Computer Modeling of the Semi-Solid Metal Manufacturing Process

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Computer Modeling of the Semi-Solid Metal Manufacturing Process
In the die casting industry, computer simulation methods have been developed to predict mold filling and solidification patterns. These programs are now routinely used to optimize die designs and minimize defects in aluminum and magnesium die cast parts. However, the newer Semi Solid Metal (SSM) and Thixomolding (TM) processes present some challenges to modeling which must be considered when applying these methods. In particular, it is essential to select an appropriate fluid dynamics model for the SSM and Thixomolding processes.

EKK has been developing and marketing solidification, mold filling and stress analysis software for the die casting industry since 1991. Based on the finite element method, these packages have set the standard for accuracy and efficiency in the industry. In 1998, EKK began marketing efficient and highly accurate algorithms for SSM and Thixomolding (TM) processes. EKK also offers consulting services using these software tools.


Semi Solid Metals
Semi Solid Metal (SSM) forming is a manufacturing process for metallic materials which was invented at M.I.T. in the 1970’s and has undergone substantial development since. In the original M.I.T. SSM forming method, a billet of specially prepared alloy is heated to a temperature between the liquidus and solidus. In this semi-solid state, the billet can be handled without deformation, but at a sufficiently high level of shear stress, the agglomerated solid structure breaks up and the fluid-solid mixture can be formed into a near net shape product by pressing it into a die cavity.

The more recent Thixomolding (TM) method was invented by Dow Chemical in the mid-1980’s and commercialized by Thixomat, Inc. in the 1990’s. In this method, the billet is replaced by granules of magnesium alloy, which are injected into a die cavity. (For the sake of clarity, both SSM castings and Thixomolded parts will be referred to as SSM products).

In comparison to castings produced via the die casting process, SSM products typically have reduced porosity levels and superior mechanical properties. This is due not only to the reduction in the volume of material which must undergo shrinkage during solidification, but also to a more uniform filling pattern in the die cavity. The mechanical properties of SSM products are often nearly equivalent to forgings, but the SSM products can be made with a greater degree of geometrical complexity.


Computer Simulations

In the die casting industry, computer simulations of the manufacturing process have been used effectively to predict die filling, solidification behavior and dimensional characteristics of cast parts. These software tools are based on either the finite element method (FEM) or the finite difference method (FDM). FDM programs are generally simple to write and the mesh is easy to create. Unfortunately, FDM meshes tend to be crude (Figure 1) and the simulation results are consequently less accurate [1].
Figure 1. Casting model created using the Finite Difference Method.
  On the other hand, FEM is geometrically more flexible than FDM, thus better suited for simulation of thin-walled parts. Until recently, FEM meshes were difficult to create. Fortunately, with the advent of Auto-meshing this complaint is now moot. With FEM, it is possible to create one mesh, having accurate surfaces, to perform the die filling, solidification and thermal stress analysis.(Figure 2)

Since solidification and stress analysis of SSM processes are similar to those of die casting processes, we will focus on the SSM capabilities in WRAFTS, the FEM software used by EKK for mold filling simulations.


Figure 2. The same geometry meshed using Finite Elements.

Mold Filling

Mold filling simulation programs currently used by the die casting industry are generally based on the three-dimensional Navier-Stokes equations, which is the scientifically accepted mathematical model for fluid dynamics. Motivating reasons for using these programs vary, but can include the following:

•  Minimizing high velocities and recirculation zones in the runner systems.
• &nbspredicting where liquid metal fronts will meet in the cavity
•  Advising the die designer of proper locations for vents and overflows.
•  Predicting fluid temperatures during filling and the subsequent solidification patterns.


The utility of the predictions generated by the simulation software is proportional to the accuracy of the simulation. If the software is inaccurate due to simplifying assumptions made during its development, then the predicted flow patterns will be inaccurate and of little value. Consequently, it is important to use numerical algorithms in the simulation software which are of the highest possible accuracy, while simultaneously minimizing the computer time necessary for solution.

For die castings, the Newtonian viscosity model generally used for mold filling simulations. In contrast, SSM materials have a much more complex rheology. This complexity is needed to describe not only the increase in viscosity created by the existence of solid alpha-phase "particles" in the mixture, but also the kinetics behind the formation and fragmentation of a network of weldments between the solid particles. A number of researchers in this field have reported that the filling patterns in SSM casting are "laminar" relative to conventional die casting [2]. This is reasoned to be a result of the markedly different rheology of the SSM materials. Hence an accurate prediction of the filling patterns in SSM castings mandates a rheological model which includes the effect of the solid phase.

Recently, some Non-Newtonian models have been proposed for SSM materials that are dependent on solids concentration and on the non-linear thixotropic nature of the material [3]. However these models have been poorly understood, to the extent that it is still common (and of little value) for a simple Power Law model to be recommended for SSM simulations. It is only recently that newer, more powerful thixotropic algorithms have become available in commercial mold filling programs [4].

