# Fatigue Calculation

User selection

Surface flaw

Embedded flaw

User input

Surface flaw

‘ai’ – flaw height for surface flaw and half height for embedded flaw in mm.

c’-Half flaw length in mm

‘p’-Shortest distance from material surface to embedded flaw in mm

D- Outer diameter of the pipe in mm

t- Thickness of the pipe in mm

Calculated parameters

B- Section thickness in plane of flaw (the remaining thickness not containing the flaw) in mm.

W- Circumference of the pipe in mm.2?r0

‘ro’-outer radius in mm from outer diameter of the pipe inputted by the user.

Constants

?- ?/2

Embedded flaw

‘a’-Half depth or height of flaw for embedded in mm

‘c’-Half flaw length in mm

‘p’-Shortest distance from material surface to embedded flaw in mm

D- Outer diameter of the pipe in mm

Calculated parameters

B’ – Effective thickness in mm B’ = 2a+2p

W- circumference of the pipe 2?r0

‘ro’-outer radius in mm from outer diameter of the pipe inputted by the user.

Constants

?- ?/2

Computation of Y

Y =M fw Mm

Mm – stress intensity magnification factor

fw – finite width correction factor

M – Bulging correction factor

Computation of fw

fw = [ sec( ?A1 / 2 A2 )]0.5

A2 = BW (for flaw)

A1 = 2ac (for surface flaw)

A1 = 4ac (for embedded flaw)

B- Thickness of the pipe in mm

W- Circumference of the pipe in mm.

Computation of M

M=(1-[a/(BM_T )])/(1-(a/B))

M_T=?{1+3.2(c^2/(2r_m B))}?^0.5

MT- Stress magnification factor

‘a’ – flaw height for surface flaw and half height for embedded flaw in mm.

B- Section thickness in plane of flaw (the remaining thickness not containing the flaw) in mm.

W –circumference of the pipe

Computation of Mm

‘a’-Half depth or height of flaw for embedded in mm

‘c’-Half flaw length in mm

‘p’-Shortest distance from material surface to embedded flaw in mm

? - parametric angle to identify position along an elliptical flaw front in radians .Assumed to ?/2

B’ – Effective thickness in mm

W- Circumference of the pipe in mm

The following condition apply

0? a/2c?1.0

0 ? ?? ?

a/B < 1.25(a/c +0.6) for 0? a/2c?0.1

a/B< 1.0 for 0.1?a/2c?1.0

Mm = {M1+M2(a/B)2+M3(a/B)4}gf?/?

M1 = 1.1.3 – 0.09(a/c) For 0?a/2c?0.5

M1 = (c/a)0.5{1+0.04(c/a)} For 0.5?a/2c?1.0

M2 = [[url removed, login to view] {0.2+ (a/c)}][url removed, login to view] For 0?a/2c?0.5

M2 = 0.2(c/a)4 For 0.5<a/2c?1.0

M3 =0.5 -1/ {0.65 + (a/c)} + 14{1-(a/c)}24 For a/2c?0.5

M3 = [url removed, login to view](c/a)4 For 0.5<a/2c?1.0

g = 1+ {0.1 + 0.35(a/B)2}(1-sin?)2 For a/2c ? 0.5

g = 1+ {0.1 + 0.35(c/a)(a/B)2}(1-sin?)2 For 0.5<a/2c?1.0

f? = {(a/c)2 cos2? + sin2?}0.25 For 0?a/2c?0.5

f? = {(c/a)2 sin2? + cos2?}0.25 For 0.5<a/2c?1.0

? = {1+ 1.464(a/c)1.65}0.5 For 0?a/2c?0.5

? = {1+ 1.464(c/a)1.65}0.5 For 0.5<a/2c?1.0

Mm- Stress intensity magnification factor

‘a’ – crack depth in mm

‘c’ –half flaw length for surface or embedded crack in mm

B- Section thickness in plane of flaw

? - parametric angle to identify position along an elliptical flaw front in radians .Assumed to ?/2

For embedded Flaw

0? a/2c?1.0

2c/W< 0.5

-? ????

a/B’ < 0.625 (a/c+0.6) for 0? a/2c?0.1

B’ = 2a+2p

Hence equation for Mm is

Mm = {M1 + M2(2a/B’)2 +M3(2a/B’)4}gf?/?

? = {1+ 1.464(a/c)1.65}0.5 For 0?a/2c?0.5

? = {1+ 1.464(c/a)1.65}0.5 For 0.5<a/2c?1.0

M1 = 1 for 0?a/2c?0.5

M1 = (c/a)0.5 For 0.5<a/2c?1.0

M_2=(0.05)/(0.11+(?a/c)?^(1.5) )

M_3=(0.29)/(0.23+?(a/c)?^(1.5) )

g=1-[((2a/B^' )^4 {2.6-(4a/B^' )}^(0.5))/(1+4(a/c))]|cos?? |

f? = {(a/c)2 cos2? + sin2?}0.25 0?a/2c?0.5

f? = {(c/a)2 sin2? + cos2?}0.25 0.5<a/2c?1.0

‘a’-Half depth or height of flaw for embedded in mm

‘c’-Half flaw length in mm

‘p’-Shortest distance from material surface to embedded flaw in mm

? - parametric angle to identify position along an elliptical flaw front in radians .Assumed to ?/2

B’ – Effective thickness in mm

W- Circumference of the pipe in mm

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