Simulation of crack propagating in discontinuously reinforced metal matrix composite

A fracture mechanics-based numerical simulation of a crack propagating under mode I loading through discontinuously reinforced metal matrix composites (MMCs) is presented. Microcrack initiation due to debonding and breakage of reinforcements, shielding and antishielding effects caused by both microcracks and the reinforcements, the effect of crack deflection, and growing crack singularity are considered in the calculation of local crack tip driving forces. Statistical variations of spatial distribution and strength of the reinforcements are also considered. The essential feature of the model is to predict crack initiation toughness and crack path morphologies using a mixed-mode crack propagation criterion. Application of the program to predict crack growth behavior in an SiC whisker/Al alloy composite is presented. Microcracking far ahead of the tip of a main crack, crack deflection toward the microcracks, and subsequent incorporation of the microcracks which most affect the main crack are well simulated. The predicted microcrack distribution and variation of mixed-mode crack tip driving forces with crack growth are also evaluated.     

Fluid flow through a solid-liquid dendritic interface

Fluid flow through a dendritic solid-liquid interfacial zone, during solidification, has been observed in a series of Sn-Pb alloys. It was found that liquid penetrates only a short distance into the zone, relative to the total thickness of the zone. The amount of solid present at the point of maximum penetration varies from 12 to 22 pct, and depends on the alloy concentration. Flow due to volume shrinkage, thermal convection, or solute convection well inside the zone, was not detected. Fluid flow through a wire mesh model of a thin section of the solid-liquid dendritic zone was examined. The results are not in agreement with that predicted for flow through a porous barrier, which had been found applicable to interdendritic fluid flow. Formerly Graduate Student, University of British Columbia, Vancouver, British Columbia, Canada     

Fluid flow in porous systems

Nuclear magnetic resonance (NMR) measurements of water velocity flowing through glass bead packs with a bead diameter of 10 mm have been made using the phi echo-planar imaging (PEPI) sequence. These results indicate that for various flow rates the flow variance is proportional to the mean flow velocity in agreement with the Mansfield-Issa equation. The velocity distributions are approximately Gaussian. Investigation of the slopes of the variance vs. velocity curves as a function of slice thickness indicate some coherence effects in the connectivity of the glass bead system. An extension of an earlier intervoxel coupling model is presented, which seems to explain the observed coherence effects.     

Fluid flow in filling ladles

The fluid flow generated during the course of tapping operations from Basic Oxygen Furnaces was analyzed. Mathematical models of the filling process were developed, and their predictions checked with experimental values obtained using a one-tenth scale model of the ladle. Reasonable agreement was achieved. Based on the full scale predictions, it is suggested that the magnitude of flow velocities are technologically significant in terms of their effect on ferro-alloy immersion times and recoveries. Formerly a Research Associate at McGill University.     

Fluid flow in filling ladles

The fluid flow generated during the course of tapping operations from Basic Oxygen Furnaces was analyzed. Mathematical models of the filling process were developed, and their predictions checked with experimental values obtained using a one-tenth scale model of the ladle. Reasonable agreement was achieved. Based on the full scale predictions, it is suggested that the magnitude of flow velocities are technologically significant in terms of their effect on ferro-alloy immersion times and recoveries.     

Fluid flow phenomena in a single phase coreless induction furnace

New measurement techniques for local velocity, magnetic field, and current density have been applied to the study of electromagnetic and hydrodynamic phenomena in a coreless induction furnace containing an aluminum alloy. The action of electromagnetic shields on the intensity and the structure of the liquid metal flow is reported. It is shown that the direction of the fluid flow and the number and sizes of the recirculating cells may be significantly modified; the electromagnetic stirring may also be practically canceled. The influence of the dimensions of the screens on the structure of the liquid metal flow is examined. Finally, the modification of the fluid flow phenomena is explained by the evolution of the electromagnetic force patterns.     