Rheological Models

Various fluid dynamic models that have been used for the SSM process are available within WRAFTS. These include a non-Newtonian Bingham Plastic / Power Law model shown in equation 1, and the Internal Variable Model [3] for which the fluid viscosity is derived from equation 2.
  
Equation 1: Bingham / Power Law ( Herschel Bulkley) Viscosity Model
   


Equation 2: Internal Variable Viscosity Model

  In these equations,  is the stress tensor,  u is the symmetric strain rate tensor, and II is the second invariant of the strain rate tensor. 0 is a yield stress below which a Bingham plastic will deform only in an elastic manner. The coefficient "n" is the power-law coefficient; for n > 1 the fluid viscosity is increasing, while for n < 1 the fluid viscosity is decreasing. For n = 1, and 0= 0, the Bingham / Power Law model reduces to a conventional Newtonian fluid model.

For the internal variable model, the first term is a conventional viscosity expression for non-interacting particulate suspensions. The second term modifies the viscosity based on the effect of clumping together of solid particles. The variable "s" is called an agglomeration function and varies between 0 and 100%. For s=100%, the semi-solid material is fully agglomerated - the network of weldments between the solid particles is complete.

The agglomeration variable s can vary depending on the processing conditions applied to the material. Consequently, it can be modeled as a chemical concentration, with a convective transport equation for its spatial and temporal variation, equation 3.
It is this transport equation for s that provides thixotropic behavior to the fluid dynamic model, and allows it to outperform the more common Power Law models.
  
  
Equation 3: Transport Equation for the Agglomeration Function
Applications:SSM
  
Mold filling results for a Semi Solid Metal casting are shown in figures 3 and 4 below. The part has a "hat" design, and was cast in 356 SSM aluminum alloy at a solid volume fraction of 55%. The shot speed at the plunger tip was 11 m/sec.

Both the Power Law model and the Internal Variable model were applied within WRAFTS to simulate the mold filling process. Property data for the Bingham Plastic / Power Law model were drawn from various sources, and consisted of a yield stress of 120,000 dyne/cm2, a coefficient m = 10.0 g/cm, and a shear thinning Power Law exponent n = 0.95.

A significant difference was found between the results from Power Law model (figure 3) and the Internal Variable model (figure 4). Due to the breakdown of the agglomerates in the runner system and the capability of the Internal Variable model to accurately track this phenomenon, the Internal Variable model shows recirculation at the top of the part. The Power Law model failed to predict this recirculation. Experiments showed that the recirculation does occur (figure 5), confirming the superior accuracy of the Internal Variable model.


Figure 3: Fluid Front for Die Filling with Power Law Model


Figure 4: Fluid Front for Die Filling with Internal Variable Model
(Note the prediction of a recirculation region at the top of the part)


Figure 5: Experimental Hat Die SSM Casting
showing Trapped Gas due to Recirculation
  
Applications: Thixomolding

A relatively new development in Thixomolding(TM) consists of the application of hot runner technology, adapted from the plastics industry. SSM modeling capabilities in WRAFTS were evaluated on this technology. In figure 6, mold filling simulation results are shown for the Thixomolding(TM) process using a spiral fluidity mold with a conventional sprue and runner design.


Figure 6: Final Temperature Profile for Mg Thixomolding at 20% solid fraction.


  
Figure 7. Experimental Thixomolded part.

As can be judged by a photograph of a casting made under the same process conditions used in the simulation, agreement with experimental results was excellent.
The analysis was subsequently modified by adding a hot runner to the design, replacing the conventional sprue / runner design. The effect on mold filling behavior was remarkable. Rather than freezing off prematurely, the filling process continued until the entire spiral was filled (figure 8).


Figure 8: Final Temperature Profile for Mg Thixomolding with Hot Runner

CONCLUSIONS
•  The geometrically flexible finite element method is better suited to SSM simulation.
•  The Internal Variable viscosity model describes the filling pattern in SSM simulation more accurately than the Power Law model.
•  Thixomolding (TM) process can be simulated by Internal Variable model.
Acknowledgments

The authors are grateful for the assistance of CMI (now Hayes Lemmerz) and Thixomat, Inc. with this work.


List of References

1) S. Mahaney and C.W. Kim, Modelling of the Die Cast Process: A Finite Element Method Approach , Die Casting Engineer, (1996)

2) L. Pasternak, R. Carnahan, R. Decker and R. Kilbert, Semi-Solid Production Processing of Magnesium Alloys by Thixomolding, Proceedings of the 2nd Intl. Conference on the Processing of Semi-Solid Alloys and Composites, S.B.Brown and M. Flemings, eds., TMS, 1992, pp.159-169

3) P. Kumar, C.L. Martin and S.B. Brown, Flow Behavior of Semi-Solid Materials,
Proceedings of the 2nd Intl. Conference on the Processing of Semi-Solid Alloys and Composites, S.B.Brown and M. Flemings, eds., TMS, 1992, pp. 250-262

4) G. Backer, Computer Aided Engineering Software for the Semi Solid Metal Manufacturing Process, JOM, (1998)

5) G. Backer, WRAFTS Users Manual, (2001)