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.
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--`,,,,``,```,`,``,,,,,,,,,``,``-`-`,,`,,`,`,,`---

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.