Strain rate can predict defects in AZ 91 magnesium alloy castings.

A Modern Casting Staff Report 

(Click here to see the story as it appears in the October issue of Modern Casting.)

Hot tearing is one of the most frequent defects in castings, and it is important to predict its occurrence as early as in the design stage of a product. There is no unique explanation of the root cause for this defect, although many predictive models exist. One of the reasons is that hot tearing is a material-specific problem.
Researchers Milan Rakita, Qingyou Han and Z. Liu, Purdue University, Mechanical Engineering Technology, West Lafayette, Ind., compared simulation results for magnesium alloy
AZ 91 with prior experimental work. They found strain rate can be used in simulations to predict locations susceptible to hot tearing in this alloy. Their paper, “Strain Rate as a Predictor of Hot Tearing in AZ 91 Magnesium Alloy,” provides their analysis of the study.

Question

Given the random appearance and extent of hot tearing, what reliable predictive model can be developed for magnesium alloy AZ 91?

1. Background

Hot tearing criteria can be roughly compiled in several main groups: stress-based, strain-based, strain rate-based and nonmechanical. The basic assumption in many hot tearing models is that this defect occurs when feeding stops to accommodate the casting shrinkage.

A combination of inadequate feeding and the strain rate has been qualitatively described as a cause of hot tearing. Rappaz, Drezet, and Gremaud gave a quantitative description of conditions that can cause nucleation of hot tears, usually called RDG criterion. According to the model, if the pressure drop caused by applied strain rate goes below a critical value, a hot tear will nucleate.

A modified form of RDG criterion assumes strain rate to be independent of temperature. There, the limits of integration are taken to be the mass feeding temperature and the temperature when bridging between dendrite arms occur. A study involving several hot tearing tests concluded the RDG model has the greatest potential of predicting hot tearing, but only on qualitative basis. The strain rate-based hot tearing models are tested on aluminum alloys, frequently Al-4.5% Cu, known for its susceptibility to hot tearing.

It is a well known practical observation that hot tearing can be reduced or eliminated in controlled casting conditions that prevent formation of large temperature and stress gradients. In line with that, preheating permanent molds to a high enough temperature is done to alleviate or eliminate hot tearing.

If feeding serves only to close the space between separated dendrites, inadequate feeding cannot be the reason for hot tearing; there are open and filled hot tears. Feeding is not considered in this work, although it is implied by the RDG model, which will be used here.

Experiments in which several magnesium alloys were poured into preheated molds determined the critical preheat temperature above which hot tearing does not occur. Magnesium alloy AZ 91 did not experience hot tearing if the mold was preheated to 635F (335C) or more. Among magnesium alloys tested, AZ 91 had the lowest susceptibility to hot tearing.

The researchers tried to simulate similar conditions and determine what hot tearing criterion matches prior experimental observations. To test the sensitivity of the prediction, AZ 91 alloy was simulated because it has relatively low susceptibility to hot tearing and a somewhat lower pouring temperature, which sometimes help decrease the danger of hot tears. Other hypotheses also tested were the relation between thermal stresses and mechanical properties of the mushy zone, and mismatch between expansion of the mold and casting shrinkage. As the results of this simple simulation showed, strain rate could be used as a reliable predictor of hot tearing in simulations of casting magnesium alloys.

2. Procedure

Commercial casting simulation software was used, with properties for AZ 91 adopted from its database. Liquidus and solidus temperatures of AZ 91 are 1,114F (601C) and 797F (425C), respectively. Pouring temperature was set to 1,292F (700C), although previous researchers used 257F to 320F (125C to 160C) superheat.

The simulation model, Fig. 1, resembles roughly the one of two molds used in the prior studies. The dimensions are reproduced while those not given are made to resemble the photographic record. This type of specimen, sometimes referred to as “harp” casting, frequently is used for determining hot tearing susceptibility.

Venting holes, which continue from the tip of spherical ends, are added in the simulation software to avoid an unnecessarily large number of control volumes. However, it was found their existence does not affect the results presented here. Control points are placed between the rod and the radius at both ends of all the rods, around 0.008 in. (0.2 mm) from the surface, in the casting and mold. The data presented in the Results section are obtained from these points. The casting alone is modeled with 150,610 metal cells, while the complete model has 5,528,736 control volumes.

Instead of finding the pressure drop under applied strain rate, the critical strain rate that causes hot tearing was estimated. It is not easy to determine the critical strain rate precisely. It can be hard to determine exact values of the temperature gradient and the solidification rate. The biggest problems seem to be viscosity and especially the cavitation threshold. It is well known that the magnitude of cavitation threshold is highly variable and unpredictable, partly because a valid model for the existence of cavitation nuclei still does not exist.

