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1T. Kim Parnell; May 3, 1999

Fracture Mechanics

Overview & Basics

T. Kim Parnell, Ph.D., P.E.

May 3, 1999


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MotivationMotivation

Brittle failure at low stress in low-strength steels

WWII era Liberty Ships Welded structures

Ductile/Brittle transition temperature too high

The occurrence of failure at low stressin high-strength materials spurred

Fracture Mechanicsfurther NBS economic study in 1978 estimated

the cost of fracture at $119 Billionin the

U.S. (about 4% of the GNP)

Brittle failure at low stress in low-strength steels

WWII era Liberty Ships Welded structures

Ductile/Brittle transition temperature too high

The occurrence of failure at low stressin high-strength materials spurred

Fracture Mechanicsfurther NBS economic study in 1978 estimated

the cost of fracture at $119 Billionin the

U.S. (about 4% of the GNP)


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Fracture v Strength CriteriaFracture v Strength Criteria


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Historical DevelopmentHistorical Development

A.A. Griffith work on brittle fracture

G.R. Irwin extended Griffiths work toductile materials

A.A. Griffith work on brittle fracture

G.R. Irwin extended Griffiths work toductile materials


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Work of GriffithWork of Griffith A. A. Griffith started his work in around the 1920s.

At this time, it was accepted that the theoreticalstrength of a material was taken to be E/10, where

E is Young's Modulus for the particular material.He was only considering elastic, brittle materials,in which no plastic deformation took place.However, it was observed that the true values of

critical strength was as much as 1000 times lessthan this predicted value, and Griffith wished toinvestigate this discrepancy.

He discovered that there were many microscopiccracks in every material which were present at alltimes. He hypothesized that these small cracksactually lowered the overall strength of the

material because as a load is applied to thesecracks, stress concentration is experienced.

A. A. Griffith started his work in around the 1920s.At this time, it was accepted that the theoreticalstrength of a material was taken to be E/10, whereE is Young's Modulus for the particular material.He was only considering elastic, brittle materials,in which no plastic deformation took place.However, it was observed that the true values of

critical strength was as much as 1000 times lessthan this predicted value, and Griffith wished toinvestigate this discrepancy.

He discovered that there were many microscopiccracks in every material which were present at alltimes. He hypothesized that these small cracksactually lowered the overall strength of the

material because as a load is applied to thesecracks, stress concentration is experienced.


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Work of IrwinWork of Irwin

G. R. Irwin, in the 1950s, began to see how thetheory outlined by Griffith would apply to ductilematerials.

He determined that there was also a certainenergy from plastic deformation that had to beadded to the strain energy originally considered

by Griffith in order for the theory to work forductile materials.

Irwin developed the concept of the strain energy

release rate.

G. R. Irwin, in the 1950s, began to see how thetheory outlined by Griffith would apply to ductilematerials.

He determined that there was also a certainenergy from plastic deformation that had to beadded to the strain energy originally considered

by Griffith in order for the theory to work forductile materials.

Irwin developed the concept of the strain energyrelease rate.


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Concepts & PrinciplesConcepts & Principles Crack tip stress distribution

1/rsingularity at the crack tip (LEFM) Energy Release Rate is related to the

Stress Intensity Factor

Condition at the crack tip ischaracterized by the Stress Intensity

Factor, KI Fracture toughness is a material

property, KIc.

Crack tip stress distribution

1/rsingularity at the crack tip (LEFM) Energy Release Rate is related to the

Stress Intensity Factor

Condition at the crack tip ischaracterized by the Stress Intensity

Factor, KI Fracture toughness is a material

property, KIc.


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Three Modes of CrackingThree Modes of Cracking

Mode I - opening mode

Mode II - in-plane

shearing/sliding modeMode III - out-of-plane

shearing/tearing mode

Mode I - opening mode

Mode II - in-planeshearing/sliding mode

Mode III - out-of-planeshearing/tearing mode

Deal with Mode I most frequently


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Stress ConcentrationStress Concentration

MaximumStress

0.120

+==t

m aK

StressConcentration

Factor

002

+=t

M

a002

+=

tM

a


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Crack Tip StressesCrack Tip Stresses

