Prevention and Control of Fracture in Metal Structures

Prevention and Control of Fracture in Metal Structures

Dr. Ayman A. Shama PhD, PE

Summary of the Cracking Problem in Structures

Types of Cracks

Corrosion Fatigue

Environmental Effects

Corrosion-Fatigue Cracking

Stress-Corrosion Cracking

Crack growth

Member Fracture Structural Failure

Material Properties related to Crack Propagation

Ductile Versus Brittle Behavior of Material

Possible Failure modes for metals

Ductile Brittle

General Comparison

Ductile Fracture Process

Brittle Fracture Process

Toughness of Material

Defined as the energy of mechanical deformation per unit volume prior to fracture

Units: Inch. Pound force per cubic inch

It is usually characterized by the area under a stress-strain curve in a slow tension test.

f

0

dvolume

energy = strain

f = strain at failure

= stress

Notch Toughness of Material

Charpy V-notch (CVN) impact test is widely used to evaluate notch toughness

Ductile-to-Brittle Transition

One of the primary functions of the Charpy test is to determine whether a material experiences a ductile-to-brittle transition with decreasing temperature.

Evaluation of Crack Growth using Principles of Fracture Mechanics

What is Fracture Mechanics? Fracture mechanics is an approach to evaluate the fracture

behavior of structural members characterized by pre-existing flaws or notches.

It is based on a stress analysis in the vicinity of the notch.

Practical design information required are:

The fracture toughness of the material as obtained from fracture-mechanics tests

The nominal stress on the structural member being analyzed

Flaw size and geometry of the structural member being analyzed

The three basic modes of crack surface displacement are:

Mode I: opening or tensile mode

Mode II: sliding mode

Mode III: tearing mode

In isotropic materials, brittle fracture usually occurs in Mode I

Brittle Fracture of Cracked Members

An applied stress may be amplified or concentrated at the tip of a crack, the magnitude of this amplification depends on crack orientation.

Flaws are sometimes referred to as stress raisers

Stress Concentration


t

m

a2

= the magnitude of the nominal applied tensile stress t= the radius of curvature of the crack tip a = the length of a surface crack, or half the length of an internal crack


The ratio m/ is denoted the stress concentration factor kt:

t

mt

a2k

1. The main principle of fracture mechanics is to establish parameters to represent the driving force or applied stress.

2. For linear fracture mechanics a parameter namely stress intensity factor (K) relates the stress field magnitude in the vicinity of a crack tip; size; shape; and orientation of the crack

3. Since brittle fracture usually occurs in Mode I for isotropic materials then K will be further denoted as KI

4. The calculation of KI is analogous to the stress demand in traditional and represent the driving force.

5. Another parameter needs to be evaluated , which is a measure of fracture toughness, analogous to the member capacity and represents the resistance force to crack extension Kc.

6. To prevent brittle fracture, the engineer keeps the calculated applied stress intensity factor , KI, below the measured fracture toughness, Kc

7. Other parameters such as the J-integral (J) and the crack-tip-opening displacement (CTOD) are also established for the elastic-plastic regime.

Fracture Mechanics Methodology

Irwin (1957) defined the stress intensity factor by means of the following limit for mode crack I:

m0

I2

limK

If we consider the line crack to be the limiting case of the elliptical hole then

a2m

therefore

aa

22

limK0

I

Stress Intensity factor

KI has units of : mMPa.inksi

All Structural members that have flaws can be loaded to various levels of KI

KI should always be kept below a limiting (critical) value Kc to prevent fracture

The solutions of the stress intensity factors have been obtained for a wide variety of problems.

aKI

Infinite-width plate containing a through-thickness crack

)b/a(faKI

Finite-width plate containing a through-thickness crack

32ba525.1ba288.0ba128.01)b/a(f

a12.1KI

Infinite-width plate containing an edge crack

)b/a(faKI

Finite-width plate containing an edge crack

432ba39.30ba72.21ba55.10ba231.012.1)b/a(f

)b/a(faKI

Finite-width plate containing a double edge crack

32ba93.1ba197.1ba203.012.1)b/a(f

4/1

2

2

22

I cosc

asin

Q

aK

Embedded Elliptical Crack in Infinite Plate

Surface Crack in Infinite Plate

kI MQ

a12.1K

5.0

t

a2.10.1Mk

)b/a(faKI

Edge crack in beam in bending

432ba14ba08.13ba33.7ba40.112.1)b/a(f

tb

M62

The stress intensity factor for the centrally applied tension load is

)b/a(fabt

PK aa

I

Superposition of stress Intensity factor Edge crack subjected to tension plus bending loads

The stress intensity factor for the bending moment is:

