RESIDUAL LIFE ASSESSMENT OF ELBOW WITH VOLUMETRIC SURFACE DEFECT

UNDER CYCLIC INNER PRESSURE

Yukhymets Petr Sergejevich

Paton Welding Institute (Kiev)

yukhymets@paton.kiev.ua

RESIDUAL LIFE ASSESSMENT

Defect and its modeling with half-ellipsoid

functioncurvitywhere

cb

hb

hb

cb

cb

cb

db

325

175,011

2313,048,012,12

12

)(

fKwhere

eeforKee

eeforee

e

ykaei

k

ykai

k

Stress concentation factor

Cyclic stress range

Fatigue curve

[N]

Nominal strains

ei

straight pipe (circular ring, h=const) elbow (circular ring, h=const)

Torus geometry

Elbows measuring results

Elbow №

Dmax, mm

Dmin, mm

Ovalityα*, %

Thickness range h, mm

I 109,7 108,0 ~1,6 5,7-6,4

II 109,1 108,1 ~0,9 5,4-6,8

III 109,6 108,2 ~1,3 5,8-6,7

IV 109,7 108,4 ~1,2 5,4-6,8

nD

DD

DD

DD minmax

minmax

minmax 100200

5.5

6

6.5

76.7

5.8

h2

U2 x( )

7

4

0 1 x

Th

icn

ess

, m

m

φ, rad

Elbow III thickness distributionextended zone

compressed zone

Torus damage modeling

Experimental and calculated strains

1.57 0 1.57 3.14 4.71 6.2820

40

60

80

100

120

140

160141.3

27.123

ek1

ek2

ek3

ek4

a

os 1( )

oc ( )

ov ( )

oo ( )

o1s ( )

upr ( )

6.283

2

3 3 3 3 1

σφ,

MP

a

φ, rad

Cross section model Cross section scheme

Circular ring,

h = const

Circular ring,

h = variable

Elliptical ring, h = const

Elliptical ring, h = variable

NNP NNP corrected

Experiment details

Nominal stress determination method

Δek х10-6

NNP 17,77

NNP corrected 13.12

Elliptical cross-section, h = const

12,07

Experiment 8,27

Strain rate on the defect surface (P=0.1 MPa)

Fatigue crack

Ni, cycle Stress concentration, ασ

ΔP, MPa

10 000 2,53 6

6 500 5,25 19

Load history

Fatigue damage estimation

Method Damage,

df

NNP 20,20

NNP corrected 4,60

Elliptical,

h = const

3,08

1 10 100 1 103

1 104

1 105

1 106

1 103

1 104

1 105

1 106

3.388 105

2.433 103

a1 N( )

10000001 N

σa,

MP

a

N, cycle

Fatigue curve (σt = 524 MPa, σy = 327 MPa, Ψ = 49%)