Markl, SIFs, and ASME VIII-2 Fatigue Design
Did you know that PRG has the only automated FEA Stress Intensification
Factor (SIF) calculator in the world?
PRG software has been automatically calculating SIFs for
varieties of piping components for more than fifteen years.
This brief article addresses the question of "What are SIFs,
where did they come from, and how do they relate to ASME
Section VIII-2 fatigue designs?"
Since B31.3 2007 (and earlier) references finite element
methods and ASME Section VIII-2 fatigue methods in Appendices
4 and 5, this is information that should be understood by
every senior piping designer.
Markl, FEA, and Div 2. Appendix 5
One benefit of PRG software is the automated calculation of piping
stress intensification factors (SIFs). SIFs are automatically
calculated in FE-SIF, Nozzle/PRO, and FE/Pipe.
In fact, there is no
other FEA software in the world that provides automatic SIF
calculations.
FE-SIF is specially designed for these calculations and intended to be
an “everyday product” for piping engineers to utilize in concert with
their usual piping analysis software.
This topic will provide a brief introduction to how SIFs are calculated,
how they relate to ASME Section VIII Division 2 fatigue design, and where
did SIFs come from.
A Stress Intensification Factor (SIF) is defined as the ratio between
the peak stress and average stress in a given component:
SIF = Actual Peak Stress / Nominal Stress in Part
A. R. C. Markl and his team (1950’s) developed the original SIFs
still used in ASME piping Codes today.
In his study, Markl determined that girth butt-welds typically
resulted in stresses approximately 1.7 to 2.0 times the stress in
non-welded piping. As a result, all of the piping codes have been
“base lined” to include the factor of 2.0 for girth welds:
|
B31.3 SIF =
|
Actual (Peak Stress) due to Moment M |
|
Stress in Girth Butt Weld due to Moment M |
OR
|
B31.3 SIF =
|
Actual (Peak Stress) due to Moment M |
|
2 * (Moment M) / (Section Modulus Z) |
In terms of ASME Section 8, Division 2, Appendix 5 and
finite element analysis (FEA) work, we could use the following
equation interchangeably with the previous equations:
|
SIF =
|
Range of Peak Stress due to M |
|
2 * (Moment M) / (Section Modulus Z) |
|
= |
2 * (Pl+Pb+Q+F) |
|
2 * (M / Z) |
OR
|
SIF =
|
Alternating Peak Stress due to M |
|
(Moment M) / (Section Modulus Z) |
|
= |
(Pl+Pb+Q+F) |
|
(M / Z) |
The peak alternating stress (PL+PB+Q+F) is usually determined
from finite element analysis. Normally, the peak stress is the
product of the secondary stress and a fatigue strength reduction
factor (FSRF). For instance:
PL+PB+Q+F = (PL+Pb+Q)*FSRF / 2.0
FSRFs are determined from testing or taken from references such
as WRC 432.
As discussed in NUREG/CR-3243, the mean curve fitted to Markl’s
fatigue test data gives a relationship between the stress range
in a butt weld pipe and the number of cycles to cause a thru-wall
fatigue failure:
i * M / Z = Sf = 490000 * (N)-0.20 (Equation 1)
where
i = stress intensification factor
M = bending moment
Z = section modulus
N = expected number of cycles
Sf = allowable cycling stress
The mean curve described by Equation 1 is shown in the figure below.
Equation 1 has been normalized based on the peak stress range in a
girth butt-weld (i.e. i = 1.0). As a result, there is an inherent
factor on the peak stress range “S” of 0.50. All peak stresses given by
Markl SIFs are half of their actual values due to Markl’s use of girth
butt-welds as a baseline.
The factor of two makes the alternating peak stresses used in Division 2
Appendix 4 & 5 very easy to implement in terms of the Markl failure
criteria (Equation 1). One could conclude that by using a factor of 0.50
on peak stress, Markl has essentially reduced the stress range to an
alternating stress component. Using this conclusion, we can use
Division 2 Appendix 4 & 5 peak stresses with the following equation:
Pl+Pb+Q+F = 490000 * (N)-0.20 (Equation 2)
N = (Pl+Pb+Q+F / 490000)-0.20 (Equation 3)
Equation 2 gives the ASME Section 8, Division 2 alternating
peak stress (Pl+Pb+Q+F) that would cause a through-wall fatigue
failure with a 50% probability of failure.
Equation 3 gives the number of cycles to failure for a given
ASME Section 8, Division 2 alternating peak stress (Pl+Pb+Q+F).
FE-SIF automates these calculations and provides accurate SIFs
for all piping components, regardless of their geometry or design.