)b/a(fatb

M6K b

2

bI

The total stress intensity factor of this case is:

a)b/a(fb

e6)b/a(f

bt

PKKK bab

IaII

2

ysy

K

2

1r

For plane-stress conditions For plane-strain conditions

2

ysy

K

6

1r

Crack-Tip Deformation and Plastic Zone size

Adopting Irwin approach

2/12

ys

app

appIeff

5.01

aK

for app = 0.75 ys

a18.1K appIeff

for app = ys

a40.1K appIeff

A large plate containing a 0.2 in. center crack is subjected to a tensile stress of σ0 = 30 ksi .

a.) Determine the plastic zone size for (σys = 80 ksi ) steel and (σys = 40 ksi ) steel

inksi81.161.030aK5.0

0I

Example

.in007.080

81.16

2

1K

2

1r

22

ys

Iy

Step-1 evaluate the stress intensity factor

for (σys = 80 ksi ) steel app = 0.375 ys no need to use K Ieff Step-2

.in039.040

835.19

2

1K

2

1r

22

ys

Ieffy

for (σys = 40 ksi ) steel app = 0.75 ys use K Ieff

inksi835.1981.16X18.1K18.1K IIeff

Plastic zone size is about 20% of the crack size !!

The J-integral represents a way to calculate the strain energy release rate , or work per unit fracture surface area, in a material.

The J-Integral

the strain energy stored in the member

P2

1U

the strain energy release rate

a

U

t

1

A

UG

For linear-elastic behavior, the J-integral is identical to G:

E

K1GJ

2I

2

II

For nonlinear behavior, the J-Integral is determined using computational methods such as the finite element method

The Crack-Tip Opening Displacement (CTOD)

sys

2I

IE

K

The CTOD relationship for a center crack in a wide plate is

Estimation of Force Resistance Parameters-Kc- Jc- c )

For LEFM we are concerned with SIF therefore emphasis will be first on Kc

Fracture toughness, Kc, is defined as the resistance to the propagation of a crack in structural member.

Factors affecting Fracture Toughness Temperature

As the temperature increases, fracture toughness increases

Loading rate

)ondsecper.in/.in(ratestrain

Fracture toughness of structural materials increases with decreasing loading rate

Loading rate and temperature combined

The temperatures at which the fracture toughness levels begins to increase significantly depend upon the loading rate

Constraint

Constraint

As the thickness is increased, the constraint increases, and the flow stress curve is raised.

Fracture toughness of structural materials increases with decreasing constraint.

Under conditions of low temperature, rapid loading, or high constraint, ductile materials may not exhibit any deformations before fracture.

Conclusion

Fracture Toughness Testing

The maximum KIC and KJC capacities that can be measured for a specimen of thickness B are:

sysIC5.2

BK

30

EBK

sysJC

ASTM Standard Fracture Tests

ASTM Test Method E-399: Standard Test Method for Plane Strain Fracture Toughness of Metallic Materials

For the determination of KIC Plane-strain critical fracture toughness value is

obtained at slow loading rates. Fracture is sudden, resulting in unstable brittle

fracture with little or no deformation.


ASTM Test Method E-399--Annex A7. Special Requirements for Rapid Load Plane-Strain Fracture Toughness KIC(t) Testing

For the determination of KIC(t) Plane-strain critical fracture toughness value is

obtained at intermediate loading rates, where t = time to maximum load in seconds.

Constraint is maximum and failure is sudden, resulting in unstable brittle fracture with little or no deformation.


ASTM Test Method E-1221: Standard Test Method for Determining Plane-Strain Crack-Arrest Fracture Toughness, K la, of Ferritic Steels

For the determination of KIa (KID) (crack-arrest toughness).

Linear-elastic behavior during dynamic or impact loading results in rapid unstable brittle fracture.


ASTM Test Method E-813: Standard Test Method for JIc, A Measure of Fracture Toughness

For the determination of JIc JIc is a measure of the fracture toughness at the

onset of slow stable crack extension. Behavior is non-linear elastic plastic.


ASTM Test Method E-1737: Standard Test Method for J-Integral Characterization of Fracture Toughness

A new test method has been developed to cover all J-integral test results such as Jc, JIc, in one standard.

Behavior would be elastic-plastic with or without stable crack extension.

ASTM Standard Fracture Tests ASTM Test Method E-1820-96: Standard Test Method for Measurement of Fracture Toughness

For the determination K, J, CTOD (): This test is developed for materials where the

type of behavior and thus the type of test needed also is not known before testing.

A bend or compact specimen is tested and the P-DCMOD and records are analyzed to determine either K, J, or values.

KIC Critical Stress Intensity Factor (Fracture Toughness)

A Fracture criterion determines how much fracture toughness is necessary for a particular structural application.

