1. MECHANICAL FAILURE
Need to understand mechanisms of various fracture modes
Fracture, fatigue & creep
Will study
Simple fracture (brittle & ductile)
Fundamentals of fracture mechanics
Impact fracture testing
Ductile to brittle transitions
Fatigue & creep
Ship-cyclic loading
from waves.
Computer chip-cyclic
thermal loading.
Hip implant-cyclic
loading from walking.
R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and Sons, Inc., 1996.
Adapted from Fig W(b), Callister 6e. (Fig W(b) is courtesy of National Semiconductor Corporation.)
Adapted from Fig.
17.19(b), Callister 6e.

2. FRACTURE Separation of a body into two or more pieces
in response to an imposed stress that is static (i.e., constant or slowly varying in time)
At temperatures << melting temperature
Applied stress may be tensile, shear, compressive or torsional (we will focus on uniaxial tension)
Two types of fracture
Ductile fracture: in materials that display substantial plastic deformation with high energy absorption before fracture
Brittle fracture: little or no plastic deformation & low energy absorption prior to fracture
Note: ductility & brittleness are relative
Ductility measured in terms of % elongation
or % reduction in area, and is a strong function
of temperature, strain rate & stress state

3. FRACTURE (contd) Occurs in two steps Ductile fracture Brittle fracture
Crack formation
Crack propagation
Ductile fracture
Extensive plastic deformation in vicinity of advancing crack
Occurs relatively slowly
Crack is said to be “stable”, i.e., resists any further extension in crack unless there is an increase in applied stress
There will be evidence of appreciable plastic deformation
Brittle fracture
Cracks spread extremely rapidly, with very little plastic deformation (“unstable”)
Crack propagation will proceed spontaneously without any increase in applied stress
Ductile fracture preferred over brittle fracture because:
Brittle fracture occurs spontaneously without warning, but ductile fracture provides warning (through perceptible deformation)
More strain energy required to induce ductile failure
Most metals are ductile, ceramics brittle, polymers can be ductile/brittle

4. DUCTILE VERSUS BRITTLE FRACTURE

5. DUCTILE FRACTURE Also called cup-and-cone fracture
Generally, moderate amount of necking
Fracture occurs in several stages
After necking, small cavities or microvoids form in the interior
Microvoids enlarge, come together & coalesce to form an elliptical with long axis perpendicular to stress direction
Shear deformation at a 45 degree angle at the outer perimeter of neck
Central region of fractured surface has irregular & fibrous appearance (due to plastic deformation)
Spherical dimples in the center, C-shaped elongated dimples in outer perimeter

6. DUCTILE FAILURE • Evolution to failure: • Resulting fracture surfaces
50 mm
• Resulting
fracture
surfaces
(steel)
50 mm
100 mm
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 )
Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

7. BRITTLE FRACTURE
No appreciable plastic deformation, rapid crack propagation
Direction of crack propagation perpendicular to applied stress  yields a flat fracture surface
Corresponds to repeated and successive breakage of atomic bonds along specific crystallographic planes
Transgranular: crack passes through (or across) grains; macroscopically, fracture surface will have grainy or facetted texture
Intergranular: crack propagates along grain boundaries; can see the 3-D nature of grains; occurs when grain boundary region has been weakened or embrittled

8. BRITTLE FRACTURE SURFACES
• Intergranular
(between grains)
• Transgranular
(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.)
160mm
4 mm
Polypropylene
(polymer)
Reprinted w/ permission from R.W. Hertzberg, "Defor-mation 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.)
3mm
1 mm
(Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p )

9. IDEAL VS REAL MATERIALS
• Stress-strain behavior (Room T):
TS << TS
engineering
materials
perfect
DaVinci (500 yrs ago!) observed...
the longer the wire, the smaller the load to fail it
Reasons:
flaws cause premature failure
Larger samples are more flawed!

10. FRACTURE MECHANICS
Measured fracture strengths for most materials are significantly lower than those predicted by theory based on atomic bonding energies (except in very small & defect free metallic and ceramic “whiskers”)
Discrepancy explained by the presence of very small, microscopic flaws at the material surface and interior
Applied stress amplified at crack tips, the magnitude of amplification depending on crack orientation and geometry
Fracture mechanics: a major field by itself, involves a quantification of the relationships between material properties, stress level, flaws, and crack propagation mechanisms

11. STRESS CONCENTRATION AT CRACKS
For an elliptical crack, can approximate stress in the neighborhood of crack
In ductile materials, yielding (or plastic deformation) will occur when sm > sy
In brittle materials, when sm > sc (critical stress), crack propagation will occur
Not so bad
Bad!
Avoid sharp corners
Young’s modulus
Surface energy

12. FRACTURE TOUGHNESS Fracture toughness: Kc = Ysc(pa)0.5 = Y(2Egs)0.5
Kc is a material property
Y ~ 1, depends on geometry
Adapted from Fig. 8.8, Callister 6e.

13. FRACTURE TOUGHNESS increasing Based on data in Table B5, Callister 6e.
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

14. DESIGN AGAINST CRACK GROWTH
• Crack growth condition:
K ≥ Kc
• Largest, most stressed cracks grow first!
--Result 1: Max flaw size
dictates design stress.
--Result 2: Design stress
dictates max. flaw size.

