1. 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.

2. Figure 6-34 Fracture toughness versus strength of different engineered materials. (Source: Adapted from Mechanical Behavior of Materials, by T.H. Courtney, 2000, p. 434, Fig Copyright © 2000 The McGraw-Hill Companies. Adapted with permission.)

3. Section 6.11 The Importance of Fracture Mechanics
Selection of a Material
Design of a Component
Design of a Manufacturing or Testing Method
Griffith flaw - A crack or flaw in a material that concentrates and magnifies the applied stress.

4. Figure 6.35 Schematic diagram of the Griffith flaw in a ceramic
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Figure Schematic diagram of the Griffith flaw in a ceramic

5. Section 6.12 Microstructural Features of Fracture in Metallic Materials
Transgranular - Meaning across the grains (e.g., a transgranular fracture would be fracture in which cracks would go through the grains).
Microvoids - Development of small holes in a material.
Intergranular - In between grains or along the grain boundaries.
Chevron pattern - A common fracture feature produced by separate crack fronts propagating at different levels in the material.

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(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

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

8. Figure 6. 47 Fatigue fracture surface
Figure 6.47 Fatigue fracture surface. (a) At low magnifications, the beach mark pattern indicates fatigue as the fracture mechanism. The arrows show the direction of growth of the crack front, whose origin is at the bottom of the photograph. (Image (a) is from C.C. Cottell, ‘‘Fatigue Failures with Special Reference to Fracture Characteristics,’’ Failure Analysis: The British Engine Technical Reports, American Society for Metals, 1981, p. 318.) (b) At very high magnifications, closely spaced striations formed during fatigue are observed (x 1000)

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 Schematic representation of a fatigue fracture surface in a steel shaft, showing the initiation region, the propagation of fatigue crack (with beam markings), and catastrophic rupture when the crack length exceeds a critical value at the applied stress

10. 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.

11. 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 )

12. 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

13. 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

14. Section 6.15 Fatigue
Fatigue is the lowering of strength or failure of a material due to repetitive stress which may be above or below the yield strength.
Creep - A time dependent, permanent deformation at high temperatures, occurring at constant load or constant stress.
Beach or clamshell marks - Patterns often seen on a component subjected to fatigue.
Rotating cantilever beam test - An older test for fatigue testing.
S-N curve (also known as the Wöhler curve) - A graph showing stress as a function of number of cycles in fatigue.

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

16. Section 6.17 Application of Fatigue Testing
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Figure 6.51 Examples of stress cycles. (a) Equal stress in tension and compression, (b) greater tensile stress than compressive stress, and (c) all of the stress is tensile

17. Section 6.16 Results of the Fatigue Test
Endurance limit - An older concept that defined a stress below which a material will not fail in a fatigue test.
Fatigue life - The number of cycles permitted at a particular stress before a material fails by fatigue.
Fatigue strength - The stress required to cause failure by fatigue in a given number of cycles, such as 500 million cycles.
Notch sensitivity - Measures the effect of a notch, scratch, or other imperfection on a material’s properties, such as toughness or fatigue life.
Shot peening - A process in which metal spheres are shot at a component.

18. 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

19. Figure 6.49 Geometry for the rotating cantilever beam specimen setup
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Figure Geometry for the rotating cantilever beam specimen setup

20. (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 stress-number of cycles to failure (S-N) curves for a tool steel and an aluminum alloy

21. 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

22. 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

23. 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

24. 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.

25. Section 6.18 Creep, Stress Rupture, and Stress Corrosion
Stress-rupture curve - A method of reporting the results of a series of creep tests by plotting the applied stress versus the rupture time.
Stress-corrosion - A phenomenon in which materials react with corrosive chemicals in the environment leading to the formation of cracks and lowering of strength.

26. Figure 6.54 Creep cavities formed at grain boundaries in an austentic stainless steel (x 500). (From ASM Handbook, Vol. 7, (1972) ASM International, Materials Park, OH )
Figure 6.55 Photomicrograph of a metal near a stress-corrosion fracture, showing the many intergranular cracks formed as a result of the corrosion process (x 200). (From ASM Handbook, Vol. 7, (1972) ASM International, Materials Park, OH )

27. Section 6.19 Evaluation of Creep Behavior
Creep test - Measures the resistance of a material to deformation and failure when subjected to a static load below the yield strength at an elevated temperature.
Climb - Movement of a dislocation perpendicular to its slip plane by the diffusion of atoms to or from the dislocation line.
Creep rate - The rate at which a material deforms when a stress is applied at a high temperature.
Rupture time - The time required for a specimen to fail by creep at a particular temperature and stress.

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(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
Figure A typical creep curve showing the strain produced as a function of time for a constant stress and temperature

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(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
Figure 6.59 Results from a series of creep tests. (a) Stress-rupture curves for an iron-chromium-nickel alloy and (b) the Larson-Miller parameter for ductile cast iron