1. Week 5 Fracture, Toughness, Fatigue, and Creep
Materials Science

2. Mechanical Failure 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?
Mechanical failure is the change in the structure/material that refrains the specimen to perform its intended operation
Flaws include micro-cracks, voids, stress concentrations, etc
Ship-cyclic loading
from waves.
Computer chip-cyclic
thermal loading.
Hip implant-cyclic
loading from walking.

3. What is a Fracture?
Fracture is the separation of a body into two or more pieces in response to an imposed stress that is static and at temperatures that are low relative to the melting temperature of the material.
The applied stress may be tensile, compressive, shear, or torsional
Any fracture process involves two steps—crack formation and propagation—in response to an imposed stress.
(i.e., constant or slowly changing with time).
the present discussion will be confined to fractures that result from uniaxial tensile loads

4. Fracture mechanisms Ductile fracture Brittle fracture
Occurs with plastic deformation
Brittle fracture
Little or no plastic deformation
Catastrophic
0. Classification is based on the ability of a material to experience plastic deformation.
1. Ductile materials typically exhibit substantial plastic deformation with high energy absorption before fracture

5. Ductile vs Brittle Failure
• Classification:
Very
Ductile
Moderately
Brittle
Fracture
behavior:
Large
Moderate
%AR or %EL
Small
• Ductile
fracture is usually
desirable!
Ductile:
warning before fracture
Brittle: No warning

6. Example: Failure of a Pipe
• Ductile failure:
--one/two piece(s)
--large deformation
• Brittle failure:
--many pieces
--small deformation

7. Moderately Ductile Failure
• Evolution to failure:
void
nucleation
void growth
and linkage
shearing
at surface
necking s
fracture
• Resulting
fracture
surfaces
(steel)
50 mm
particles
serve as void
nucleation
sites.
100 mm

8. Ductile vs. Brittle Failure
2. Brittle fracture takes place without any appreciable deformation, and by rapid crack propagation. The direction of crack motion is very nearly perpendicular to the direction of the applied tensile stress and yields a relatively flat fracture surface, as indicated in Figure
cup-and-cone fracture
brittle fracture

9. Transgranular vs Intergranular Fracture
1. For most brittle crystalline materials, crack propagation corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes (Figure a); such a process is termed cleavage. This type of fracture is said to be transgranular, because the fracture cracks pass through the grains.
2. In some alloys, crack propagation is along grain boundaries this fracture is termed intergranular
3. Scanning electron fractograph showing an intergranular fracture surface. 50 magnification
Intergranular Fracture
Transgranular Fracture

10. Brittle Fracture Surfaces
• Intergranular
(between grains)
• Transgranular
(within grains)
304 S. Steel (metal)
316 S. Steel (metal)
160 mm
4 mm
Polypropylene
(polymer)
Al Oxide
(ceramic)
3 mm
1 mm

11. Ideal vs Real Materials
• Stress-strain behavior (Room T):
TS << TS
engineering
materials
perfect s e
E/10
E/100
0.1
perfect mat’l-no flaws
carefully produced glass fiber
typical ceramic
typical strengthened metal
typical polymer
• DaVinci (500 yrs ago!) observed...
-- the longer the wire, the
smaller the load for failure.
• Reasons:
-- flaws cause premature failure.
-- Larger samples contain more flaws!
Steel Young’s Modulus Elasticity is 200,000MPa and UTS is 800MPa
Da Vinci -> Italian scientist, inventer

12. Flaws are Stress Concentrators!
Results from crack propagation
Griffith Crack
where t = radius of curvature
so = applied stress
sm = stress at crack tip
Kt = Stress concentration factor t
The measured fracture strengths for most brittle materials are significantly lower than those predicted by theoretical calculations based on atomic bonding energies. This discrepancy is explained by the presence of very small, microscopic flaws or cracks that always exist under normal conditions at the surface and within the interior of a body of material. These flaws are a detriment to the fracture strength because an applied stress may be amplified or concentrated at the tip, the magnitude of this amplification depending on crack orientation and geometry. This phenomenon is demonstrated in Figure.
Due to their ability to amplify an applied stress in their locale, these flaws are sometimes called stress raisers.

