11 Fracture Mechanisms 2notes

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Objectives

1. Explain the effect of experimental variables on

fracture test results.

2. Understand and use the critical stress intensity

approach to predict linear elastic fracture.

3. Describe the Charpy transition temperature

approach to fracture testing.

4. Explain the role of state of stress, grain size,and test rate in the DBTT of metals.

5. Calculate the plastic zone size ahead of a

crack.



Why Fracture Mechanics?

WWII Liberty Ship

Welded Construction

New workers

High rate of steel

production quality problems

Cyclic wave action Hatch Openings

“Broke in Two”



Fracture Mechanics

1. No load transfer across

crack/hole.

2. Stress higher than

3. Water analogy



1. Crack is sharp discontinuity



1. Crack is sharp discontinuity

2. Crack grows under action of stress

3. Controlling Factor

Available energy > required work to createnew surface



Flaws are Stress Concentrators!Griffith Crack

where

t = radius of curvature

o = applied stress

m = stress at crack tip

o t

/

t

o m K

a

21

2

t

Adapted from Fig. 8.8(a), Callister 7e.



Concentration of Stress at Crack

Tip

Adapted from Fig. 8.8(b), Callister 7e.



Engineering Fracture Design

r /h

sharper fillet radius

increasing w /h

0 0.5 1.0 1.0

1.5

2.0

2.5

Stress Conc. Factor, K t max

o

=

• Avoid sharp corners!

Adapted from Fig.

8.2W(c), Callister 6e. (Fig. 8.2W(c) is from G.H.

Neugebauer, Prod. Eng. (NY), Vol. 14, pp. 82-87

1943.)

r , fillet

radius

w

h

o

max



Crack Propagation

Crack propagation depends on sharpness of crack tip

A plastic material deforms at the tip, “blunting”

the crack.

deformedregion

brittle

Blunting has two effects – reduces stress

concentration, absorbs energy in plastic work.

plastic



Flow of Energy/Work in Fracture

WORK of

External

Force, P*d

Elastic

Energy Crack Surface

Energy

Plastic

Work

As a crack grows, the stress behind the tip

falls to zero, releasing the stored elastic

energy in the material, this energy can be

used to do the plastic or surface work of

fracture



When Does a Crack Propagate?

Crack propagates if above critical stress

where E = modulus of elasticity

s = specific surface energy

a = one half length of internal crack

For ductile => replace s by s + p

where p

is plastic deformation energy

21

2/

s

c a

E

i.e., m > c



Mode I Westegaard Solution



Stress Intensity Factor

Let = 0 and we get

= K /2r

where K = Y a



What is K?

-Stress Intensity Factor

-Represents Intensity of Field At Tip

-Shape of Distribution Given by 1/ 2r

-Represents the energy available in the near field

to do the work of fracture!



Crack Growth CriteriaIf K APPLIED > K C

A Crack Will Grow



1. Mathematically, what happens to

yy = k/ 2r as r 0?

2. Actual stress distribution



Plastic Zone at Crack Tip



3. Rearranging the Westegard solution and

setting the stress equal to the yield strength:

In front of crack:



Question

If increasing the loading rate increases the yield

(flow) stress of most materials, what will

happen to the plastic zone at a crack tip as the

rate is increased?a. Zone decreases in size

b. Zone increases in size

c. Zone doesn’t change



Effect of Strength on Toughness

Sourcebook on Industrial Alloy and

Engineering Data, ASM International



Effect of Test Variables

A. Temperature

K C

Temperature

FCC

BCC & HCP




A. Temperature

B. Crack Tip Radius

C. Specimen Thickness




A. Temperature

B. Crack Tip Radius

C. Specimen ThicknessD. Strain Rate

= d /dt



Loading Rate

• Increased loading rate... -- increases y and UTS

-- decreases %EL

• Why? An increased rategives less time for

dislocations to move past

obstacles.

y

y

TS

TS

larger

smaller

C i i l S I i



Critical Stress Intensity

Factor- K IC

This is the value of K at crack advance for

-Mode I (opening mode)

-Plain strain (thick specimens)-Sharp crack

You will need to have K IC values for the particular

strain rate, temperature, and environment for which

you are engineering.

