David Spencer (MIT) developed semi-solid material processing through an accidental observation he made while dealing with the processing of metals in their mushy state. The semi-solid material process basically consists of two stages: pre-processing and processing. During pre-processing, the manufacturer heats the material to a liquid state. While it cools, the manufacturer breaks the material up, usually by mechanical means. The result is a mushy material with a very uniform microstructure consisting mainly of round crystals. Then, in the processing stage, the manufacturer forces the mushy material into a die where it is allowed to fully cool.

Semi-solid processing has numerous advantages over liquid casting. With liquid casting, the material is heated to extremely high temperatures to reach a liquid state. Then, while the material is hot, it is injected into a die to create a part. This approach potentially introduces tiny gas bubbles into the material, degrading structural integrity, increasing the possibility of shrinkage and cracking while cooling, and putting considerable wear on the die due to the high processing temperatures.

Semi-solid processing attempts to eliminate these problems. The lower processing temperature causes less shrinkage and cracking while the die-cast product cools. The lower temperature also results in less wear on the die because the conditions are less extreme. Another advantage is that the finished product has better material properties due to the material's microstructure and the lower likelihood of gas-bubble entrapment. Though the advantages over traditional methods are clear, understanding the complex behavior of materials in this state has been the stumbling block to the advancement of this technology. Being able to effectively model these processes is vital to the development of this concept.

The case studied here examines numerically a simple 2D flow from a larger reservoir region into a die. The model uses a continuous Herschel-Bulkley fluid model that is based on the continuous Bingham model Papanastasiou (1987) proposed. Alexandrou, at Worcester Polytechnic Institute, pioneered the use of this model to simulate the material behavior during these processes. The Herschel-Bulkley model combines both the non-linear deformation and the existence of a finite yield stress shown by many experimental studies with semi-solid metals during processing. The model is a combination of the power-law model, for non-linear deformation, and the Bingham model, for the existence of the finite yield stress.

For simplicity of calculation, it is assumed that the flow was steady state and isothermal. Although the material properties depend on temperature - and in a full analysis one would include temperature dependence for completeness - for the purpose of this work , inclusion of temperature was unnecessary. Also, most die filling processes occur very quickly, therefore excluding the steady-state case for direct comparison. However, it is intended that the case studied here allow examination, in a simple way, of the bulk flow characteristics and identify where problem areas may occur during an actual die filling process. With that in mind, the case studied provides results that serve this purpose fairly well.

In the past, researchers have modeled semi-solid materials in many different ways, including complex two-phase analysis. These models have proven deficient in numerically capturing the full behavior of the material, which is solid-like in some regions, and liquid in others. Many experimental studies have shown that the Herschel-Bulkley fluid model approximates general flow characteristics well, but the discontinuity of the finite yield stress has made numerical study difficult. The continuous, or "regularized" Herschel-Bulkley model smoothes over this discontinuity with an exponential term in the shear stress relation. A model parameter, known as the stress growth exponent, controls how closely the relation captures the discontinuity. The higher the parameter is, the closer the approximation to the ideal behavior, with a correspondingly higher difficulty of convergence.

The continuous Herschel-Bulkley model does a very good job of capturing one of the most interesting and important flow characteristics - the yield surface - for this type of problem. Yield surface is the interfacial boundary between regions of materials that behave and deform as a liquid, and those that experience virtually no deformation and behave as a solid. Knowing where the solid-like, or "unyielded" regions exist is extremely important to processing. Large, unyielded zones lying on walls, for example, can result in large amounts of material becoming thermally welded in place. Therefore, knowing where these problem areas could arise is crucial for flow control during the process.

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