fracture mechanics based life assessment … · – develop generic residual stress profiles for...

FRACTURE MECHANICS BASED LIFE ASSESSMENT PROCEDURES FOR

FRACTURE IN WELDMENTS

Kamran Nikbin

http://www3.imperial.ac.uk/mestructuralintegrity

Objectives in VAMAS TWA31 and ASTM

o A collaborative effort of testing inhomogeneous weldments or pre-cracked specimens

o Weldment crack growth testing – Round Robino Weldment crack growth testing – Round Robin

o Consider 316H, P22, P91, P92

o Consider different geometries

o Weldment modelling

o Measurement and evaluation the effects of residual stressstress

o Probabilistic considerations to treat scatter

o Validating correlating parameters for weldment test

Based on the results make recommendation for Standards and codes development

What needs to be considered in VAMAS TWA312

• Geometry, load and weld configuration

• Failure mechanism, -Fracture, Fatigue or Creep

• Should residual stress be taken into account• Should residual stress be taken into account

• Appropriate correlation parameters

- K, J, C*• Treatment of crack initiation and growth rate

• Profiling and quantifying residual stresses in • Profiling and quantifying residual stresses in specimens and components

• Predictive models for Crack Growth

recommendation for Standards and Codes

What is needed for Fracture Based Assessment

• Parameters appropriate for Fracture and Fatigue

– Eta factors for welds mismatch

– Residual stress effects on K– Residual stress effects on K

• Model and quantify

– residual stresses

– Weld properties

• Quantify Residual stress in components• Quantify Residual stress in components

– Develop generic residual stress profiles for welded components

– Implement in Standards and Life assessment Codes

ASTM E1457 schematic of weldment CT specimen

b) Thin section testing HAZ region a) Weld/HAZ/Base

c)Thin section testing weld region d) Electron beam type thin weld/HAZ region

Weld region HAZ region Base region

For Fracture Toughness

Fracture, creep, fatigue cracking mechanisms

( , )r

mat

K P aK

K

PL

=

=For Fatigue :Paris Law

For Creep Time dependent parameter

φ*/ DCdtda =

mKCdNda ∆=/

( , )r

L y

PL

P a σ=

and creep Fatigue can be added linearly giving

φ*/ DCdtda =

m*KCf/DCdN/da ∆φ +=

Evaluation of Fracture Mechanics Parameters for

Welded Compact Tension Specimens

ηP∆

=dP1 L−=η

J derivation is given as Where

• Using FEM for J Estimation Methods, η Factor

for Weldments can be obtained

• To cover

ηHaWB

PJ

N )( −∆

=d(a/W)

dP

P

1 L

L

−=η

• To cover

– Crack Length and work hardening effects

– Weld Width effects

– Mismatch Ratio Effects7

Mismatch factors in welds

� Mismatch factor, M, ratio of the weld metal (WM) to the

homogeneous base metal’s (BM) yield strength

WMMσ

=

� Weldments are often in an over-matched condition

� The yield strength of the weld metal is higher than that of

the base material

� Promotes gross section yielding of the base metal

� Facilitate a shift of plastic zone from the weld to the base

WM

BM

Mσσ

=

8

� Facilitate a shift of plastic zone from the weld to the base

materials

� Therefore reduces the probability of structural failure

originating from an undetected weld defect in operation

J Estimation Methods• Experimentally, non-linear (plastic) component

of J (and C*) determined using the η factor

( )

2p

e p

AKJ J J η= + = +

′ −η : Geometry dependent function

( )e pJ J J

E B W aη= + = +

′ −

� Power-law hardening materials may be represented by the Ramberg-Osgood material model

0

0

N

E E

σσ σε α

σ

= +

E : Elastic Modulus

N : Power law hardening exponent

: Normalising (yield) stress

: Yield offset

0σ

α

η : Geometry dependent function

9

0

� For power-law hardening materials of C(T) specimen

1 ( )

p

p

PNJ

N B W aη

∆=

+ − 1p p

NA P

N= ∆

+

Ce

Ce

P

∆p∆

η Factor for Weldments• Previous work to determine the η factors mainly

for homogenous materials

• Limited work has been performed on • Limited work has been performed on

weldments.