The critical strain rate increases with the increase in cavitation threshold and secondary dendrite arm spacing. It is evident that this model predicts that material becomes very intolerable to imposed strain rate and very susceptible to hot tearing as the temperature approaches solidus. The critical strain rate asymptotically approaches zero around solidus, meaning inevitable hot tearing, which is not physically real. This suggests the critical strain rate should be looked for around temperatures where the fraction of the solid phase is approximately 0.9, not around solidus temperature.

Strain rate is the highest in the mold preheated to 392F (200C) and drops down with increasing preheat temperature. The main feature is a distinct difference in strain rates in the casting when molds preheated to 626F (330C) and 644F (340C). Strain rates next to the spherical ends were even slightly negative around solidus temperature when the mold was preheated to 644F (340C). It is interesting that, except in the shortest rod next to the riser, strain rates were higher if the mold was preheated further to 698F (370C). Experiments were performed up to around 707F (375C) for this alloy, and no hot tearing was reported. Hence, we can assume strain rate developed when the mold was preheated to 698F (370C).

It is reasonable to expect that the thin liquid films between solid grains need higher cavitation threshold due to lack in cavitation nuclei, like gas bubbles and dissolved gases. The ratio of cooling rates between mold and casting also has been examined. The underlying hypothesis is that hot tearing may be avoided if thermal expansion and shrinkage of the mold and casting occur simultaneously. If the mold is preheated to an insufficiently high temperature, it still will expand while the casting is shrinking. This increases stress buildup in the casting, which leads to cracking in the final stages of solidification, when the material starts to gain mechanical strength.

To estimate the difference in shrinkage, it would be ideal to compare a variation in the length between characteristic points in the mold with the variation of unconstrained length in the casting. The latter is, however, very hard to determine. For that reason, the cooling rates at adjacent points in the mold and in the casting are compared.

As shown in Fig. 2, this result does not give a conclusive proof of hot tearing. The ratio is positive, meaning both casting and mold shrink at these points when the casting is around solidus temperature. Also, the distance between the control points in the mold decreases when the casting is below 932F (500C). Even if the mold shrinks, it can impose significant constraint if the unconstrained casting would have shrunk at the faster rate.

In any case, the effect of the shrinkage mismatch should be well captured by the strain rate. One expects these two are in direct
proportion.

The ratio of cooling rates is slightly negative at the beginning of cooling, indicating its expansion, but in all cases the ratio reaches positive values when the casting is at around 932F (500C). Therefore, according to the simulation, mold expands while castings shrink when the fraction of the solid phase is around 0.75, when the danger of hot tearing is not so great. There are occasional large negative peaks that show up and disappear within 50F to 59F (10C to 15C) before the ratio turns to positive values. Occurrence of these peaks does not depend on the preheating temperature. In conclusion, the effect of the shrinkage mismatch could not be clearly evidenced in this simulation.

Simulated stresses show only negligible plastic deformations in short rods during a very small temperature range below solidus temperature, and only in the mold preheated to 392F (200C). So, the simulation would show no danger of hot tearing if this result was used as a prediction.

3. Results and Conclusions

Simulated strain rates in the “harp” type casting with the mold preheated to 644F (340C) show distinctively lower values than for the mold preheated to 626F (330C). This is in acceptable agreement with prior experimental results in which hot tearing did not occur in molds preheated above 635F (335C).

This is a good indication that the strain rate can be used in simulations of real castings from AZ 91 magnesium alloy to predict possible hot tearing and in finding a solution as early as in the design phase. One can make a conjecture that the strain rate can be used as a predictor of hot tearing in magnesium alloys in general. Further work is required to prove this assertion.

The RDG criterion was used in its differential form and viscosity was calculated to obtain the critical strain rate. This procedure needs further justification to be more rigorous. Nevertheless, the calculated limiting strain rate falls with the range that separates strain rates in the mold preheated to 626F and 644F (330C and 340C). Because the critical strain does not show physically realistic behavior near the solidus, its value should be determined at lower values of solid fraction.

In conclusion, it is recommended that the critical strain rate is determined by combining the “harp” casting tests, the simulation of the same tests and the set of Equations used in this study. This result can be used in simulations of real castings from that alloy to optimize process parameters to decrease the risk of hot tearing, or completely avoid it.  

For more details, see the original version of this paper, 13-1340, published in the proceedings of the 2013 AFS Metalcasting Congress, at www.afsinc.org.