*There is a similar K IIC for Mode II fracture.



Fracture Toughness

Based on data in Table B5,

Callister 7e .Composite reinforcement geometry is: f

= fibers; sf = short fibers; w = whiskers;

p = particles. Addition data as noted

(vol. fraction of reinforcement):1. (55vol%) ASM Handbook , Vol. 21, ASM Int.,

Materials Park, OH (2001) p. 606.

2. (55 vol%) Courtesy J. Cornie, MMC, Inc.,

Waltham, MA.

3. (30 vol%) P.F. Becher et al., Fracture Mechanics of Ceramics , Vol. 7, Plenum Press

(1986). pp. 61-73.4. Courtesy CoorsTek, Golden, CO.

5. (30 vol%) S.T. Buljan et al., "Development of

Ceramic Matrix Composites for Application in

Technology for Advanced Engines Program",

ORNL/Sub/85-22011/2, ORNL, 1992.

6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci.Proc., Vol. 7 (1986) pp. 978-82.

Graphite/Ceramics/Semicond

Metals/ Alloys

Composites/fibers

Polymers

5

K I c ( M P a · m 0 .

5 )

1

Mg alloys

Al alloys

Ti alloys

Steels

Si crystal

Glass - soda Concrete

Si carbide

PC

Glass 6

0.5

0.7

2

4

3

10

2 0

3 0

<100>

<111>

Diamond

PVC PP

Polyester

PS

PET

C-C (|| fibers) 1

0.6

67

4 0

506 07 0

100

Al oxide Si nitride

C/C ( fibers) 1

Al/Al oxide(sf) 2

Al oxid/SiC(w) 3

Al oxid/ZrO 2 (p) 4

Si nitr/SiC(w) 5

Glass/SiC(w) 6

Y 2 O 3 /ZrO 2 (p) 4



I. Approaches To Fracture

A. Fracture Mechanics

1. Linear Elastic F.M.

2. Elastic Plastic F.M.

B. Transition Temperature (older)

1. Charpy

2. Drop weight tear

3. Dynamic tear



II. Methods of Testing

1. LEFM: ASTM E399

2. E-P: ASTM E-813

3. Charpy: ASTM E-23



III. Transition Temperature Approach

A. Standard Charpy V- Notch

Result: Total Energy of Fracture



Charpy Testing

final height initial height

• Impact loading: -- severe testing case

-- makes material more brittle

-- decreases toughness

Adapted from Fig. 8.12(b),

Callister 7e. (Fig. 8.12(b) is

adapted from H.W. Hayden,

W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials , Vol. III, Mechanical Behavior , John Wiley and Sons,

Inc. (1965) p. 13.)

(Charpy)




Plot Impact E versus Temperature



• Increasing temperature...

--increases %EL and K c

• Ductile-to-Brittle Transition Temperature (DBTT)...

Temperature

BCC metals (e.g., iron at T < 914°C)

I m p a c t E n e r g y

Temperature High strength materials ( y > E /150) polymers

More Ductile Brittle

Ductile-to-brittletransition temperature

FCC metals (e.g., Cu, Ni)

Adapted from Fig. 8.15,

Callister 7e.




Define DBTT:

1. 50% Fracture AppearanceTemperature (FATT)

2. Midpoint in Energy

3. Lateral contraction method




Problem: Service experience doesn’t

necessarily match experiment.

1. Specimens are thin – structures may not be--- lack of constraint

2. Specimen tip is blunt --- real cracks are

usually sharp

Charpy may yield Non-Conservative estimates

of DBTT!!!



DBTT Design

Allowable Stress -Usually - Sy / F.S.(F.S.= Factor of Safety)

DBTT +40C – use Sallowable

DBTT +30C to +40C – use .90 Sallowable



less than DBTT +10 –

Not Allowed

11 Fracture Mechanisms 2notes

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