Some researchers have experimented with tool diameter to shoulder diameter ratio, but is there any standard relationship between pin length and pin diameter in FSW tool
Pin's length is determined by the weld metal thickness. Pin's diameter is determined by the required pin's strength and wear resistance, Therefore, we finally come to the shoulde/pin diameter ratio.
Dear Sergei answered very brief and nice. For completing his answer, there is a lot of papers optimizing the tool dimensions. Also, the majority of the investigators use the 1/4 or 1/3 for the pin/shoulder ratio.
Since there is no standard available for FSW.. Its one of the parameter, you can consider for the test.. it always depend upon other parameters and materials to be welded..
For micro friction stir welding, the diameter of the pin is small and for general FSW the diameter is the range of 6-10mm. the diameter depends upon the process. There is no barrier of range of diameter (perhaps not studied) from micro to general FSW process.
Coming to length, for proper FSW having good weld, the length of the pin should be slightly less than the metal thickness( again not much studied in this area) for proper dynamic crystallization process and makes better weld quality.
Finally, these are two two independent parameter ( i guess) and their ratio will not help in proper dynamic re crystallization of the joint . More taughts welcome