to 5.1% (1.9×) by solution treating, whereas the highest value was raised from 5% as-cast to 13% in the solution treated condition (2.6×).
For the T4 and T6 tempers, the values of Weibull modulus for both tensile strength and Ef
were improved following
ageing from the solution treated condition meaning the flaw size distribution decreased. For the fully hardened T6 temper tensile strengths, for example, m was equal to 61 and the position parameter, σo
, the values of Weibull modulus and posi- was 438 MPa. This repre-
tion parameters were decreased only slightly from solution treated, to T4, to T6 conditions, depicted by the failure probability plots shown in Figure 3 (d) and summarised in Table 5.
Quality charts and Equivalent Defect fractions Derived from the ludwik-Holloman Equation
All tensile data were converted to true stress and true strain values, and the strain hardening exponent n was calculated from the slope of the log-log plot of the average stress-strain curve, based on this data. This value of n was then used to find the average strength coefficient, K, in the same manner used pre- viously.1
The model flow curve was thereby deter-
mined, and the experimental true stress-true strain data are overlaid with these model curves in Figure 4. Values of the strain hardening exponent, n, and the strength coefficient, K, for each of the conditions are provided in Table 5.
Quality curves based on the data of Figure 4 for the as-cast and solution treated condition are compared di- rectly in Figure 5. These two con- ditions display only a small differ- ence in the values of strain harden- ing exponent n, at 0.261 and 0.282 respectively. The values of strength coefficient K do however display greater differences; the as-cast value was 872.1, but the solution treated material displayed a value of 729.2. This change in strength coefficient has offset the entire flow curve downwards (Figure 5). What
52
Figure 4. Model flow curves derived using the Ludwik- Holloman equation for the values of strain hardening exponent, n, and strength coefficient, K, presented in Table 5. (Note that the Portevin Le Chatelier effect, which is observed in the solution treated condition, is neglected for the purpose of this derivation).
Table 5. Values for Weibull Modulus, Position Parameter, Strain Hardening Exponent and Strength Coefficient, for Evaluating Casting Quality
sents an improvement to Weibull modulus, (m) above the as-cast (42.3), solution treated (30), and T4 (37) condi- tions, and hence a substantial improvement in qual- ity. For Ef
single marker on the line) was much greater. This means that, although all elongation results were improved, the best quality samples would appear to be improved propor- tionately more. For example, examining only the highest and lowest values, Tables 1 and 2 show that the lowest value of Ef
for the as-cast condition was raised from 2.7%
is perhaps most significant, was the change in relative qual- ity, and therefore the corresponding equivalent defect frac- tion present on the fracture surface, determined by solving Eqn 8. In regards to quality (q) for the as-cast material, most values were between q=0.1 and q=0.2.1
For the so-
lution treated condition the values were mostly between q=0.2 and q=0.4. The equivalent defect fraction present on the fracture surface derived using Eqn 8 is 0.21-0.32 for the as-cast condition; this was reduced to 0.07-0.23 for the solution treated condition.
This change in the equivalent defect fraction present on the fracture surface was a particularly interesting result, because the amount of features such as porosity, Fe-bearing particles, and oxide flakes for example, were not expected to be de- creased by solution treatment. Although there is clearly the potential to increase porosity by blistering during long times or high temperatures of solution treatment, the procedures
International Journal of Metalcasting/Fall 2011
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