13. Concentration of Stress at Crack Tip

14. Engineering Fracture Design
• Avoid sharp corners! s
r/h
sharper fillet radius
increasing
w/h
0.5
1.0
1.5
2.0
2.5
Stress Conc. Factor, K t s
max o =
r ,
fillet
radius w h o s
max
Explain effect of increasing W/h on Kt

15. 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
Blunt -> make less intense
Elastic strain energy is also called as Resilience energy

16. When Does a Crack Propagate?
Crack propagates if above critical stress
where
E = modulus of elasticity
s = specific surface energy (J/m2)
a = one half length of internal crack
For ductile => replace gs by gs + gp
where gp is plastic deformation energy
i.e., sm > sc
All brittle materials contain a population of small cracks and flaws that have a variety of sizes, geometries, and orientations.When the magnitude of a tensile stress at the tip of one of these flaws exceeds the value of this critical stress, a crack forms and then propagates, which results in fracture

17. Fracture Toughness: Design Against Crack Growth
• Crack growth condition:
K ≥ Kc =
• Largest, most stressed cracks grow first!
--Result 1: Max. flaw size
dictates design stress. s
amax no
fracture
--Result 2: Design stress
dictates max. flaw size.
amax s no
fracture
Kc is the fracture toughness
Y is a dimensionless parameter or function that depends on both crack and specimen sizes and geometries, as well as the manner of load application. Relative to this Y parameter, for planar specimens containing cracks that are much shorter than the specimen width, Y has a value of approximately unity. For example, for a plate of infinite width having a through-thickness crack Y=0; whereas for a plate of semi-infinite width containing an edge crack of length Y=1.1

18. Fracture Toughness
For relatively thin specimens, the value of Kc will depend on specimen thickness. However, when specimen thickness is much greater than the crack dimensions, Kc becomes independent of thickness.
The Kc value for this thick-specimen situation is known as the plane strain fracture toughness KIC

19. Fracture Toughness ) (MPa · m K 0.5 Ic Kc = Graphite/ Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers 5 K Ic
(MPa · m
0.5 ) 1
Mg alloys
Al alloys
Ti alloys
Steels
Si crystal
Glass -
soda
Concrete
Si carbide PC 6
0.7 2 4 3 10
<100>
<111>
Diamond
PVC PP
Polyester PS
PET
C-C
(|| fibers)
0.6 7
100
Al oxide
Si nitride
C/C
( fibers)
Al/Al oxide(sf)
Al oxid/SiC(w)
Al oxid/ZrO
(p)
Si nitr/SiC(w)
Glass/SiC(w) Y O
/ZrO
Kc =

20. Design Example: Aircraft Wing
• Material has Kc = 26 MPa-m0.5
• 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 = ?
• Use...
• Key point: Y and Kc are the same in both designs.
9 mm
112 MPa
4 mm
--Result:
Pay off -> Yield a profit or result
Answer:
• Reducing flaw size pays off!

21. Loading Rate s sy e -- increases sy and TS gives less time for
• Increased loading rate...
-- increases sy and TS
-- decreases %EL
• Why? An increased rate
gives less time for
dislocations to move past
obstacles and form into a crack. s e sy TS
larger
smaller
That’s why a piece ruptured by impact loading doesn’t show much plastic deformation before getting ruptured

22. Impact Testing -- severe testing case -- makes material more brittle
• Impact loading:
-- severe testing case
-- makes material more brittle
-- decreases toughness
(Charpy)
final height
initial height

23. Impact Tests
A material may have a high tensile strength and yet be unsuitable for shock loading conditions
Impact testing is testing an object's ability to resist high-rate loading.
An impact test is a test for determining the energy absorbed in fracturing a test piece at high velocity
Types of Impact Tests -> Izod test and Charpy Impact test
In these tests a load swings from a given height to strike the specimen, and the energy dissipated in the fracture is measured
3. Impact energy is a measure of the work done to fracture a test specimen
4. Izod -> (notched or unnotched)
5. The test is particularly useful in showing the decrease in ductility and impact strength of materials of bcc structure at moderately low temperatures

24. A. Izod Test
The Izod test is most commonly used to evaluate the relative toughness or impact toughness of materials
Izod test sample usually have a V-notch cut into them
Metallic samples tend to be square in cross section, while polymeric test specimens are often rectangular
It is used more as a comparative test rather than a definitive test
… although specimens with no notch as also used on occasion

25. Izod Test - Method
It involves striking a suitable test piece with a striker, mounted at the end of a pendulum
The test piece is clamped vertically with the notch facing the striker.
The striker swings downwards impacting the test piece at the bottom of its swing.