Fluid flow in solidifying monotectic alloys

Use of a two-wavelength holographic technique results in a simultaneous determination of temperature and composition profiles during directional solidification in a system with a miscibility gap. A shadowgraph technique is employed for flow visualization. By these methods, flow regimes are identified and related to particular melt compositions. We discuss the relationships among fluid flow, phase separation, and mass transport during the solidification of the monotectic alloy. The primary sources of fluid motion in this system are buoyancy and thermocapillary forces. These forces act together when phase separation results in the formation of droplets (this occurs at the solid-liquid interface and in the bulk melt). While buoyancy forces arise due to density differences between the droplet and the host phase, thermocapillary forces (associated with temperature gradients in the droplet surface) may predominate. In the absence of phase separation, buoyancy results from density gradients related to temperature and compositional gradients in the single-phase bulk melt. The effects of buoyancy are especially evident in association with water- or ethanol-rich volumes created at the solid-liquid growth interface.     

Fluid flow from a low to a higher density liquid

The penetration of liquid from a low density brine solution into a higher density solution below it has been measured as a function of vertical flow velocity and the density difference of the two solutions. The flow velocity was produced by a horizontal disc rotating in the low density liquid. The results show the penetration distance and penetration rate are dependent on flow velocity and in particular are very sensitive to small changes in the density difference between the two liquids. The observations are considered in relation to liquid penetration into dendritic arrays, and fluid flow in the pool of ingots and continuously cast steel billets, during solidification.     

Fluid flow into a dendritic array under forced convection

The flow of liquid into the solid-liquid region of AISi, AlCu, and AlMg alloys, freezing upward, has been examined using radioactive tracers. With the liquid stirred by a rotating disc, it was found that the liquid penetrated a relatively short distance into the solid-liquid region, the penetration increasing a small amount with increasing flow velocity. The volume fraction liquid at maximum penetration was large, greater than 0.63. Flow into the solid-liquid region in AlMg was similar to that observed in AISi, but flow in AlCu was less. A water model containing solid dendrites, simulating the metal system, was used to observe directly fluid flow in a simplified solid-liquid region. The results showed that flow into the solid-liquid region increased appreciably when either the flow velocity was strongly increased or the temperature difference between the interdendritic liquid and free flowing liquid decreased. The penetration was not significantly changed with changes in dendrite morphology or the length of the solid-liquid region.     

单流板坯连铸中间包流体流动控制与效果

通过物理模拟实验,研究了南钢板坯连铸不同结构中间包的流动特性,优化了中间包结构.中间包结构优化后,最小停留时间提高120%,浓度峰值时间提高97%,死区体积分率降低72%.实验结果表明,开发的异型边结构的湍流控制器可以更好地改善单流中间包的流体流动特性.现场实际应用的结果表明,中间包结构优化后,铸坯夹杂物面积比下降了32%.     

Fluid flow and mixing in secondary metallurgy

Mixing in metallurgical vessels is determined by bulk flow, turbulence and diffusion. In this presentation, the main features of mixing liquid steel by gas stirring are discussed. The criteria for bubbling and jetting during gas injection are considered including interaction of powder load on flow regimes. It is of interest to know the domains of bubbling and jetting behaviour in order to minimize the effect of back attack which is responsible for additional wear of bottom linings and tuyere pipes. Quantitative information is given on velocity, the radius and the pumping capacity of the buoyant plume. The relations lead to the conclusion that the gas flow should be apportioned to two or more plugs in order to increase the efficiency of the pumping effect. Furthermore, the macroscopic flow pattern is substantially influenced by the ratio of height to diameter of the ladle. Especially at high ratios dead volumes near the ladle bottom are observed. Further examples for the influence of fluid flow on reactions, dispersing and separating in the ladle and tundish are given. At first approach, mixing time depends on the gas flow rate or on the specific power input. But the details are much more complicated. It is shown that the mixing process can be described by two types of models among others: the turbulent recirculation model and the model of partial volumes. The comparison of calculated concentration-time-dependencies with plant results confirms the practicability and usefulness of the model of partial volumes. It is also concluded that the water model results for ladles may be transferred to plant conditions. In total all examples that are discussed emphasize the great significance of model simulations and model calculations as instruments for process improvement and process development.     

