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Materials Engineering DISCUSSION
I want to lighten a machine frame by changing some steel parts to aluminium. Aluminium has about one third of the density of steel, but also about one third of the Young's modulus, so it looks as if any weight saved is lost again when the sections are made thicker to get the stiffness back.
Is that right for every kind of part? The frame has tie rods in tension, rectangular beams in bending and some flat cover panels, and deflection rather than strength is the limit in all of them.
For the tie rods you are right. Axial stiffness is E × A / L, so the mass needed for a given stiffness scales with ρ / E. Steel: E about 200 GPa, ρ about 7850 kg/m³, giving E/ρ = 25.5 MN·m/kg. Aluminium: 70 GPa and 2700 kg/m³, giving 25.9. They are practically the same, so an aluminium tie rod of equal stiffness needs about three times the area and weighs the same as the steel one.
The same near-equality holds for titanium and magnesium alloys, which is a well-known coincidence among the common structural metals.
Bending is different because stiffness depends on the second moment of area, which grows faster than the area when you make a section deeper. For a beam whose section is scaled up in proportion, the mass for a given bending stiffness goes with ρ / √E; for a flat panel where only the thickness can change it goes with ρ divided by the cube root of E.
Panel example: equal stiffness needs E × t³ constant, so the aluminium panel must be (200 / 70)^(1/3) = 1.42 times thicker. Its mass is 1.42 × 2700 / 7850 = 0.49 of the steel panel. For the scaled beam the ratio is √(200 / 70) × 2700 / 7850 = 0.58. So the covers can lose about half their weight and the beams about 40 percent.
That saving only exists if the part is allowed to grow. If the outer dimensions of a beam are fixed by the space available, and you can only change wall thickness, a hollow aluminium section of the same outer size needs roughly three times the wall thickness and ends up near the same weight, exactly like the tie rod. Check the envelope before counting on the benefit.
For a fixed-height beam it can even be better to stay with steel and remove material where it does little: thinner webs, lightening holes near the neutral axis, or a deeper section with thinner flanges.
Do not let stiffness be the only check once the material changes. Common structural aluminium such as 6061-T6 has a yield strength around 240 to 275 MPa, which is similar to mild steel, but welding it softens the heat-affected zone considerably, so welded joints are designed with reduced strength. Aluminium also has no true endurance limit, so a vibrating frame needs a fatigue check at the expected number of cycles.
Two more differences show up in machines: thermal expansion is about twice that of steel (roughly 23 against 12 µm/m per °C), which matters where aluminium parts are bolted to steel ones, and threads in aluminium strip more easily, so use longer engagement or thread inserts.
