Numerical simulation and experimental study of solidification of squeeze cast aluminum composites in the presence of cooled fibers

In order to improve the material properties of fiber-reinforced aluminum composites, experimental research has been carried out to create finer matrix microstructures and novel interfaces between aluminum matrix (A2014) and carbon fibers using a modified pressure infiltration technique. In this novel process the ends of the fibers extending outside the mold are cooled by using a variety of heat sinks. Solidification microstructures show that the dendrite arm spacing in between and around the fibers are much finer than in the region where there are no fibers. This suggests the possibility of refining the matrix microstructures by cooling the fibers extending out of the mold. A numerical simulation is also performed to study the solidification process of aluminum matrix by finite volume method. The cooling curves obtained by the simulation are compared with the experimentally measured cooling curves in order to validate the numerical model. It is found that the simulation result closely matches the experimentally obtained data.     

Simulation of metal matrix composite solidification in the presence of cooled fibers

Metal matrix composite (MMC) has been well known for its superior material properties compared with traditional composite. A new method is introduced to improve the properties of MMC in the sense that the ends of the reinforcement phase of the composite are allowed to extend out of the mold and cooled by a heat sink in order to promote the rate of heat transfer through the fibers and promote the formation of primary alpha phase around the reinforcement. This paper presents the experimental results obtained from the foundry in the University of Wisconsin-Milwaukee and some numerical simulation results of the solidification process in the cast mold.     

双周期圆截面纤维复合材料平面问题的解析法

结合双准周期Riemann边值问题理论与Eshelby等效夹杂原理，为双周期圆截面纤维复合材 料平面问题发展了一个实用有效的解析方法，获得了问题的全场级数解并与有限元结果进行 了比较. 该方法为非均匀材料的力学性质分析和复合材料等新材料的微结构设计提供了 一个有效的计算工具，也可用来评估有限元等数值与近似方法的精度.     

Creep-rupture lifetime simulation of unidirectional metal matrix composites with and without time-dependent fiber breakage

A numerical simulation for predicting the axial creep-rupture lifetime of continuous fiber-reinforced metal matrix composites is proposed, based on the finite element method. The simulation model is composed of line elements representing the fibers and four-node isoparametric plane elements representing the matrix. While the fibers behave as an elastic body at all times, the matrix behaves as an elasto-plastic body at the loading process and an elasto-plastic creep body at the creep process. It is further assumed in the simulation that the fibers are fractured not only in stress criterion but time-dependently with random nature. Simulation results were compared with the creep-rupture lifetime data of a boron-aluminum composite with 10% fiber volume fraction experimentally obtained. The simulated creep-rupture lifetimes agreed well with the averages of the experimental data. The proposed simulation is further carried out to predict a possibility of creep-rupture for the composite without time-dependent fiber breakage. It is finally concluded that the creep-rupture of a boron-aluminum composite is closely related with the shear stress relaxation occurring in the matrix as well as time-dependent fiber breakage.     

有限长滚子黏滑接触分析

有限长线接触在齿轮传动与滚子轴承中广泛存在,滚子端部的应力集中严重影响机械零件的疲劳寿命. 本文中基于矩阵法和重叠半空间模型方法建立了有限长滚子黏滑接触的数值计算模型,利用共轭梯度法和快速傅里叶变换方法对模型进行了求解;并且分析了滚子自由端面和不同切向力对滚子黏滑接触的影响. 结果表明:当两有限长滚子的自由端面完全重合时,切应力在端面不会出现应力集中现象,端面的黏着区域相比于中间截面的黏着区会缩小. 此外,随着切向力的增大,端面黏滑区域的切应力增大.      

Second-order estimate of the macroscopic behavior of periodic hyperelastic composites: theory and experimental validation

This paper deals with some theoretical and experimental aspects of the behavior of periodic hyperelastic composites. We focus here on composites consisting of an elastomeric matrix periodically reinforced by long fibers. The paper is composed of three parts. The first part deals with the theoretical aspects of compressible behavior. The second-order theory of Ponte Castañeda (J. Mech. Phys. Solids 44 (1996) 827) is considered and extended to periodic microstructures. Comparisons with results obtained by the finite element method show that the composite behavior predicted by the present model is much more accurate for compressible than for incompressible materials. The second part deals with the extension of the method to incompressible behavior. A mixed formulation (displacement-pressure) is used which improves the accuracy of the estimate given by the model. The third part presents experimental results. The composite tested is made of a rubber matrix reinforced by steel wires. Firstly, the matrix behavior is identified with a tensile test and a shear test carried out on homogeneous samples. Secondly, the composite is tested under shearing. The experimentally measured homogenized stress is then compared with the predictions of the model.     

