Mode I crack tip field with strain gradient effects

A plane strain mode I crack tip field with strain gradient effects is investigated. A new strain gradient theory is used. An elastic-power law hardening strain gradient material is considered and two hardening laws, i.e. a separation law and an integration Law are used respectively. As for the material with the separation law hardening, the angular distributions of stresses are consistent with the HRR field, which differs from the stress results([19]); the angular distributions of couple stresses are the same as the couple stress results([19]). For the material with the integration law hardening, the stress field and the couple stress field can not exist simultaneously, which is the same as the conclusion([19]), but for the stress dominated field, the angular distributions of stresses are consistent with the HRR field; for the couple stress dominated field, the angular distributions of couple stresses are consistent with those in Ref. [19]. However, the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only, while the crack tip field of mode I is dominated by the tension gradient, which will be shown in another paper.

The Influence of Strain Gradient on the shear Band in a Saturated Soil

The dynamic localization of saturated soil is investigated by considering the influence of higher strain gradient. It is shown that the strain gradient has a significant influence on the evolution of shear band in saturated soil and that the width of shear band is proportional to the square root of the strain gradient softening coefficient. The numerical simulation is processed to investigate the influences of shear strain gradient and other factors on the evolution of shear band.

What Do We Know about Long Laminar Plasma Jets?

Silent and stable long laminar plasma jets can be generated in a rather wide range of working parameters. The laminar flow state can be maintained even if considerable parameter fluctuations exist in the laminar plasma jet or if there is an impact of laterally injected particulate matter and its carrier gas. The attractive special features of laminar plasma jets include extremely low noise level, less entrainment of ambient air, much longer and adjustable high-temperature region length, and smaller axial gradient of plasma parameters. Modeling results show that the laminar plasma jet length increases with increasing jet inlet velocity or temperature and the effect of natural convection on laminar plasma jet characteristics can be ignored, consistent with experimental observations. The large difference between laminar and turbulent plasma jet characteristics is revealed to be due to their different laws of surrounding gas entrainment. Besides the promising applications of the laminar plasma jet to remelting and cladding strengthening of the metallic surface and to thermal barrier coating preparation, it is expected that the laminar plasma jet can become a rather ideal object for the basic studies of thermal plasma science owing to the nonexistence of the complexity caused by turbulence.

In situ formation by laser cladding of a TiC composite coating with a gradient distribution

An in situ method was developed to produce an Ni alloy composite coating reinforced by in situ reacted TiC particles with a gradient distribution, using one-step laser cladding with a pre-placed powder mixture on a 5CrMnMo steel substrate. Dispersed and ultra-fine TIC particles were formed in situ in the coating. Most. of the TiC particles, with a marked gradient distribution, were uniformly distributed within interdendritic regions because of the trapping effect of the advancing solid-liquid interface. In addition, the TiC-gamma-Ni interfaces generated in situ were found to be free from any deleterious surface reaction. Finally, the microhardness also showed a gradient variation, with the highest value of 1250 Hv0.2 and the wear properties of the coating were significantly enhanced.

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.

Comparative Study Of The Influence Of Natural Convection On Directional Solidification Of Al-3.5 Wt% Ni And Al-7 Wt% Si Alloys

We present numerical simulations of thermosolutal convection for directional solidification of Al-3.5 wt% Ni and Al-7 wt% Si. Numerical results predict that fragmentation of dendrite arms resulting from dissolution could be favored in Al-7 wt% Si, but not in Al-3.5 wt% Ni. Corresponding experiments are in qualitative agreement with the numerical predictions. Distinguishing the two fragmentation mechanisms, namely dissolution and remelting, is critical during experiments on earth, when fluid flow is dominant. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Anisotropic, gradient and metal-like mechanical behaviors of teeth and their implications on tooth functions

The anisotropy and gradient of the elastic modulus and the hardness of teeth were investigated by means of instrumented indentation method. Such properties are attributed to the unique microstructures of teeth based on scanning electron microscopic analysis. By comparing the relationship between the ratio of hardness to the reduced elastic modulus and the ratio of elastic unloading work to the total work of teeth in course of indentation to those of other materials, we found that the material behaviors of teeth display metal-like characteristics rather than ceramics as considered traditionally. These material behaviors and relevant functions are discussed briefly.

Deflections and curvatures of a film-substrate structure with the presence of gradient stress in MEMS applications

The close form solutions of deflections and curvatures for a film-substrate composite structure with the presence of gradient stress are derived. With the definition of more precise kinematic assumption, the effect of axial loading due to residual gradient stress is incorporated in the governing equation. The curvature of film-substrate with the presence of gradient stress is shown to be nonuniform when the axial loading is nonzero. When the axial loading is zero, the curvature expressions of some structures derived in this paper recover the previous ones which assume the uniform curvature. Because residual gradient stress results in both moment and axial loading inside the film-substrate composite structure, measuring both the deflection and curvature is proposed as a safe way to uniquely determine the residual stress state inside a film-substrate composite structure with the presence of gradient stress.

