Friction stir welding plasticizes metal by frictional/deformational heating under a rotating pin tool, then carries it around the pin and forges it back together behind the tool. In the reference frame that moves with the tool (a standard simplification, e.g. Nunes/Seidel–Reynolds analytical flow models), the process looks like a steady 2-D velocity field: cold material streams in from upstream at the traverse speed, gets swept around the pin, and exits behind it.
r = √(x²+y²), ω signed (rad/s, + = CCW)
Rotational term (solid body inside the pin,
decaying vortex outside it — the classic two-zone
approximation of the stirred/TMAZ region):
DF(r) = 1 for r ≤ R
= (R/r)·exp(−(r−R)/L) for r > R
(u_rot, v_rot) = (−ω·y, ω·x) · DF(r)
Small radial term (models forging-driven outward/
rearward extrusion that builds the onion-ring bands):
(u_out, v_out) = k·(x, y)·exp(−r/2L)
Total field: u = v_travel + u_rot + u_out
v = v_rot + v_out
Because this field is steady in the tool frame, particle pathlines coincide exactly with streamlines — playback runs at a fraction of real time purely for legibility, but that uniform time-scaling leaves every path's shape (and the dimensionless ratio λ = ωR/v that controls it) exactly unchanged.
- Advance ratio λ = ωR/v — the standard FSW parameter comparing tool surface speed to travel speed; higher λ means more material rotations per millimetre of weld travel, i.e. more thorough stirring.
- Advancing side (orange) is where the pin's rotational surface velocity adds to the traverse velocity; retreating side (blue) is where it opposes it. Real FSW welds show measurably different grain flow, defect rates and onion-ring spacing between the two sides — this asymmetry is exactly why FSW tool rotation direction matters.
- The pin-radius and RPM sliders reproduce the tradeoff real welding engineers face: too little stirring (low λ) leaves unbonded "kissing-bond" defects, too much (very high λ) overheats and thins the joint.