How do Materials Break?

Chapter 8: Failure

Ductile vs. brittle fracture

Principles of fracture mechanics

Stress concentration

Impact fracture testing

Fatigue (cyclic stresses)

Cyclic stresses, the SN curve

Crack initiation and propagation

Factors that affect fatigue behavior

Creep (time dependent deformation)

Stress and temperature effects

Alloys for high-temperature use NOT tested:

8.14 Data extrapolation methods

8.15 Alloys for high-temperature use

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2

Fracture Modes

Simple fracture is the separation of a body into 2 or more pieces in response to an applied stress that is static

(constant) and at temperatures that are low relative to the

Tm of the material.

Classification is based on the ability of a material to experience plastic deformation.

Ductile fracture

Accompanied by significant plastic deformation

Brittle fracture

Little or no plastic deformation

Sudden, catastrophic

2

Fracture Mechanism Steps : crack formation crack propagation

Ductile vs. brittle fracture

Ductile - most metals (not too cold):

Extensive plastic deformation before crack

Crack stable: resists extension unless applied stress is increased

Brittle fracture - ceramics, ice, cold metals:

Little plastic deformation

Crack unstable: propagates rapidly without increase in applied stress

Ductile fracture is preferred in most applications

3

Ductile vs Brittle Failure

Very

Ductile

Moderately

Ductile Brittle

Fracture

behavior:

Large Moderate %AR or %EL Small

Ductile fracture is usually more desirable

than brittle fracture!

Ductile:

Warning before

fracture

Brittle:

No

warning

4

5

Evolution to failure:

Moderately Ductile Failure

necking void

nucleation

Resulting fracture

surfaces

(steel)

50 mm

particles

serve as void

nucleation

sites.

50 mm

From V.J. Colangelo and F.A. Heiser, Analysis of

Metallurgical Failures (2nd ed.), Fig. 11.28, p. 294, John

Wiley and Sons, Inc., 1987. (Orig. source: P. Thornton, J.

Mater. Sci., Vol. 6, 1971, pp. 347-56.)

100 mm

Fracture surface of tire cord wire loaded in tension.

Courtesy of F. Roehrig, CC Technologies, Dublin, OH.

Used with permission.

fracture Crack

propagation Coalescence

of cavities

5

Ductile failure: -- one piece

-- large deformation

Example: Pipe Failures

Brittle failure: -- many pieces

-- small deformations

6

Ductile Fracture

(Cup-and-cone fracture in Al)

Scanning Electron Microscopy. Spherical dimples micro-cavities that initiate crack formation.

7

Crack propagation is fast

Propagates nearly perpendicular to direction of

applied stress

Often propagates by cleavage - breaking of atomic

bonds along specific crystallographic planes

No appreciable plastic deformation

Brittle Fracture (Low Dislocation Mobility)

Brittle fracture in a mild steel

8

9

Brittle Fracture Arrows indicate point at failure origination

Distinctive pattern on the fracture surface: V-shaped

chevron markings point to the failure origin.

9

A. Transgranular fracture: Cracks pass through grains. Fracture surface: faceted texture because of different

orientation of cleavage planes in grains.

B. Intergranular fracture: Crack propagation is along grain boundaries (grain boundaries are weakened/embrittled by

impurity segregation etc.)

Transgranular fracture

Brittle Fracture

10

Intergranular fracture

Stress Concentration

The measured fracture strengths for most brittle materials are significantly lower than those

predicted by theoretical calculations based on

atomic bond energies.

This discrepancy is explained by the presence of very small microscopic flaws or cracks that are

inherent to the material.

The flaws act as stress concentrators or stress raisers, amplifying the stress at a given point.

This localized stress diminishes with distance away from the crack tip.

11

t

Flaws are Stress Concentrators!

If the crack is similar to an elliptical hole through plate, and is oriented

perpendicular to applied stress, the

maximum stress m=

where

t = radius of curvature

so = applied stress

sm = stress at crack tip

a = length of surface crack or length of internal crack

stress concentration factor:

2/1

t0

mt

a2K

s

s

sm 2soa

t

1/ 2

Ktso

12

Concentration of Stress at Crack Tip

13

Crack Propagation

Cracks having sharp tips propagate easier than cracks

having blunt tips

A plastic material deforms at a crack tip, which blunts the crack.

ductile

deformed

region

brittle

14

When Does a Crack Propagate?

Crack propagates if crack-tip stress (sm) exceeds a critical stress (sc)

where E = modulus of elasticity

s = specific surface energy

a = one half length of internal crack

For ductile materials => replace s with s + p

where p is plastic deformation energy

2/12

s

as

cE

i.e., sm > sc

15

Fracture Toughness

Fracture toughness measures a materials resistance to brittle fracture when a crack is present.

Indication of the amount of stress required to propagate a pre-existing flaw.

Assume that flaws (cracks, voids, etc.) are present.

Evaluate the ability of a component containing a flaw to resist fracture.