Discrete modeling of crack bridging by a discontinuous platelet with a controlled interface

Crack bridging by discontinuous fibers can make brittle materials tougher by transferring stresses from the crack tip to elsewhere in the matrix material. One important aspect of crack bridging is the nature of the interface between the fibers and the matrix material. In this paper, a two-dimensional numerical model of bridging a Mode I loaded crack by linear elastic discontinuous platelets is developed for two different types of interfaces. The first type is a perfectly bonded interface. The second type is an imperfect interface described as a stick–slip interface. A shear-lag model to predict platelet pullout is developed in detail to verify the numerical implementation of the stick–slip interface. An example of a crack tip bridged by a platelet is examined for both interfaces. The perfectly bonded interface will reduce the Stress Intensity Factor (SIF) of the crack greatly but introduces new stress concentrations at the platelet ends. The stick–slip interface can be tailored to also reduce the SIF while not introducing new stress concentrations.     

THERMOMECHANICAL RESPONSE OF SMA FIBER COMPOSITES WITH NON-UNIFORM TEMPERATURE DISTRIBUTION

A micromechanics method based on the High-Order-Theory developed by Aboudi et al. is used to predict the thermomechanical response of composites reinforced by shape memory alloy (SMA) fibers, and the non-uniform thermal distribution in composite arising from the process of heating or cooling is considered. The numerical development based on this model was coded to predict the thermomechanical response of shape memory alloy fiber/elastomer matrix composite subjected to thermal cycle loading. When the composite is heated, two heating ways, thermal gradients and heat source by passing an electric current through the SMA fibers are imposed on the composite respectively. Upon cooling, the first thermal boundary condition and the second thermal boundary condition are subjected to the composite respectively. A series of stress distributions and temperature distributions for different instants are calculated to reveal the interaction between the SMA material and matrix. It is useful to analyze and design the SMA actuator driven by heat source or the surface temperature.     

多尺度嵌入式离散裂缝模型模拟方法

天然裂缝性油藏和人工压裂油藏内裂缝形态多样,分布复杂,传统的离散裂缝模型将裂缝作为基岩网格的边界,采用非结构化网格进行网格划分,其划分过程复杂,计算量大。嵌入式离散裂缝模型划分网格时不需要考虑油藏内的裂缝形态,只需对基岩系统进行简单的网格剖分,可以大大降低网格划分的复杂度,从而提高计算效率。然而,在油藏级别的数值模拟和人工压裂裂缝下的产能分析中,仍然存在计算量巨大、模拟时间过长的问题。本文提出嵌入式离散裂缝模型的多尺度数值计算格式,使用多尺度模拟有限差分法研究嵌入式离散裂缝模型渗流问题。通过在粗网格上求解局部流动问题计算多尺度基函数,多尺度基函数可以捕捉裂缝与基岩间的相互关系,反映单元内的非均质性,因此该方法既有传统尺度升级法的计算效率,又可以保证计算精度,数值结果表明这是一种有效的裂缝性油藏数值模拟方法。     

Molten droplet solidification and substrate remelting in microcasting Part I: numerical modeling and experimental verification

This paper presents a numerical model of a molten metal droplet impinging, solidifying and bonding to a solid substrate. The physical and numerical model includes dissimilar materials, multi-dimensional axisymmetric heat transfer, tracking of solid/liquid interfaces during remelting and solidification, and coupled treatment of the continuous droplet/substrate region. The numerical model solves for the evolution of the temperature distribution in the droplet and substrate, predicts the position of the remelting and solidification fronts, and accounts for convective motion. The effect of the convection induced by the droplet spreading is modeled through a time-dependent effective thermal conductivity. High-speed filming of the molten droplet impinging and spreading on the substrate is performed to obtain the required parameters to determine this time dependent effective conductivity. The accuracy of the model is investigated with experimental techniques. This research is directly related to the development of microcasting Shape Deposition Manufacturing (SDM) which is a process for automatically fabricating complex multi-material objects by sequentially depositing material layers. Microcasting is a molten metal droplet deposition process in SDM, which is able to create fully dense metal layers with controlled microstructure. Important issues in the production of high quality objects manufactured with microcasting SDM are: attainment of interlayer metallurgical bonding through substrate remelting, control of both substrate and droplet cooling rates, and minimization of residual thermal stresses. To validate experimentally the numerical modeling approach, predicted cooling rates are compared with thermocouple measurements and substrate remelting depths are verified through optical metallographic techniques. Received on 10 June 1998     

