Micromechanics analyses of interface crack

A new mechanics model based on Peierls concept is presented in this paper, which can clearly characterize the intrinsic features near a tip of an interfacial crack. The stress and displacement fields are calculated under general combined tensile and shear loadings. The near tip stress fields show some oscillatory behaviors but without any singularity and the crack faces open completely without any overlapping when remote tensile loading is comparable with remote shear loading. A fracture criterion for predicting interface toughness has been also proposed, which takes into account for the shielding effects of emitted dislocations. The theoretical toughness curve gives excellent prediction, as compared with the existing experiment data. The project supported by the National Natural Science Foundation of China     

Two-phase displacement of non-newtonian fluid

This paper considers the problem of non-Newtonian oil displa-cement by water in porous media.adopting the linear permea-tion law with initial pressure gradient.For one-dimensionalflow,the basic equation of non-Newtonian oil displacement bywater in sandstone reservoirs and fractured reservoirs is de-rived and numerical solutions are obtained.The results arecompared with the corresponding ones for Newtonian oil dis-placement to show the essential characteristics of non-Newto-nian oil displacement by water.     

A micromechanical analysis of the nonlinear elastic and viscoelastic constitutive relation of a polymer filled with rigid particles

Micromechanical theory is applied to study the nonlinear elastic and viscoelastic constitutive relations of polymeric matrix filled with high rigidity solid particles. It is shown that Eshelby's method can be extended to the case of nonlinear matrix and Eshelby's tensor still exists provided that Poisson's ratio of the nonlinear matrix assumes constant value in deforming process and the rigidity of elastic filling particles is much higher than that of the matrix. A new method for averaging process is proposed to overcome the difficulty that occured in applying the ordinary equivalent inclusion method or the self-consistant method to nonlinear matrices. A rather simple constitutive equation is obtained finally and the strengthening effect of solid particles to composites is investigated. The work supported by the LNM, Institute of Mechanics, Chinese Academy of Sciences and by the National Natural Science Foundation of China     

The crack tip zone shielding effect for ductile particle reinforced brittle materials

The crack tip zone shielding effect for the ductile particle reinforced brittle materials is analyzed by using a micromechanics constitutive theory. The theory is developed here to determine the elastoplastic constitutive behavior of the composite. The elastoplastic particles, with isotropic or kinematical hardening, are uniformly dispersed in the brittle elastic matrix. The method proposed is based on the Mori-Tanaka's concept of average stress in the composite. The macroscopic yielding condition and the incremental stress strain relation of the composite during plastic deformation are explicity given in terms of the macroscopioc applied stress and the microstructural parameters of the composite such as the volume fraction and yield stress of ductile particles, elastic constants of the two phases, etc. Finally, the contribution of the plastic deformation in the particles near a crack tip to the toughening of the composite is evaluated. The project supported by National Natural Science Foundation of China     

Effective viscoelastic behavior of particulate polymer composites at finite concentration

Polymeric materials usually present some viscoelastic behavior. To improve the mechanical behavior of these materials, ceramics materials are often filled into the polymeric materials in form of fiber or particle. A micromechanical model was proposed to estimate the overall viscoelastic behavior for particulate polymer composites, especially for high volume concentration of filled particles. The method is based on Laplace transform technique and an elastic model including two-particle interaction. The effective creep compliance and the stress and strain relation at a constant loading rate are analyzed. The results show that the proposed method predicts a significant stiffer response than those based on Mori-Tanaka's method at high volume concentration of particles.     

Subcritical stable growth of a penny-shaped crack in an aging viscoelastic body with cylindrical anisotropy

The paper studies the subcritical stable growth of a penny-shaped mode I crack in an aging linear viscoelastic body with cylindrical anisotropy under tensile loads applied at infinity. The equations of quasistatic crack growth are derived using the Volterra principle for a modified Dugdale model and the critical crack opening displacement as a failure criterion. The kernel of the operator that describes the viscoelastic crack opening is found using operator-valued continued fractions. As an example, the subcritical stable growth of a crack in a specific material is studied numerically __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 1, pp. 82–92, January 2007.     

