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Semisolid materials are suspensions of metal alloys which are processed while in a mushy state. In this state, the suspensions behave as viscoplastic materials with time-dependent material properties. During processing, the material is injected at high speed into a mold cavity with the process lasting only fractions of a second. The short-term transient material response is thus very important for the understanding of the rheology and the further development of the process. A theory based on the Herschel-Bulkley flow model appropriate for the short-term breakage of welded bonds in semisolid metal slurries is proposed. The "strength" of the slurry due to these bonds is assumed to be a function of a coherency parameter which is proportional to the number of welded bonds that break during the application of shear. The evolution of this parameter is described by a first-order kinetics. Using a novel and simple computational method, well suited for free and moving-boundary problems, we study the flow between two coaxial cylinders and obtain accurate results for the evolution of the structure, the extent of the yielded domain and the evolution of the stress. The results and conclusions apply directly to the design and analysis of rotational rheometer experiments for semisolid metal slurries and suspension systems exhibiting similar behavior. © 2006 Elsevier B.V. All rights reserved. 142 1-3 199 206 Cited By :16

Systematic experimental work and modeling efforts have been conducted to characterize the yield behavior of commercial aluminum alloys in the semisolid state. In this study, extensive compression experiments were performed to measure the yield stress of semisolid aluminum slurries at high solid fractions (0.5 to 1.0), and a cone penetration method was employed to measure yield stress at low solid fractions (

The quasi-conservative stochastic averaging (QCSA) method is applied to a Bouc-Wen-Baber hysteretic system (BWB) under Gaussian white noise excitations. The stationary probability density of the system's response amplitude and energy is obtained for different excitation levels and different damping ratios. These results are compared with the studies presented by Cai and Lin in A New Solution Technique for Randomly Excited Hysteretic Structures, Technical Report on Grant No. NCEER-88-0012, State University of New York, Buffalo, NY, 1988. The first-passage time problem for the hysteretic system is also studied using the method of QCSA. The results for the expected time to failure as a function of the initial total energy are shown, for different excitation levels and for different threshold values of energy. The relationship between the expected time to failure when initial total energy is zero and excitation level is shown for a wide range of hysteresis shape parameters. © 1995. 10 161 170 161-170

The finite element method was used to study steady, incompressible, laminar flow in porous tube systems. The Navier-Stokes equations were used to describe the flow phenomena in the tube and shell space while the continuum theory of Brinkman was used to describe flow in the porous tube wall. The solution method, based on the Galerkin finite element and Newton iteration techniques, provided velocities and pressures for a wide range of Reynolds numbers and operational modes. the Darcy permeability was the only adjustable parameter used in the model and it was calculated a priori. The approach was justified by a comparison to previous experimental results for flow in a porous ceramic tube and shell system. The model was then used to investigate the effect of shell diameter and tube length on the flow field for closed shell, closed end, and cross flow operation. © 1991. 46 2847 2855 2847-2855

When SSM material is subjected to a sudden transient the rate of buildup (aging) is negligible compared to the rate of breakdown (shear rejuvenation). While this is generally true, due to prolonged processing or the geometry the local shear rate in some regions may become equal or lower than the critical value, where aging becomes as important as shear rejuvenation. In this work we simulate in detail shear rejuvenation and aging in semisolid slurries. Using a standard thixotropic model used widely for modeling SSM suspensions but a novel computational method we reveal and confirm numerically for the first time shear banding. The phenomenon is found to be time dependent where the material first yields fully and then, after a certain time the yielded front retreats to form two distinct bands -one yielded and one unyielded. This phenomenon must be accounted for in the evaluation of the material constants since the time scale of the process is similar to the time scale of the phenomenon. 141-143 313 318 Sponsors: Conference code: 74970

The time-dependent, compressible extrusion of a Carreau fluid is solved over the reservoir-die-extrudate region using finite elements in space and a fully implicit scheme in time. A nonmonotonic slip law based on experimental data on polyethylene melts is assumed to hold along the die wall and the velocity at the entrance of the reservoir is taken to be fixed and uniform. As in the case of the extrudate-swell flow, the combination of compressibility and nonlinear slip leads to self-sustained oscillations of the pressure drop and of the mass flow rate in the unstable regime. The effects of the reservoir volume, the imposed flow rate, and the capillary length on the amplitude and the frequency of the pressure and free surface oscillations are studied and comparisons are made with experimental observations. © 2006 Elsevier B.V. All rights reserved. 146 1-3 30 44 Cited By :16