Drop migration of middle Reynolds number in a vertical temperature gradient

The experimental investigation of the thermocapillary drop migration in a vertical temperature gradient uns performed on ground. Silicon oil and pure soybean oil were used as experimental medium in drops and as continuous phases, respectively, in the present experiment. The drop migration, under the combined effects of buoyancy: and thermocapillarity, was studied for middle Reynolds numbers in order of magnitude O(10(1)). The drop migration velocities depending on drop diameters were obtained. The present experimental results show relatively small migration velocity in comparison with the one suggested by Young et nl. for linear theory of small Reynolds number. An example of flow patterns inside the drop was observed by PIV method.

The motion of solid particles in a liquid with vertical temperature-gradient

A ground-experiment study on the motions of solid particles in liquid media with vertical temperature gradient is performed in this paper. The movement of solid spheres toward the heating end of a close cell is observed. The behavior and features of the motions examined are quite similar to thermocapillary migration of bubbles and drops in a liquid. The motion velocities of particles measured are about 10(-3) to 10(-4) mm\s. The velocity is compared with the velocity of particles floated in two liquid media. The physical mechanism of motion is explored.

A simple approach to solve boundary-value problems in gradient elasticity

We outline a procedure for obtaining solutions of certain boundary value problems of a recently proposed theory of gradient elasticity in terms of solutions of classical elasticity. The method is applied to illustrate, among other things, how the gradient theory can remove the strain singularity from some typical examples of the classical theory.

Approximate theory of natural-convection with small grashof number

To gain some insight into the behaviour of low-gravity flows in the material processing in space, an approximate theory has been developed for the convective motion of fluids with a small Grashof number Gr. The expansion of the variables into a series of Gr reduces the Boussinesq equation to a system of weakly coupled linearly inhomogeneous equations. Moreover, the analogy concept is proposed and utilized in the study of the plate bending problems in solid mechanics. Two examples are investigated in detail, i. e. the 2-dimensional steady flows in either circular or square infinite closed cylinder, which is horizontally imposed at a specified temperature of linear distribution on the boundaries. The results for stream function ψ, velocity u and temperature T are provided. The analysis of the influences of some parameters such as the Grashof number Gr and the Prandtl number Pr, on motions will lead to several interesting conclusions. The theory seems to be useful for seeking for an analytical solutions. At least, it will greatly simplify the complicated problems originally governed by the Navier-Stokes equation including buoyancy. It is our hope that the theory might be applicable to unsteady or 3-dimensional cases in future.

Transient Flows in Low Permeability Porous Media with Composite Start-Up Pressure Gradient

A new mathematical model for the transient flow in the composite low permeability is established. It is solved by FEM with different boundary conditions such as infinite, circular closed and constant pressure boundary conditions. The typical curves for transient wellbore pressure have been presented. It is shown that the pressure and pressure derivative curves with composite start-up pressure gradients have different slopes which are depended on the start-up pressure gradients and the mobility radios in different regions. The boundary effects are the same as the normal reservoirs without start-up pressure gradients. The study provides a new tool to analyze the transient pressure test data in the low permeability reservoir.

Simulation of Natural Gas Production in Hydrate Reservoirs

This paper simulates a one-dimensional physical model of natural gas production from hydrate dissociation in a reservoir by depressurization. According to the principles of solid hydrate decomposition in stratum and flow of natural gas in porous medium, the pressure governing equations for both gas zone and hydrate zone are set up based on the physical production model. Using the approximation reported by N. N. Verigin et al. (1980), the nonlinear governing equations are simplified and the self-similar solutions are obtained. Through calculation, for different reservoir parameters, the distribution characters of pressure are analyzed. The decline trend of natural gas production rate with time is also studied. The simulation results show that production of natural gas from a hydrate reservoir is very sensitive to several reservoir parameters, such as wellbore pressure and stratum porosity and permeability.

What Do We Know about Long Laminar Plasma Jets?

Silent and stable long laminar plasma jets can be generated in a rather wide range of working parameters. The laminar flow state can be maintained even if considerable parameter fluctuations exist in the laminar plasma jet or if there is an impact of laterally injected particulate matter and its carrier gas. The attractive special features of laminar plasma jets include extremely low noise level, less entrainment of ambient air, much longer and adjustable high-temperature region length, and smaller axial gradient of plasma parameters. Modeling results show that the laminar plasma jet length increases with increasing jet inlet velocity or temperature and the effect of natural convection on laminar plasma jet characteristics can be ignored, consistent with experimental observations. The large difference between laminar and turbulent plasma jet characteristics is revealed to be due to their different laws of surrounding gas entrainment. Besides the promising applications of the laminar plasma jet to remelting and cladding strengthening of the metallic surface and to thermal barrier coating preparation, it is expected that the laminar plasma jet can become a rather ideal object for the basic studies of thermal plasma science owing to the nonexistence of the complexity caused by turbulence.