Chapter 8 -

Materials Engineering – Day 3

• Quick Review of Hardness & Hardness Testing

• Big problem: when ductile materials go brittle…

• Impact Testing• Ductile to Brittle Transition Temperature• Introduction to Fracture. See how far we

get.

Chapter 8 - 2

ISSUES TO ADDRESS...

• How do flaws in a material initiate failure?• How is fracture resistance quantified; how do different material classes compare?• How do we estimate the stress to fracture?• How do loading rate, loading history, and temperature affect the failure stress?

Ship-cyclic loadingfrom waves.

Computer chip-cyclicthermal loading.

Hip implant-cyclicloading from walking.

Adapted from Fig. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.)

Adapted from Fig. 22.26(b), Callister 7e.

Chapter 8: Mechanical Failure

Adapted from chapter-opening photograph, Chapter 8, Callister 7e. (by Neil Boenzi, The New York Times.)

Chapter 8 -

Ductile vs. Brittle Behavior

• Let us look at some pictures of failure in metal.

Here they are.• Notes on Brittle

1. Gross deformation is not great2. Failure is by cleavage mechanism3. Fracture surface is faceted and shiny

• Notes on Ductile1. Gross deformation is visible2. Failure is by microvoid coalescence3. Fracture surface is dimpled and dull

Chapter 8 - 5

Ductile vs Brittle Failure

Very Ductile

ModeratelyDuctile BrittleFracture

behavior:

Large Moderate%AR or %EL Small• Ductile fracture is usually desirable!

Adapted from Fig. 8.1, Callister 7e.

• Classification:

Ductile: warning before

fracture

Brittle: No

warning

Chapter 8 - 6

• Ductile failure: --one piece --large deformation

Figures from V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.1(a) and (b), p. 66 John Wiley and Sons, Inc., 1987. Used with permission.

Example: Failure of a Pipe

• Brittle failure: --many pieces --small deformation

Chapter 8 - 8

Ductile vs. Brittle Failure

Adapted from Fig. 8.3, Callister 7e.

cup-and-cone fracture brittle fracture

Chapter 8 - 9

Brittle Failure

Arrows indicate pt at which failure originated

Adapted from Fig. 8.5(a), Callister 7e.

Chapter 8 -metallurgist.com/.../Fractography.htm

Chapter 8 -

http://pwatlas.mt.umist.ac.uk/internetmicroscope/micrographs/failure/brittle-steel.html

Chapter 8 -

Stress Concentration

What is it? Changes in geometry (holes, fillets, threads, notches) can cause local increases in stress (stress raisers) For example: Near a small hole in a large plate, the stress at the edge of the hole is three times as high as the stress away from the hole.

Chapter 8 - 15

Concentration of Stress at Crack Tip

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

Chapter 8 - 16

Engineering Fracture Design

r/h

sharper fillet radius

increasing w/h

0 0.5 1.01.0

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

Chapter 8 -

More on Stress Concentration Factor

• Importance:1. high-strength, low ductility materials can

crack2. cyclic stress coupled with stress

concentration is typical for fatigue failures• Quantifying:

Stress Concentration Factor, K=max/nominal

where: – K is from published charts– nominal is the stress ignoring the stress

concentration– max is the highest local stress due to the

concentration

Chapter 8 - 18

Loading Rate

• Increased loading rate... -- increases y and TS -- decreases %EL

• Why? An increased rate gives less time for dislocations to move past obstacles.

y

y

TS

TS

larger

smaller

Chapter 8 - 19

Impact 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)

Chapter 8 - 20

• Increasing temperature... --increases %EL and Kc

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

Temperature

BCC metals (e.g., iron at T < 914°C)

Imp

act

Ene

rgy

Temperature

High strength materials (y > E/150)

polymers

More Ductile Brittle

Ductile-to-brittle transition temperature

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

Adapted from Fig. 8.15, Callister 7e.

Chapter 8 -

Effect of Radiation on Charpy Energy

www.msm.cam.ac.uk/.../Irradiated_Steel.html

Chapter 8 -

Chapter 8 - 23

• Pre-WWII: The Titanic • WWII: Liberty ships

• Problem: Used a type of steel with a DBTT ~ Room temp.

Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard, The Discovery of the Titanic.)

Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Earl R. Parker, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.)

Design Strategy:Stay Above The DBTT!

Chapter 8 - 25

Crack Propagation

Cracks propagate due to sharpness of crack tip • A plastic material deforms at the tip, “blunting” the

crack.

deformed region

brittle

Energy balance on the crack• Elastic strain energy-

• energy stored in material as it is elastically deformed• this energy is released when the crack propagates• creation of new surfaces requires energy

plastic

Chapter 8 - 26

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

– Kc = c/0

For ductile => replace s by s + p

where p is plastic deformation energy

212

/

sc a

E

i.e., m > c

or Kt > Kc

Chapter 8 - 27

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

KIc

(MP

a ·

m0

.5)

1

Mg alloys

Al alloys

Ti alloys

Steels

Si crystalGlass -soda

Concrete

Si carbide

PC

Glass 6

0.5

0.7

2

4

3

10

20

30

<100>

<111>

Diamond

PVC

PP

Polyester

PS

PET

C-C(|| fibers) 1

0.6

67

40506070

100

Al oxideSi nitride

C/C( fibers) 1

Al/Al oxide(sf) 2

Al oxid/SiC(w) 3

Al oxid/ZrO 2(p)4Si nitr/SiC(w) 5

Glass/SiC(w) 6

Y2O3/ZrO 2(p)4

Chapter 8 -

Example Problem

• A large, thick plate is fabricated from a steel alloy that has a plane strain fracture toughness of 55 MPA m1/2. If, during service, the plate is exposed to a tensile stress of 200 MPA, determine the minimum length of a surface crack that would lead to failure?

• Ans. About 24 mm.

Chapter 8 - 31

• Two designs to consider...Design A --largest flaw is 9 mm --failure stress = 112 MPa

Design B --use same material --largest flaw is 4 mm --failure stress = ?

• Key point: Y and Kc are the same in both designs.

Answer: MPa 168)( B c• Reducing flaw size pays off!

• Material has Kc = 26 MPa-m0.5

Design Example: Aircraft Wing

• Use...max

cc

aY

K

c amax A

c amax B

9 mm112 MPa 4 mm --Result:

Chapter 8 - 32

• Engineering materials don't reach theoretical strength.

• Flaws produce stress concentrations that cause premature failure.

• Sharp corners produce large stress concentrations and premature failure.

• Failure type depends on T and stress:

- for noncyclic and T < 0.4Tm, failure stress decreases with:

- increased maximum flaw size, - decreased T, - increased rate of loading.- for cyclic : - cycles to fail decreases as increases.

- for higher T (T > 0.4Tm): - time to fail decreases as or T increases.

SUMMARY