1. Shrinkage by Thermal Analysis
A Thermal Analysis approach by
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2. Heat absorbing events in Metal
Most events in the solidification of metal are exothermic or heat producing events. Shrink and gas holes are endothermic or heat absorbing events. To form an interior surface, atoms have to be pulled away from other atoms. In thermodynamic terms this is called “work” and requires or absorbs energy. In effect, it speeds cooling the sample rather than heating or slowing the cooling of the sample. On the cooling curve, this can be seen as an unexpected increase or upward movement of the rate of cooling.
Gas bubble formation also requires work to form and produces an upward movement of the cooling rate, but at a different point in the cooling curve.
Shrink
Gas

3. Gas vs. Shrink vs. Suck-in
Gas will come out of the metal as the solubility of the gas falls off with decreasing temperature. The metal is generally still mostly liquid so this occurs in the early part of the eutectic reaction.
Shrink is caused by stress forming in the casting because of a loss of volume. As the atoms form crystals, they go from a “5 nearest neighbors” (a liquid) to a more compact “6 nearest neighbors” (a crystal). If the walls of the casting are weak, they may move inward and we will have suck-in. But if the walls are strong, then shrinkage can result. There is a third possibility that gives us solid castings…more on this later.

4. Stress caused cracking
It is not common, but in white irons, stresses due to solidification can also result in micro-cracking. In this case below, the matrix included a small number of dendrites that tore under stress. The left “micro” shows a dendritic crack within a gray iron matrix, and the right “micro” shows a dendritic crack in a chilled matrix.
The green cooling curve and the blue 2nd derivative curves show multiple inflections as energy is absorbed by the tearing process.

5. Physics of forming an interior surface
Forming an interior surface removes energy (endothermic). It can be see as a
small inflection in the first and second derivatives toward the end of the eutectic.
The green curve is the rate of cooling or 1st derivative, and the blue is the 2nd
derivative.

6. Quantifying Shrink
Higher order derivatives provide the means to find the beginning and ending of
a shrinkage thermal event. Below the third derivative curve (in black)
is passing downward through zero at the start and end of a clear shrink arrest.

7. Calculating the energy of Shrink
Determine that a shrink arrest has occurred.
From the center of the shrink, backtrack to a negative-passing 3rd derivative to find the start of the shrink energy.
From the center of the shrink, go forward to a negative-passing 3rd derivative to find the end of the shrink energy.
Find the equation of the line connecting start and end points.
Integrate the area under the Rate of Cooling curve and above this line for the energy in degrees per second squared.
Ratio that energy by dividing by the energy of the heat of fusion of the entire sample to come up with a % of total energy.

8. Small Shrinkage
Zero curve in magenta, rate of cooling in green. Temperatures (deg. C) of Shrink arrest and copper arrests, and percent of heat of fusion for both copper and shrink (shrink is negative energy)

9. Large Shrinkage
Zero curve in magenta, rate of cooling in green. Temperatures (deg. C) of Shrink arrest and copper arrests, and percent of heat of fusion for both copper and shrink (shrink is negative energy)

10. Shrinkage in Iron
Shrinkage in iron is generally less than in aluminum, and therefore more difficult to detect. The green curve (rate of cooling/1st derivative) magnifies the cooling curve 100 times. The blue curve (2nd derivative) magnifies changes in the cooling curve 1,000 times and makes things even more apparent.

11. The Role of Stress in shrinkage
When there is not enough metal to fill the space, stress is the first thing to happen. As stress accumulates pent up energy, one of several things may happen.
The stress may be partially removed by a gas hole forming.
The stress may be partially removed by a shrink hole forming.
The stress may be partially removed by micro-porosity forming.
The stress may be partially removed by micro-cracking of the weakest component of the matrix.
The stress may be partially removed by forming a suck-in defect.
The stress can be distributed evenly throughout the grain boundaries and form no defects.
Part of what decides which of these will occur, is the rate of the growth of graphite which goes from zero volume in the liquid to about 10% volume at room temperature. Another possibility is the formation of a stress riser that encourages the formation of shrink.

12. The role of Graphite in Shrink
Graphite starts out as a dissolved carbon in the liquid. Here it fits between the larger iron atoms and does not affect the volume of the liquid. As the iron cools, the distance between the iron atoms decreases and the carbon is squeezed out. It then forms graphite within the metal which does occupy space and has volume. A typical ductile iron will have between 9 and 11% graphite by volume. The 9% is more typical of a pearlitic iron, and 11% is more typical of a heat treated ferritic iron. In the wonderful world of ductile iron, steel, which is the matrix of ductile, shrinks approximately 10%.
The problem in ductile iron arises because the graphite does not form rapidly enough to offset the shrinkage of the steel matrix. In gray iron, the graphite forms more rapidly and so those castings require less risering and have fewer problems with shrink.

13. Corrective action for Ductile Iron
Ductile has always been a challenge to make without significant shrink. The solution is complicated, but thermal analysis can help in some ways. We need to break the problem down first into two broad categories:
We cannot make this part
Sometimes it comes out right.
If it is number 1, then gating and risering may still be an issue. If number two, then you probably have a good gating system, though pouring temperature may be an issue.
Next, after eliminating everything else, we might assume the reason we sometimes get bad castings is the iron. For that we need to break the problem down into two new categories:
Large castings
Small castings.

14. Large ductile castings and Shrink
Large Castings are typically poured with hypo-eutectic iron. This means that there will be dendrites that form in the casting giving the casting wall strength to fight suck-in. These kind of castings generally get in trouble if the C.E. (carbon equivalent) gets too high and you move closer to a eutectic form of freezing.
The dendrites will block feeding and choke off the gates, so gating has to be designed larger for that issue.
Overall, there will be shrinkage in these large castings. The trick is to keep it controlled and in locations that do not hurt the strength or integrity of the castings. Chills, extra risers and gate size along with pouring as-cold-as-possible will help.

15. Small iron castings and Shrink
Small Castings freeze off much faster and can utilize higher C.E.s. The additional carbon provides more early graphite to offset the shrinkage. These castings are generally poured with a C.E. between 4.35 and 4.55 with the higher values for the smaller castings. Some very thin castings may be successfully poured with as high as a 4.8 C.E. but these will be prone to shrink if they have any thicker sections.
Gray iron does not have the same shrinkage levels as ductile does. I believe that is because the gray iron graphite comes out completely at the eutectic temperature, while the ductile graphite continues to grow down to the eutectoid temperature of about 1400 F. This slower evolution of graphite puts more stress on the casting to compensate for volume loss and leads to one of these earlier mentioned stress related defects.

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