Fracture criteria are related to the three levels of fracture performance, namely plane strain, elastic plastic, or fully

plastic

Fracture-Criteria

Originally established for large welded ship hull structures and then adopted for usage in other classes of structures.

Assumes brittle fracture is not likely to occur in an element if the material absorbs more than 15 ft-lb Charpy V-notch impact energy at the anticipated operating temperature

The 15-ft-lb CVN Impact Criterion

Transition-Temperature Criterion Fracture characteristics is described in terms of the transition

from brittle to ductile behavior as measured by Charpy V-notch impact test

In addition to notch toughness this criterion uses also a transition-temperature to specify the level of performance.

Through-Thickness Yielding Criterion

This criterion is based on two observations :

First, increasing the design stress in a particular application results in more stored energy in a structure

Second, increasing plate thickness promotes a more severe state of stress, namely, plane strain.

This criterion requires that in the presence of a large sharp crack in a large plate, through-thickness yielding should occur before fracture

For through-thickness yielding to occur in the presence of a large sharp crack in a large plate, plane stress conditions are required:

.in2tfortK ysc

The equation defines the plane stress condition at which considerable through-thickness yielding begins to occur.

To ensure linear elastic (plane strain) state of stress at the crack tip and KI = KIc at initiation of crack propagation:

2

ys

IcK5.2t,a

KIc = Critical value of SIF (fracture toughness)

ys = Yield strength of the material

the leak-before-break criterion assumes that a crack of twice the wall thickness in length should be stable at a stress equal to the nominal design stress

Leak-Before-Break Criterion

2ys

22I

)/(5.01

tK

At fracture , KI = Kc and because standard material properties were usually obtained in terms of KIc, the following relation between Kc and KIc has to be used:

)4.11(KK 22Ic

2C and

2

ys

IcK

t

1

Therefore

2

2ys

2Ic2

Ic2ys

2

t

K4.11K

)/(5.01

t

Examples

1-fracture load for a cracked beam under bending

A rectangular section beam has a depth 2c = 150 mm, width t = 25 mm, and length L = 2.0 m. The beam is loaded as simply supported with a concentrated load P at the center. A notch is machined into the beam on the tension side opposite the point of application of P. The depth of the notch was increased by fatigue loading until a = 15 mm. The beam is made of 17-7PH precipitation hardening steel with fracture toughness 77 MPa (m)0.5 and yield stress 1145 MPA. a. Determine whether or not plane strain conditions are satisfied for the beam. b. Determine the fracture load P.

04.1ba14ba08.13ba33.7ba40.112.1)b/a(f432

10.0150

15

b

a

mm31.111145

1000775.2

K5.2t,a

22

ys

Ic

Plane strain conditions are satisfied

)b/a(fa

Kor)b/a(faK Ic

Ic

tb2

PL3

tb4

PL6

tb

M6222

Therefore

)b/a(faL3

tKb2P

)b/a(fa

K

tb2

PL3 Ic2

Ic

2

kN9.65N6585604.1(15)1000X2(3

)100077)(25()150(2

)b/a(faL3

tKb2P

2Ic

2

2: Evaluation of the Fracture Load for a Mechanical Tool A mechanical tool as shown in Fig. is made of AISI 4340. The dimensions of the tool are d = 250 mm, b = 60 mm, and the width t = 25 mm. Determine the magnitude of the fracture load P for the crack length of a = 5 mm. Describe the stress field condition in the vicinity of the crack.

By using the superposition method for :

)b/a(faKI

Case of finite-width plate containing an edge crack

432ba39.30ba72.21ba55.10ba231.012.1)b/a(f

and

)b/a(faKI

Case of Edge crack in beam in bending

432ba14ba08.13ba33.7ba40.112.1)b/a(f

tb

M62

Therefore,

For the crack length of a = 5 mm, a / b = 5 / 60 = 0.0833

163.1ba39.30ba72.21ba55.10ba231.012.1)b/a(f432a

047.1ba14ba08.13ba33.7ba40.112.1)b/a(f432b

a)b/a(fb

e6)b/a(f

bt

PKKK bab

IaII

a)b/a(fb

e6)b/a(f

bt

PKKK bab

IaII

From table the critical fracture toughness factor of this material is 59 MPa (m)0.5

Therefore,

1000/5047.160

250x6163.1

25x60

10Px100059

6

kN8.25P

The total maximum stress is

tb

Pe6

bt

P2m

25x60

250x1000x8.25x6

25x60

1000x8.252

MPa1503MPa2.447 ys

3- Prioritize structural repairs at a site An engineer inspected two structures in a site. The first structure is a truss made up of Aluminum tubular sections each has an outside diameter of 4 in. and wall thickness of 0.25 in. The inspection revealed circumferential through-thickness cracks of 0.60 in. length. A recent load rating of this structure showed that these members are currently carrying 47 kips tension loads. The second structure is a high strength steel pressure vessel that is carrying 5000 psi of internal pressure and has 30 in. nominal diameter, and 0.60 in. wall thickness. Inspection of this structure revealed a surface flaw of length 2 in. and an a/2c ratio of 0.25. Which structure should be repaired first?

