A note on the effect of surface energy and void size to void growth

Recent studies revealed that rapid void growth is the dominant failure mechanism in an elasto-plastic solid under high mean tensile stress. This paper studies the effect of the surface energy and void size to the void growth. The models of a thick spherical shell and a thick spherical column in void growth are analyzed and numerically estimated. The main conclusion from this study is that, for typical metals, the surface energy effect is negligible for voids larger than 100 nm in size, but it may become significant when the void size is on the order of 10 nm.     

Influences of microscope size effect of matrix on plastic potential and void growth of porous materials

Based on approximate theoretical analyses on a typical spherical cell containing a spherical microvoid, the influences of matrix materials' microscopic scale on the macroscopic constitutives potential theory of porous material and microvoid growth have been investigated in detail. By assuming that the plastic deformation behavior of matrix materials follows the strain gradient (SG) plastic theory involving the stretch and rotation gradients, the ratio (λ=l/a) of the matrix materials' intrinsic characteristic lengthl to the microvoid radiusa is introduced into the plastic constitutives potential and the void growth law. The present results indicate that, when the radiusa of microvoids is comparable with the intrinsic characteristic lengthl of the matrix materials, the influence of microscopic size effect on neither the constitutive potential nor the microvoid evolution predicted can be ignored. And when the void radiusa is much lager than the intrinsic characteristic lengthl of the matrix materials, the present model can retrogress automatically to the improved Gurson model that takes into account the strain hardening effect of matrix materials. Project supported by the National Natural Science Foundation of China (No. A10102006).     

Coupling effects of void size and void shape on the growth of prolate ellipsoidal microvoid

The combined effects of void size and void shape on the void growth are studied by using the classical spectrum method. An infinite solid containing an isolated prolate spheroidal void is considered to depict the void shape effect and the Fleck-Hutchinson phenomenological strain gradient plasticity theory is employed to capture the size effects. It is found that the combined effects of void size and void shape are mainly controlled by the remote stress triaxiality. Based on this, a new size-dependent void growth model similar to the Rice-Tracey model is proposed and an important conclusion about the size-dependent void growth is drawn: the growth rate of the void with radius smaller than a critical radius r_c may be ignored. It is interesting that r_c is a material constant independent of the initial void shape and the remote stress triaxiality.The project supported by the National Natural Science Foundation of China (A10102006) and the New Century Excellent Talents in Universities of China. The English text was polished by Keren Wang.     

Influences of reinforcing particle and interface bonding strength on material properties of Mg/nano-particle composites

In the present study, an effective model is proposed to predict the effective elastic behavior of the three-phase composite containing spherical inclusions, each of which is surrounded by an interphase layer. The constitutive equations are derived for the stress and strain of each phase of the composite subjected to a far-field tension. Based on these constitutive laws, the effective bulk, shear and Young’s modulus are obtained. A statistical debonding criterion is adopted to characterize the varying probability of the evolution of interphase debonding. Influences of debonding damage, particle volume fraction, interphase properties and bonding strength on overall mechanical behavior of composites are also discussed. Numerical analyses are carried out on particle-reinforced composites and the predictions have a good agreement with the experimental results.     

Effect of particle polydispersity on particle concentration measurement by using laser Doppler anemometry

Measurement of particle concentration by laser Doppler anemometry (LDA) is studied on a vertical air jet seeded by a powder disperser with controlled particle and air flow rates. Particle arrival rate is utilized to retrieve particle number densities from conventional LDA operation. The effect of polydisperse nature of the particles is assessed. Comparisons between measured and estimated particle number densities suggest that only a certain portion of the particle population with a particle size to fringe spacing ratio around unity can be detected. Results indicate that reliable measurement of absolute particle concentration is possible for a particle population of narrow size distribution with an average diameter equivalent to fringe spacing. Present number density measurement technique which is useful for practical purposes with conventional LDA systems is found to yield physically reasonable profiles in both laminar and turbulent regimes.     

Hydrodynamic action of the fluid slowly flowing around a spheroidal particle covered by a viscous film

A steady problem of a slow axisymmetric flow of a viscous incompressible fluid around an oblate spheroid covered by a viscous film is solved analytically with the use of the Stokes approximation. Surface tension on the interface between the fluids is taken into account. Expressions for velocity components and stream functions are presented. A formula for determining the force action of the incoming flow onto the oblate spheroid is derived.     