16

Fracture Toughness

Mode I fracture is the condition where the crack plane is normal to the direction of largest tensile loading. This is the most commonly encountered mode.

Fracture toughness is a function of loading, crack size, and structural geometry.

KC = asY

Kc is the fracture toughness in or

Y is a crack length and component geometry factor that is different for each

specimen, dimensionless.

is the applied stress in MPa or psi a is the crack length in meters or inches

mMPa inpsi

17

Crack growth condition:

Largest, most highly stressed cracks grow first!

As Engineers we must Design

Against Crack Growth

K Kc = asY

--Scenario 1: Max. flaw size dictates design stress.

maxas

Y

Kcdesign

s

amax no fracture

fracture

--Scenario 2: Design stress dictates max. flaw size.

2

max

1

s

design

c

Y

Ka

amax

s no fracture

fracture

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Design Example: Aircraft Wing

Answer: MPa 168)( B sc

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 KIc are the same for both designs.

Material has KIc = 26 MPa-m0.5

Use... maxa

sY

KIcc

B max Amax

aa cc ss

9 mm 112 MPa 4 mm --Result:

= a = sY

KIc constant

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Lets look at Another Situation

Steel subject to tensile stress of 1030 MPa, it

has KIc of 54.8 MPa(m) a handbook value, Y = 1.

If it has a largest surface crack 0.5 mm (.0005 m) long will it grow and

fracture?

What crack size will

result in failure?

1

1

1*1030* 3.141*.0005 40.82

Since K < K the part won't fail!

a a

a

a c

K Y a

here

Y

Y a

s

s

1

22

1 54.81*1030

3.1416

.0009 .9

c c

c

c

K Y a

KY

a

a m mm

s

s

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Impact Testing

final height initial height

Two standard tests: Charpy and Izod.

Measure the impact energy (energy required to fracture a test piece under an impact load), also called the notch

toughness.

(Charpy)

testing fracture characteristics: high strain rates

Energy ~ h - h

21

As temperature decreases a ductile material can become brittle

Effect of temperature on the impact energy:

Ductile-to-Brittle Transition

22

http://www.mechlook.com/ductile-brittle-transition/

Many materials experience a shift from ductile to brittle behavior if the temperature is

lowered below a certain point.

The temperature at which this shift occurs varies from material to material.

23

It is sometimes defined DBTT as the temperature at which the material absorbs 15 ft*lb of impact energy during

fracture.

We ideally want the DBTT to be as low as possible for low-temperature design.

Metals such as aluminum, gold, silver, and copper have an FCC (face-centered cubic) crystal lattice structure, and

most do not experience a shift from ductile to brittle

behavior.

Metals, such as iron, many steels, chromium, and tungsten, have a BCC (body-centered cubic) crystal

structure and experience a sharp, often non-linear shift in

ductility.

Many components on a crane have even a DBTT for instance many blocks are rated with a service temperature

of -20 C.

DBTT values are usually determined through a standardized Charpy (or similar) impact test at varying

temperatures.

Ductile to Brittle Transition Temperature

(DBTT)

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Pre-WWII: The Titanic WWII: Liberty ships

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.)

Ductile to Brittle Transition Temperature

(DBTT)

Disastrous consequences for a welded transport ship,

suddenly split across the entire girth of the ship (40F).

Problem: Steels were used having DBTTs just below room temperature.

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Under fluctuating / cyclic stresses, failure can occur at considerably lower loads than tensile or yield strengths

of material under a static load.

Causes 90% of all failures of metallic structures (bridges, aircraft, machine components, etc.)

Fatigue failure is brittle-like (relatively little plastic deformation) - even in normally ductile materials. Thus

sudden and catastrophic!

Fatigue Failure under fluctuating stress

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Fatigue behavior Fatigue = failure under cyclic stress

tension on bottom

compression on top

counter motor

flex coupling

specimen

bearing bearing

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Fatigue corresponds to the brittle fracture of an alloy after a total of N

cycles to a stress below the tensile strength.

Fatigue: Cyclic Stresses

Cyclic stresses characterized by maximum, minimum and mean

stress, the range of stress, the stress amplitude, and the stress ratio

Mean stress sm = (smax + smin) / 2

Range of stress sr = (smax - smin)

Stress amplitude sa = sr/2 = (smax - smin) / 2

Stress ratio R = smin / smax

Convention: tensile stresses positive

compressive stresses negative 27

Fatigue

Fracture surface with crack initiation at top.

Surface shows

predominantly dull

fibrous texture where

rapid failure occurred

after crack achieved

critical size.

Fatigue failure

1. Crack initiation

2. Crack propagation

3. Final failure

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Fatigue failure is brittle in nature, even in

normally ductile materials; there is very little

plastic deformation associated with the failure.

The image shows fatigue striations (microscopic).

Striations are close

together indicating

low stress, many cycles.

Widely spaced striations

mean high stress few

cycles.

