Guinier
A chain of physical models that follows an aluminium alloy from the melt to the finished sheet.
Thermodynamics, precipitation, strength, multi-alloy sheet: each step is taken from the published literature and checked against measurements before the next one is built on it.
To begin with
As a rolling ingot solidifies, the liquid enriched in alloying elements moves relative to the growing crystals. The centre ends up a few percent poorer in magnesium and silicon than the rest. Can a long anneal even it out?
What casting leaves in the ingot stays in the sheet: the centre of the ingot becomes the centre of the sheet. Questions like this one are what Guinier is for.
Questions it answers
Every figure below is produced by Guinier as it stands, by one of its documented examples.
AA6016 is a common alloy for car body panels. To harden it, it must first be heated until its Mg2Si particles dissolve, but never until it starts to melt.
The thermodynamic model puts that window between 503 and 583 °C. The iron-rich particles never dissolve, at any temperature.
Recycled scrap brings iron, and iron cannot be removed by heat treatment. Simulating the solidification of an AA6016 ingot shows the coarse iron-rich particles tripling, from 0.4 to 1.3 % of the mass, as the iron rises from 0.10 to 0.40 %.
These particles later decide where new grains form during annealing, and where cracks start when the sheet is bent.
Ageing at 175 °C fills the alloy with needle-shaped precipitates a few nanometres across, and they make it strong. After 8 hours, the model gives needles of 1.9 nm radius occupying 1.5 % of the volume. Neutron scattering and electron microscopy measured 1.7 to 2.0 nm and 1.6 %.
The parameters are the published ones; none was adjusted to obtain this agreement.
Next to a weld, the metal is heated for a few seconds only. That is enough: above about 450 °C the precipitates dissolve, and the sheet falls back to a third of its strength.
Below 300 °C, nothing happens. The model follows the measured trend, and is somewhat too strong between 300 and 400 °C, where more stable phases the model does not represent start to form.
Iron-rich particles also hold silicon, which would otherwise go into the hardening precipitates. Chaining the thermodynamic model to the precipitation model puts a number on it. From 0.10 to 0.55 % iron, an aged 6061 loses about 60 MPa.
The same chain tells how much silicon to add back.
An ingot can be cast with a strong core and a softer skin, then rolled into one sheet. Three things follow, all three computed.
One furnace temperature has to suit both alloys (here 547–591 °C). The interfaces blur over 13 µm, set by the last 30 seconds of heat treatment rather than the 10 hours spent in the ingot, because rolling squeezes the earlier mixing by a factor of 600. And in bending the surface yields first: a softer skin lowers that limit by the same amount however thin it is.
$ python ex06_multilayer_sheet.py Multi-alloy sheet: AA6061 core, AA6063 skins, 1 mm AA6061 Mg2Si solvus 546.5 °C, solidus 600.9 °C AA6063 Mg2Si solvus 504.2 °C, solidus 619.3 °C common solution window: 547 - 591 °C (44 K, feasible) MG: mixed zone 12.7 µm; share of Dt: homogenisation 0.3 %, solution treatment 99.7 % SI: mixed zone 15.1 µm; share of Dt: homogenisation 0.3 %, solution treatment 99.7 % skins 5 % each: tension 96.1 %, plastic moment 92.6 %, first-yield moment 61.0 % skins 10 % each: tension 92.2 %, plastic moment 86.0 %, first-yield moment 61.0 % skins 20 % each: tension 84.4 %, plastic moment 75.0 %, first-yield moment 61.0 %
How it works
Each model reads what the previous one produced and adds its own part: which phases, how much solute is left in the matrix, which precipitates of which size, what strength.
Equilibrium phases and Scheil solidification (CALPHAD, COST 507 database, pycalphad).
Nucleation, growth and coarsening of needle-shaped β″ (Kampmann–Wagner numerical model).
Dislocations shearing small precipitates and bypassing large ones, plus solid solution.
Interdiffusion at the interfaces, strength through the thickness, tension and bending.
Every model and every parameter comes from a cited paper or database.
Each model has a validation notebook that compares it with published measurements, and automated tests keep the comparison true.
When a database cannot represent a phase, or a model does not transfer to another alloy, the notebook shows it and explains why.