MICROMECHANICS ANALYSIS ON EVOLUTION OF CRACK IN VISCOELASTIC MATERIALS

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Conservation Law and Application of J-Integral in Multi-Materials

The conservation law of J-integral in two-media with a crack paralleling to the interface of the two media was firstly proved by analytical and numerical finite element method. Then a schedule model was established that an interface crack is inserted in four media. According to the J-integral conservation law on multi-media, the energy release ratio of Ⅰ-type crack was considered to be conservation when the middle medium layers are very thin. And the conservation law was also convinced by numerical method. By means of the dimension analysis on the model, the asymptotic results and formula calculating the energy release ratio and complex stress intensity factor are presented.     

The high accuracy explicit difference scheme for solving parabolic equations 3-dimension

ＩｎｔｒｏｄｕｃｔｉｏｎＦｒｏｍｐｒａｃｔｉｃａｌｐｒｏｂｌｅｍ,ｗｅｃｏｕｌｄｃｏｎｃｌｕｄｅｍａｎｙｐｒｏｂｌｅｍｓａｂｏｕｔｓｏｌｖｉｎｇｐａｒａｂｏｌｉｃｐａｒｔｉａｌｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ．Ｎｏｗｔｈｅｒｅａｒｅｍａｎｙｎｕ...     

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.     

PREDICTION OF MODE Ⅰ CRACK PROPAGATION DIRECTION IN CARBON-FIBER REINFORCED COMPOSITE PLATE

A newly developed Z fracture criterion for the composite materials was introduced, the new concepts of in-plane average strain, in-plane dilatational strain energy density factor and reciprocal characteristic function were presented. Many experimental results show that the Z fracture criterion can be well used to predict the crack propagating direction for mode f crack in carbon-fiber reinforced composite laminates.     

Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts

Summary  The dynamic response of an interface crack between two dissimilar piezoelectric layers subjected to mechanical and electrical impacts is investigated under the boundary condition of electrical insulation on the crack surface by using the integral transform and the Cauchy singular integral equation methods. The dynamic stress intensity factors, the dynamic electrical displacement intensity factor, and the dynamic energy release rate (DERR) are determined. The numerical calculation of the mode-I plane problem indicates that the DERR is more liable to be the token of the crack growth when an electrical load is applied. The dynamic response shows a significant dependence on the loading mode, the material combination parameters as well as the crack configuration. Under a given loading mode and a specified crack configuration, the DERR of an interface crack between piezoelectric media may be decreased or increased by adjusting the material combination parameters. It is also found that the intrinsic mechanical-electrical coupling plays a more significant role in the dynamic fracture response of in-plane problems than that in anti-plane problems. Received 4 September 2001; accepted for publication 23 July 2002 The work was supported by the National Natural Science Foundation under Grant Number 19891180, the Fundamental Research Foundation of Tsinghua University, and the Education Ministry of China.     

DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL

The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli’s gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.     

An analytic and application to state space reconstruction about chaotic time series

The state space reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: N.H.Packard, F.Takens, M. Casdagli, J.F.Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time τ were identified. The influence for state space reconstruction of lag time τ was discussed. The result tells us that is a good practical method for state space reconstruction.     

An automatic constraint violation stabilization method for differential/ algebraic equations of motion in multibody system dynamics

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Computer simulated analyses on deformation and fracture of non-cracked and cracked specimens

A unified damage and fracture model, the combinatory work density model, which is suitable for either non-cracked body or cracked body has been suggested^[t−7]. In the present paper, the deformation and fracture of the two kinds of tensile spceimen and TPB specimen made of 40Cr steel have been simulated by using the new model together with the large elastic-plastic deformation finite element method. The results give a good picture of the whole deformation and fracture processes of the specimens in experiments; especially, the results on the TPB specimen can be used to obtain the relationship between load and displacement at the loading pointP-Δ, and between crack extension and displacement at the loading point Δa-Δ, the resistance curveJ _R -Δa and the fracture toughnessJ _1C . All the results are in remarkable agreement with those obtained by experiments. Therefore the model suggested here can be used to simulate crack initiation and propagation in non-cracked body and fracture initiation and crack stable propagation in cracked body. The project supported by National Natural Science Foundation of China     

The investigation on dynamic fracture behavour of materials under compressive-shear combined stress waves

In this paper, an improved plate impact experimental technique is presented for studying dynamic fracture mechanism of materials, under the conditions that the impacting loading is provided by a single pulse and the loading time is in the sub-microsecond range. The impacting tests are carried out on the pressure-shear gas gun. The loading rate achieved is dK/dt∼10⁸ MPa m^1/2s⁻¹. With the elimination of influence of the specimen boundary, the plane strain state of a semi-infinite crack in an infinite elastic plate is used to simulate the deformation fields of crack tip. The single pulses are obtained by using the “momentum trap” technique. Therefore, the one-time actions of the single pulse are achieved by eradicating the stress waves reflected from the specimen boundary or diffracted from the crack surfaces. In the current study, some important phenomena have been observed. The special loading of the single pulse can bring about material damage around crack tip, and affect the material behavior, such as kinking and branching of the crack propagation. Failure mode transitions from mode I to mode II crack are observed under asymmetrical impact conditions. The mechanisms of the dynamic crack propagation are consistent with the damage failure model. The project supported by the National Natural Science Foundation of China (No. 19672066 and 18981180-4) and the Key Project of Chinese Academy of Sciences (No. KJ951-1-20)     