• Aim of this work was to determine the η factor

on C(T) specimen geometries for a range of:

– Crack lengths, a

Mismatch ratios,

PW2

LLD∆

– Mismatch ratios, M

– Weld widths, h

– Stress states : Plane Stress and Plane Strain

– Power-law hardening exponents, N10

P

a

2H 2h

2

LLD∆

Finite Element Model

• Half (2D) symmetry model

• Bi-material model (no material property gradient to represent HAZ)represent HAZ)

• Focused crack tip mesh design

� Ramberg-Osgood material model

� N = 5 and N = 10

� E = 200 GPa

� = 1

� Weld Metal = 629 MPaα

0σ

Analysis Matrix

Weld Metal Base metalCrack length

a/W

Weld Width h and

(2h/2H)

Stress State(MPa) N (MPa) N

WM

BM

Mσσ

=

• Review of literature solutions for the η factor have

0.5

6295

10

1258

510

0.350.400.45

0.500.600.70

1.25 (0.04)2.50 (0.08)5.00 (0.16)

Plane strain

&

Plane stress

1.0 619

1.5 417

2.0 314

• Review of literature solutions for the η factor have been performed

– Compared to the results obtained from this work

12

P

a

PW

2H 2h

2

LLD∆

2

LLD∆

Specimen Geometries DefinitionSEN(T) M(T) DEN(T)

C(T) CS(T)SEN(B)

13P

a

PW

2H 2h

2

LLD∆

2

LLD∆

C(T): Best fits ηLLD

2.2

2.4

2.6

� For a given a/W and M for the conditions examined, η values found

to differ by a maximum of 12% of

0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.751.4

1.6

1.8

2.0

2.2

a/W

ηL

LD

M=0.5

M=1.0

M=1.5

M=2.0

to differ by a maximum of 12% of

the mean value

� Mean values can describe

� a/W dependency of η

� influence of M for a given a/W

• ηmay be considered to be somewhat insensitive to

crack length for 0.4 ≤ a/W ≤ 0.7, for all M values

• For a given a/W , η decreases as M increases

14

CS(T): Best fits ηLLD and ηCMOD

2.6

2.8

3.0

L/W=2, h=2.5 mm

Plane stress and plane strain

with N= 5, 10, 20 M=0.5

M=1.0

M=1.5

M=2.0 4.2

4.4

4.6

4.8

5.0L/W=2, h=2.5 and 5 mm


with N= 5, 10, 20 M=0.5

M=1.0

M=1.5

M=2.0

0.2 0.3 0.4 0.5 0.6 0.7

1.6

1.8

2.0

2.2

2.4

ηLLD

a/W

M=2.0

0.2 0.3 0.4 0.5 0.6 0.7

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

ηC

MO

D

a/W

15

• The investigations do not consider the different weld width.

• For a given crack length, the η solutions of the under-matched and over-

matched conditions show a less than 10% variation to homogeneous

material.

• Due to the good trends on both ηLLD and ηCMOD , both methods can be used to evulate J and C*.

SEN(B) : Best fits for ηLLD and ηCMOD

1.0

1.2

1.4

L/W=2, h=2.5 mm


with N= 5, 10, 20

1.0

1.2

1.4

1.6L/W=2, h=2.5 mm


with N= 5, 10, 20

• The data are not same as Catrin’s

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.2

0.4

0.6

0.8

ηC

MO

D

a/W

M=0.5

M=1.0

M=1.5

M=2.0

M=1.0 Catrin's

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.0

0.2

0.4

0.6

0.8

1.0

M=0.5

M=1.0

M=1.5

M=2.0

M=1.0 Catrin's

ηLLD

a/W

16

• The data are not same as Catrin’s

• The investigations do not consider the different weld width.

