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 ‘rm’ –mean radius in mm from mean of outer radius and inner radius ‘ro’-outer radius in mm from outer diameter of the pipe inputted by the user. ‘ri’- inner radius of the pipe in [login to view URL] radius - thickness 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. ‘rm’ –mean radius 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 = [0.89/ {0.2+ (a/c)}]-0.54 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 = -0.11(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