Scattering of anti-plane shear waves by a single crack in an unbounded trasversely isotropic electro-magneto-elastic medium

A theoretical treatment of the scattering of anti-plane shear (SH) waves is provided by a single crack in an unbounded transversely isotropic electro-magneto-elastic medium. Based on the differential equations of equilibrium, electric displacement and magnetic induction intensity differential equations, the governing equations for SH waves were obtained. By means of a linear transform, the governing equations were reduced to one Helmholtz and two Laplace equations. The Cauchy singular integral equations were gained by making use of Fourier transform and adopting electro-magneto impermeable boundary conditions. The closed form expression for the resulting stress intensity factor at the crack was achieved by solving the appropriate singular integral equations using Chebyshev polynomial. Typical examples are provided to show the loading frequency upon the local stress fields around the crack tips. The study reveals the importance of the electro-magneto-mechanical coupling terms upon the resulting dynamic stress intensity factor. Contributed by SHEN Ya-peng Foundation item: the National Natural Science Foundation of China (10132010, 50135030) Biographies: DU Jian-ke (1970∼)     

A class of nonlinear boundary value problems for the second-order<Emphasis Type="Italic">E</Emphasis><Subscript>2</Subscript> class elliptic systems in general form

A class of nonlinear boundary value problems (BVP) for the second-order E₂ class elliptic systems in general form is discussed. By introducing a kind of transformation, this kind of BVP is reduced to a class of generalized nonlinear Riemann-Hilbert BVP. And then some singular integral operators are introduced to establish the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of the properties of singular integral operators and the function theoretic methods. Foundation items: the National Natural Science Foundation of China (19671056); Shanghai Municipal Natural Scientific Foundation (99ZA14030, 01ZA14023); Jiangxi Provincial Natural Scientific Foundation (981102, 0211014) Biographies: LI Ming-zhong (1935−); XU Ding-hua (1967−)     

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR＇ E SYSTEMS

An impulsive control scheme of the Lur‘e system and several theorems on stability of impulsive control systems was presented, these theorems were then used to find the conditions under which the Lur‘e system can be stabilized by using impulsive control with varying impulsive intervals. The parameters of Lur‘e system and impulsive control law are given, a theory of impulsive synchronization of two Lur‘e system is also presented. A numerical example is used to verify the theoretical result.     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOWWATER EQUATIONS INCLUDING CURRENT AND SILTSEDIMENTATION （Ⅱ）——THE DISCRETE-TIMECASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation systemconsisting of water dynamics equations, silt transport equation, and the equation of bottomtopography change were derived. A fully discrete MFE scheme for the discrete-time alongcharacteristics is presented and error estimates are established. The existence andconvergence of MFE solution of the discrete current velocity, elevation of the bottomtopography, thickness of fluid column, and mass rate of sediment is demonstrated.     

Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes

Summary  In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular integral equations. Numerical results illustrate the effect of the loading combination parameter λ, material property distribution and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of applied electric impact. Received 4 December 2001; accepted for publication 9 July 2002 This work is supported by the National Natural Science Foundation of China through Grant No. 10132010.     

Theoretical analysis on the local critical stress and size effect for interfacial debonding in particle reinforced rheological materials

The mechanisms of interfacial debonding of particle reinforced rheological materials are studied. Based on an energy criterion, a simple formula of local critical stress for interfacial debonding is derived and expressed in terms of the interfacial energy. The particle size effect on interface debonding can then be analyzed easily owing to the fact that critical stress is inversely proportional to the square root of particle radius. By taking PP/CaCO₃ system as an example, the present energy criterion is compared with the mechanical debonding criterion, and it is found that under the condition that bond strength is equal to matrix strength and particle radius not over 0.2μm, the mechanical debonding criterion can be automatically satisfied if the energy criterion is satisfied. A relation between critical time and interface energy is calculated by using the energy criterion. The influences of the particle volume fraction and the parlicle size, the loading rate and the relaxation time of the matrix on the critical time of interfacial debonding are also discussed. Supported by the National Natural Science Foundation of China (19632030 and 19872007) and Natural Science Foundation of Jiangsu Province.     

MAXIMAL ELEMENTS FOR GB-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature. Contributed by DING Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province of China ([2000]25) Biography: DING Xie-ping (1938∼)     

Stress analysis for an infinite strip weakned by periodic cracks

Stress analysis for an infinite stripcracks were assumed in a horizontal position,weakened by periodic cracks is studied. The and the strip was applied by tension “p“ in y-direction. The boundary value problem can be reduced into a complex mixed one. It is found that the EEVM ( eigenfunction expansion variational method) is efficient to solve the problem. The stress intensity factor at the crack tip and the T-stress were evaluated. From the deformation response under tension the cracked strip can be equivalent to an orthotropic strip without cracks. The elastic properties in the equivalent orthotropic strip were also investigated. Finally, numerical examples and results were given.     

MAXIMAL ELEMENTS FOR G-B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅱ)

By applying existence theorems of maximal elements for a family of G_B-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces. These theorems improve and generalize many important known results in literature. Contributed by Duping Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province ([2000]25) Biography: Duping Xie-ping (1938∼), Professor (E-mail: dingxip@sichu.edu.cn)