Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.

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.

Singularity of Stress Field Around Interface Crack Between Viscoelastic Bodies

研究两半无限大黏弹性体间Griffith界面裂纹在简谐载荷作用下裂纹尖端动应力场的奇异特性.通过引入裂纹张开位移和裂纹位错密度函数,相应的混合边值问题归结为一组耦合的奇异积分方程.渐近分析表明裂尖动应力场的奇异特征完全包含在奇异积分方程的基本解中.通过对基本解的深入分析发现黏弹性材料界面裂纹裂尖动应力场具有与材料参数和外载荷频率相关的振荡奇异特性.以标准线性固体黏弹材料为例讨论了材料参数和载荷频率对奇性指数和振荡指数的影响.

Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known -1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.

Fracture analysis for 3-dimensional bodies with a surface crack

This paper deals with fracture analyses in 3-dimensional bodies containing a surface crack. A general solution of stress-strain fields at crack tip is proposed. Based on the stress-strain fields obtained, a high-order 3-dimensional special element is established to calculate the stress intensity factors in a plate with a surface crack. The variation of stress intensity factors with geometric parameters is investigated.

Thermophoretic deposition of particles onto cold surfaces of bodies in two-dimensional and axisymmetric flows

The problem of thermophoretic deposition of small particles onto cold surfaces is studied in two-dimensional and axisymmetric flow fields. The particle concentration equation is solved numerically together with the momentum and energy equations in the laminar boundary layer with variable density effect included. It is shown explicitly to what extent the particle concentration and deposition rate at the wall are influenced by the density variation effect for external flow past bodies. The general numerical procedure is given for two-dimensional and axisymmetric cases and is illustrated with examples of thermophoretic deposition of particles in flows past a cold cylinder and a sphere.

Study on cracked plates, shells and 3 dimensional bodies

This paper presents a summary of the authors' recent work in following areas: (1) The stress-strain fields at crack tip in Reissner's plate. (2) The calculations of the stress intensity factors in finite size plates. (3) The stress-strain fields at crack tip in Reissner's shell. (4) The calculations of the stress intensity factors and bulging coefficients in finite size spherical shells. (5) The stress-strain fields along crack tip in three dimensional body with surface crack. (6) The calculation of stress intensity factors in a plate with surface crack.

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Characteristics of Wake Flow in Long Bluff Bodies

Vortex shedding is the main characteristics of bluff bodies, which will cause the bluff bodies to vibrate and sometimes result in the structures failure. In this paper the wake flow characteristics of 21 bluff bodies with rectangular, rounded and angular profiles and the length-to-width ratio in the range of 4~12 were deeply studied by Micro ADV. Two parameters, namely the relative intensity of the load due to Karman vortices and the large scale vortex intensity, were introduced to measure the wake flow intensity. Generally, the values of these parameters for different bluff bodies are consistent with each other. The experiment results showed that the key factor affecting the wake flow characteristics is the bluff edge, especially the leading edge geometry. The wake flow in bluff bodies with rounded edge profiles has more regular vortices and becomes more periodic than that in bluff bodies with rectangular ones. A bluff body with angular edged profile was witnessed to have not only small wake loading but small hydraulic resistance also.

In situ nutrient removal from aquaculture wastewater by aquatic vegetable Ipomoea aquatica on floating beds

Nutrient-rich effluents caused rising concern due to eutrophication of aquatic environment by utilization of a large amount of formula feed. Nutrient removal and water quality were investigated by planting aquatic vegetable on artificial beds in 36-m(2) concrete fishponds. After treatment of 120 days, 30.6% of total nitrogen (TN) and 18.2% of total phosphorus (TP) were removed from the total input nutrients by 6-m(2) aquatic vegetable Ipomoea aquatica. The concentrations of TN, TP, chemical oxygen demand (COD) and chlorophyll a in planted ponds were significantly lower than those in non-planted ponds (P<0.05). Transparency of water in planted ponds was much higher than that of control ponds. No significant differences in the concentration of total ammonia nitrogen (TAN), nitrate nitrogen (NO3-N) and nitrite nitrogen (NO2--N) were found between planted and non-planted ponds. These results suggested that planting aquatic vegetable with one-sixth covered area of the fishponds could efficiently remove nutrient and improve water quality.

Allelopathic effects of phenolic compounds present in submerged macrophytes on Microcystis aeruginosa

In laboratory studies, the allelopathic effects of 3 (Hydrocharitaceae family) submerged macrophytes (Elodea nuttallii (Planch) St. John, Hydrilla verticillata (L.f.) Royle and Vallisneria spiralis L.) were investigated on two strains of Microcystis aeruginosa. Both aqueous methanol extracts and exudates of three macrophytes inhibited the growth of both strains of Microcystis aeruginosa, After 3-days culture, E nuttallii, H. verticillata and V. spiralis excreted 0.8, 0.3 and 1.0% of total phenolic compounds (TPC), respectively, into the surrounding water. After removing phenolic compounds by polyvinylpolypyrrolidone (PVPP)), the plant exudates showed very weak activity. The inhibitory rates of exudates of E. nuttallii, H. verticillata and V. spiralis, against non-toxic M. aeruginosa were decreased by 35.7, 43.4 and 59.1% respectively. Thus 3 submerged macrophytes released the phenolic compounds into the surrounding water, to inhibit the growth of M. aeruginosa. This information may help us in understanding the mechanism of allelopathy in aquatic ecosystems and to control the algal bloom in eutrophic water bodies.

Trends of Superoxide Dismutase and Soluble Protein of Aquatic Plants in Lakes of Different Trophic Levels in the Middle and Lower Reaches of the Yangtze River, China

A limnological study was carried out to determine the responses of superoxide dismutase (SOD) activities and soluble protein (SP) contents of 11 common aquatic plants to eutrophication stress. Field investigation in 12 lakes in the middle and lower reaches of the Yangtze River was carried out from March to September 2004. Our results indicated that non-submersed (emergent and floating-leafed) plants and submersed plants showed different responses to eutrophication stress. Both SOD activities of the non-submersed and submersed plants were negatively correlated with their SP contents (P < 0.000 1). SP contents of non-submersed plants were significantly correlated with all nitrogen variables in the water (P < 0.05), whereas SP contents of submersed plants were only significantly correlated with carbon variables as well as ammonium and Secchi depth (SD) in water (P < 0.05). Only SOD activities of submersed plants were decreased with decline of SD in water (P < 0.001). Our results indicate that the decline of SOD activities of submersed plants were mainly caused by light limitation, this showed a coincidence with the decline of macrophytes in eutrophic lakes, which might imply that the antioxidant system of the submersed plants were impaired under eutrophication stress.