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored. This work was supported by the National Natural Science Foundation of China (No.19772064) and by the project of CAS KJ 951-1-20     

Comparison between the dynamic moduli of fully non-linear and quasilinear viscoelastic materials

This paper deals with the non-linear viscoelastic model with multiple hereditary integrals (MHI) in the frequency domain and the conditions that it reduces to single hereditary integral or the quasilinear viscoelastic (QLV) model. It is shown that when the higher order complex moduli are related to the first-order modulus as the MHI model reduces to the QLV model. The coefficients of quasilinearity should be real and independent of amplitude and frequency.     

A numerical method for crack growth analysis in linearly viscoelastic materials

This paper presents a numerical method for the analysis of crack initiation and extension in linearly viscoelastic materials undergoing Mode I plane stress deformation. Plastic deformation near the crack tip is considered by a strip-yielding model. The crack initiation and growth are taken to follow a critical energy release rate fracture criterion, and the plastic work per unit crack extension is included in the calculation of the total energy release rate. The resulting numerical method is presented in algorithmic form and two example problems are solved to demonstrate its application. The two example problems represent unstable and stable crack propagations respectively. The results obtained lend insight into the effect of creep deformation on the initiation and growth of a crack.     

Crack propagation in the power-law nonlinear viscoelastic material

I.IntroductionCrazingdamageisacommonphenon1enonoffractureofpolymericmaterials.Theformationofcrazezoneisamid-stateinthefractureprocessofthematerialsfromperfectstatetofaiIurc.Microscopically,inthisregionthereexistssomefibrilslinkingthetwocracksurfacesandres…     

Characterization of viscoelastic properties of polymeric materials through nanoindentation

Nanoindentation testing was used to determine the dynamic viscoelastic properties of eight polymer materials, which include three high-performance polymers and five densities of high-density polyethylene. It was determined that varying the harmonic frequency of nanoindentation does not have a significant effect on the measured storage and loss moduli of the polymers. Agreement was found between these nanoindentation results and data from bulk dynamic mechanical testing of the same materials. Varying the harmonic amplitude of the nanoindentation had a limited effect on the measured viscoelastic properties of the resins. However, storage and loss moduli from nanoindentation were shown to be sensitive to changes in the density of the polyethylene.     

The energy release rate for linear viscoelastic materials

For viscoelastic materials, the energy release rate is a fairly important parameter for determining whether the crack extends, but so far its meaning for viscoelastic materials is not yet clear enough. In this paper, the thermodynamic mechanical theory is used to derive the local and global energy release rate of viscoelastic materials when constitutive equations are given. Moreover, the method of deriving the viscoelastic energy release rate is discussed. The relation between the energy release rate and internal energy, Helmholz free energy is described. The equivalence between the local and global energy release rates is also proved after some doubts in previous papers are dispelled, although the upshot is not original. Furthermore, the concrete forms of the energy release rate for anisotropic, orthotropic and isotropic viscoelastic media are presented. The forms of the local and global energy release rates in the failure zone are discussed and the difference between the equation presented here and the one given in previous papers is pointed out.     

Time-temperature-stress equivalence and its application to nonlinear viscoelastic materials

Stress-dependence of the intrinsic time of viscoelastic materials is investigated. The influence of stress level on the intrinsic time is considered to be similar to that of temperature, pressure, solvent concentration, damage and physical aging. The time-temperature-stress equivalence principle is proposed, by employing which, the creep curves at different temperatures and stress levels can be shifted into a master curve at reference temperature and stress level. Thus the long-term creep behavior of viscoelastic materials at a lower temperature and stress can be predicted from the short-term one at a higher temperature and stress. As an example, the nonlinear creep behavior of high-density polyethylene (HDPE) at room temperature is studied using the time-temperature-stress equivalence principle presented. Project supported by the National Natural Science Foundation of China (No. 19632030, 50003005) and by the Education committee of Human Province (No. 99C122).     

Finite element analysis of mode III steady crack growth in anisotropic hardening materials

In this paper, the steady crack growth of mode III under small scale yielding conditions is investigated for anisotropic hardening materials by the finite element method. The elastic-plastic stiffness matrix for anisotropic materials is given. The results show the significant influences of anisotropic hardening behaviour on the shape and size of plastic zone and deformation field near the crack tip. With a COD fracture criterion, the ratio of stress intensity factorsk _ss/k_c varies appreciably with the anisotropic hardening parameterM and the hardening exponentN.     

