This problem assumes that this is a design without documented experience within

This problem assumes that this is a design without

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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 (K Ic ) = 104 ksi-in 0.5 (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 MDT No reproduction or networking permitted without license from IHS --`,,,,``,```,`,``,,,,,,,,,``,``-`-`,,`,,`,`,,`---
PTB-5-2013 49 Figure 31 – E-KD-3.1.1-1 – Stress Distribution in Vessel Wall STEP 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 K Ic . 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 MDT No reproduction or networking permitted without license from IHS --`,,,,``,```,`,``,,,,,,,,,``,``-`-`,,`,,`,`,,`---
PTB-5-2013 50 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, G 0 and G 1 are given by: Where Table C.12 provides the A i,j coefficients and equation C.96 is used for the value of β as: 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-in 0.5 . Therefore, the criterion is not satisfied.