Material ys (ksi ) Kic (ksi.in0.5)

Aluminum alloy 64 21

High strength steel 180 220

)b/a(faKI

a= 0.30 in.

b= 5.8875 in.

a/b= 0.30/5.8875=0.051

Truss Structure

01.1ba525.1ba288.0ba128.01)b/a(f32

Therefore

ksi4.21)01.1(30.0

21

)b/a(fa

KIc1max

since

Therefore

)b/a(faKI

222 .in94.25.344

area

kips36.51)4.2(4.21AP

Therefore the maximum tension load the member can sustain is:

Factor of safety against fracture: 093.147

36.51FOS 1structure

kI MQ

a12.1K

The general relation among KI , , and a for a surface flaw

k

Ic2max

M.a12.1

QK

and

Pressure Vessel Structure

from the figure try a value of 1.4 for a//2c=0.25

396.1)5.083.0(2.115.0t

a2.10.1Mk

.in5.0a.in2c2for25.0c2/a

psi5320)30(

)1000)(60.0)(133(2

d

t2p 2max

For the first trial assume Mk =1.396 and Q=1.4, therefore

ksi133396.1.)5.0)(14.3(12.1

4.1220

M.a12.1

QK

k

Ic2max

The maximum internal pressure p that can be sustained

t2

pd2max

For p = 5320 psi 74.0180

133

ys

2max

Therefore from figure Q=1.35

Using Mk=1.396 and Q=1.35, try a second iteration

ksi5.130396.1.)5.0)(14.3(12.1

35.1220

M.a12.1

QK

k

Ic2max

psi5220)30(

)1000)(60.0)(5.130(2

d

t2p 2max

For p = 5220 psi 725.0180

5.130

ys

2max

Therefore from figure Q=1.36

Using Mk=1.396 and Q=1.36, try a third iteration

ksi8.130396.1.)5.0)(14.3(12.1

36.1220

M.a12.1

QK

k

Ic2max

psi5232)30(

)1000)(60.0)(8.130(2

d

t2p 2max

For p = 5232 psi 726.0180

8.130

ys

2max

Therefore from figure Q = 1.365 no further iterations are required

Factor of safety against fracture:

0464.15000

5232FOS 2structure

093.1FOS0464.1FOS 1structure2structure

Therefore structure-2 should be repaired first

Fracture-Control Plans

A fracture-control plan is a specific set of guidelines and recommendations developed for a particular structure. They include but not limited to:

1. Knowledge of the service conditions to which the structure will be subjected.

2. The use of structural materials with adequate fracture toughness.

3. Elimination or minimization of stress raisers.

4. Control of welding procedures,.

5. Proper inspection plans of the structure.

References

1. Anderson, T.L. “ Fracture Mechanics: Fundamentals and Applications”, Taylor and Francis, 2005

2. Tada, H., Paris, P., and Irwin, G. “The Stress Analysis of Cracks Handbook”, ASME Press, 2000

3. Paris, P. and Sih, G. “Stress Analysis of Cracks”, Research Report, Department of Mechanical Engineering, Lehigh University, 1967

4. Irwin, G. “ Analysis of stresses and Strains Near the End of a Crack Transversing a Plate”, Journal of Applied Mechanics, Vol. 24, 1957

5. Wells, A., “Unstable Crack Propagation in Metals:”, Cranfield Crack Propagation Symposium, Vol 1, 1961

7. Rolfe, S. and Barsom, J, “ Fatigue and Fracture and Fatigue Control in Structures” ASTM, 1999

8. E 399-90 (Reapproved 1997). Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials, ASTM, Vol. 03.01.

9. E 399-A-7. Special Requirements for Rapid-Load Plane-Strain Fracture Toughness KIc(t ) Testing, ASTM, Vol. 03.01.

10. E 1221-96. Standard Test Method for Determining Plane-Strain Crack-Arrest Fracture Toughness of Ferritic Steels, ASTM, Vol. 03.01.

11. E 813-89. Standard Test Method for JIc, A Measure of Fracture Toughness, ASTM, Vol. 03.01.

12. E 1737-96. Standard Test Method for J-Integral Characterization of Fracture Toughness, ASTM, Vol. 03.01.

References-continued

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Prevention and Control of Fracture in Metal Structures