The effects of casting speed on steel continuous casting process

A three dimensional simulation of molten steel flow, heat transfer and solidification in mold and “secondary cooling zone” of Continuous Casting machine was performed with consideration of standard k−ε model. For this purpose, computational fluid dynamics software, FLUENT was utilized. From the simulation standpoint, the main distinction between this work and preceding ones is that, the phase change process (solidification) and flow (turbulent in mold section and laminar in secondary cooling zone) have been coupled and solved jointly instead of dividing it into “transient heat conduction” and “steady fluid flow” that can lead to more realistic simulation. Determining the appropriate boundary conditions in secondary cooling zone is very complicated because of various forms of heat transfer involved, including natural and forced convection and simultaneous radiation heat transfer. The main objective of this work is to have better understanding of heat transfer and solidification in the continuous casting process. Also, effects of casting speed on heat flux and shell thickness and role of radiation in total heat transfer is discussed.     

Deterministic physical influence control of interfacial motion in thermal processing of solidified materials

In this paper, a new experimental method of phase interface motion control with time dependent boundary cooling is presented for ice–water solidification problems. A numerical method for inverse heat transfer problems was developed to predict the transient boundary conditions, which produce a prescribed phase interface motion. In the experimental study, the predicted boundary temperatures from the numerical simulation were used to control the ice–water interface movement for various specified interface motions. Two cases of different phase interface velocities were considered. Water supercooling was observed during each experiment. A time delay in the thermal control was calculated based on an analytical solution. Close agreement between measured data and specified interface motion was achieved for the ice–water solidification problems.     

Numerical simulation and experimental investigation of the elastocaloric cooling effect in sputter-deposited TiNiCuCo thin films

The exploitation of the elastocaloric effect in superelastic shape memory alloys (SMA) for cooling applications shows a promising energy efficiency potential but requires a better understanding of the non-homogeneous martensitic phase transformation. Temperature profiles on sputter-deposited superelastic \({\mathrm {Ti_{55.2}Ni_{29.3}Cu_{12.7}Co_{2.8}}}\) shape memory alloy thin films show localized release and absorption of heat during phase transformation induced by tensile deformation with a strong rate dependence. In this paper, a model for the simulation of the thermo-mechanically coupled transformation behavior of superelastic SMA is proposed and its capability to reproduce the mechanical and thermal responses observed during experiments is shown. The procedure for experiment and simulation is designed such that a significant temperature change from the initial temperature is obtained to allow potential cooling applications. The simulation of non-local effects is enabled by the use of a model based on the one-dimensional Müller–Achenbach–Seelecke model, extended by 3D mechanisms such as lateral contraction and by non-local interaction, leading to localization effects. It is implemented into the finite element software COMSOL Multiphysics, and comparisons of numerical and experimental results show that the model is capable of reproducing the localized transformation behavior with the same strain rate dependency. Additionally to the thermal and the mechanical behavior, the quantitative prediction of cooling performance with the presented model is shown.     

Helical Fiber Pull-out in Biological Materials

Many biological materials, such as wood and bone, possess helicoid microstructures at microscale, which can serve as reinforcing elements to transfer stress between crack surfaces and improve the fracture toughness of their composites. Failure processes, such as fiber/matrix interface debonding and sliding associated with pull-out of helical fibers, are responsible mainly for the high energy dissipation needed for the fracture toughness enhancement. Here we present systemic analyses of the pull-out behavior of a helical fiber from an elastic matrix via the finite element method(FEM) simulation, with implications regarding the underlying toughening mechanism of helicoid microstructures. We find that, through their uniform curvature and torsion, helical fibers can provide high pull-out force and large interface areas, resulting in high energy dissipation that accounts, to a large extent, for the high toughness of biological materials. The helicity of fiber shape in terms of the helical angle has significant effects on the force-displacement relationships as well as the corresponding energy dissipation during fiber pull-out.     