Study of possible void nucleation and growth in solids in the framework of the Davis-Nadai deformation theory

In the framework of the Davis-Nadai deformation theory, we study the problem of a ball with a central cavity subjected to internal and external pressure. The solution is constructed in the reference configuration for the polynomial material deformation law with possible regard to matter conservation inside the cavity. The obtained solution is analyzed; it is mathematically proved that the limit load exists in the case of uniform compression, and a method for determining this load is given. It is also proved that a new void can be formed in a solid ball in the case of its extension, and the critical load of void formation is estimated. It is shown that the already existing spherical void cannot completely disappear under the action of external pressure (assuming that its shape is preserved and remaining in the framework of the continuity hypothesis).     

In-line imaging measurements of particle size,velocity and concentration in a particulate two-phase flow

A novel method is developed for in-line measurements of particle size, velocity and concentration in a dilute, particulate two-phase flow based on trajectory image processing. The measurement system consists of a common industrial CCD camera, an inexpensive LED light and a telecentric lens. In this work, the image pre-processing steps include stitching, illumination correction, binarization, denoising, and the elimination of unreal and defocused particles. A top-hat transformation is found to be very effective for the binarization of images with non-uniform background illumination. Particle trajectories measured within a certain exposure time are used to directly obtain particle size and velocity. The particle concentration is calculated by using the statistics of recognized particles within the field of view. We validate our method by analyzing experiments in a gas-droplet cyclone separator. This in-line image processing method can significantly reduce the measurement cost and avoid the data inversion process involved in the light scattering method.     

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.     

Vapor pressure and void size effects on failure of a constrained ductile film

To achieve certain properties, semiconductor adhesives and molding compounds are made by blending filler particles with polymer matrix. Moisture collects at filler particle/polymer matrix interfaces and within voids of the composite. At reflow temperatures, the moisture vaporizes. The rapidly expanding vapor creates high internal pressure on pre-existing voids and particle/matrix interfaces. The simultaneous action of thermal stresses and internal vapor pressure drives both pre-existing and newly nucleated voids to grow and coalesce causing material failure. Particularly susceptible are polymeric films and adhesives joining elastic substrates, e.g. Ag filled epoxy. Several competing failure mechanisms are studied including: near-tip void growth and coalescence with the crack; extensive void growth and formation of an extended damaged zone emanating from the crack; and rapid void growth at highly stressed sites at large distances ahead of the crack, leading to multiple damaged zones. This competition is driven by the interplay between stress elevation induced by constrained plastic flow and stress relaxation due to vapor pressure assisted void growth.A model problem of a ductile film bonded between two elastic substrates, with a centerline crack, is studied. The computational study employs a Gurson porous material model incorporating vapor pressure effects. The formation of multiple damaged zones is favored when the film contains small voids or dilute second-phase particle distribution. The presence of large voids or high vapor pressure favor the growth of a self-similar damage zone emanating from the crack. High vapor pressure accelerates film cracking that can cause device failures.     

Experimental investigations and modeling of volume change induced by void growth in polyamide 11

Polymers are known to be sensitive to hydrostatic pressure. The influence of stress triaxiality ratio on cavitation and damage has been highlighted in numerous studies. This paper proposes experimental investigations allowing the control of both the stress triaxiality ratio and the void distribution via microscopic observations of microtome-cut surfaces from interrupted tests. With the help of a finite element code, the Gurson–Tvergaard–Needleman model was calibrated by using these multi-scale experimental data. Then comparison between both numerical and analytical models and experimental data was performed. Bridgman formulae were reported to be valid up to the peak load. Moreover, a better understanding of the time evolution of significant parameters such as the porosity (volume change) and the stress triaxiality ratio (hydrostatic pressure), was highlighted.     

Effect of the porosity and particle size of materials on sound-wave velocity

Methods were developed to measure longitudinal and transverse sound velocities in porous materials — various Zn-S mixtures and KBr samples. It is shown that, on exposure to ultrasound with a wavelength far exceeding the pore size in pressed samples, a porous body behaves as a continuous medium. Sound velocity in a porous material was found to depend on the quantitative ratio of vacuum, air, and toluene in the pores. Bulk sound velocities estimated using an additive method agree with experimental data within an error not more than 10%. It was found that removal of moisture traces from porous samples led to significant absorption of sound waves. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 121–127, July–August, 2009.     

