In this article we will discuss about the solidification of metals:- 1. Mechanism of Solidification 2. Rate of Solidification 3. Solidification of a Large Casting in an Insulating Mould 4. Solidification with Predominant Interface Resistance 5. Solidification with Constant Casting Surface Temperature 6. Solidification with Predominant Resistance in Mould and Solidified Metal.
Contents:
- Mechanism of Solidification
- Rate of Solidification
- Solidification of a Large Casting in an Insulating Mould
- Solidification with Predominant Interface Resistance
- Solidification with Constant Casting Surface Temperature
- Solidification with Predominant Resistance in Mould and Solidified Metal
1. Mechanism of Solidification:
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Pure Metals:
Liquids need to be cooled below their freezing points before the solidification begins. This is because energy is required to create surfaces for new crystals. The degree of super-cooling necessary is reduced by the presence of other surfaces (particles) which serve as the initial nuclei for crystal growth.
When a liquid metal is poured into a mould, initially (at time t0 in Fig. 2.14) the temperature everywhere is θ0. The mould face itself acts as the nucleus for crystal growth, and if the conductivity of the mould is high, randomly-oriented small crystals grow near the mould face.
Subsequently, a temperature gradient results within the casting, as indicated in Fig. 2.14 for t1and t2. As the solidification progresses gradually inwards, long columnar crystals, with their axes perpendicular to the mould face, grow. This orientation of crystal growth is desirable from the point of view of strength of the casting.
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Alloys:
An alloy, unlike a pure metal, does not have a sharply defined freezing temperature. The solidification of an alloy takes place over a range of temperature. During this process, the solids separating out at different temperatures possess varying compositions.
Due to pit these facts, the direction of crystal growth in an alloy depends on various factors, such as:
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(i) The composition gradient within the casting,
(ii) The variation of solidus temperature with composition, and
(iii) The thermal gradient within the mould.
We shall discuss each of these factors by considering the example of a solid solution alloy whose phase diagram is shown in Fig. 2.15.
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Let the liquid alloy have the composition C0 (of B in A). Also, let θf be the freezing point of pure metal A, and θ0 and θ’0, respectively, be the liquidus and the solidus temperatures of the alloy of composition C0.
As the liquid alloy is cooled down to the temperature 0O, solids start to separate out. The concentration of B in these solids is only C1(<C0) as is evident from Fig. 2.15. As a result, the concentration of B in the liquid, near the solid-liquid interface, increases to a value more than C0. Figure 2.16 shows this for the situation where solidification front has progressed up to some distance d from the mould face.
Now, let us consider two points P and Q within the liquid alloy, P being just beyond the solid-liquid interface, as indicated in Fig. 2.16. The solidus temperatures corresponding to the compositions at P and Q are θ’P and θ’Q, respectively (see Fig. 2.15). Let θP and θQ be the actual temperatures at the points P and Q, respectively. θQ is greater than θP due to the thermal gradient within the casting (see Fig. 2.14). If both θa and θP lie in the range θ’P to θ’Q, then the liquid at Q is supercooled, whereas that at P is not. This implies that the crystallization starts at Q sooner than at P. If this difference is very prominent, then the columnar growth of crystals starting from the mould surface is hampered. The crystal growth in such a situation may appear as in Fig. 2.17. Thus, a dendritic
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Thus, a dendritic structure is produced. If the crystallization at Q gets completed before it starts at P (due to a very small thermal gradient, with a very high concentration difference and a very slopy solidus line), then randomly-oriented crystals may appear inside the casting. Moreover, the presence of solid crystals ahead of the solid-liquid interface makes feeding of the liquid metal more difficult. This also implies greater risk of having voids within the casting, normally referred to as centre-line shrinkage.
One remedy to avoid the aforestated problem is to produce a large thermal gradient within the mould by providing a chill (cooled metal block with high thermal conductivity) at the mould’s end. If θP is considerably below 6q, then the degree of supercooling is not significantly different at P and Q and a gradual progress of the solid-liquid interface is ensured. The problem is obviously less critical for alloys having a small temperature difference between the liquidus and the solidus lines.
The freezing patterns of a chilled and an ordinary mould are shown in Fig. 2.18. In Fig. 2.18a, the solidification starts at the centre line of the mould before the solidification is complete even at the mould face. In the chilled mould (Fig. 2.18b), on the other hand, due to rapid heat extraction, a narrow liquid- solid zone quickly sweeps across the molten metal.
The difficulty of feeding a given alloy in a mould is expressed by a quantity, called Centre-Line Feeding Resistance (CFR). It is defined as –
2. Rate of Solidification:
A reservoir of liquid metal, called riser is used to compensate for the shrinkage that takes place from the pouring temperature up to solidification. In this respect, grey cast iron is an interesting exception where solidification occurs in two stages.
The shrinkage associated with the first stage may well be compensated by the expansion that takes place during the second stage, and as such, a riser may not be necessary. To ensure that the riser does not solidify before the casting, we should have an idea of the time taken by the casting to solidify.
Moreover, the placement (location) of the riser can be judiciously chosen if an estimate of the time taken by the casting to solidify up to a certain distance from the mould face is available.
The heat rejected by the liquid metal is dissipated through the mould wall. The heat, released as a result of cooling and solidification of the liquid metal, passes through different layers. The temperature distribution in these layers, at any instant, is schematically shown in Fig. 2.19.
The thermal resistances which govern the entire solidification process are those of the liquid, the solidified metal, the metal-mould interface, the mould, and the ambient air. These five different regions are indicated by the numbers 1 to 5 in Fig. 2.19. The solidification process is quite complicated especially when complex geometry, freezing of alloys, or temperature dependence of thermal properties is considered.
