Chapter%207%20Fracture:%20Macroscopic%20Aspects

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Chapter 7Fracture Macroscopic Aspects
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Goofy Duck Analog for Modes of Crack Loading
Goofy duck analog for three modes of crack
loading. (a) Crack/beak closed. (b) Opening
mode. (c) Sliding mode. (d) Tearing mode.
(Courtesy of M. H. Meyers.)
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Theoretical Tensile Strength
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Theoretical Cleavage Strength
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Stress Concentration
Lines of force in a bar with a side notch. The
direction and density of the lines indicate the
direction and magnitude of stress in the bar
under a uniform stress s away from the notch.
There is a concentration of the lines of force at
the tip of the notch.
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Inglis Stress Concentration
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Stress Concentration due to a Circular Hole

• Stress distribution in a large plate containing a
  circular hole.
• (b) Stress concentration factor Kt as a function
  of the radius of a circular hole in a large plate
  in tension.

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Stress Concentration due to an Elliptical Hole
Stress concentration at an elliptical hole for a
3b.
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Griffith Criterion of Crack Propagation
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Crack in Thin and Thick Plates
Crack in (a) thin (t1) and (b) thick (t2) plates.
Note the plane-stress state in (a) and the
plane-strain state in (b).
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Dislocation Emission at Crack Tip
Dislocations emitted from a crack tip in copper.
TEM. (Courtesy of S. M. Ohr.)
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Plane Stress and Plane Strain
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Linear Elastic Fracture Mechanics
Inherent material resistance to crack growth, KR
and its relationship to the applied stress s and
crack size a.
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Three Modes of Fracture
The three modes of fracture. (a) Mode I opening
mode. (b) Mode II sliding mode. (c) Mode III
tearing mode.
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Stress Field at a Crack Tip
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Crack Tip Stress Field
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Some Crack and Loading Configurations
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Plastic Zone Correction
Plastic-zone correction. The effective crack
length is (a ry).
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DugdaleBilbyCottrellSwinden Model of a Crack.
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Plastic Zone at Crack Tip Plane Stress and Plane
Strain
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Variation of Fracture Toughness with Thickness
(a) Variation infracture toughness (Kc) with
plate thickness (B) for Al 7075-T6 and H-11
Steel. (Reprinted with permission from J. E.
Srawley and W. F. Brown, ASTM STP 381
(Philadelphia ASTM, 1965), p 133, and G. R.
Irwin, in Encyclopaedia of Physics, Vol. VI
(Heidelberg Springer Verlag, 1958). (b)
Schematic variation of fracture toughness Kc and
percentage of flat fracture P with the plate
thickness B.
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Elastic Body with a Crack

• Elastic body containing a crack of length 2a
  under load P.
• (b) Diagram of load P versus displacement e.

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Crack Extension Force
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Crack Opening Displacement
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Crack Opening Displacement
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Body under External Forces
A body subjected to external forces F1, F2, . .
., Fn and with a closed contour .
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J Integral
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J Integral
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R Curves for Brittle and Ductile Material
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Different Parameters for Fracture Toughness
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Fracture Toughness vs. Yield Stress
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Fracture Toughness Effect of Impurities
Variation of fracture toughness KIc with tensile
strength and sulfur content in a steel. (Adapted
from A. J. Birkle, R. P. Wei, and G. E.
Pellissier, Trans. ASM, 59 (1966) 981.)
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Plane Strain Fracture Toughness
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Fracture Toughness vs. Yield Strength for
Different Alloys
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Measures of Crack Tip Opening Displacement
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Strength Distribution for a Brittle and Ductile
Solid
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Weibull Distribution
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Typical Values of Weibull Modulus
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Weibull Plots for Steel and Two Alumina samples
Weibull plots for a steel, a conventional
alumina, and a controlled-particle-size (CPS)
alumina. Note that the slope (Weibull modulus
m)?8 for steel. For CPS alumina, m is double that
of conventional alumina. (After E. J. Kubel, Adv.
Mater. Proc., Aug (1988) 25.)
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Probability of Failure for Three Ceramics
Probability of failure of flexural strength
(4-point bend test with inner and outer spans 20
and 40 mm, respectively, and cross section of 3
4 mm) for three ceramics. (Courtesy of C. J.
Shih.)