Numerical simulation of heat,mass and momentum transport behaviours in directionally solidifying alloy castings under electromagnetic fields using an extended Direct‐SIMPLE scheme

A Direct‐SIMPLE scheme is further extended for numerical simulations of heat and species mass transfer, and liquid flow behaviours in solidification processes of shaped alloy castings under various electromagnetic (EM) fields, based on a binary continuum model (a solidification transport phenomena/processes (STP)‐based dendrite solidification model). Unlike in a SIMPLE scheme, no iterative computations are needed to achieve the final pressure and velocity corrections in the extended Direct‐SIMPLE procedure, therefore extremely high computational efforts can be avoided. Using three different types of model alloys, pseudo‐binary In718 base‐4.85 wt% Nb, γ(TiAl)‐55 at% Al and Al‐4.5 wt% Cu systems, sample computations for solving strongly coupled solidification transport phenomena in directionally solidifying shaped castings under static and harmonic EM‐fields of different strengths are carried out, to demonstrate the feasibility and efficient calculation performance of the present model and numerical methods. Copyright © 2004 John Wiley & Sons, Ltd.     

A Numerical Investigation of Transpiration Cooling with Liquid Coolant Phase Change

This article presents a numerical approach to investigate the transpiration cooling problems with coolant phase change within porous matrix. A new model is based on the coupling of the two-phase mixture model (TPMM) with the local thermal non- equilibrium (LTNE), and used to describe the liquid coolant phase change and heat exchange processes in this article. The effects of thermal conductivity, porosity, and sphere diameter of the porous matrix on the temperature and saturation distributions within the matrix are studied. The results indicate that an increase in the porosity or sphere diameter can lead to an area dilation of two-phase region and a rise of liquid temperature; whereas an increase in the thermal conductivity of the porous matrix results only in a rise of liquid temperature, but drops of solid temperature and temperature gradient on the hot surface. The influence of hot surface pressure on cooling effect is discussed by numerical simulations, and numerical results show that the effect of the transpiration cooling will be worse under higher pressure. The investigation also discovers an inverse phenomenon to the past investigations on the transpiration cooling without coolant phase change, namely in two-phase region, coolant temperature may be higher than solid temperature. This inversion can be captured only by the new LTNE–TPMM.     

Direct 2D simulation of small gas bubble clusters: from the expansion step to the equilibrium state

A numerical strategy, based on an adaptive finite element method, is proposed for the direct two‐dimensional simulation of the expansion of small clusters of gas bubbles within a Newtonian liquid matrix. The velocity and pressure fields in the liquid are first defined through the Stokes equations and are subsequently extended to the gas bubbles. The liquid–gas coupling is imposed through the stress exerted on the liquid by gas pressure (ruled by an ideal gas law) and by surface tension. A level set method, combined with a mesh adaptation technique, is used to track liquid–gas interfaces. Many numerical simulations are presented. The single bubble case allows to compare the simulations to an analytical model. Simulations of the expansion of small clusters are then presented showing the interaction and evolution of the gas bubbles to an equilibrium state, involving topological rearrangements induced by Plateau's rule. Copyright © 2006 John Wiley & Sons, Ltd.     

STATISTIC MODELING OF THE CREEP BEHAVIOR OF METAL MATRIX COMPOSITES BASED ON FINITE ELEMENT ANALYSIS

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Numerical investigation of transpiration and ablation cooling

To predict the integral performance of transpiration and ablation cooling during the reentry of hypersonic vehicles, an unsteady numerical model based on the assumption of thermal equilibrium is presented. The non-thermal equilibrium model and the thermal equilibrium model are coupled by the effective thermal properties of the porous matrix and the coolant. The calculation using the thermal equilibrium model shows the influence of the variation of the effective thermal properties on the numerical results by a comparison between constant and variable thermal properties. The comparison indicates that near the melting temperature of the porous matrix, the position of the moving boundary due to ablation is sensitive to the temperature, therefore, the variation of the thermal properties are considered in this paper. The process of ablation and transpiration cooling is simulated under different numerical conditions. The simulations demonstrate that the injection rate of coolant mass flow and initial temperature of cooling are important parameters for the control of the ablation process.     

A dual-scale coupled micro/macro segregation model for dendritic alloy solidification

The present article reports on the formulation, numerical implementation, and application of a single-domain coupled micro/macroscopic model for simulation of dendritic alloy solidification. Microscopic solutal non-equilibrium effects have been included in the macroscopic modeling of solidification by using a fixed grid dual scale numerical approach. Salient features of the present approach include a continuum model for conservation of mass, momentum, energy and species on the macroscopic scale, a microscopic solute redistribution model, and the solution procedure and auxiliary equations necessary for coupling between the two models. The coupling between macro and micro scale models is practically made possible by introducing an iterative micro/macro time step scheme. The local solidification rate is calculated by implicit iterations of macroscopic conservation equations and the microscopic solute redistribution model. The present model is capable to simulate eutectic reaction, local re-melting, and account for the inter-linkage between micro and macroscopic solute redistribution (micro and macrosegregation).