These comments are for US use only.
I just quoted this paragraph in a previous post. This is from ASME B31.3, (year 2004):
(a) Pressure relieving devices required by para. 301.2.2(a) shall be in accordance with the BPV Code, Section VIII, Div. 1, UG-125(c), UG-126 through UG-128, and UG-132 through UG-136, excluding UG-135(e) and UG-136(c). The terms "design pressure" and "piping system" shall be substituted for "maximum allowable working pressure" and "vessel," respectively ...
What this says is that some kind of pressure relieving device is required, but it specifically excludes the need for an ASME rated valve by excluding paragraphs UG-135(e) and UG-136(c). I don't have the BPV code handy to verify that, but I'm 99.9% sure my memory hasn't failed me there because we use non-code rated RV's for piping. Note however that an ASME code RV is needed to protect pressure vessels in the US. Not sure what is needed in other areas of the world.
Also, some of these "adjustable cracking pressure check valves" are specifically intended for use on instrument lines or any small diameter pipe or tube system. For example, Nupro (one of the Swagelok companies) makes a
CPA Series "adjustable check valve". Another company, Generant, makes the "ACV" series which is a knock off of the Nupro CPA series. Both companies market these as relief devices for small diameter lines, for pressure up to 600 psi. I'm sure there are other manufacturers out there as well. Here's Generant's web page (can't seem to find the Nupro one.)
Note however that Air Products and Chemicals, Inc. has found that some of these very small relief valves (check valves) fail to operate well at low pressure. They tend to stick shut, and has suggested they not be used below 100 psig. See public disclosure here:
So to answer the question, adjustable check valves are actually allowed by ASME B31.3 piping code and there are companies that make such things. They are not however, allowed for any ASME rated pressure vessel.