I think that's a lot of tribal knowledge. A good place to start would be to snag a copy of a D1.1 and take a look at the prequalified joint conifgurations that would give you a good starting point for allowable sizes of configurations in relation to material thickness.
I could be wrong but I've never seen a formulas or ratios for bevels and angles and the likes, too many variables like material, process, heat input etc.
All of the replies to fatehy's question are correct, but they don't answer what he's actually looking for.
Fatehy wants a standard, or table, or graph, or etc, saying that for a given pipe thickness the selected pipe end is this one.
Fatehy, I'm sorry to tell you that there's no official standard or whatever official publication that says what's the correct pipe end shape for a given thickness.
By "official" I mean a professional organization like AWS, ASME. API or others that have published standards, Codes or any printed material sold to the public, where their (the organizations') experience is condensed and made available to the interested persons.
What exist are General Specifications for Piping Systems issued by project engineering firms that are handed to their clients as part of their (the firms') services. In fact, when a client appoints a project engineering firm to undertake the design of a new plant or the revamp of an existing one, the project engineering firm hands to the client a whole set of documents, including, if it is the case, piping documents: General Piping Specification, Piping Detailed Specifications, List of Lines, Piping Layout, Isometrics and so on. These documents are confidential and are given to the client as part of the project engineering services. When receiving them, the client promises (usually in writing) not to disclose any document to unauthorized third parties. Back in my days of erector and project engineer dozens of General Piping Specs passed under my eyes.
Well, fatehy, it's on these General Piping Specs that you will find what you're looking for; it's these documents that, in most cases (but not always) state the type of welding end to be selected for a given thickness. Unfortunately for you, these documents are not sold to the public, for they're confidential information that belongs to the project engineering firm and makes part of its knowledge and experience.
I'll give you a couple of clues, based on my personal experience of the many years I spent erecting and designing industrial plants. K and X joints are unfeasible for piping, because you won't be able to weld them by the inside, unless the piping diameter is large enough to allow a welder to get into it (the pipe). J joints must be machined, they can't be cut with the torch. So they're feasible for thicknesses of, say, one inch and above in piping prefabricating shops, where there's a lathe available at hand. J joints don't compensate their cost for lower thicknesses. If the pipes are to be cut to length at the job site, where there's not a lathe easily available, then the best solution is to cut a V bevel with the torch, no matter the thickness.
Giovanni S. Crisi
Sao Paulo - Brazil