1. 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!

2. 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

3. 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.

4. 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. (c)2003 Brooks/Cole, a division of Thomson Learning, Inc
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
Figure When a ductile material is pulled in a tensile test, necking begins and voids form – starting near the center of the bar – by nucleation at grain boundaries or inclusions. As deformation continues a 45° shear lip may form, producing a final cup and cone fracture

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

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

9. (c)2003 Brooks/Cole, a division of Thomson Learning, Inc
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
Figure The Chevron pattern in a 0.5-in.-diameter quenched 4340 steel. The steel failed in a brittle manner by an impact blow

10. 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 )

11. 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

12. 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.

13. 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. 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.

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

18. 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 )

19. 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

20. 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

21. Section 6.10 Fracture Mechanics
Fracture mechanics - The study of a material’s ability to withstand stress in the presence of a flaw.
Fracture toughness - The resistance of a material to failure in the presence of a flaw.

22. (c)2003 Brooks/Cole, a division of Thomson Learning, Inc
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
Figure Schematic drawing of fracture toughness specimens with (a) edge and (b) internal flaws

23. (c)2003 Brooks/Cole, a division of Thomson Learning, Inc
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
Figure The fracture toughness Kc of a 3000,000psi yield strength steel decreases with increasing thickness, eventually leveling off at the plane strain fracture toughness Klc

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. 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

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

29. 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

30. 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

31. 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.

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

33. 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

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

35. 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.