• For a given crack length, the η solutions of the under-matched and

over-matched conditions show a less than 10% variation to

homogeneous material.

• it is recommended that J or C* values for the SENB specimen are

evaluated using the crack mouth opening displacement, CMOD due

to the limited deviations.

SENT: Best fits for ηLLD and ηCMOD

• In Load control

3.5 1.25

1.30

L/W=2, h=5 mm

0.5

1.0

1.5

2.0

2.5

3.0

3.5

L/W=2, h=2. 5 and 5 mm

with N= 5, 10, 20

in Plane stress and Plane strain

ηLLD M=0.5

M=1.0

M=1.5

M=2.0

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25L/W=2, h=5 mm

with N= 5, 10, 20

in Plane stress and Plane strain

ηC

MO

D

M=0.5

M=1.0

M=1.5

M=2.0

17

0.1 0.2 0.3 0.4 0.5 0.6 0.70.0

0.5

a/W

0.1 0.2 0.3 0.4 0.5 0.6 0.70.70

0.75

a/W

M=2.0

• When a/W0.4, both ηCMOD and ηLLD can be used.

• For a given crack length and weld width, the η solutions of the under-

matched and over-matched conditions examined show a variation of 15%

from the mean value.

Results –put in ASTM E1457

hFLD

a/W C(T) baseUnder-match

(M=0.5)

Over-match

(M=1.5)Over-match (M=2)

error (±0.08) error (±0.12) error (±0.08) error (±0.12)

0.4 2.15 2.41 2.05 1.94

0.42 2.21 2.46 2.09 2.040.42 2.21 2.46 2.09 2.04

0.44 2.23 2.47 2.1 2.06

0.46 2.24 2.48 2.12 2.07

0.48 2.26 2.49 2.14 2.08

0.5 2.26 2.48 2.13 2.08

0.52 2.26 2.475 2.13 2.08

0.54 2.27 2.47 2.12 2.09

0.56 2.27 2.465 2.12 2.09

2.28 2.47 2.12 2.10.58 2.28 2.47 2.12 2.1

0.6 2.27 2.45 2.1 2.08

0.62 2.26 2.43 2.1 2.06

0.64 2.25 2.41 2.1 2.04

0.66 2.24 2.39 2.1 2.02

0.68 2.23 2.39 2.1 2.02

0.7 2.23 2.39 2.1 2.02

Quantitative measurements of residual stress

in Compact Tension specimens

• Examples of residual stress in CT and

welded components welded components

• Implications for

– Fracture parameters– Fracture parameters

– Life assessment

– Codes of practice

Inducing residual stress by pre-compression

800

-600

-400

-200

0

200

400

600

800

Str

ess (

MP

a)

x = 2.3 mm , y = z = 0

x

σ

normal stress, σ 22

relaxation

heat up

precompress

� Modelled sequence of loading and relaxation

-1000

-800

-2.0 -1.0 0.0 1.0 2.0 3.0 4.0

log10time (hours)

xσ

Residual stress due to welding

Starter Crack

Parent Metal

W

P

W

P

HAZ

a) b)

� 316L Weld Metal, P22, P91, P92 HAZ and weld test

� EDM notch located in Heat Affected Zone (HAZ)

Weld Metal

a

P

a

P

� EDM notch located in Heat Affected Zone (HAZ)

� EDM or Pre-fatigued starter crack

� As-welded condition (non-stress relieved)

� Size and geometry effects

Example of weld 316 specimen and test rig

a) b)

Complications of fabrication due to insufficient material

-EB welding

-Specimen size, geometry

Measurement Details

Parent

2 mm 4 mm

EB WeldScan II EB Weld

(a)(b)

