What is the Stress Intensification Factor or SIF?
The Stress Intensification Factor or SIF, as defined by Code ASME Section III, is a Fatigue Correlation Factor that compares the fatigue life of Piping Components, such as Tees and branch connections, to that of girth butt welds in straight pipe subjected to bending moments. This factor is often confused with stress concentration factors, stress coefficients, or other stress indices used in various mechanical design and fracture mechanics problems.
History of Stress Intensification Factor
The Stress Intensification Factor in piping stress analysis provides the fatigue correlation of piping elbow and branch connections for evaluating moment loading. This approach is based on the Markl stress intensity factor which is defined as: iS = 245,000N-2, where i=(CN-2)/S and C=245,000 for carbon steel materials, N=Cycles to failure and S=Nominal stress amplitude.
Stress Intensification Factor Equation
According to Section III, for class 2 & 3 piping and B31.1, the calculated stress S is determined by the equation:
S = i*M / Z,
where M = (Mx2 + My2 + Mz2)1/2 and Z=Section Modulus.
The thermal expansion stress SE is determined by the equation: SE = {(Sb)2 + 4(St)2}1/2, where Sb=resultant bending stress and St=torsional stress = Mt/2Z.
The resultant bending stress is calculated by Sb= [((iiMi)2 + (ioMo)2)1/2]/Z, where ii= in-plane bending stress intensification factor and io= out-of-plane stress intensification factor.
Calculating Elbow without Flange
R1:
The radius of the elbow is calculated by multiplying the pipe size with 1.5. For a 12” Std schedule long radius elbow, R1 is equal to 18”.
T:
The thickness of the elbow is equal to the thickness of the pipe. Assuming the same thickness for both, the thickness of the elbow (T) is equal to 0.375”.
r2:
The radius of the elbow at the end is calculated by subtracting the thickness from the outside diameter and then dividing the result by 2. In this case, for a 12” Std schedule long radius elbow, the radius of the elbow at the end (r2) is equal to 6.1875”.
h:
The height of the elbow is calculated by dividing the radius of the elbow (R1) by the square of the radius at the end (r2). For a 12” Std schedule long radius elbow, the height of the elbow (h) is equal to 0.176.
ii and io:
The ii and io values are calculated by dividing 0.9 and 0.75 respectively by the cube of the height of the elbow (h). For a 12” Std schedule long radius elbow, the ii and io values are equal to 2.86 and 2.4 respectively.
- R1 = 1.5(12) = 18”
- T = 0.375” (Std) Assume the same thickness for pipe & elbow
- r2 = ( OD-T)/2 = 6.1875”
- h = (TR1 )/(r2)2= 0.176 (From table D-300 of B31.3)
- ii = 0.9 / h2/3 = 2.86
- io = 0.75/ h2/3 = 2.4
Calculating Elbow with Flange
C1:
When one end of the elbow has a flange, a correction factor C1 is applied. This is calculated by dividing the height of the elbow (h1) by 6. For a 12” Std schedule long radius elbow, the correction factor C1 is equal to 0.7486.
ii and io:
The ii and io values are recalculated by multiplying the correction factor C1 with 0.9 and 0.75 respectively and then dividing the result by the cube of the height of the elbow (h). For a 12” Std schedule long radius elbow, the ii and io values are equal to 2.14 and 1.797 respectively.
- ii = C1 ( 0.9 ) / h2/3 = 0.7486 x 2.86 = 2.14
- io = C1 ( 0.75)/ h2/3 = 0.7486 x 2.4 = 1.797
Pressure vs Stress Intensification Factor
Analytical Methods for Stress Intensification Factor Calculation
Analytical methods for calculating Stress Intensity Factor (SIF) are defined by piping codes and are used to accurately estimate the stress levels of pipe systems. These methods involve the application of a moment through the nominal attached pipe and the determination of the highest stress from the resulting plot. This stress can then be divided by M/Z to get the SIF.
FEM Techniques for Stress Intensification Factor Calculation
Finite Element Methods (FEM) software can also be used to calculate Stress Intensity Factors. Popular software packages such as FE-pipe and Ansys are used to build models and calculate SIFs. The software takes into account the geometry of the pipe system, material properties, and loading conditions to provide a detailed analysis of the system.
What is Stress Intensification Factor (SIF)?
Stress Intensification Factor (SIF) is a measure of the amount of stress in a part relative to the amount of stress in a girth (circumferential) butt weld due to a similar moment “M”. It is defined as the ratio of the actual peak stress in the part to the nominal stress in the part for a piping component subject to bending loads. SIF= (Actual Peak Stress in Part)/( Nominal Stress in Part).
Calculation of SIF:
When Stress Intensity Factors are needed for a large D/T “Wye” Fitting, usually four SIFs are involved: one for the in-plane moment about the wye, one for the out-plane moment for both the main header and branch sections. As an example, the calculation for a 32×0.375 wye fitting is given below. According to Markl’s definition, the SIF is calculated as: B31 Stress Intensity Factor (SIF) = Actual Stress in Part (due to M)/ Stress in Girth Butt Weld (due to M).
Load Cases in FE/Pipe Modeling
FE/Pipe is a powerful tool for creating models related to piping systems. It automatically sets up two load cases for the model: Operating and Occasional.
Displacements and Stresses of the Load Cases
Various displacements and stresses from each load case can be seen in below Fig. Depending on the type of model and the loads applied, these displacements and stresses can vary greatly. It is important to analyze these data to ensure that the model is performing as expected.