Development of numerical models to simulate flow characteristics of semi-solid metals in the die cavity requires a good understanding of the transient and equilibrium flow properties of semi-solids and knowledge of the basic parameters that control the process. This paper presents transient rheology behavior of a MHD A356 aluminum alloy under constant rotational speed conditions. Transient flow properties of the alloy were measured as a function of rotational speed using a high temperature rheometer equipped with a vane-cup system. 167 172 167-172

An essential element for the integration of the semisolid metal (SSM) process in the production of complex commercial components is the availability of accurate mathematical and computational tools that could describe both the material characteristics and the dynamics of semisolid slurries during die filling. Computational simulation and modeling is also a powerful and an effective tool that can be used to understand complex physical phenomena, such as those observed with semisolid slurries, and to support theoretical models describing them. We show how important physics can be revealed using experiments combined with numerical simulations. More specifically, we investigate the flow details and the shape evolution during the compression of a finite amount of a Herschel-Bulkley fluid, and the flow of such a material in a rotational viscometer. These two flows relate to popular experiments that are commonly used to determine rheological constants of semisolid slurries. The goal is to use mathematical and computational tools to test postulates for physical and theoretical models used to describe semisolid slurry behavior. The ultimate objective of this work is to contribute to the development of a methodology, which relates simulations to actual experimental results in order to determine the material constants of semisolid slurries. 359 361 Sponsors: American Foundry Society (AFS) American Society for Metals International (ASM) The Institute of Materials, Minerals and Mining (IOM3) North American Die Casting Association (NADCA) Conference code: 66060 Cited By :1 Centre Technique des Industries de la Fonderie (CTIF)

The focus of this paper is compression molding of semi-concentrated fiber suspensions. During compression molding a premeasured amount of raw material (charge) is placed between two halves of a die. The die is then closed so that the charge is compressed, thus taking the shape of the die. In this paper we used the theory developed by Dinh and Armstrong for semi-concentrated fiber suspensions, although the theoretical background and numerical procedures developed in this paper can be extended to other theories as well. The constitutive equations are expressed in terms of the flow kinematics through the use of Finger and Cauchy finite deformation tensors which are approximated numerically using a semi-implicit finite difference scheme. The full unsteady form of the governing equations are formulated using a mixed Eulerian-Lagrangian description and solved using a classical Galerkin Finite Element Method. Results are shown for the filling of a two-dimensional cavity under various process conditions such as constant compression rate, constant compression force and at different fiber concentrations and fiber aspect ratios. 175 177 185 177-185

Processing of metal alloys in their mushy state represents a new trend in metal processing. The process produces components with low porosity, high crack resistance along with fine microstructure and mechanical properties that are better than those produced by liquid casting, and comparable to those of forged alloys. In the present work, a summary of the current understanding on the rheology of semisolid slurries is presented. This is followed by an overview of the different mathematical models proposed by the authors to describe the experimentally observed behavior of the material, and salient numerical results including die filling. Copyright © 2000 Society of Automotive Engineers, Inc.

Understanding the time-dependent flow behavior of metal alloys in semisolid state is essential for the further development of the process. In the present investigation, the thixotropic behavior of semisolid slurries is modeled using conservation equations and the Herschel-Bulkley fluid model. The rheological parameters are assumed to be functions of the solid volume fraction, and of a structural parameter that changes with processing history. The evolution of the structural parameter is described by a first order kinetic differential equation that relates the rate of build-up and break-down of the solid skeleton. The model is implemented into a computer code to predict die filling. 578 475 480 475-480

