3 ,',& ,
Chapter 3 Flow
3.3 Fluidity (maximum fluidity length) Lf
3.3.5 Comparison of fluidity tests
The second type of filling, fillability, occurs at higher mould and/or metal temperatures where the heat content of the system is sufficiently high that solidification is delayed until after filling has come to a stop. Studies of the microstructure of the castings confirm that the grains are large and randomly oriented, as would be expected if the metal were stationary during freezing. Filling is then controlled by a mechanical balance of forces. The mode of solidification and further increases of temperature of the metal and the mould play no part in this phase of filling.
In a fluidity test of simpler geometry consisting of straight strips of various thickness, the linear plots of fluidity Lf versus thickness x and superheat ATs are illustrated in Figures 3.15 and 3.16 for Al- 7Si alloy and cast iron in sand moulds. It is easy to combine these plots giving the resultant three- dimensional pyramid plot shown in Figure 3.17.
The plot is based on the data for the A1 alloy in Figure 3.15. In terms of the pressure head h, and the intercepts ATo and xo defined on fluidity plots 3.15 and 3.16, the equation describing the slightly skewed surface of the pyramid is
(3.15) Where C i s a constant with dimensions of reciprocal temperature. For the A1 alloy, C i s found from Figure 3.15 to have a value of about 1.3 f 0.1 K-I, ATo = 30 f 5 , y = 2 Nm-' allowing for contribution of oxide film to the surface tension, p = 2500 kgm-3, g = 10 msK2 and h = 0.10 m. We can then write an explicit equation for fluidity (mm) in terms of superheat (degrees Celsius) and section thickness (mm):
Lf = C(ATs
+
ATO)(X - (2y/pgh))Lf = 1.3(ATs
+
3 0 ) ( ~ - 1.6)For a superheat ATs = 100°C and section thickness x = 2 mm we can achieve a flow distance Z+ = 68 mm for AI-7Si in a sand mould. If the head h were increased, fluidity would be higher, as indicated by Equation 3.15 (but noting the limitations discussed in section 3.3.2).
As we have seen, in these thin section moulds both heat transfer and surface tension contribute to limit the filling of the mould, their relative effects differ in different circumstances. This action of both effects causes the tests to be complicated, but, as we have seen, not impossible to interpret. Further practical examples of the simultaneous action of heat transfer and surface tension will be considered in the next section.
Flow 93
ZA 27 alloy.
Green sand VK Strip test. (1959)
200
I
temp. Pouring ("C) 0 /0 0.5 1 .o 1.5
Strip thicknesdmm.
and 2 . 0 m m . (These rounded values are chosen simply for convenience.) The individual lengths in each section have been plotted separately, not added together to give a total as originally suggested by Kondic. (Totalling the individual lengths seems to be a valid procedure, but does not seem to be helpful, and simply adds to the problem of disentangling the results.) Interestingly all the results extrapolate back to a common value for zero fluidity at the melting point for the alloy, 490°C. This is a surprising finding for this alloy. Most alloys extrapolate to a finite fluidity at zero superheat because the metal still takes time to give up its latent heat, allowing the metal time to flow. The apparent zero fluidity at the melting point in this alloy requires further investigation.
Also shown in Figure 3.22 are fluidity spiral results. An interesting point is that, despite his earlier concerns, I am sure VK would have been reassured that the percentage scatter in the data was not significantly different to the percentage scatter in the strip test results.
The further obvious result from Figure 3.22 shows how the fluidity length measurements of the spiral are considerably higher than those of the strip tests. In a qualitative way this is only to be expected because of the great difference in the cross- sections of the fluidity channels. We can go further, though, and demonstrate the quantitative equivalence of these results.
In Figure 3.23, the spiral and strip results are all reduced to the value that would have been obtained if the spiral and the strip tests all had sections of 2 mm x 17 mm.
Figure 3.21 Fluidity of ZA27 alloy cast in greensand using the VK fluidity strip test ( 2 ) using data ,from Sahoo and Whiting (1984).
2.0
This is achieved by reducing the spiral results by a factor 4.44 to allow for the effect of surface tension and modulus, making the results equivalent to those in the 2 mm thick cast strip. The 2 mm section results remain unchanged of course. The 1.5 and 1.0 mm results are increased by factors 1.75 and 4.12 respectively. These adjustment factors are derived below.
Taking Equation 3.1 (Equation 3.2 can be used in its place, since we are to take ratios), together with Equations 3.5 and 3.6, and remembering that the velocity is given approximately by (2gH)'/*
then we have for sand moulds:
Lf = kmn( 2gH)
= k m n ( 2 g ( ~ - (y/rpg)))"2 (3.16) where n is 1 for interface controlled heat flow, such as in metal dies and thin sand moulds, and n is 2 for mould control of heat flow, such as in thick sand moulds.
Returning now to the comparison of fluidity tests, then by taking a ratio of Equation 3.16 for two tests numbered 1 and 2, we obtain:
For the work carried out by Sahoo and Whiting on both the spiral and strip tests, the ratio given in Equation 3.17 applies as accurately as possible, since the liquid metal and the moulds were the same in each case. Assuming the moduli were 1.74 and 0.985 mm respectively, and the radii were 4
800
700
600
500
E E
.g 40C E G
.
3
30C
20c
1 oc
C
Spiral
I I I I I
I 2.0 mm
'
I
I Fluidity /@
I strips
I I I I / I / I I I
I A
1.0 mm
a / m -
-.---
500 550
Temp "C
and 1 mm respectively, y = 1.9 Nm-'? and p = 5714 kgm-3, and the height of the sprue in each case approximately 0.1 m, it follows
Lfl
={ [
0.1 - 0.00847Lfz 0.895 0.1 - 0.0339
= 3.77 x 1.18
= 4.44
The calculation is interesting because it makes clear that the largest contribution towards increased fluidity in these thin section castings derives from
600
Figure 3.22 Results of Figure 3.21 replotted to show the effect of superheat explicitly, as though from strips of section thickness 1.0, 1.5 and 2.0 mm.
together with results of the spiral fluidity test.
their modulus (i.e. their increased solidification time). The effect of the surface tension is less important in the case of the comparison of the spiral with the 2 mm section. If the spiral of modulus 1.74 mm had been compared with a thin section fluidity test piece of only 1 mm thick, then:
LfllLf2 = 13.6 X 1.68 = 9.25
Thus although the surface tension factor has risen in importance from 1.18 to 1.68, the effect of freezing time is still completely dominant, rising from 3.77 to 13.6.
The dominant effect of modulus over surface
Flow 95
200
._ a
-
L v, 15C E E cuc 0
-
Ev E 1oc
-
==.._ 0 - LL
5c
0 Spiral lengthd4.44
0 2.0 Effective strip thickness mm A 1.5 Strip/0.572
0 1 .o Strip/0.243
y 8
1 4 I I I I I
500 550 600
Temp. ("C) tension appears to be a general phenomenon in sand moulds as a result of the (usually) small effect of surface tension compared to the head height.
The accuracy with which the spiral data is seen to fit the fluidity strip test results for the Zn-27A1 alloy when all are adjusted to the common section thickness of 2 mm x 17 mm (Figure 3.23) indicates that, despite the arguments that have raged over the years, both tests are in fact measuring the same physical phenomenon, which we happen to call fluidity, and both are in agreement.
9.97 AI
140
401
20
1
9 12 16 % Si
Figure 3.23 Data from the spiral and strip tests shown in Figure 9, reduced by the factors shown to simulate results as though all the tests had been curried out in a similar size mould, of section 2 mrn x 17 mm. All results are seen to agree, confirming the validity of the comparison.