1. Chapter 8: Mechanical Failure & Failure Analysis
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 loading
from waves.
Computer chip-cyclic
thermal loading.
Hip implant-cyclic
loading from walking.
Adapted from chapter-opening photograph, Chapter 8, Callister 7e. (by Neil Boenzi, The New York Times.)
Adapted from Fig (b), Callister 7e. (Fig (b) is courtesy of National Semiconductor Corporation.)
Adapted from Fig (b), Callister 7e.

2. Fracture mechanisms Ductile fracture Brittle fracture
Occurs with plastic deformation
Brittle fracture
Occurs with Little or no plastic deformation
Thus they are Catastrophic meaning they occur without warning!

3. Ductile vs Brittle Failure
Very
Ductile
Moderately
Brittle
Fracture
behavior:
Large
Moderate
%Ra or %El
Small
• Ductile fracture is nearly always desirable!
Ductile:
warning before fracture
Brittle: No warning

4. Example: Failure of a Pipe
• Ductile failure:
--one piece
--large deformation
• Brittle failure:
--many pieces
--small 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., Used with permission.

5. Moderately Ductile Failure
• Evolution to failure:
void
nucleation
void growth
and linkage
shearing
at surface
necking s
fracture
• Resulting
fracture
surfaces
(steel)
50 mm
Inclusion
particles
serve as void
nucleation
sites.
From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig , p. 294, John Wiley and Sons, Inc., (Orig. source: P. Thornton, J. Mater. Sci., Vol. 6, 1971, pp )
100 mm
Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

6. Ductile vs. Brittle Failure
cup-and-cone fracture
brittle fracture
Adapted from Fig. 8.3, Callister 7e.

7. Brittle Failure Arrows indicate point at which failure originated
Adapted from Fig. 8.5(a), Callister 7e.

8. Brittle Fracture Surfaces: Useful to examine to determine causes of failure
• Intergranular
(between grains)
• Intragranular
(within grains)
304 S. Steel (metal)
Reprinted w/permission from "Metals Handbook", 9th ed, Fig. 633, p Copyright 1985, ASM International, Materials Park, OH. (Micrograph by J.R. Keiser and A.R. Olsen, Oak Ridge National Lab.)
316 S. Steel (metal)
Reprinted w/ permission from "Metals Handbook", 9th ed, Fig. 650, p Copyright 1985, ASM International, Materials Park, OH. (Micrograph by D.R. Diercks, Argonne National Lab.)
160 mm
4 mm
Polypropylene
(polymer)
Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.35(d), p. 303, John Wiley and Sons, Inc., 1996.
Al Oxide
(ceramic)
Reprinted w/ permission from "Failure Analysis of Brittle Materials", p. 78. Copyright 1990, The American Ceramic Society, Westerville, OH. (Micrograph by R.M. Gruver and H. Kirchner.)
3 mm
1 mm
(Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p )

10. Failure Analysis – Failure Avoidance
Most failure occur due to the presence of defects in materials
Cracks or Flaws (stress concentrators)
Voids or inclusions
Presence of defects is best found before hand and they should be determined non-destructively
X-Ray analysis
Ultra-Sonic Inspection
Surface inspection
Magna-flux
Dye Penetrant

11. Ideal vs Real Materials
• Stress-strain behavior (Room Temp):
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!
Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig John Wiley and Sons, Inc., 1996.

12. Considering Loading Rate Effect
• Increased loading rate...
-- increases sy and TS
-- decreases %EL
• Why? An increased rate
allows less time for
dislocations to move past
obstacles. s e sy TS
larger
smaller

13. Impact (high strain rate) Testing
• Impact loading (see ASTM E23 std.):
-- severe testing case
-- makes material act more brittle
-- decreases toughness
Useful to compare alternative materials for severe applications
(Charpy Specimen)
final height
initial height
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.)

14. Considering Temperature Effects
• 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
High strength materials ( s y
> E/150)
Adapted from Fig. 8.15, Callister 7e.
Temperature
Ductile-to-brittle
transition temperature

16. Figure Variation in ductile-to-brittle transition temperature with alloy composition. (a) Charpy V-notch impact energy with temperature for plain-carbon steels with various carbon levels (in weight percent). (b) Charpy V-notch impact energy with temperature for Fe–Mn–0.05C alloys with various manganese levels (in weight percent).
(From Metals Handbook, 9th ed., Vol. 1, American Society for Metals, Metals Park, OH, 1978.)

18. Design Strategy: Build Steel Ships Quickly!
• Pre-WWI: 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., (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., (Orig. source: Earl R. Parker, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.)
• Problem: Used a type of steel with a DBTT ~ Room temp.
As a Designer: Stay Above The DBTT!

19. Flaws are Stress Concentrators!
Results from crack propagation
Griffith Crack Model:
where t = radius of curvature of crack tip
so = applied stress
sm = stress at crack tip t
Stress concentrated at crack tip
Adapted from Fig. 8.8(a), Callister 7e.

