Andrew Wasylyk UNTF 2011

Understanding of the limiting condition for ductile components

Andrew Wasylyk

UNTF 2011

plastic zone

Fracture process areaPlastic zone

Defining Limiting Condition

Ductile components

• Primary pipe work is fabricated from Grade 304 stainless steel

• Typical yield stress250MPa

• Typical ductility60 - 70%

Aim

Define cases under which structural integrity of ductile components may be solely assessed on plastic collapse

criteria, whilst maintaining the integrity of the plant

Fracture above limit load

From SPECIMEN to STRUCTURE

Size effect!

Defining Fracture

• J-integral– Conventional methodology to

define critical crack tip stress field– Validity limits– Dependence on global plasticity

0 2 4 6 8 10 120.0

0.5

1.0

1.5

LEFM+EPFM Defined Fracture

fracture can be defined by :K, J,J-T,J-Q

Lr

crac

k le

ngth

cor

rect

edLLD (mm)

ASME TES

How do we define fracture?

Limit Load

Ductile Fracture

• Local Approach– Rice & Tracey local approach– Defined for ductile behaviour, growth of a void to

a critical void volume fraction.– Proportional to stress, strain and triaxiality ahead

of the crack tip– Will account for constraint effects.

Fracture Toughness Specimens:

• a/W=0.55

• Unloading compliance methodology• Crack propagation proportional to elastic unload• Global J proportional to area under the load

displacement curve• Tracking of plasticity development using Digital Image

Correlation

Experiments

Aim Analyse fracture under a range of Plasticity conditions Compare methodologies defining fracture under large plasticity conditions

Experimental results

0.0 0.5 1.0 1.5 2.0 2.50

1000

2000 25mmCT ASTM 1820 Validity limit 15mmCT ASTM 1820 Validity limit 10mmCT ASTM 1820 Validity limit

J0.2BL=160 MPa mm

J0.2BL=300 MPa mm

B=10 mm

J

(M

Pa

mm

)

a (mm)

B = 25mm

B=15 mm

J0.2BL

=700 MPa mm

25mmCT

15mmCT

10mmCT

0.0 0.5 1.0 1.5 2.00

50

100

150

200

250

300

350

400

450

500

J

(MP

a m

m)

a (mm)

4-10a

c

b

e

d

f hg

k

a

c

b

g

f

h

d

e

25mmCT 15mmCT

10mmCT

Finite Element Analysis• Boundary Layer analysis • 3D Compact Tension

Local Approach

Rice and Tracey Ductile criterion

pmm d

R

R f

0

0 2

3cosh**008.0

2

3sinh*558.0ln

Void growth in triaxial stress fieldGeneralised form based on a

range of shape factors

Local Approach

B = 10 mm B = 15 mm B = 25 mm

J (MPa mm)

0 200 400 600 8000.00

0.02

0.04

Ge

ne

ral R

ice

& T

race

y (p

er

un

it vo

lum

e)

Conclusion

Fracture behaviour of small scale specimens can be defined using a modified Rice and Tracey

approach

Small scale specimen can be used to define fracture behaviour without over-conservatism

Plasticity is self similar in all specimens

THANK YOU FOR YOUR ATTENTION!Any Questions?

Image Correlation

• Optical tracking of local displacement of features on the surface of the specimen

• Surface preparation:– 25mm CT: White paint coating with

random black speckles– 15mmCT & 10mmCT: Oxalic Acid

electro-etching, I=6V,t=12min

0 2 4 6 8 10 120.0

0.5

1.0

1.5

LEFM+EPFM Defined Fracture

fracture can be defined by :K, J,J-T,J-Q

Lr

cra

ck le

ng

th c

orr

ect

ed

LLD (mm)

ASME TES

How do we define fracture?

Limit Load

Fracture above limit load

Region I: LEFM

Region II: EPFM

Region III: J-QLocal ApproachEnergy Dissipation