Semisolid metal processing is gaining interest very rapidly in the casting industry. It offers distinct advantages over other near-net-shape technologies, such as a more homogeneous microstructure, less porosity and thus improved mechanical properties. A perfect control of die filling during processing is however necessary, especially in the case of semisolid forming of aluminum, where a non-controlled die filling can lead to oxide inclusions. Numerical simulation can be used to predict die filling, and hence to optimize the die design. However, the constitutive behavior of semisolid metals is quite complex. Their non-Newtonian behavior depends not only on the volume fraction of liquid, but also on the metal’s history prior to processing, and the processing conditions. In this study, a “Bingham type”, or Herschel–Bulkley constitutive relation is introduced, capable of describing correctly the bulk behavior of the semisolid slurry. This constitutive equation is implemented in a modified version of the casting simulation package PAM CAST SIMULOR. Simulations for the filling of 2-D and 3-D cavities using different injection speeds and material parameters are presented. The results are in good agreement with experimental evidences featuring similar geometric characteristics. Optimization of die design using numerical simulation is also introduced.

Understanding the time-dependent flow behavior of semisolid materials (SSM) is essential for the simulation of semisolid processes. During processing, the structure of the material changes with the processing history due to agglomeration and di-agglomeration of particles or inter-particle interactions. Analysis of experimental data shows that the transient behavior of SSM at constant structure is shear thickening, and there exists a shear dependent finite yield stress. The flow of SSM is modeled using the Herschel-Bulkley fluid model. The yield stress, the consistency index, and the power-law index are assumed to be functions of the solid volume fraction and a structural parameter that changes with the processing history. The evolution of the structural parameter is described by a first-order kinetic differential equation. The model is then implemented into a 3-d computer code to predict the flow field, yield surfaces, and distribution of parameters in a channel flow. 755 760 755-760

The flow of Herschel-Bulkley fluids through a sudden 3-D square with expansion height ratio of 2:1 is studied numerically by solving the mass and momentum conservation equations along with a continuous constitutive relation. Solutions are obtained for a Reynolds number equal to 1, and a wide range of dimensionless pressure gradient and rheological parameters on both unsteady and steady laminar flows with constant fluid properties. The solution was obtained using a classical Galerkin finite element formulation with a segregated solution procedure. Results are shown for the evolution in time of yielded/unyielded regions and the influence of the different parameters on the shape and extent of these regions and the volume flow rate at steady flow.

The importance of processing of metal and metal matrix composites in semisolid state is increasing quite rapidly due to the distinct advantages it offers over similar methods of near-net-shape making. In this investigation we are using a two-phase model to predict the behavior of SSM in a three-dimensional isothermal flow through a sudden square expansion. The model is implemented computationally using a classical Galerkin-Finite element formulation with a segregated solution procedure. The model captures relative motion and particle crowding. 1081 1086 1081-1086

A constitutive relation is proposed that is capable of predicting a wide range of experimental rheological behavior depending on the proper choice of the parameters. The model represents the otherwise discontinuous Bingham behavior as a continuous model. This model is simple and easy for numerical implementation and therefore can be used in the modeling of other materials processing problems. 807 811 807-811

Processing of metals and metal matrix composites in the semi-solid state is an emerging new technology and is becoming increasingly popular. This method provides several advantages over the traditional liquid state processing including better control over the viscosity and final microstructure and reduced solidification shrinkage. A two-dimensional simulation of the injection molding filling process for semi-solid materials is presented. The material is modeled as a homogeneous incompressible fluid and the stress tensor is expressed using a shear rate thickening Bingham fluid model. This article shows the filling of a standard tension test specimen from one end. Due to symmetry, only one half of the geometry is modeled. Results are presented for filling rates as functions of the inlet velocity and pressure conditions. The effects of the adjustable parameters of the constitutive relation (yield stress, Bingham exponent, power-law index) are investigated. These results are presented and discussed. The effectiveness of the shear-thickening Bingham fluid model in representing the material behavior is also discussed. 231 159 170 159-170