On a case of crack path bifurcation in cohesive materials

Summary Experimental, theoretical and numerical investigations show that crack kinking and crack branching can be observed and simulated in brittle solids and in the fast dynamical propagation of quasi-brittle fractures. The present study shows that kinking and branching may also occur in the quasi-static regime when an isotrophic or equi-biaxial tensile state of stress arises at the tip of a cohesive crack, and may represent alternative itineraries (i.e. path bifurcation) of the fracture process. Specific reference is made to the common but meaningful case of the three-point-bending test. Various numerical techniques apt to capture the above occurrence are comparatively presented, and the influence of path bifurcation on the overall behaviour of the specimen is discussed. Received 8 October 1997; accepted for publication 22 January 1998     

Limiting velocity of crack propagation in elastic materials

A crack is represented as a continuous set of linear dislocations. Simple analytical expressions are obtained for the potential and kinetic energies of the environment of moving cracks and the attached mass of cracks for an arbitrary form of the stress applied to the crack P(x). It is shown that the indicated analytical expressions are bilinear integrals of the functions P(x) and ∂P(x)/∂x. These integrals are calculated in explicit form for a constant stress over the entire crack length and the stress due to the action of molecular adhesion forces in a narrow region near the crack openings. It is shown that the calculation results does not depend on the form of molecular adhesion forces. The proposed approach to describing cracks and calculations based on it has made it possible for the first time to obtain a complete analytical expression for the limiting crack propagation velocity in elastic materials as a function of the main mechanical characteristics of such materials. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 158–166, July–August, 2009.     

Penny-shaped crack in transversely isotropic piezoelectric materials

Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the displacement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another form of the general solution is obtained under cylindrical coordinate system by introducing three quasi-harmonic functions into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore, the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The results show that the stress and the electric displacement components near the crack tip have (r ^−1/2) singularity. The project supported by the Natural Science Foundation of Shaanxi Province, China     

非均匀弹性材料中反平面的运动裂纹

用解析方法研究了非均匀弹性材料中反平面运动裂纹问题。首先采用余弦变换求解非均匀材料的基本方程，然后根据混合边值条件建立裂纹运动的对偶积分方程，再把对偶积分方程化为第二类Fredholm积分方程。给出了数值算例，计算结果表明材料的非均匀性对动应力强度因子有较大的影响。     

Growth of a mode II crack in an orthotropic plate made of a viscoelastic composite material

The growth of a straight mode II crack in a viscoelastic orthotropic plate is examined. The plate material is modeled by a viscoelastic anisotropic medium. The shear displacement in the fracture process zone is determined as a function of time using the corresponding elastic solution, the Volterra principle, and the method of operator continued functions. The time dependence of the crack length is constructed as integral equations of three phases of stable growth. The solution of these equations gives kinetic curves __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 89–97, September 2006.     

粘弹性岩体中支护圆形洞室施工过程的解析分析

地下洞室的开挖与支护是逐步的连续过程。对具有流变效应的粘弹性岩体,流变时效与施工效应发生耦合,变形与时间相关。针对深埋圆形洞室的施工,用半径时变函数模拟断面开挖过程。当岩体模拟为任一粘弹性材料时,将方程进行拉普拉斯变换求得位移通解,逆变换后代入边界条件确定待定函数,最终得到用洞周面力表达的围岩应力、位移统一解。区分开挖与支护时段,将半径时变函数、洞周面力不同表达式代入,利用支护后围岩与弹性支护接触条件建立关于支护力的Volterra积分方程。当岩石模拟为Boltzmann粘弹模型时,代入材料参数可求解积分方程得到支护力的确切表达,并进一步求得开挖过程及任意时刻支护后应力、位移分段解析表达式。表达式和算例分析表明:加支护后的径向位移增长呈指数形式变化且最终稳定于某一数值。最终洞型相同时,采用不同断面开挖速度且挖完立即支护时,开挖较快的情况位移变化较剧烈,而支护后最终稳定位移较小;但是,相应支护阶段产生的位移较大,支护力也较大。文中给出的方法可用于计算圆形洞室半径任意开挖并加支护后的应力、位移,适用于任一粘弹模型岩体的施工分析。