Predicting a superalloy's shrinkage-porosity tendency from its residual liquid

Shrinkage porosity is one of the most stubborn defects in superalloy castings. It forms at the very end of solidification, when most of the metal is already solid and the residual liquid is trapped between dendrites. Metal shrinks as it freezes, and that shrinkage has to be made up by feeding – liquid flowing to the freezing site through narrow channels between dendrite arms. Where feeding cannot keep up, a pore remains.

An alloy's porosity tendency is usually judged by experience or by its freezing range: the wider the range, the longer and more tortuous the feeding path. Authors at the University of Science and Technology Beijing set out to reduce it to a few measurable properties of the residual liquid itself – and to obtain a method that ranks alloys before the first pour.

How feeding works

This section is our explanation, to show why the authors chose these parameters; it is not in the abstract.

At the end of solidification the mushy zone is like a sponge: a dendrite framework with liquid in its pores. Flow through such a porous medium follows Darcy's law: the flow rate is proportional to the pressure drop and the permeability of the medium and inversely proportional to the liquid's viscosity. Permeability is set by the framework geometry – dendrite arm spacing and liquid fraction. The less liquid is left and the finer the dendrites, the narrower the channels.

How much liquid has to be fed is set by the solid–liquid density difference: the larger it is, the more the metal shrinks on freezing. How easily the liquid passes is set by viscosity and permeability. If the required flow exceeds what the channels can pass under the available pressure drop, the liquid pressure falls and a pore appears. Hence the interest in the properties of the residual, last liquid: segregation makes its composition very different from the master alloy, and with it the density and viscosity change.

What was studied

Five alloys of different chemistry – from the well-known GH4169 to the highly alloyed GH4975 and GH4065. Porosity tendency was measured with poured test pieces. Structure and segregation in the final stage of solidification were studied in three ways: isothermal quenching during solidification (to freeze the liquid at the right moment and measure its composition), directional solidification and differential scanning calorimetry.

From the measured solid and liquid compositions at the end of solidification, the authors calculated the characteristics of the residual liquid thermodynamically. Together with dendrite arm spacing and the difficult-feeding temperature range, they then quantified the combined effect on porosity.

What was found

Two factors lead – the solid–liquid density difference and the viscosity of the residual liquid. On that basis the authors built a Darcy-law method that ranks alloys by porosity tendency. They report that the predicted tendency for the different alloys agrees well with experiment, and that the method provides a basis for designing multi-component alloy compositions and optimising the process.

We give no numbers: the paper is behind a paywall, this reading is based on the abstract, and the figures are in the full text.

Limits

Five alloys are few for a general criterion. The paper deals with ingots of wrought alloys, and feeding in an ingot and in a thin-walled cored blade differs a great deal: a blade has its own hot spots, risers and feeding path, and directional solidification itself changes both PDAS and permeability. So applying the method to blade-casting alloys is a hypothesis, even though the physics is the same.