26. Determination of Izod Impact Energy
At the point of impact, the striker has a known amount of kinetic energy.
The impact energy is calculated based on the height to which the striker would have risen, if no test specimen was in place, and this compared to the height to which the striker actually rises.
Tough materials absorb a lot of energy, whilst brittle materials tend to absorb very little energy prior to fracture

27. B. Charpy Test
Charpy test specimens normally measure 55 x 10 x 10mm and have a notch machined across one of the larger faces
The Charpy test involves striking a suitable test piece with a striker, mounted at the end of a pendulum.
The test piece is fixed in place at both ends and the striker impacts the test piece immediately behind a machined notch.
… A V-shaped notch, 2mm deep, with 45° angle and 0.25mm radius along the base
The impact energy for Charpy test is calculated in the same manner as for Izod test

28. Factors Affecting Impact Energy
For a given material the impact energy will be seen to decrease if the yield strength is increased
The notch serves as a stress concentration zone and some materials are more sensitive towards notches than others
Most of the impact energy is absorbed by means of plastic deformation during the yielding. Therefore, factors that affect the yield behavior (and hence ductility) of the material such as temperature and strain rate will affect the impact energy
if the material undergoes some process that makes it more brittle and less able to undergo plastic deformation. Such processes may include cold working or precipitation hardening.
The notch depth and tip radius are therefore very important
This type of behaviour is more prominent in materials with a body centred cubic structure, where lowering the temperature reduces ductility more markedly than face centred cubic materials

29. Effect of Temperature on Toughness
• Increasing temperature...
--increases %EL and Kc
• Ductile-to-Brittle Transition Temperature (DBTT)...
FCC metals (e.g., Cu, Ni)
BCC metals (e.g., iron at T < 914°C)
polymers
Impact Energy
Brittle
More Ductile
Kc -> fracture toughness
A material experiences a ductile-to-brittle transition with decreasing temperature.
At higher temperatures the CVN (Charpy V-Notch) energy is relatively large, in correlation with a ductile mode of fracture. As the temperature is lowered, the impact energy drops suddenly over a relatively narrow temperature range, below which the energy has a constant but small value; that is, the mode of fracture is brittle
High strength materials ( s y
> E/150)
Temperature
Ductile-to-brittle
transition temperature

30. Fatigue Test
Fatigue is concerned with the premature fracture of metals under repeatedly applied low stresses
A specified mean load (which may be zero) and an alternating load are applied to a specimen and the number of cycles required to produce failure (fatigue life) is recorded.
Generally, the test is repeated with identical specimens and various fluctuating loads.
Data from fatigue testing often are presented in an S-N diagram which is a plot of the number of cycles required to cause failure in a specimen against the amplitude of the cyclical stress developed
3. Loads may be applied axially, in torsion, or in flexure. Depending on amplitude of the mean and cyclic load, net stress in the specimen may be in one direction through the loading cycle, or may reverse direction
4. The cyclical stress represented may be Stress Amplitude (One-half the range of fluctuating stress developed in a specimen in a fatigue test.), maximum stress or minimum stress. Each curve in the diagram represents a constant mean stress. Most fatigue tests are conducted in flexure, rotating beam, or vibratory type machines.

31. Fatigue Testing Equipment
2. Consider a rotating beam of circular cross-section and carrying a load W

32. Fatigue Loading

33. Fatigue Test - S-N Curve
This S–N diagram indicates that some metals can withstand indefinitely the application of a large number of stress reversals, provided the applied stress is below a limiting stress known as the endurance limit
0. The standard method of studying fatigue is to prepare a large number of specimens free from flaws, and to subject them to tests using a different range of stress, S, on each group of specimens. The number of stress cycles, N, endured by each specimen at a given stress level is recorded and plotted, as shown in Figure
Endurance limit -> it is the maximum stress to which a metal can be subjected for indefinitely long periods without damage. Endurance limit for Carburized iron plot (in figure above) is 200MNm-2 and for Decarburized iron is 110MNm-2

