This problem assumes that this is a design without documented experience within industry. The failure mode to be analyzed is a semi-elliptical surface connected flaw in the ID of the wall in the radial- axial plane. Vessel Data: •Material = SA-705 Gr. XM-12 Condition H1100 •Design Temperature = 70°F •Critical Stress Intensity Factor (KIc) = 104 ksi-in0.5(based on minimum fracture toughness and specification minimum yield strength – see methodology in problem E-KM-2.1.2) •Inside Diameter = 6.0 in •Outside Diameter = 12.0 in •Diameter Ratio (Y) = 2.0 [KD-250] •Design Pressure = 50,581 psi (problem E-KD-2.1.1) •Yield Strength = 115,000 psi @ 70°F per Table Y-1 of Section II, Part D •Tensile Strength = 140,000 psi @ 70°F •Assumed Crack Aspect Ratio (2c/a) = 3:1 per KD-410(b) The stress in the wall of this pressure vessel is a combination of the pressure stress and the residual stresses induced during autofrettage. The residual stresses were calculated in E-KD-5.1.1. The pressure stress distribution was also calculated here using the methods of KD-250. The principal of superposition was used to combine the two for the total stress at design conditions. Figure E-KD-3.1.1-1 shows a plot of these stresses at the design condition. Copyright ASME International Provided by IHS under license with ASME Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 04/10/2013 00:12:21 MDTNo reproduction or networking permitted without license from IHS--`,,,,``,```,`,``,,,,,,,,,``,``-`-`,,`,,`,`,,`---
PTB-5-201349 Figure 31 – E-KD-3.1.1-1 – Stress Distribution in Vessel WallSTEP 1– Determine if the stress intensity factor for a crack at 80% of the wall thickness will result in brittle failure Many of the available methods for calculating stress intensity factors are not accurate beyond 80% of the wall. The stress intensity factor at this depth must be less than KIc. The stress intensity factor is to be calculated in accordance with the methods found in API 579-1 / ASME FFS-1 per KD-420(a). The stress intensity factor solutions are found in Appendix C. Specifically, C.5.10 has a solution for “Cylinder – Surface Crack, Longitudinal Direction – Semi-Elliptical Shape, Internal Pressure (KCSCLE1)”. Figure E-KD-3.1.1-2 shows the crack being analyzed. Copyright ASME International Provided by IHS under license with ASME Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 04/10/2013 00:12:21 MDTNo reproduction or networking permitted without license from IHS--`,,,,``,```,`,``,,,,,,,,,``,``-`-`,,`,,`,`,,`---
PTB-5-201350 Figure 32 – E-KD-3.1.1-2 – Cylinder – Surface Crack, Longitudinal Direction Semi-Elliptical Shape (API 579-1 / ASME FFS-1 Figure C.15)Paragraph C.5.10.1 is for a Mode I Stress Intensity Factor for an inside surface , including pressure in the crack face. Equation C.186 gives: Where the influence coefficients, G0and G1are given by: Where Table C.12 provides the Ai,jcoefficients and equation C.96 is used for the value of βas: Influence coefficients G2, G3, and G4 are then determined by the methods found in paragraph C.14.3 or C.14.4, typically using the weight function approach. The value of Q is determined with equation C.15: Using this methodology, the stress intensity factor for a crack with a depth of 2.4 inches is 285,100 psi-in0.5. Therefore, the criterion is not satisfied.