈｉｃｈｔｈｅｄｉｍｅｎｓｉｏｎｏｆＳ13(△ )ｄｏｅｓｎｏｔｄｅｐｅｎｄｏｎｔｈｅｇｅｏｍｅｔｒｉｃａｌｃｈａｒａｃｔｅｒｏｆｔｒｉａｎｇｕｌａｔｉｏｎｉｓｐｒｅｓｅｎｔｅｄ .Ｗｅａｎａｌｙｚｅ…