Solidification structure
5.2 Development of matrix structure
5.2.4 Disintegration of the solid
Nordland's results fall into a regime of frequency and amplitude where the vibrational energy is too low for damage to occur to the dendrites (Figure 5.22).
5.2.3.1 Dendrite arm spacing (DAS)
In the metallurgy of wrought materials, it is the grain size of the alloy that is usually the important structural feature. Most metallurgical textbooks therefore emphasize the importance of grain size.
In castings, however, grain size is sometimes important (as will be discussed later), but more often it is the secondary dendrite arm spacing (sometimes shortened merely to dendrite arm spacing, DAS) that appears to be the most important structural length parameter.
The mechanical properties of most cast alloys are seen to be strongly dependent on secondary arm spacing. As DAS decreases, so ultimate strength, ductility and elongation increase. Also, since homogenization heat treatments are dependent on the time required to diffuse a solute over a given average distance d, if the coefficient of diffusion in the solid is D, then from the order-of-magnitude relation we have
d = (Dt)'/* (5.21)
Thus finer DAS results in shorter homogenization times, or better homogenization in similar times;
the cast material is more responsive to heat treatment, giving better properties or faster treatments.
It is now known that DAS is controlled by a coarsening process, in which the dendrite arms first grow at very small spacing near the tip of the dendrite. As time goes on, the dendrite attempts to reduce its surface energy by reducing its surface area. Thus small arms preferentially go into solution while larger arms grow at their expense, increasing the average spacing between arms. The rate of this process appears to be limited by the rate of diffusion of solute in the liquid as the solute transfers between
c n l
dissolving and growing arms. From an equation such as 5.21, and assuming the alloy solidifies in a time t f , we would expect that DAS would be proportional to ti1*, since tf is the time available for coarsening. In practice it has been observed that DAS is actually proportional to
t"
where n usually lies between 0.3 and 0.4. Figure 5.23 shows the magnificent research result, that the relation between DAS and tf continues to hold for A l 4 . 5 C u alloy over eight orders of magnitude. Interestingly, however, a plot of grain size on the same figure shows that grain size is completely scattered above the DAS line. Clearly, a grain cannot be smaller than a single dendrite arm, but can grow to unlimited size in some situations.In summary, DAS is controlled by solidification time. Grain size, on the other hand, is controlled by a number of quite different processes, some of which are discussed further in the following section.
Solidification 5tructure I37
isolated grains in the growing forest of columnar dendrites. The directional heat flow that they will then experience will grow them unidirectionally, converting them to columnar grains. However. a sufficient deluge of equiaxed grains will swamp the progress of the columnar zone, converting the structure to equiaxed.
The columnar to equiaxed transition has been the subject of much solidification research. In summary it seems that the transition is controlled by the numbers of equiaxed grains that are available.
This in turn is controlled by the casting temperature and the G/V ratio. The work by Spittle and Brown ( I 989) illuminates the concepts admirably (Figure 5.24). The interested reader is recommended to consult the original publications.
In large steel ingots the columnar grains can reach lengths of 200 mm or more. These long cantilevered projections from the mould wall are under considerable stress as a result of their weight, and the additional weight of equiaxed grains, en route to the bottom of the ingot, that happen to settle on their tips. Under this weight, the grains will therefore bend by creep, possibly recrystallizing at the same time, allowing the grains that grow beyond a certain length to sag downwards at various angles. This mechanism seems consistent with the structure of the columnar zone in large castings, and explains the so-called branched columnar zone.
The straight portions of the columnar crystals near the base have probably resisted bending by the support provided by secondary arms, linked to form transverse supporting structures.
Growing dendrites can be damaged or fragmented in other ways to create the seeds of new grains.
Mould coatings that contain materials that release gas on solidification, and so disturb the growing crystals, are found to be effective grain refiners (Cupini et al. 1980). Although these authors do not find any apparent increase of gas take-up by the casting, it seems prudent to view the 10 per cent increase in strength as hardly justifying such a risk until the use of volatile mould dressings is assessed more rigorously.
The application of vibration to solidifying alloys is also successful in refining grain size. The author admits that it was hard work reviewing the vast amount of work in this area (Campbell 1981). It seems that all kinds of vibration, whether subsonic, sonic, or ultrasonic, are effective in refining the grain size of most dendritically freezing materials providing the energy input is sufficient (Figure 5.22).
The product of frequency and amplitude has to exceed 0.01 ms-’ for 10 per cent refinement i 0.02 ms-’ for SO per cent refinement, and 0.1 ms- for 90 per cent refinement (Campbell 1980). It is possible that at the free liquid surface of the metal the energy required to fragment dendrites is much less than this, as Ohno (1987) points out. This is operating, the experimental results on a wide variety
of metals that solidify in a dendritic mode from A1 alloys to steels could be summarized to a close approximation by:
, f . n = 0. 10 ms-’
This relation describes the product of frequency (Hz) and amplitude (m) that represents the critical threshold for grain fragmentation. It seems to be valid over the complete range of experimental conditions ever tested, from subsonic to ultrasonic frequencies, and from amplitudes of micrometres to centimetres.
