A constitutive model for cavitation and cavity growth in rubber-like materials under arbitrary tri-axial loading

In this paper, we attempted to construct a constitutive model to deal with the phenomenon of cavitation and cavity growth in a rubber-like material subjected to an arbitrary tri-axial loading. To this end, we considered a spherical elementary representative volume in a general Rivlin's incompressible material containing a central spherical cavity. The kinematics proposed by [Hou, H.S., Abeyaratne, R., 1992. Cavitation in elastic and elastic-plastic solids. J. Mech. Phys. Solids 40, 571-722] was adopted in order to construct an approximate but optimal field. In order to establish a suitable constitutive law for this class of materials, we utilized the homogenisation technique that permits us to calculate the average strain energy density of the volume. The cavity growth was considered through a physically realistic failure criterion. Combination of the constitutive law and the failure criterion enables us to describe correctly the global behaviour and the damage evolution of the material under tri-axial loading. It was shown that the present models can efficiently reproduce different stress states, varying from uniaxial to tri-axial tensions, observed in experimentations. Comparison between predicted results and experimental data proves that the proposed model is accurate and physically reasonable. Another advantage is that the proposed model does not need special identification work, the initial Rivlin's law for the corresponding incompressible material is sufficient to form the new law for the compressible material resulted from cavitation procedure. (C) 2007 Elsevier Ltd. All rights reserved.

Dynamic properties and asymmetry of tension and compression of metal matrix composites under impact loading

The mechanical behaviors of 2124, Al-5Cu, Al-Li and 6061 alloys reinforced by silicon carbide particulates, together with 15%SiCw/6061 alloy, were studied under the quasi-static and impact loading conditions, using the split Hopkinson tension/compression bars and Instron universal testing machine. The effect of strain rate on the ultra tensile strength (UTS), the hardening modulus and the failure strain was investigated. At the same time, the SEM observations of dynamic fracture surfaces of various MMC materials showed some distinguished microstructures and patterns. Some new characteristics of asymmetry of mechanical behaviors of MMCs under tension and compression loading were also presented and explained in details, and they could be considered as marks to indicate, to some degree, the mechanism of controlling damage and failure of MMCs under impact loading. The development of new constitutive laws about MMCs under impact loading should benefit from these experimental results and theoretical analysis.

Real-Time Measurement on Deformation Fields of Hole-Excavated Samples under Impact Tension

In this paper, the real-time deformation fields are observed in two different kinds of hole-excavated dog-bone samples loaded by an SHTB, including single hole sample and dual holes sample with the aperture size of 0.8mm. The testing system consists of a high-speed camera, a He-Ne laser, a frame grabber and a synchronization device with the controlling accuracy of I microsecond. Both the single hole expanding process and the interaction of the two holes are recorded with the time interval of 10 mu s. The observed images on the sample surface are analyzed by newly developed software based on digital correlation theory and a modified image processing method. The 2-D displacement fields in plane are obtained with a resolution of 50 mu m and an accuracy of 0.5 mu m. Experimental results obtained in this paper are proofed, by compared with FEM numerical simulations.

Surface Tension and Its Temperature Coefficient of Molten Tin Determined with the Sessile Drop Method at Different Oxygen Partial Pressures

The surface tension of molten tin has been determined by the sessile drop method at The surface tension of molten tin has been determined by the sessile drop method at temperatures ranging from 523 to 1033 K and in the oxygen partial pressure (P-O2) range from 2.85 x 10(-19) to 8.56 x 10(-6) MPa, and its dependence on temperature and oxygen partial pressure has been analyzed. At P-O2 = 2.85 x 10(-19) and 1.06 x 10(-15) MPa, the surface tension decreases linearly with the increase of temperature and its temperature coefficients are -0.151 and -0.094 mNm(-1) K-1, respectively. However, at high P-O2 (3.17 x 10(-10), 8.56 x 10(-6) MPa), the surface tension increases with the temperature near the melting point (505 K) and decreases above 723 K. The surface tension decrease with increasing P-O2 is much larger near the melting point than at temperatures above 823 K. The contact angle between the molten tin and the alumina substrate is 158-173degrees, and the wettability is poor.