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Federal investigators say metal fatigue caused a hole to rip open in the roof of a Southwest Airlines jet as it cruised at 35,000 feet in 2009. The National Transportation Safety Board says the 14-inch crack developed in a spot where two sheets of aluminum skin were bonded together on the Boeing 737 jet.

The pilot made an emergency landing in Charleston, W.Va. There were no injuries among the 126 passengers and five crew members. Two months after the scare, Boeing told all airlines with 737s to conduct repeated inspections of the top of the fuselage near the vertical tail fin. The Federal Aviation Administration has since made those inspections mandatory.

Southwest got the plane in 1994 it's much older than the average Southwest jet and had flown it for 50,500 hours and made 42,500 takeoffs and landings before it sprang a hole in the roof, according to the safety board report. The safety board said it found signs of metal fatigue by magnifying the area in front of the tail fin. In a 3-inch stretch, the crack penetrated completely through the aluminum skin.

FAA records showed that eight cracks had been found and repaired in the fuselage during the plane's 14-year checkup.

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S-N Curves

Fatigue limit, Sfat: --no fatigue if S < Sfat

Sfat

case for steel (typ.)

N = Cycles to failure 10

3 10

5 10

7 10

9

unsafe

safe

S =

str

ess a

mplit

ude

SN curve becomes

horizontal at large N

Stress amplitude below which

the material never fails, no

matter how large the number

of cycles is

For some materials, there is no fatigue limit!

case for Al (typ.)

N = Cycles to failure 10

3 10

5 10

7 10

9

unsafe

safe

S =

str

ess a

mplit

ude

Fatigue strength: stress at which

fracture occurs after specified

number of cycles

Fatigue life: Number of cycles to

fail at specified stress level 31

Example 1

2 5max 3

2min 3

Given: 2014-T6 Alum. Alloy bar (6.4 mm )

find its fatigue life if a part is subject to loads:

5340 - tensile then compressive

5340 5340 165.993.22 106.4*10

2

5340 53403.6.4*10

2

N

MPa

s

s

5

max min

min

6

165.9922 10

165.99 165.990

2 2

331.99

165.992

Examining Fig (right) at S = 165.99

Fatigue Life = Cycles to Failure 7 10

m

r Max

ra

MPa

MPa

MPa

S MPa

s ss

s s s

ss

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Example 2

33

The fatigue data for a brass alloy are given as follows,

(a) Determine the fatigue strength at 5 105 cycles.

(b) Determine the fatigue life for 200 MPa.

(a) As indicated by the A set of dashed lines on the plot, the fatigue strength at 5 105 cycles [log (5 105) = 5.7] is about 250 MPa.

(b) As noted by the B set of dashed lines, the fatigue life for 200 MPa is about 106.3 = 2 106 cycles (i.e., the log of the lifetime is about 6.3).

Answer:

Improving Fatigue Life

Remove stress

concentrators

bad

bad

better

better

shot

peening put

surface into

compression

shot carburizing

C-rich gas

Polishing (removes machining flaws etc.)

Impose compressive surface stresses (to suppress surface

cracks from growing)

--Shot Peening

--Case Hardening

Optimize geometry

--Avoid internal corners, notches etc.

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Case Hardening Case hardening is a technique where both

surface hardness and

fatigue life are improved

for steel alloys.

Both core region and carburized outer case

region are seen in image.

Knoop microhardness

shows case has higher

hardness (smaller indent).

A carbon or nitrogen rich outer surface layer (case)

is introduced by atomic

diffusion from the

gaseous phase. The case

is typically 1mm deep and

is harder than the inner

core material.

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Creep

Creep testing

Furnace

Time-dependent and permanent deformation of materials subjected to a constant load at high

temperature (> 0.4 Tm).

Examples: turbine blades, steam generators.

Creep testing:

36

Stages of creep Sample deformation at a constant stress (s) vs. time

Primary Creep: slope (creep rate)

decreases with time.

Secondary Creep: steady-state

i.e., constant slope De/Dt).

Tertiary Creep: slope (creep rate)

increases with time, i.e. acceleration

of rate.

1. Instantaneous deformation, mainly elastic.

2. Primary/transient creep. Slope of strain vs. time decreases with

time: work-hardening

3. Secondary/steady-state creep. Rate of straining constant: work-

hardening and recovery.

4. Tertiary. Rapidly accelerating strain rate up to failure: formation of

internal cracks, voids, grain boundary separation, necking, etc. 37

Creep: stress and temperature effects

With increasing stress or temperature:

The instantaneous strain increases

The steady-state creep rate increases

The time to rupture decreases

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Summary

Brittle fracture

Charpy test

Corrosion fatigue

Creep

Ductile fracture

Ductile-to-brittle transition

Fatigue

Fatigue life

Fatigue limit

Fatigue strength

Impact energy

Intergranular fracture

Izod test

Stress raiser

Thermal fatigue

Transgranular fracture

Make sure you understand language and concepts:

39

Homework: 8.5, 8.10, 8.20 (deadline 3/11)

ANNOUNCEMENTS

Reading: chapter 9

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