Just so I am understanding this question correctly, you're looking for the smallest size welding specimen that can be used for destructive testing Such as bend tests and tensile pulls?
Do you have any more information on the process or material as this varies somewhat by code and process.
The size of the specimen is dicated by the welding code governing the applications, such as ASME Section IX, AWS D1.9 (for Ti), B2.1 (as Al mentioned), etc. You can't generally pick a code based on the sample sizes you want. However, that is only if you are building something to the code. I see that you are from a university though, and could be perhaps just doing research? If that is the case, there isn't much difference between the AWS type codes structural codes. They generally require rectangular full thickness tensile tests. However, ASME allows turned specimens and has specimen sizes down to .188" diameter with a length of "the width of the weld plus 2D".