Recently the importance of processing metals and metal matrix composites in semi-solid state is growing rapidly. Performing the shape making operations in the semi-solid state provides a better opportunity to control the microstructure of the final product. In this paper we are presenting a numerical approach to simulate the compression molding of semi-solid materials. A phenomenological constitutive relation based on the Bingham fluid model and the Power-law model is proposed. The model has four adjustable parameters. These parameters are evaluated by comparing with the experimental results. Results are presented for Sn-15%Pb alloy system. The model is then used to describe the unsteady flow of semi-solid materials in compression molding. The Generalized Eulerian-Lagrangian (GEL) formulation is used to locate the free surface while maintaining the solid boundaries. Yielded and unyielded portions of the charge are identified. 179 83 87 83-87

Vortex lock-on phenomena in flow past a circular cylinder with a periodic component superimposed on the mean free stream flow is investigated using concepts from dynamical systems (chaos) theory. Numerical results show that in addition to classical lock-on phenomenon (where the wake and forcing frequencies coincide or lock-on in a subharmonic multiple) regions are observed in which the wake frequency locks-on to a fractional ratio of the freestream oscillation frequency. The observed phenomena are compared to qualitative predictions of circle map theory. A possible general framework for understanding lock-on phenomena using circle map theory is discussed. 157 183 188 183-188

A mathematical and a numerical approach to model the injection mold filling stage is presented. The approach is based on a Generalized Eulerian Lagrangian (GEL) formulation. In purely Lagrangian formulations the solution is obtained at mesh points which follow the local fluid velocity. On the other hand, in Eulerian formulations the mesh is fixed and the solution is obtained at fixed spatial locations. In injection molding different parts of the flow domain are best analyzed by one but not both formulation methods. The Generalized Eulerian Lagrangian formulation combines the advantages of both formulations: In the same flow problem but different regions the GEL formulation allows the selective application of an Eulerian, Lagrangian, or a mixture of the two formulations. In this work the melt is described using the White‐Metzner constitutive relation and results are shown and discussed for the filling of a cavity from a single gate and from a fully open end under different process conditions. Copyright © 1993 Society of Plastics Engineers 33 1055 1064 1055-1064

Direct chill (DC) casting is used extensively in the production of wrought nonferrous metals and alloys, particularly in the aluminum industry. For alloys, a semi-solid region known as the “mushy zone” and defined by the liquidus and solidus temperatures, marks the solidification front. The liquidus and solidus isotherms represent respectively the onset and completion of solidification. Pure metals exhibit no mushy zone while alloys with increasing freezing ranges exhibit larger mushy zones. In this work, a two-dimensional Eulerian steady-state finite element model is used to analyze the melt flow as well as the mushy region during continuous casting. The simultaneous solution to the melt flow problem and the non-uniform release of latent heat in the mushy region is achieved using an inverse approach. This is a novel method in the numerical modelling of DC casting which offers distinct advantages over other methods of solution. In this analysis we are including the effects of the mushy region in an idealized continuous casting problem of an Al-.7% Mg alloy. Specifically, we are investigating the effects of the temperature field, melt flow, and the casting and cooling rates on the position and shape of the solidification front. 513 531 513-531

The focus of this paper is unsteady flow of semi-dilute fiber suspensions in complex geometries. These flows are typical of injection molding problems in which the raw material in granular form, usually plastic resin mixed with fibers of certain concentration and aspect ratio, is heated above the melting point, and forced into the mold cavity by means of pressure. When the mold cavity is filled, additional material is supplied to compensate for shrinkage due to cooling. The injection is then cut off, the mold is allowed to cool, and the piece is removed from the mold. The duration, temperature and pressure at each stage are adjusted to suit individual requirements. In this paper we used the theory developed by Dinh and Armstrong for semi-dilute fiber suspensions, although the theoretical background and numerical procedures developed in this paper can be extended to other theories as well. The constitutive equations are expressed in terms of the flow kinematics through the use of the Finger and Cauchy finite deformation tensors which are approximated numerically using a semi-implicit time integration scheme. The full unsteady form of the governing equations are formulated using a mixed Eulerian-Lagrangian description and solved using a classical Galerkin Finite Element Method. The accuracy of the numerical solution is compared to exact solutions for an equivalent radially diverging source flow. Results are shown for the filling of a two-dimensional cavity under various process conditions such as constant flow rate, constant pressure and at different fiber concentrations and fiber aspect ratio. 153 103 111 103-111