Slice cut line

62.5 mm Scan IV

� Specimen EB1 � Specimen EB2

Parent

x 11

x 22

x 33

EB Weld

x 11 = 0

Scan I

Scan II

Parent

EB Weld

x 11 = 0

Scan III

Parent

EDM 1

EDM 2

Slice cut line

MMA Weld MMA Weld

60 m

m

• Specimen EB1 unslit

• EDM slit in specimen EB2

– EDM1 : a/W = 0.5

– EDM2 : a/W = 0.57

• Measurement along expected crack path 23

x 11 = 0 x 11 = 0

Residual Stress in welded CT

600

800

σ22

σ33

σ11

EB1(b)

σ 22

σ 33

σ 11400

600

800

σ22

σ33

σ11

EB2 EDM1(b)

σ 22

σ 33

σ 11

-400

-200

0

200

400

Str

ess

(MP

a)

-400

-200

0

200

400

-30.0 -20.0 -10.0 0.0 10.0 20.0 30.0

Str

ess

(MP

a)

24

-30.0 -20.0 -10.0 0.0 10.0 20.0 30.0

Distance from EB Weld (mm)

-30.0 -20.0 -10.0 0.0 10.0 20.0 30.0

Distance from EB Weld (mm)

• Significant stress relaxation with EDM slit introduction 30-50 % reduction

Effect of Residual Stress

400

600

800

Re

sid

ual

Str

ess (

MP

a)

s22 Stress-Spec no crack

s22 Stress-Spec crack

s22 Stress-Spec crack 2

Crack 1

EB Weld

Weld multipass region (see Fig. 5.1)

σ22: no crackσ22: crack 1σ22: crack 2

Measurement line

x

-400

-200

0

200

0 10 20 30 40 50 60

Position (mm)

Re

sid

ual

Str

ess (

MP

a)

Crack 2

HAZ

a

12.5 mm

� residual stress profiles before testing in a weldment

� Large effect due to the EB weld reduces with crack growth

� Most of the residual stress is removed when crack is extended

Measured residual stresses

1,0

1,5

0,0

0,5

1,0

0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

CT1: pre-compress +

thermal soak,1000 hrs

yσσ22

26-1,5

-1,0

-0,5

x / W

∆a= 4

W

σ22σ22x


1,0

1,5

CT2: Pre-compress + EDM 2 mm crack

0,0

0,5

1,0

0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

yσσ22

27-1,5

-1,0

-0,5

x / W

∆a= 2

W

σ22σ22x


1,0

1,5

CT2: Pre-compress + EDM 2 mm crack +

primary load, 650°C, 1000 hrs

0,0

0,5

1,0

0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

yσσ22

primary load, 650°C, 1000 hrs

28-1,5

-1,0

-0,5

x / W

∆ a = 15W

σ22σ22x


1,0

1,5

0,0

0,5

1,0

0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

yσσ22

29-1,5

-1,0

-0,5

x / W

W

σ22σ22x


1,0

1,5

� An upper-bound linear distribution can be used to envelope the measured

residual stress

Uniform membrane stress

0,0

0,5

1,0

0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

yσσ22


Upper-bound linear

distribution

30-1,5

-1,0

-0,5

x / W

∆ a = 15W

σ22σ22x


1,0

1,5

� Upper-bound linear distribution to envelope the measured residual stress

� Upper-bound uniform membrane stress- no stress relaxation


0,0

0,5

1,0

0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

yσσ22


Upper-bound linear

distribution

31-1,5

-1,0

-0,5

x / W

∆ a = 15W

σ22σ22x

Upper-bound linear profile

σ22σ22x

σy

W

x/W

32

a/W = 0.4

x/W0.4 0.7


σ22σ22x

σy

W

x/W

0.67σy

33

a/W = 0.5

x/W

0.5 0.7


σ22σ22x

σy

W

x/W

0.67σy

0.33σy

34

a/W = 0.6

x/W

0.6 0.7

Introduction of residual stress� Residual stress introduced as an initial stress distribution using the