Governing Equations and Numerical Solutions of Tension Leg Platform with Finite Amplitude Motion

It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

Viscosity, Surface Tension, and Atomization of Water-Methanol and Diesel Emulsions

This article is the result of experimental studies of the rheologv, viscosities, surface tensions, and atomization of water-methanol and diesel emulsions. The Span 80 and Tween 60 are employed to make three emulsifying agents, Y01, Y02, and Y03, with viscosity of 1.32-1.5 Pa s and HLB values of 5.36, 4.83, and 4.51, respectively. In the water-in-oil emulsions, the aqueous phase is between 10% and 50%; the agent concentration added is 0.8-8.0%. The viscosity of the emulsions is 0.003-0.02 Pa s, and the surface tens ion is 0.04-0.1 N/m. The types and concentrations of agents significantly influence the viscosity of the emulsions, and the higher concentration of the aqueous phase (<50%) in creases the viscosities of the emulsions, especially for higher agent concentration. Interfacial membrane and HLB values of the agents can explain all these phenomena. Higher aqueous phase concentration and agent viscosity results in larger Sauter mean diameter.

Combined effect of surface tension, gravity and van der Waals force induced by a non-contact probe tip on the shape of liquid surface

Aiming at understanding how a liquid film on a substrate affects the atomic force microscopic image in experiments, we present an analytical representation of the shape of liquid surface under van der Waals interaction induced by a non-contact probe tip. The analytical expression shows good consistence with the corresponding numerical results. According to the expression, we find that the vertical scale of the liquid dome is mainly governed by a combination of van der Waals force, surface tension and probe tip radius, and is weekly related to gravity. However, its horizontal extension is determined by the capillary length.

Real-Time Measurement on Deformation Fields of Notched Samples Under Impact Tension

In this paper, a real-time and in situ optical measuring system is reported to observe high-velocity deformations of samples subjected to impact loading. The system consists of a high-speed camera, a He-Ne laser, a frame grabber, a synchronization device and analysis software based on digital correlation theory. The optical system has been adapted to investigate the dynamic deformation field and its evolution in notched samples loaded by an split Hopkinson tension bar, with a resolution of 50 pin and an accuracy of 0.5 mum. Results obtained in experiments are discussed and compared with numerical simulations. It is shown that the measuring system is effective and valid.

On failure modes and strength characterization of brittle disordered materials under uniaxial compression and tension

With a newly developed Material Failure Process Analysis code (MFPA(2D)), influence of hetero geneity on fracture processes and strength characterization of brittle disorder materials such as rock or concrete is numerically studied under uniaxial compression and tension conditions. It is found th at, due to the heterogeneity of the disordered material, relatively more diffused micro-fractures appear in the early stage of loading. Different from homogeneous materials such as glass, macro-crack nucleation starts well before the peak stress is reached and the crack propagation and coalescence can be traced, which can be taken as a precursory to predict the macro-fracture of the material. The presence of residual strength in the post-peak region and the resemblance in the stress-strain curves between tension and compression are significant results and are found to be dependent on the heterogeneity of the specimens. Examples showing the tentative applications of MFPA(2D) in modeling failure of composite materials and rock or civil engineering problem are also given in this paper.

