Using a combination of theoretical and experimental techniques, the critical depth of a long, internal or external surface flaw in an internally pressurized cylinder can be found. The theoretical study is performed using nonlinear finite-element methods. Assuming an infinitely long, axially oriented, surface crack in the wall of a pressure tube, a quarter of the tube cross section was modeled in plane strain. Three different crack penetrations were examined by specifying crack depth to wall thickness ratios (a/t) equal to 0.25, 0.5, and 0.75. The crack-tip stress-strain field was simulated using collapsed isoparametric elements containing a 1/r singularity.

The J-integral, and thus the stress-intensity factor, was found using the virtual crack extension method. Initially, elastic values were calculated, but, as the tube is manufactured from a zirconium alloy having a work-hardening material behavior, the analyses were extended into the elastic-plastic regime. Choosing the J-integral as the crack-driving force parameter, elastic and elastic-plastic theoretical crack-driving force curves were produced for internal and external surface flaws.

Experimental J-resistance curves have previously been determined using small-specimen test pieces. In the experimental tests, various property states of the zirconium alloy, such as unirradiated versus irradiated conditions and different levels of hydrogen concentrations, have been examined. Using the theoretically derived crack-driving force curve for an internal or external surface flaw, and the appropriate experimental J-resistance curve, an estimate of the critical depth can be obtained. The depth values obtained using this method compare very favorably with the result of a recent experimental burst test of a pressure tube containing a long external surface flaw.