Table of Contents

## Stress Intensity Factor Meaning

**As per Code ASME Section III, Stress Intensity Factor or SIF is defined as the Fatigue Correlation Factors that compare the fatigue life of Piping Components (Tees, branch connections) to that of girth butt welds in straight pipe subjected to bending moments.** This is also widely known as Stress Intensification Factor.

Note that, Stress Intensity factors are often confused with stress concentration factors, stress coefficients, or other stress indices used in various mechanical design and fracture mechanics problems. Stress intensification factor in piping stress analysis provides the fatigue correlation of piping elbow and branch connections for evaluating moment loading.

## History of Stress Intensity Factor

### Markl Fatigue Curve for Straight Pipe (Fig. 1):

Markl stress intensity factor : iS = 245,000N^{-0.2}

i =( CN^{-0.2})/S

Where

- i=Stress intensity factor
- C=245,000 for carbon steel materials
- N=Cycles to failure
- S=Nominal stress amplitude

Markl Stress Intensity Factor is based on deflection control, fully reversed, cyclic bending fatigue tests.

## Stress Intensity Factor Equation

### As per Section III, for class 2 & 3 piping and B31.1

Calculated stress S = i*M / Z

where

- M = (M
_{X}^{2 }+ M_{Y}^{2}+ M_{Z}^{2})^{1/2} - Z=Section Modulus
- i= Stress intensity factor

This approach is conservative.

Thermal expansion stress S_{E} = (S_{b}^{2} + 4S_{t}^{2})^{1/2}

where

- S
_{b}=resultant bending stress - S
_{t}=torsional stress = M_{t}**/**2Z

The resultant bending stress is calculated by

S_{b}= [((i_{i}M_{i})^{2 }+ (i_{o}M_{o})^{2})^{ ½}]**/**Z

where

- i
_{i }= in-plane bending stress intensification factor (Refer Fig. 3) - i
_{o}= out-of-plane stress intensification factor (Refer Fig. 3) - M
_{i }= in-plane bending moment (Refer Fig. 2) - M
_{o }= out-of-plane bending moment (Refer Fig. 2)

**Eg: ****For 12” Std schedule long radius elbow**.

a)Elbow without flange

- R
_{1 }= 1.5(12) = 18” - T = 0.375” (Std) Assume same thk for pipe & elbow
- r
_{2 }= ( OD-T)/2 = 6.1875” - h = (TR
_{1})/(r_{2})^{2}= 0.176 (From table D-300 of B31.3) - i
_{i }= 0.9 / h^{2/3}= 2.86 - i
_{o }= 0.75/ h^{2/3}= 2.4

b)If one end is flanged the correction factor C_{1} = h^{1/6 }= 0.7486

- i
_{i }= C_{1}( 0.9 ) / h^{2/3}= 0.7486 x 2.86 = 2.14 - i
_{o }= C_{1}( 0.75)/ h^{2/3}= 0.7486 x 2.4 = 1.797

## Pressure vs Stress Intensity Factor

### Effect of Pressure on Stress Intensity Factor:

## Finite Element Methods for Stress Intensity Factor Calculation

The various methods for calculating Stress Intensity Factor are

- Analytical Methods defined by Piping Codes
- FEM techniques

The user can see that the basic SIF procedure is:

- Build the model.
- Apply a moment through the nominal attached pipe.
- Read the highest stress from the result plot.
- Divide by M/Z to get the SIF.

The Fem Softwares widely used for calculating Sif are

- FE-pipe
- Ansys

### Stress Intensity Factor Calculations

The basic definition of a stress intensity factor (SIF) is:

**SIF = (Actual Peak Stress in Part)/( Nominal Stress in Part)**

The nominal stress in the part for a piping component subject to bending loads is M/Z where “M” is the moment that the pipe exerts on the component, and Z is the section modulus of the matching pipe welded to the part being analyzed.

**Example Case:**

For example, when Stress Intensity Factors are needed for a large D/T “Wye” Fitting, there are usually four SIFs involved.

- one for the in-plane moment about the wye,
- one for the out-plane moment
- For both the main header and branch sections.

An example, demonstrating this calculation for a 32×0.375 wye fitting is shown in the example.

Markl’s definition of the SIF is the ratio of the actual stress in the part due to a moment “M”, divided by the nominal stress in a girth (circumferential) butt weld due to a similar moment “M”.

B31 Stress Intensity Factor (SIF) = Actual Stress in Part (due to M)/ Stress in Girth Butt Weld (due to M)

Two load cases for the model are setup automatically by FE/Pipe.

They are

- Operating, and
- Occasional

Various displacements and stresses from each load case are shown in Fig 6 and Fig 7.

Some more Resources that may be of your interest

Piping Elbow or Bend SIF (Stress Intensification Factor)

How to use ASME B31J-2017 and FEM for SIF and k-factors for Stress Analysis

ASME B 31J & B 31J Essentials: Why these are useful in Piping Stress Analysis?

Thanks for explaining that the nominal stress can be found by dividing the moment of the pipe by the section modulus of the matching pipe that’s welded to that part. Lately I’ve been interested in learning more about the future of welding technology. It’s was interesting to learn about some of the math involved in welding, so I’m glad you shared!