In single-crystal growth it seems that the damage to a dendrite arm may not be confined to breaking off the arm. Simply bending an arm will cause that part of the crystal to be misaligned with respect to its neighbours. Its subsequent growth might be in a favourable direction, causing it to grow to the size of a significant defect. Vogel and colleagues ( 1977) propose that given a sufficiently large angle of bend, the plastically deformed material will recrystallize rapidly. The newly formed grain boundary, having a high energy, will be preferentially wetted by the melt, which will therefore propagate along the boundary and detach the arm. The arm now becomes a free-floating grain.
In the pouring of conventional castings, Ohno ( 1987) has drawn attention to the way in which the grains of some metals grow from the nucleation site on the mould wall. The grains grow from narrow stems that make the grains vulnerable to plastic deformation and detachment. Thus as metal washes over the mould surface, thousands of crystals are washed into the melt, the nucleation sites that continue to be attached to the mould wall presumably seeding strings of replacement crystals, one after another. There is an element of runaway catastrophe in this process; as one dendrite is felled, it will lean on its neighbours and encourage their fall.
The fragments of crystals that are detached in this way may dissolve once again as they are carried off into the interior of the melt if the casting temperature is too high. The interior of the casting may therefore become free of so-called equiaxed grains. Finally, the structure of the casting will consist only of columnar grains that grow inwards from the mould wall.
However, if the casting temperature is not too high, then the detached crystals will survive, forming the seeds of grains that subsequently grow freely in the melt. The lack of directionality and the equal length of the axes of these crystals have given them the name ‘equiaxed’ grains. At very low casting temperatures, perhaps together with sufficient bulk turbulence, the whole of the casting may solidify with an equiaxed structure.
In mixed situations where modest quantities of equiaxed grains exist, they may be caught up as
sometimes known as shower nucleation, as proposed by the Australian researcher, Southin, although it is almost certainly not a nucleation process at all.
Most probably it is a dendrite fragmentation or multiplication process, resulting from the damage to dendrites growing across the cool surface liquid.
These are possibly actually attached to the floating oxide film, or growing from the side walls, but are disturbed by the washing effect of the surface waves.
If we return to Figure 5.23 and attempt to plot grain size on this diagram, it reveals that grain sizes are dotted randomly all over the upper half of the diagram, above the DAS size line. Occasionally some grains will be as small as one dendrite arm, and so will lie on the DAS line. No grain size can be lower than the line. This is because, if we could imagine a population of grains smaller than the DAS, and which would therefore find itself below the line, then in the time available for freezing, the population would have coarsened, reducing its surface energy to grow its average grain size up to the predicted size corresponding to that available time. Thus although grains cannot be smaller than the dendrite arm size, the grain size is otherwise independent of solidification time. Clearly, totally independent factors control the grain size.
It is clear, then, that the size of grains in castings results not simply from nucleation events, such as homogeneous events on the side walls, or from
Figure 5.24 Computer simulated macrostructure of growth inwards from the sides of an ingot for progressively increasing casting temperature ( a ) to (d). Reprinted with permission from J. Materials Science, Chapman & Hall, London.
chance foreign nuclei, or intentionally added grain refiners. Grain nuclei are also subject to further chance events such a s redissolution; further complications, mostly in larger-grained materials, result f r o m c h a n c e events of d a m a g e o r fragmentation from a variety of causes.
A further effect should be mentioned. The grains formed during solidification may not continue to exist down to room temperature. Many steels, for instance, as discussed in section 5.6, undergo phase changes during cooling. Even in those materials that are single phase from the freezing point down to room temperature can experience grain boundary migration, grain growth o r even wholesale recrystallizsation. Figure 5.25 shows an example of grain boundary migration in an aluminium alloy.
It bears emphasizing once again that dendrite arm spacing is controlled principally by freezing time, whereas grain size is influenced by many independent factors.
Before leaving the subject of the as-cast structure, it is worth giving warning of a few confusions concerning nomenclature in the technical literature.
First, there is a widespread confusion between the concept of a grain and the concept of a dendrite.
It is necessary to be on guard against this.
Second, the word ‘cell’ has a number of distinct technical meanings that need to be noted:
Solidification structure 139
cell count’, giving a measure of something called a ‘cell size’. In these difficult circumstances it is perhaps the only practical quantity that can be measured, whatever it really is!
I
Figure 5.25 Micrograph of AI-0.2Cu alloy showing porosity and interdendritic segregation. Some grain boundary migration during cooling is clear.
(Electropolished in perchloric and acetic acid solution and etched in ferric chloride. Dark areas are etch pitted.)
1. A cell can be a general growth form of the solidification front, as used in this book.
2. Cell is the term used to denote graphite ‘rosettes’
in grey cast irons. Strictly, these are graphite grains; crystals of graphite which have grown from a single nucleation event. They grow within, and appear crystallographically unrelated to, the austenite grains that form the large dendritic rafts of the grey iron structure. Analogous structures, again called cells, are seen in spheroidal graphite irons.
3. The term ‘cell count’ or ‘cell size’ is sometimes used as a measure of the fineness of the microstructure, particularly in aluminium alloys.
Here the distinction between primary arm, secondary arm and grain is genuinely difficult to make in randomly oriented grains, where primary and secondary arms are not clearly differentiated (see Figure 5.20). To avoid the problem of having to make any distinction, a count is made of the number of features (whether primary or secondary arms or grains) in a measured length. This is arbitrarily called ‘the