How to determine critical Marangoni number in half floating zone convection

In the present paper, the coordinated measurements of the temperature profile inside the liquid bridge and the boundary variation of Free surface, in addition to other quantities, were obtained in the same time for the half floating zone convection. The results show that the onset of free surface oscillation is earlier than the one of temperature oscillation during the increasing of applied temperature difference, and the critical Marangoni numbers, defined usually by temperature measurement, are larger than the one defined by free surface measurement, and the difference depends on the volume of liquid bridge. These results induce the question, ''How to determine experimentally the critical Marangoni number?'' Copyright (C) 1996 Elsevier Science Ltd.

Fracture criterion based on the higher-order asymptotic fields

A complete development for the higher-order asymptotic solutions of the crack tip fields and finite element calculations for mode I loading of hardening materials in plane strain are performed. The results show that in the higher-order asymptotic solution (to the twentieth order), only three coefficients are independent. These coefficients are determined by matching with the finite element solutions carried out in the present paper (our attention is focused on the first five terms of the higher-order asymptotic solution). We obtain an analytic characterization of crack tip fields, which conform very well to the finite element solutions over wide range. A modified two parameter criterion based on the asymptotic solution of five terms is presented. The upper bound and lower bound fracture toughness curves predicted by modified two parameter criterion are given. These two curves agree with most of the experimental data and fully capture the proper trend.

Effects of high-frequency vibration on critical marangoni number

The influence of vibration on thermocapillary convection and critical Marangoni number in liquid bridge of half floating zone was discussed for the low frequency range 0.4-1.5 Hz and the intermediate frequency range 2.5-15 Hz in our previous papers. This paper extends the study to high frequency range 15-100Hz. This ground based experiment was completed on the deck of an electromagnetic vibration machine. The results of our experiment shows when the frequency of the applied acceleration is high enough, the amplitude of the time varying part of the temperature response is disappear and the shape of the free surface of the liquid bridge exhibits no fluctuations due to inertia. The critical Marangoni number which is defined to describe the transitions from a peroidical convection in response to vibration to an oscillatory convection due to internal instability is nearly the same as the critical Marangoni number for oscillatory flow in the absence of vibration.

Effects of g-jitter on the critical marangoni number

A half floating zone is fixed on a vibrational deck, which supports a periodical applied acceleration to simulate the effect of g-jitter. This paper deals with the effects of g-jitter on the fluid fields and the critical Marangoni number, which describes the transition from a forced oscillation of thermocapillary convection into an instability oscillatory convection in a liquid bridge of half floating zone with top rod heated. The responses of g-jitter field on the temperature profiles and flow pattern in the liquid bridge were obtained experimentally. The results indicated that the critical Marangoni number decreases with the increasing of g-jitter effect and is slightly smaller for higher frequency of g-jitter with fixed strength of applied gravity.

Influence of buoyancy on floating-zone convection of small bond number

Gravity may influence the velocity and temperature distributions, bouyancy may induce Rayleigh instability and the instability may be excited due to the change of free surface shape associating with gravity in the thermocapillary convection. These effects have been studied in the present paper. The results show that gravity may have an important effect in thermocapillary oscillatory convection even for the cases of small Bond number experiments either on the ground or in space.

Asymptotic solution of mode-iii crack in damaged softening materials

In this paper, a constitutive model of elasticity coupled with damage suggested by Lemaitre et al, [1] is used. The macroscopic stress-strain response of the model includes two stages: strain hardening and strain softening. The basic equation is derived for the anti-plane shear problem. Several lowest order asymptotic solutions are obtained, and assembled for the crack-tip fields.

High order asymptotic field for plane stress crack problem

This paper presents an exact analysis for high order asymptotic field of the plane stress crack problem. It has been shown that the second order asymptotic field is not an independent eigen field and should be matched with the elastic strain term of the first order asymptotic field. The second order stress field ahead of the crack tip is quite small compared with the first order stress field. The stress field ahead of crack tip is characterized by the HRR field. Hence the J integral can be used as a criterion for crack initiation.

Micromechanics of elastic solids weakened by a large number of cracks

This paper presents a micromechanics analysis of the elastic solids weakened by a large number of microcracks in a plane problem. A new cell model is proposed. Each cell is an ellipse subregion and contains a microcrack. The effective moduli and the stress intensity factors for an ellipse cell are obtained. The analytic closed formulas of concentration factor tensor for an isotropic matrix containing an anisotropic inclusion are derived. Based on a self-consistent method, the effective elastic moduli of the solids weakened by randomly oriented microcracks are obtained.

An asymptotic analysis for one dimensional stress wave propagation in damaged viscoelastic media

A regular perturbation technique is suggested to deal with the problem of one dimensional stress wave propagation in viscoelastic media with damage. Based upon the first order asymptotic solution obtained, the characteristics of wave attenuation are studied. In fact, there exist three different time-dependent phenomena featuring the dynamic response of the materials, the first expressing the characteristics of wave propagation, the second indicating the innate effect of visco-elastic matrix and the third coming from the time dependent damage. The comparision of first order asymptotic solution with the numerical results calculated by a finite difference procedure shows that the perturbation expansion technique may offer a useful approach to the problem concerned.