34. Fatigue Mechanism --crack grew even though Kmax < Kc
• Crack grows incrementally
typ. 1 to 6
increase in crack length per loading cycle
crack origin
• Failed rotating shaft
--crack grew even though
Kmax < Kc
--crack grows faster as
• Ds increases
• crack gets longer
• loading freq. increases.
ΔK is the change in the stress intensity factor

35. Improving Fatigue Life
1. Impose a compressive
surface stress
(to suppress surface
cracks from growing)
N = Cycles to failure
moderate tensile s m
Larger tensile
S = stress amplitude
near zero or compressive
Increasing m
--Method 1: shot peening
put
surface
into
compression
shot
--Method 2: carburizing
C-rich gas
Residual compressive stresses are commonly introduced into ductile metals mechanically by localized plastic deformation within the outer surface region. Commercially, this is often accomplished by a process termed shot peening. Small, hard particles (shot) having diameters within the range of 0.1 to 1.0 mm are projected at high velocities onto the surface to be treated. The resulting deformation induces compressive stresses to a depth of between one-quarter and one-half of the shot diameter.
A carbon- or nitrogen-rich outer surface layer (or “case”) is introduced by atomic diffusion from the gaseous phase. The case is normally on the order of 1 mm deep and is harder than the inner core of material. The improvement of fatigue properties results from increased hardness within the case, as well as the desired residual compressive stresses the formation of which attends the carburizing or nitriding process. This process increases bonding strength among molecules at surface, thus, giving rise to compressive stress
2. Remove stress
concentrators.
bad
better

36. 4. Creep Test
Creep is defined as plastic (or irrevresible) flow under constant stress
Creep is high temperature progressive deformation at constant stress
A creep test involves a tensile specimen under a constant load maintained at a constant temperature.
At relatively high temperatures creep appears to occur at all stress levels, but the creep rate increases with increasing stress at a given temperature.
2. Another definition of term “creep”
3. … Measurements of strain are then recorded over a period of time

37. Creep Test
Creep occurs in three stages: Primary, or Stage I; Secondary, or Stage II, and Tertiary, or Stage III
Figure (top) shows the characteristics of a typical creep curve
Bottom graph -> On y-axis replace “creep” with “strain”

38. Creep Test
Stage I occurs at the beginning of the tests, and creep is mostly transient, not at a steady rate.
In Stage II, the rate of creep becomes roughly steady
In Stage III, the creep rate begins to accelerate as the cross sectional area of the specimen decreases due to necking decreases the effective area of the specimen
… or Primary creep …
Resistance to creep increases until Stage II is reached. … or Secondary creep. …. This stage is often referred to as steady state creep.
… or tertiary creep … If stage III is allowed to proceed, fracture will occur.
The creep test is usually employed to determine the minimum creep rate in Stage II. Engineers need to account for this expected deformation when designing systems.

39. Creep • Occurs at elevated temperature, T > 0.4 Tm tertiary primary
secondary
elastic

40. Secondary Creep s stress exponent (material parameter)
• Strain rate is constant at a given T, s
stress exponent (material parameter)
activation energy for creep
(material parameter)
strain rate
material const.
applied stress
• Strain rate
increases
for higher T, s 10 2 4 -2 -1 1
Steady state creep rate (%/1000hr) e s
Stress (MPa)
427°C
538 °C
649
R is the Boltzman Constant having units J/mol.K

41. Creep Failure S-590 Iron, T = 800°C, s = 20 ksi g.b. cavities applied
along grain boundaries.
time to failure (rupture)
function of
applied stress
temperature
applied
stress
g.b. cavities
• Time to rupture, tr
• Estimate rupture time
S-590 Iron, T = 800°C, s = 20 ksi
L(10 3
K-log hr)
Stress, ksi
100 10 1 12 20 24 28 16
data for
S-590 Iron
1073K
Ans: tr = 233 hr
24x103 K-log hr
Larson-Miller Parameter
22.37 = 20 + log tr
tr = antilog (2.37) = 233

42. Numerical Problems
Problems 8.1 – 8.10; 8.14 – 8.23; and 8.27