I don't have a set of ASME code books in front of me to pull the section number, but I remeber writing a PVC welding spec to ASME requirements about 10 years ago.
A quick ASME search brought up this:
Committee on Nonmetallic Pressure Piping Systems Standards Established
ASME Standards and Certification has chartered a new standards committee to develop the first comprehensive standards covering design, joining, fabrication, installation, examination, and testing for thermoplastic and fiberglass reinforced plastic piping systems. The committee will also develop and maintain nonmetallic material specifications for nonmetallic materials other than wood, glass, and concrete for pressure applications. More than 50 committee volunteers have been appointed to this committee and its subcommittees supported by manufacturers, engineering contractors, end users, trade associations and regulatory agencies. It is anticipated that these standards will facilitate the Interchangeability of nonmetallic piping components and the compatibility of material chemistries and composition.
For more information, contact Daniel Sharp (+1.212.591.8538).
NACE is also involved in plastics:
http://www.onepetro.org/mslib/servlet/onepetropreview?id=NACE-00536And so is AWS:
http://www.aws.org/w/a/technical/g1/Tim