Stability Of Adhesion Clusters And Cell Reorientation Under Lateral Cyclic Tension

This work is motivated by experimental observations that cells on stretched substrate exhibit different responses to static and dynamic loads. A model of focal adhesion that can consider the mechanics of stress fiber, adhesion bonds, and substrate was developed at the molecular level by treating the focal adhesion as an adhesion cluster. The stability of the cluster under dynamic load was studied by applying cyclic external strain on the substrate. We show that a threshold value of external strain amplitude exists beyond which the adhesion cluster disrupts quickly. In addition, our results show that the adhesion cluster is prone to losing stability under high-frequency loading, because the receptors and ligands cannot get enough contact time to form bonds due to the high-speed deformation of the substrate. At the same time, the viscoelastic stress fiber becomes rigid at high frequency, which leads to significant deformation of the bonds. Furthermore, we find that the stiffness and relaxation time of stress fibers play important roles in the stability of the adhesion cluster. The essence of this work is to connect the dynamics of the adhesion bonds (molecular level) with the cell's behavior during reorientation (cell level) through the mechanics of stress fiber. The predictions of the cluster model are consistent with experimental observations.

Role Of Vertical Component Of Surface Tension Of The Droplet On The Elastic Deformation Of Pdms Membrane

Poly(dimethylsiloxane) (PDMS) has been widely used in lab-on-a-chip and micro- total analysis systems (mu-TAS), thus wetting and electrowetting behaviors of PDMS are of great importance in these devices. PDMS is a kind of soft polymer material, so the elastic deformation of PDMS membrane by a droplet cannot be neglected due to the vertical component of the interfacial tension between the liquid and vapor, and this vertical component of liquid-vapor surface tension is also balanced by the stress distribution within the PDMS membrane. Such elastic deformation and stress distribution not only affect the exact measurement of contact angle, but also have influence on the micro-fluidic behavior of the devices. Using ANSYS code, we simulated numerically the elastic deformation and stress distribution of PDMS membrane on a rigid substrate due to the liquid-vapor surface tension. It is found that the vertical elastic deformation of the PDMS membrane is on the order of several tens of nanometers due to the application of a droplet with a diameter of 2.31 mm, which is no longer negligible for lab-on-a-chip and mu-TAS. The vertical elastic deformation increases with the thickness of the PDMS membrane, and there exists a saturated membrane thickness, regarded as a semi-infinite membrane thickness, and the vertical elastic deformation reaches a limiting value when the membrane thickness is equal to or thicker than such saturated thickness. (C) Koninklijke Brill NV, Leiden, 2008.

Effect Of A Negative Poisson Ratio In The Tension Of Ceramics

The effect of a negative Poisson ratio is experimentally revealed in the tension deformation of a natural layered ceramic. This effect can increase the volume strain energy per unit volume by 1100% and, simultaneously, decrease the deformation strain energy per unit volume by about 44%, so that it effectively enhances the deformation capacity by about 1 order of magnitude in the tension of the material. The present study also shows that the physical mechanisms producing the effect are attributed to the climbing on one another of the nanostructures in the natural material, which provides a guide to the design of synthetic toughening composites.

Experimental Investigation Of Influence Of Interfacial Tension On Convection Of Two-Layer Immiscible Liquid

Benard-Marangoni convections of two-layer fluids heated from the bottom are investigated experimentally with a particle imagine velocimetry. The flows are visualized from the side, and various velocity fields near the onset of convection, such as three-layer vortex convective patterns, are observed when the depth ratio varies in a wide range. A new classification of the convective patterns is proposed with more detail than in previous studies. The analysis of the results indicates that the interface tension greatly influences the motion intensities of the bottom and top layers. The dimensionless wave number increases with the Bond number when the motion in the top layer is not more intense than that in the bottom layer, which agrees with the theoretical prediction.

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Numerical analyses for the material bifurcation in plane sheet under tension

The various patterns (shear banding, surface wrinkling and necking) of material bifurcation in plane sheet under tension are investigated in this paper by means of a numerical method. It is found that numerical analysis can provide better ground for searching for the lowest critical loads. The inhomogeneity caused by void damage and the nonuniformity in the stress distribution across sheet thickness are proved to have detrimental effects on the material bifurcation. Nevertheless, material stability can be promoted by any means of depressing void damage or alleviating stress, even locally across the thickness. Besides, the peculiar behaviour of material bifurcation under slight biaxiality state is demonstrated. Copyright (C) 1996 Elsevier Science Ltd