SIGINI subroutine in Abaqus

� Arbitrary ‘balancing’ stress required to give force and moment equilibrium

0,6

0

0,1

0,2

0,3

0,4

0,5

σ2

2 /

σy

35� Two-dimensional elastic 2D elastic analysis performed

-0,3

-0,2

-0,1

0

0,5 0,6 0,7 0,8 0,9 1

σ

x/W

Introduction of crack in FE model� Crack is introduced by releasing boundary constraint on nodes

over a distance of x/W = 0.02 of crack tip

0,6

0

0,1

0,2

0,3

0,4

0,5

σ2

2 /

σy

x/W = 0.02

36

-0,3

-0,2

-0,1

0

0,5 0,6 0,7 0,8 0,9 1

x/W

Results: Residual stress alone

�� 0

) ��

��

/(�

� ��

��

37

� Upper-bound linear profile gives significant reduction in SIF compare to

membrane yield stress, for long cracks

Residual stress + primary load

F =14.5 kN

� Residual stress combined with primary load of 14.5 kN,

corresponds to Kp =15 MPa √m for a/W = 0.4

F =14.5 kN

38

� using upper-bound linear profile is too conservative

when residual stress is combined with primary load

Quantitative measurements of residual stress

ion components

• Examples of residual stress in various

components and methods of Residual components and methods of Residual

Stress measurement

• Implications on • Implications on

– K and C* parameters

– Life assessment

– Codes of practice

Residual stress determination in componentsEffect on K and C*

(a) T-plate (b) Tubular-T joint (c) Tubular-Y joint

(d) Pipe butt weld (e) Tube-on-plate (f) Bent pipe (g) Repair weld

Comparison of measured distributions

with chosen profiles

T-plate 1

1.2

∪⊥∅

∪ y

data (S E 702)

data (S 355)

R6 / B S 7910(2)re

sid

ual str

ess,

σ

σ

σ σ /

σσ σσy

0

0.2

0.4

0.6

0.8

norm

alis

ed r

esid

ual str

ess, ∪

⊥∅R6 / B S 7910(2)

B S 7910 (1)

B ilinear [3]

a

No

rmalised

resid

ual str

ess,

-0.4

-0.2

0 0.2 0.4 0.6 0.8 1y /W

norm

alis

ed r

esid

ual str

ess,

No

rmalised

Residual Stress Measurement on T-plate

1

1.5

Force balanced data (average)As received data (average)Bi-linear approximation of averageBi-linear approximation of average +0.25

No

rma

lise

d R

esid

ua

l S

tre

ss (

σre

s/σ

YP)

-0.5

0

0.5

No

rma

lise

d R

esid

ua

l S

tre

ss (

MeanMean + 2sdv

yW

� Upper bound distribution is less conservative than current

BS7910 and R6 level 1 and 2 distributions

-0.5

0 0.2 0.4 0.6 0.8 1

Normalised Position (y/w)

Dataset (Transverse residual

stresses)

� Measurement methods

� Neutron diffraction

� X-ray diffraction 0.4

0.8

1.2

norm

alis

ed r

esid

ual s

tress

T-butt

Pipe on plateTubular T

Tubular Y

Pipe ButtCold Bent tube

Repair (pipe girth)

Treatment of Residual Stress Data (Measured)

� X-ray diffraction

� Hole drilling & sectioning

� Block removal

� Trepanning etc.

� Materials : ferritic, austenitic, Cr-Mo, C-

Mn steel.

Geometries included

-0.8

-0.4

0

0.4

0 0.2 0.4 0.6 0.8 1

normalised position, y / W

norm

alis

ed r

esid

ual s

tress

� Geometries included

� Weld repair data(a) T-plate (b) Tubular-T joint (c) Tubular-Y joint

(d) Pipe butt weld (e) Tube-on-plate (f) Bent pipe (g) Repair weld

0.8

1.2

norm

alis

ed r

esid

ual s

tress

T-butt

Pipe on plateTubular T

Tubular Y

Pipe ButtCold Bent tube

Repair (pipe girth)

