Fracture mechanisms Ductile fracture –Occurs with plastic deformation Brittle fracture –Occurs...
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Transcript of Fracture mechanisms Ductile fracture –Occurs with plastic deformation Brittle fracture –Occurs...
Fracture mechanisms
• Ductile fracture– Occurs with plastic deformation
• Brittle fracture– Occurs with Little or no plastic deformation– Thus they are Catastrophic meaning they occur
without warning!
Ductile vs Brittle Failure
Very Ductile
ModeratelyDuctile BrittleFracture
behavior:
Large Moderate%Ra or %El Small
• Ductile fracture is nearly always
desirable!
Ductile: warning before
fracture
Brittle: No
warning
• 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
• Evolution to failure:
• Resulting fracture surfaces (steel)
50 mm
Inclusion particlesserve as voidnucleationsites.
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 mmFracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.
Moderately Ductile Failure
necking
void nucleation
void growth and linkage
shearing at surface fracture
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Figure 6.36 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
Ductile vs. Brittle Failure
Adapted from Fig. 8.3, Callister 7e.
cup-and-cone fracture brittle fracture
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. Thomson Learning™ is a trademark used herein under license.
Figure 6.40 The Chevron pattern in a 0.5-in.-diameter quenched 4340 steel. The steel failed in a brittle manner by an impact blow
• Intergranular(between grains)
• Intragranular (within grains)
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.)
316 S. Steel (metal)
Reprinted w/ permission from "Metals Handbook", 9th ed, Fig. 650, p. 357.
Copyright 1985, ASM International, Materials
Park, OH. (Micrograph by D.R. Diercks, Argonne
National Lab.)
304 S. Steel (metal)Reprinted w/permission from "Metals Handbook", 9th ed, Fig. 633, p. 650. Copyright 1985, ASM International, Materials Park, OH. (Micrograph by J.R. Keiser and A.R. Olsen, Oak Ridge National Lab.)
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.
3 mm
4 mm160 mm
1 mm(Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p. 1119.)
Brittle Fracture Surfaces: Useful to examine to determine causes of failure
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
• Stress-strain behavior (Room Temp):
Ideal vs Real Materials
TS << TSengineeringmaterials
perfectmaterials
E/10
E/100
0.1
perfect mat’l-no flaws
carefully produced glass fiber
typical ceramic typical strengthened metaltypical 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. 7.4. John Wiley and Sons, Inc., 1996.
• Increasing temperature... --increases %EL and Kc
• Ductile-to-Brittle Transition Temperature (DBTT)...
Considering Temperature Effects
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.
Flaws are Stress Concentrators!
Results from crack propagation• Griffith Crack Model:
where t = radius of curvature
of crack tip
o = applied stress
m = stress at crack tip
ot
/
tom K
a
21
2
t
Adapted from Fig. 8.8(a), Callister 7e.
Concentration of Stress at Crack Tip
Adapted from Fig. 8.8(b), Callister 7e.
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 G.H. Neugebauer, Prod. Eng. (NY), Vol. 14, pp. 82-87 1943.)
r , fillet
radius
w
h
o
max max is the concentrated stress in the narrowed region
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 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
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 = c/0
For ductile materials replace s by s + p
where p is plastic deformation energy
212
/
sc a
E
i.e., m > c
or Kt > Kc
21
Section 6.10Fracture 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.
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Figure 6.30 Schematic drawing of fracture toughness specimens with (a) edge and (b) internal flaws
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Figure 6.31 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
Fracture Toughness
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
K1c – plane strain stress concentration factor – with edge crack; A Material Property we use for design, developed using ASTM Std: ASTM E399 - 09 Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness K Ic of Metallic Materials
Fatigue behavior:• Fatigue = failure under cyclic stress
• Stress varies with time. -- key parameters are S (stress
amplitude), m, and frequency
max
min
time
mS
• Key points when designing in Fatigue inducing situations: -- fatigue can cause part failure, even though max < c. -- 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
(Fig. 8.18 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.)
tension on bottom
compression on top
countermotor
flex coupling
specimen
bearing bearing
Figure 8.8 Fatigue corresponds to the brittle fracture of an alloy after a total of N cycles to a stress below the tensile strength.
• Fatigue limit, Sfat: --no fatigue failure if
S < Sfat
Fatigue Limit is defined in: ASTM D671
Adapted from Fig. 8.19(a), Callister 7e.
Fatigue Design Parameters
Sfat
case for steel (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S = stress amplitude
• However, Sometimes, the fatigue limit is zero!
Adapted from Fig. 8.19(b), Callister 7e.
case for Al (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S = stress amplitude
For metals other than Ferrous alloys, F.S. is taken as the stress that will cause failure
after 108 cycles
• Cracks in Material grows incrementallytyp. 1 to 6
a~
increase in crack length per loading cycle
• Failed rotating shaft --crack grew even though
Kmax < Kc
--crack grows faster as • increases • crack gets longer • loading freq. increases.
crack origin
Adapted fromfrom D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.
Fatigue Mechanism
mKdN
da
Figure 8.11 An illustration of how repeated stress applications can generate localized plastic deformation at the alloy surface leading eventually to sharp discontinuities.
Improving Fatigue Life
1. Impose a compressive surface stresses (to suppress surface crack growth)
N = Cycles to failure
moderate tensile mLarger tensile m
S = stress amplitude
near zero or compressive mIncreasing
m
--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
bad
better
better
Adapted fromFig. 8.24, Callister 7e.
Figure 8.20 Comparison of (a) cyclic fatigue in metals and (b) static fatigue in ceramics.
• 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