Influence of the particle size and volume fraction on micro-damage of the composites

The bulk and shear modulus of metal matrix composites with various volume fractions of particles are modified based on the Eshelby’s equivalent inclusion method combined with self-consistent scheme. By introducing the modified modulus, a new model, which can predict the particle size effects on the stress–strain relation under interfacial debonding damage between matrix and particles, is established. The results obtained from the present investigation show a better agreement with the experimental data.     

A study on stress intensity factors and singular stress fields of three-dimensional interface crack

By using the finite-part integral concepts and limit technique, the hypersingular integrodifferential equations of three-dimensional (3D) planar interface crack were obtained; then the dominant-part analysis of 2D hypersingular integral was further used to investigate the stress fields near the crack front theoretically, and the accurate formulae were obtained for the singular stress fields and the complex stress intensity factors. After that, a numerical method is proposed to solve the hypersingular integrodifferential equations of 3D planar interface crack, and the problem of elliptical planar crack is then considered to show the application of the method. The numerical results obtained are satisfactory. Project supported by the Foundation of Solid Mechanics Open Research Laboratory of State Education Commission at Tongji University and the National Natural Science Foundation.     

Effect of interface stress on the fracture behavior of a nanoscale linear inclusion along the interface of bimaterials

This paper investigates the influence of residual interface tension on the fracture behavior of a nanoscale linear interface inclusion in a bimaterial matrix. Solutions to the inclusion opening displacement and the energy release rate are obtained. The results show that the interface effect on the inclusion deformation and inclusion tip field are prominent at nanoscale. Especially, the residual interface stress has a dramatic influence on the energy release rate. It is also found that the importance of the interface effect depends on the size of the inclusion, the shear modulus ratios of the bimaterial. The inclusion opening displacement and the energy release rate can be reduced considerably by decreasing the inclusion length at nanoscale.     

Effect of particle shape and size on flow properties of lactose powders

The shape and size of particles are understood to affect the bulk behaviour of powders, though there are but few studies that present quantitative information on the relationship between particle shape and the flow properties of powder. This is due in part to the lack of techniques for rapidly determining both particle shape and the range of flow characteristics that describe the response of powders to the stress and shear experienced during their processing. This study presents data that quantifies the influence of particle shape/size of three different lactose powders on their respective flow and bulk characteristics. Two of the samples differ in size but have similar shapes; the third sample is more spherical but similar in size to one of the other two samples. The results demonstrate that in addition to particle size, particle shape significantly affect the flow characteristics of a powder over a wide range of stress conditions.     

Effects of soil and operational parameters on soil-tire interface stress vectors

Normal and tangential stress vectors were measured at the soil-tire interface of a pneumatic tractor tire on firm and soft soils. Stress magnitudes were determined with a transducer which was designed to measure both normal and tangential stresses. The orientation of the transducer was determined using a 3-dimensional, sonic digitizing system which was mounted inside the air cavity of the tire. Data are presented from tests conducted at zero input torque, zero net traction, and 0.15 net traction ratio which show the effects of inflation pressure, dynamic load, and soil conditions on the stress vectors.     

Prediction of wheel performance by analysis of normal and tengential stress distributions under the wheel-soil interface

Prediction of wheel performance by analysis of normal stress distribution under the wheel-soil interface was reported by one of our research members. In this study analysis of both normal and tangential stress distributions are included for the prediction of wheel performance. A visco-elastic soil model based on a three-element Maxwell model is used to evaluate normal stress distribution under a wheel running on soft ground. The values of the parameters characterizing the visco-elastic behavior of the soil can be derived from plate penetration tests. A rigid wheel-soil interface model is used to evaluate the tangential stress distribution under the wheel-soil interface. Shear deformation modulus, cohesion and angle of internal shearing resistance of the soil are derived from shear-displacement tests. Test results indicate that both maximum normal and shear stress occur in front of the wheel axle, and the location of peak normal stress shifts backwards towards the wheel axle while that of tangential stress shifts forwards when slippage is increased from a low value. Increasing slippage also causes a decrease in normal stress and an increase in tangential stress. Coefficients of traction and tractive efficiency are low at low slippage, increase with an increase in slippage, and level off at higher slippage.