20. Concentration of Stress at Crack Tip
Adapted from Fig. 8.8(b), Callister 7e.

21. 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
max is the concentrated stress in the narrowed region
Adapted from G.H. Neugebauer, Prod. Eng. (NY), Vol. 14, pp )

22. Crack Propagation deformed region
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 is stored in material as it is elastically deformed
this energy is released when the crack propagates
creation of new surfaces requires (this) energy
plastic

23. When Does a Crack Propagate?
Crack propagates if applied stress is above critical stress
where
E = modulus of elasticity
s = specific surface energy
a = one half length of internal crack
Kc = sc/s0
For ductile materials  replace gs by gs + gp
where gp is plastic deformation energy
i.e., sm > sc
or Kt > Kc

24. Fracture Toughness ) (MPa · m K 0.5 Ic
K1c – plane strain stress concentration factor – with edge crack; A Material Property we use for design, developed using ASTM Std: ASTM E Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness K Ic of Metallic Materials
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
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
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/ /2, ORNL, 1992.
6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc., Vol. 7 (1986) pp

27. As Engineers we must 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
Y is a material behavior shape factor

28. Design Example: Aircraft Wing
• Material has Kc = 26 MPa-m0.5
• Two designs to consider...
Design A
--largest flaw is 9 mm
--failure occurs at 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:
Answer:
• Reducing flaw size pays off!

29. Let’s look at Another Situation
Steel subject to tensile stress of 1030 MPa, it has K1c of 54.8 MPa(m) – a handbook value
If it has a ‘largest surface crack’ .5 mm (.0005 m) long will it grow and fracture?
What crack size will result in failure?

30. Figure Two mechanisms for improving fracture toughness of ceramics by crack arrest. (a) Transformation toughening of partially stabilized zirconia involves the stress-induced transformation of tetragonal grains to the monoclinic structure, which has a larger specific volume. The result is a local volume expansion at the crack tip, squeezing the crack shut and producing a residual compressive stress. (b) Microcracks produced during fabrication of the ceramic can blunt the advancing crack tip

31. Fatigue behavior: • Fatigue = failure under cyclic stress
tension on bottom
compression on top
counter
motor
flex coupling
specimen
bearing
(Fig is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.) s
max
min
time m S
• Stress varies with time.
-- key parameters are S (stress amplitude), sm, and frequency
• Key points when designing in Fatigue inducing situations:
-- fatigue can cause part failure, even though smax < sc.
-- fatigue causes ~ 90% of mechanical engineering failures.
Because of its importance, ASTM and ISO have developed many special standards to assess Fatigue Strength of materials

32. Some important Calculations in Fatigue Testing

33. Figure Fatigue corresponds to the brittle fracture of an alloy after a total of N cycles to a stress below the tensile strength.

34. Fatigue Design Parameters
• Fatigue limit, Sfat:
--no fatigue failure if
S < Sfat
Fatigue Limit is defined in: ASTM D671
Sfat
case for
steel
(typ.)
N = Cycles to failure 10 3 5 7 9
unsafe
safe
S = stress amplitude
Adapted from Fig. 8.19(a), Callister 7e.
• However, Sometimes, the fatigue limit is zero!
Adapted from Fig. 8.19(b), Callister 7e.
case for Al
(typ.)
N = Cycles to failure 10 3 5 7 9
unsafe
safe
S = stress amplitude

35. Let’s look at an Example

36. For metals other than Ferrous alloys, F. S
For metals other than Ferrous alloys, F.S. is taken as the stress that will cause failure after 108 cycles

37. Figure 8.21 Fatigue behavior for an acetal polymer at various temperatures.
(From Design Handbook for Du Pont Engineering Plastics, used by permission.)
For polymers, we consider fatigue life to be (only) 106 cycles to failure thus fatigue strength is the stress that will lead to failure after 106 cycles

38. Fatigue Mechanism • Cracks in Material 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.
Adapted from
from D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.

39. Figure An illustration of how repeated stress applications can generate localized plastic deformation at the alloy surface leading eventually to sharp discontinuities.

40. Figure Illustration of crack growth with number of stress cycles, N, at two different stress levels. Note that, at a given stress level, the crack growth rate, da/dN, increases with increasing crack length, and, for a given crack length such as a1, the rate of crack growth is significantly increased with increasing magnitude of stress.

41. Improving Fatigue Life
1. Impose a compressive
surface stresses
(to suppress surface
crack growth)
N = Cycles to failure
moderate tensile s m
Larger tensile
S = stress amplitude
near zero or compressive
Increasing m
Adapted from
Fig. 8.24, Callister 7e.
--Method 1: shot peening
put
surface
into
compression
shot
--Method 2: carburizing
C-rich gas
2. Remove stress
concentrators.
Adapted from
Fig. 8.25, Callister 7e.
bad
better

42. Figure Fatigue strength is increased by prior mechanical deformation or reduction of structural discontinuities.

43. Other Issues in Failure – Stress Corrosion Cracking
Water can greatly accelerate crack growth and shorten life performance – in metals, ceramics and glasses
Other chemicals – that can generate (or provide H+ or O2-) ions – also effectively reduce fatigue life as these ions react with the metal or oxide in the material

44. Figure The drop in strength of glasses with duration of load (and without cyclic-load applications) is termed static fatigue.
(From W. D. Kingery, Introduction to Ceramics, John Wiley & Sons, Inc., New York, 1960.)

45. Figure The role of H2O in static fatigue depends on its reaction with the silicate network. One H2O molecule and one –Si– O–Si– segment generate two Si–OH units, which is equivalent to a break in the network.

46. Figure 8.20 Comparison of (a) cyclic fatigue in metals and (b) static fatigue in ceramics.

47. SUMMARY • 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 s and T < 0.4Tm, failure stress decreases with:
- increased maximum flaw size,
- decreased T,
- increased rate of loading.
- for cyclic s:
- cycles to fail decreases as Ds increases.
- for higher T (T > 0.4Tm):
- time to fail decreases as s or T increases.