];length*stress[ 5.0aCKI = ];length*stress[5.0

aCKI =

Ex: (ksi-

in, MPa-

m)Near-ti stress field LEFM

=

=

+=

2

3cos

2cos

2sin

r2

2

3sin

2

sin1

2

cos

r2

2

3sin2sin12cosr2

K

K

K

xy

x

y


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Some Applications of

Fracture Mechanics

Some Applications of

Fracture Mechanics Remaining life as a function of crack

size Crack size that can be tolerated

(critical crack size) Time for a crack to grow from an

initial size to the critical size

(inspection interval)

Remaining life as a function of crack

size Crack size that can be tolerated

(critical crack size) Time for a crack to grow from an

initial size to the critical size

(inspection interval)


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Test Techniques for

Fracture Properties

Test Techniques for

Fracture Properties Compact Tension (CT)

specimen

Charpy impactspecimen

Compact Tension (CT)

specimen

Charpy impactspecimen


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Stress Intensity Factors for CTStress Intensity Factors for CT


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Miniature SpecimensMiniature Specimens Trend:

Development oftechniques usingminiaturespecimens

Example:Small Punchprocedure for

generatingconstitutiveproperties &fracture toughness

Trend:Development oftechniques usingminiaturespecimens

Example:Small Punchprocedure for

generatingconstitutiveproperties &fracture toughness


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Piping Design:Leak Before Break CriteriaPiping Design:Leak Before Break Criteria

Desirable for pipe to be able to grow acrack through-wall (leak) withoutunstable crack growth (break).

Leak provides an opportunity todetect the crack before it becomes

long enough to be critical.

Desirable for pipe to be able to grow acrack through-wall (leak) withoutunstable crack growth (break).

Leak provides an opportunity todetect the crack before it becomes

long enough to be critical.


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Pipeline-Unstable Crack GrowthPipeline-Unstable Crack Growth 16-inch underground natural gas line 300 psi internal pressure

Poor quality welds (ERW pipe)

Fast fracture of a 40-ft. section after initial welddefects grew through fatigue to critical size

Resulting fire & explosions demolished the plant

16-inch underground natural gas line 300 psi internal pressure

Poor quality welds (ERW pipe)

Fast fracture of a 40-ft. section after initial welddefects grew through fatigue to critical size

Resulting fire & explosions demolished the plant


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Fatigue GrowthFatigue Growth

Cyclic stress intensity factor

Paris law

Integrate to get Cycles to

failure

Cyclic stress intensity factor

Paris law

Integrate to get Cycles to

failure

aYKKK ==minmax

( )mKAdN

da=

( ) ( )2/2/0f

f

0

f

0

1

amm

a

ammm

a

a

N

aY

da

AYA

dadNN

=

==


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Fatigue Fracture SurfaceFatigue Fracture Surface


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ConclusionsConclusions

Cracks are everywhere, it isjust a matter of how large!

Fracture design criteria arerequired more often inmodern design

More efficient designs withlower factors of safety drive

this trend

Cracks are everywhere, it isjust a matter of how large!

Fracture design criteria arerequired more often inmodern design

More efficient designs withlower factors of safety drive

this trend


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Selected References:

Fracture Mechanics

Selected References:

Fracture Mechanics Broek, David (1982). Elementary Engineering Fracture

Mechanics, 3rd Ed., Martinus Nijhoff Publishers.

Anderson, T.L. (1991). Fracture Mechanics:Fundamentals and Applications, CRC Press.

Dieter, George, E. (1976). Mechanical Metallurgy, 2nd

Ed., McGraw-Hill. ASTM E399-83, (1983). Standard Test Method for

Plane-Strain Fracture Toughness of MetallicMaterials., Philadelphia.

ASTM E813-87, (1987). Standard Test Method for JIC,a Measure of Fracture Toughness, Philadelphia.

ASTM E1152-87, (1987). Standard Test Method forDetermining J-R Curves, Philadelphia.

Broek, David (1982). Elementary Engineering FractureMechanics, 3rd Ed., Martinus Nijhoff Publishers.

Anderson, T.L. (1991). Fracture Mechanics:Fundamentals and Applications, CRC Press.

Dieter, George, E. (1976). Mechanical Metallurgy, 2nd

Ed., McGraw-Hill. ASTM E399-83, (1983). Standard Test Method for

Plane-Strain Fracture Toughness of MetallicMaterials., Philadelphia.

ASTM E813-87, (1987). Standard Test Method for JIC,a Measure of Fracture Toughness, Philadelphia.

ASTM E1152-87, (1987). Standard Test Method forDetermining J-R Curves, Philadelphia.

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