Caution: Scatter in Experimental and FEM results

-0.8

-0.4

0

0.4

0 0.2 0.4 0.6 0.8 1


norm

alis

ed r

esid

ual s

tress

Caution should be exercised in Life Assessment

Analysis in FEM of Measurements of

in Residual stress in Residual stress

Residual Stress Profiling

1

1.2

no

rma

lise

d r

esi

du

al

stre

ss

Mean + 2SD

-0.2

0

0.2

0.4

0.6

0.8

no

rma

lise

d r

esi

du

al

stre

ss

Master curve

Mean

Master curve

� Transverse residual stresses for a range of welded geometries

including a mean, ± 1 SD and ± 2 SD upper and lower bound fit to the data

-0.2

0 0.1 0.2 0.3 0.4 0.5


0.8

π↑°�

y

Linear Upper Bound

Linear Lower Bound

Proposed Linear (0.75)

resid

ual str

ess,

σσ σσ/ σσ σσ

y

2data (S355)Linear Upper BoundLinear Lower Bound σ σ σ σ

y√π√π √π√

πa

Effect of Residual profile on Stress Intensity Factors

linear profile (T-plate)

-0.8

-0.4

0

0.4

no

rma

lise

d r

esid

ua

l str

ess

, π↑° Proposed Linear (0.75)

Linear (0.6)

No

rma

lis

ed

resid

ual str

ess,

0.4

0.8

1.2

1.6

Linear Lower BoundProposed Linear (0.75)Linear (0.6)R6

No

rma

lis

ed

SIF

,K

I /

σ σ σ σ

-1.2

0 0.2 0.4 0.6 0.8 1

normalised position, y / WNo

rma

lis

ed

00.1 0.2 0.3 0.4 0.5

normalised crack length, a/WN

orm

ali

se

d

2

..*

=

ref

refref

KC

σεσ ɺ

Proposed linear profile (Tube)

1.3

data (crown)

BS7910

Linear Upper Bound

Effect of Residual profile on Stress Intensity Factors

0.8

y

Linear Upper Bound

Linear Lower Bound

res

idu

al s

tre

ss

, σσ σσ

/ σσ σσy

0.3

0.5

0.7

0.9

1.1

Linear Upper Bound

Proposed linear (0.75)

Linear (0.6)

No

rma

lis

ed

SIF

,K

I /

σ σ σ σy

√π√π √π√πa

-0.8

-0.4

0

0.4

0.8

no

rma

lise

d r

esid

ua

l str

ess

, π↑°�

y

Linear Lower Bound

Proposed Linear (0.75)

Linear (0.6)

No

rma

lis

ed

res

idu

al s

tre

ss

,

0.1

0.1 0.2 0.3 0.4 0.5normalised crack length, a / WN

orm

ali

se

d-1.2

0 0.2 0.4 0.6 0.8 1


No

rma

lis

ed

2

..*

=

ref

refref

KC

σεσ ɺ

To Improve Testing and Assessment Codes for Welds

• Provide comprehensive and validated data

• Provide improved parameters to assess cracks• Provide improved parameters to assess cracks

• Development of predictive numerical tools for

welds

• Validation and verification of modelling, testing • Validation and verification of modelling, testing

for component

Standards that need to be updated

• ASTM E1457-2012 ‘Creep Crack Growth testing Standard’,

• Nikbin, K. M, ‘Creep Crack Growth Life Assessment’, • Nikbin, K. M, ‘Creep Crack Growth Life Assessment’, PVRC Document’, 2007

• ISO/TTA 2007(E) – ‘Creep/Fatigue Crack growth

Testing of Components’

• ASTM E2670 ‘Creep/Fatigue Crack Growth Testing• ASTM E2670 ‘Creep/Fatigue Crack Growth Testing

• Under the auspices of VAMAS TWA31- Committee for Creep/Fatigue Cracking in Weldments

fracture mechanics based life assessment … · – develop generic residual stress profiles for...

Documents