Fluid flow in interdendritic space in cubic alloys

The permeability of interdendritic space was measured using unidirectionally frozen organic borneol-paraffin alloys whose columnar dendrite structure was the same as that of metallic alloys of f.c.c. and b.c.c. An aqueous solution containing a small amount of red ink and 25 vol.% surface active agent was made to flow in the interdendritic space in the directions parallel to and normal to columnar dendrites. In both flow cases, the permeability was approximately proportional to the cube of the fraction liquid. For flow normal to columnar dendrites, the permeability increased with primary and secondary arm spacings. When the flow direction was parallel to columnar dendrites, the permeability increased with increasing primary arm spacing but it decreased with increasing secondary arm spacing.     

Fluid flow and tracer dispersion in shallow tundishes

A mathematical model is developed to describe fluid flow and tracer dispersion in shallow tundishes. Two tundish designs are considered, namely one with a point inlet and a point outlet, and another with a point inlet and a slot outlet. Each of these designs is investigated, both in the absence and presence of flow control devices, the latter consisting of either conventional use of dams and weirs, or a magnetic field imposed perpendicularly to the main flow direction.     

Fluid flow and inclusion removal in continuous casting tundish

Three-dimensional fluid flow in continuous casting tundishes with and without flow control devices is first studied. The results indicate that flow control devices are effective to control the strong stirring energy within the inlet zone, and other zones are with much uniform streamline. By dividing tundish into two zones with different inclusion removal mechanisms the inclusion removal is calculated. Three modes of inclusion removal from molten steel in the tundish, i.e., flotation to the free surface, collision and coalescence of inclusions to form larger ones, and adhesion to the lining solid surfaces, are taken into account. The Brownian collision, Stokes collision, and turbulent collision are examined and discussed. The suitable coagulation coefficient is discussed, and a value of 0.18 is derived. Calculation results indicate that, besides flotation, collision of inclusion and adhesion to the lining solid surfaces are also important ways for inclusion removal from molten steel in tundish especially for the smaller inclusions. The flotation removal holds 49.5 pct, and the adhesion removal holds 29.5 pct for the tundish with flow control devices; the collision effect is reflected in improving flotation and adhesion. Finally, industrial experiment data are used to verify the inclusion removal model.     

Fluid flow and weld penetration in stationary arc welds

Weld pool fluid flow can affect the penetration of the resultant weld significantly. In this work, the computer simulation of weld pool fluid flow and its effect on weld penetration was carried out. Steady-state, 2-dimensional heat and fluid flow in stationary arc welds were computed, with three driving forces for fluid flow being considered: the buoyancy force, the electromagnetic force, and the surface tension gradient at the weld pool surface. The computer model developed agreed well with available analytical solutions and was consistent with weld convection phenomena experimentally observed by previous investigators and the authors. The relative importance of the influence of the three driving forces on fluid flow and weld penetration was evaluated, and the role of surface active agents was discussed. The effects of the thermal expansion coefficient of the liquid metal, the current density distribution in the workpiece, and the surface tension temperature coefficient of the liquid metal on weld pool fluid flow were demonstrated. Meanwhile, a new approach to free boundary problems involving simultaneous heat and fluid flow was developed, and the effort of computation was reduced significantly.     

Fluid flow and bath temperature destratification in gas-stirred ladles

The transient fluid flow and temperature distributions in argon-stirred ladles have been investigated. The governing equations of unsteady fluid flow and energy were solved numeri-cally with a control-volume technique, while the turbulence was modeled by the two-equationk- ∃ model. The two-phase zone was described by novel experimental equations, which char-acterize the gas-fraction distribution in the bath for a wide range of variables in both aqueous and liquid metal systems. Fully transient computational results are presented and compared against transient temperature computations based on a steady-state velocity field. The resulting mixing times compare closely with industrial experience. A.H. Castillejos E., formerly Postdoctoral Fellow, The University of British Columbia,.