15. DESIGN EXAMPLE: GAS TANK
Design pressurized spherical tank of radius r and thickness t, so that yielding occurs before failure
Fracture toughness: Kc = Ysc(pa)0.5
Need to find material in which large crack length can be tolerated
So, maximize (Kc/sy)2

16. DESIGN EXAMPLE: GAS TANK (2)
“Leak-before-break” criterion: Design pressurized spherical tank of radius r and thickness t, so that crack growth through thickness of tank occurs before rapid crack propagation
Circumferential wall stress: s = pr/(2t)
Fracture toughness: Kc = Ysc(pa)0.5
Leak-before-break criterion is met when one-half the internal crack length is equal to the thickness of the pressure vessel, i.e., a = t
Here, we need to find a material such that (Kc2/sy) is maximized
Both requirements lead to medium carbon steel as the strong candidate, which is why pressure tanks are generally made of medium carbon steel

17. LOADING RATE • Increased loading rate... • An increased rate
--increases sy and TS
--decreases %EL … Why?
• An increased rate
gives less time for disl. to
move past obstacles.
• Impact loading:
--severe testing case
--more brittle
--smaller toughness
• Impact toughness = mgDh
Adapted from Fig. 8.11(a) and (b), Callister 6e. (Fig. 8.11(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.)

18. DUCTILE-TO-BRITTLE TRANSITION
• Increasing temperature...
--increases %EL and Kc
• Ductile-to-brittle transition temperature (DBTT)...
Adapted from C. Barrett, W. Nix,
and A.Tetelman, The Principles
of Engineering Materials, Fig. 6-21, p. 220, Prentice-Hall, 1973.
Electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New
Jersey.
Note: low impact energy signifies brittle fracure
• Why do FCC metals behave differently?
• lots of close packed slip planes & directions, allow easy movement of dislocations

19. DESIGN STRATEGY: STAY ABOVE THE DBTT!
• 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., (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.

20. COMPOSITION DEPENDENCE OF DBTT
Higher the carbon content in steel
DBTT increases
Level of brittleness (strength) increases

21. FATIGUE
Failure in structures due to dynamic & fluctuating stresses  Bridges, aircrafts, machine components
Failure occurs at stress levels considerably less than Y and TS
90 % of all failures in metals due to fatigue
Brittle like, sudden & catastrophic, even in ductile materials
Mean Stress
Range of Stress
Stress Amplitude
Stress Ratio

22. FATIGUE --variation can be irregular
• Fatigue = failure under cyclic stress.
Adapted from Fig. 8.16, Callister 6e. (Fig is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.)
• Stress varies with time.
--key parameters are S and sm
--variation can be irregular
• Key points: Fatigue...
--can cause part failure, even though smax < sc. Why?
--causes ~ 90% of mechanical engineering failures.

23. FATIGUE DESIGN PARAMETERS
• Fatigue limit, Sfat:
--no fatigue if S < Sfat
Adapted from Fig. 8.17(a), Callister 6e.
• Sometimes, the
fatigue limit is zero!
Adapted from Fig. 8.17(b), Callister 6e.

24. FATIGUE Fatigue happens through: Crack Initiation Ni
Crack Propagation Np
Rapid Failure if a  aC Nr
Low Stress Level  HCF Ni > Np
High Stress Level  LCF Np > Ni
Crack Initiation usually at surfaces at points of stress concentration  surface scratches, sharp fillets, keyways, dents
Crack Propagation:
Stage I  Along crystallographic planes of high shear stress (~2 grains)
Stage II  Rate , propagation  app.
Stage III  Sudden failure

25. FATIGUE
Benchmarks
(Interruptions)
Striations

26. FATIGUE MECHANISM • Crack grows incrementally • Failed rotating shaft
typ. 1 to 6
increase in crack length per loading cycle
crack origin
Adapted from
Fig. 8.19, Callister 6e. (Fig is from D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.)
• Failed rotating shaft
--crack grew even though
Kmax < Kc
--crack grows faster if
• Ds increases
• crack gets longer
• loading freq. increases.
--Fractured surface reminiscent of tree-rings: each advancement in crack length contributes to a striation

27. Crack Propagation Rate
Crack growth stops if  < 0  if min < 0, Kmin= min = 0, K = Kmax

28. FATIGUE

29. IMPROVING FATIGUE LIFE
1. Impose a compressive
surface stress
(to suppress surface
cracks from growing)
Adapted from
Fig. 8.22, Callister 6e.
--Method 1: shot peening
--Method 2: carburizing
2. Remove stress
concentrators.
Adapted from
Fig. 8.23, Callister 6e.

30. CREEP • Occurs at elevated temperature, T > 0.4 Tmelt
• Deformation changes with time.
Adapted from
Figs and 8.27, Callister 6e.
• Primary: creep strain increase slows down (strain hardening)
• Secondary: linear, steady-state creep (strain hardening balanced by recovery)
• Tertiary: grain boundary separation, formation of voids, etc.

31. SECONDARY CREEP • Most of component life spent here.
• Strain rate is constant at a given T, s
--strain hardening is balanced by recovery
stress exponent (material parameter)
strain rate
activation energy for creep
(material parameter)
applied stress
material const. .
Adapted from
Fig. 8.29, Callister 6e.
(Fig is from Metals Handbook: Properties and Selection: Stainless Steels, Tool Materials, and Special Purpose Metals, Vol. 3, 9th ed., D. Benjamin (Senior Ed.), American Society for Metals, 1980, p. 131.)
• Strain rate
increases
for larger T, s

32. RUPTURE LIFETIME
Not all samples stressed at the same level will fail at the same time
Reliability physics (based on probability & statistics)
Extrapolation of test data to realistic operation conditions a major challenge

33. 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.