In what follows, we shall discuss the solidification of pure metals in some cases of practical interest. In doing so, we shall, depending on the situation, make simplifying assumptions to neglect the thermal resistance of one or more of the regions shown in Fig. 2.19.
3. Solidification of a Large Casting in an Insulating Mould:
During the solidification of a large casting in an insulating mould, like the one used in the sand or investment casting, almost the entire thermal resistance is offered by the mould. Hence, the analysis we give computes the freezing time by considering only the thermal resistance of region 2 (Fig. 2.19).
Consider a mould face AB shown in Fig. 2.20. The large mould, initially at a temperature θ0, is assumed to be extended up to infinity in the x-direction.
At time t = 0, the liquid metal at temperature θp is poured into the mould. We also assume that the metal just in contact with the mould face solidifies instantaneously. In other words, the temperature of the mould face is raised to θf (freezing temperature of the metal) at t=0 and is maintained at that value the completion of solidification. The temperature distribution within the till at a subsequent time t (assuming one-dimensional heat conduction in the x-direction) for such a case is given by
It should be noted that the foregoing analysis assumes a plane metal-mould interface AB, not usually encountered in engineering practice. Often, we are required to find out the freezing time of complex contours.
For such contours, all we need to do is observe (without any precise calculations) the following basic features to know whether the analysis we have given underestimates or overestimates the actual freezing time. To observe these features, we consider three types of metal-mould interfaces (see Fig. 2.21), namely, (i) convex, (ii) plane (used in our analysis), and (iii) concave.
In Fig. 2.21a, the heat flow is more divergent, and consequently the rate is somewhat more than that in Fig. 2.21b. Thus, the freezing time in such a case is overestimated by the foregoing analysis. Similarly, in Fig. 2.21c, the heat flow is more convergent, and consequently the rate is somewhat less than that in Fig. 2.21b. So, the freezing time in such a case is underestimated by the analysis we have given.
The quantitative results of the effect of the mould-casting interface on the freezing time can be obtained for some basic shapes. Before we give these results, we define two non-dimensional parameters, namely-
4. Solidification with Predominant Interface Resistance:
In some common casting processes, the heat flow is controlled significantly by the thermal resistance of the mould-metal interface. These processes include permanent mould casting and die casting.
The condition of no contact resistance exists only when the mould-metal contact is so intimate that a perfect wetting occurs, i.e., the casting gets soldered to the mould face. In such a case, the temperature distribution, assuming no superheat, is as shown in Fig. 2.23. We are considering again a problem of one-dimensional heat flow.
Equation (2.44) is helpful in estimating the solidification time of small, thin- section parts cast in a heavy metal mould as used in a die or permanent mould casting.
It may be noted at this stage that over and above the interface resistance we have discussed, there are significant differences between the solidification process in a sand mould and that in a chill or metal mould.
We give here two important ways in which the latter differs from the former:
(i) The thermal conductivity of the solidified metal may provide considerable thermal resistance, as shown by region 4 of Fig. 2.19. Because of this, the surface temperature of the casting (θs), as can be seen, becomes much lower than the freezing temperature θf.
(ii) Because of the sub cooled solidified metal, more total heat than that considered has to be removed. Thus, the heat capacity of the solidifying metal also plays an important role in the rate of solidification.
5. Solidification with Constant Casting Surface Temperature:
If a large, slab-shaped casting (say, of steel) is produced in a thin, water cooled mould made out of a metal (say, of copper) having a much higher conductivity than the solidified casting, then the thermal resistance provided by the solidifying metal itself is significant. In such a case, the predominant thermal resistance is offered by region 4 (see Fig. 2.19).
Neglecting the thermal resistances of all the other regions, the temperature distribution at any instant takes the shape shown in Fig. 2.24. Here, the mould-metal interface (or the casting surface) temperature θS can be assumed to remain constant at its initial value θ0, and θf indicates the freezing temperature of the metal and this is also taken as the pouring temperature.
At any instant t, δ(t) indicates the depth of solidification. The process can be idealized, without much error, as a one-dimensional one. Hence, the solidification time ts is obtained from δ(ts) = h/2, where h is the thickness of the slab being cast. The temperature profile within the range 0 < x < δ(t) is given by
This analysis is valid only after the initial solidification stage (0.5-1 cm) is over. Similar results for the solidification time of the other shapes can be found from the available literature.
6. Solidification with Predominant Resistance in Mould and Solidified Metal:
The copper mould is quite thick and is not water cooled. Then, the mould-metal interface temperature θS can no longer be assumed to remain at its initial value θ0. The value of θS, still assumed to be constant, is decided by the thermal properties of the mould and the solidified metal.
Moreover, after the initial stage of solidification, the interface resistance also becomes negligible. Thus, the only significant thermal resistance is offered by regions 2 and 4 (Fig. 2.19) and the resulting temperature distribution at any instant is as shown in Fig. 2.25. Assuming the mould to be a semi-infinite medium in the negative x-direction, the temperature distribution in the mould is
Now, the left-hand side and ɸ in equation (2.62) are known; so, ζ can be determined either graphically or by trial and error. In the former approach, a graph of ζeζ2 [erf (ζ) + ɸ] versus ζ should be drawn for the given value of ɸ, and ζ can then be solved for with the known value of the left-hand side of equation (2.62). Once ζ is known, the depth of solidification can be computed from equation (2.47) and the solidification time from equation (2.52). For such a casting to be feasible, it should be ensured that θS works out to be less than the melting point of the mould metal.