Modeling of shrinkage defects during solidification of long and short freezing materials

Abstract

The aim of the model presented in this paper is to capture the difference in solidification behavior of long and short freezing materials. The shrinkage defects in short freezing materials tends to be internal, as porosity, while in long freezing materials these defects tend to be external in the form of surface depressions. To achieve this, a pressure drop based 3D feeding flow model has been developed to evaluate shrinkage defects for casting alloys. A continuum formulation is used to describe the transport of mass, energy and momentum. It is assumed that during solidification the driving force for flow is shrinkage. A Darcy type source term has been included in the momentum equation to account for flow resistance in the mushy zone. A VOF free surface model has been used to describe shrinkage defects, i.e., external surface depressions and internal shrinkage porosities, while ensuring mass conservation. The model is used to calculate the shrinkage in a simple casting. The results shows internal and outside shrinkage defects depending on the freezing range of the metal. Short freezing range results mainly in internal shrinkage whereas the long freezing range results in external shrinkage. The expected shrinkage features are well described by the present model.

Introduction

Shrinkage related defects in shape casting are a major cause of casting rejections and rework in the casting industry. The most important defects that arise from shrinkage solidification are:

• External defects: pipe shrinkage and caved surfaces;

• Internal defects: macroporosity and microporosity.

Short freezing materials are more prone to internal defects, whereas long freezing materials are more prone to surface depressions. These shrinkage related defects result from the interplay of several phenomena such as heat transfer with solidification, feeding flow and its free surfaces, deformation of the solidified layers and the presence of dissolved gases.

Many attempts to model shrinkage related defects have been made. An extensive review on these models has been made by Lee et al. (2001) and later Stefanescu (2005). The initial effort of casting simulation was to develop codes that only analyze the solidification behavior by heat conduction models, solving the energy transport equations. For defects prediction they use a criteria function, empirical models for evaluation of shrinkage porosity defects, based on some relations of the local temperature gradient. The most well known is the Niyama Criterion (Niyama et al., 1982), based on finding the last region to solidify as most probable location for shrinkage defects. These and other functions have been summarized by Overfelt et al. (1997), Spittle et al. (1997) and later evaluated by Taylor and Berry (1998). Some models came up that were based on solving the heat transfer and mass conservation to predict the position of the free surface and macro-shrinkage cavity. Trovant and Argyropoulos (1996) proposed a model to account for shrinkage and consequently determine the shrinkage profile resulting from phase and density change. Beech et al. (1998) presented a method for macro-shrinkage cavity prediction based on a continuum heat transfer model which determines when an area will be completely cut off from sources of liquid metal (such as risers) where a void will form to account for volume deficit and its size is calculated through the mass conservation equation. Another approach, and more complex one, is the one, which tries to consider the feeding flow analysis. The first model that took into account feeding flow dates back to the early 1D analytic work of Piwonka and Flemings (1966). This early analytical work formed the basis of a later category of models based upon Darcy's law. Darcy's law relates the flow trough a porous media to the pressure drop across it. Kubo and Pehlke (1985) were the pioneers in presenting a 2D numerical model by coupling Darcy's law to the equations of continuity estimating the fluid flow. Later other 2D model was presented by Zhu and Ohnaka (1991) and Huang et al. (1998). In terms of 3D models, Bounds et al. (2000) presented a model that predicts macroporosity, misruns and pipe shrinkage in shaped castings. Later Sabau and Viswanathan (2002), Pequet et al. (2002) and Carlson et al. (2003) also presented 3D models that included the concept of pore nucleation and growth.

In the present model the volume deficit due to shrinkage can only be compensated by two phenomena: depression of the outside surface or by creating internal pores. The mechanism to create these defects is illustrated in Fig. 1. When the metal is still liquid after pouring the shrinkage of the material is fed from the top driven by gravity (a). At some instant a solid layer will grow inwards from the mould interface (b), enclosing a liquid region. To compensate the mass deficit within liquid region, a flow has to be generated through the solidifying layer. This flow through the emerging dendrites will observe an increasing friction, resulting in a pressure drop across the solidifying layer. When the pressure drops below a certain critical pressure a pore will open (c). After the pore has opened the pressure inside the pore is considered to be constant. So the model should allow for calculation of free surface flow through a porous medium, driven by mass continuity and gravity. This flow should be coupled to the pressure to check if it has dropped below the critical pressure.