Objectives

1
Objectives

• Explain the effect of experimental variables on
  fracture test results.
• Understand and use the critical stress intensity
  approach to predict linear elastic fracture.
• Describe the Charpy transition temperature
  approach to fracture testing.
• Explain the role of state of stress, grain size,
  and test rate in the DBTT of metals.
• Calculate the plastic zone size ahead of a crack.

2
Why Fracture Mechanics?

• WWII Liberty Ship
• Welded Construction
• New workers
• High rate of steel production ? quality problems
• Cyclic wave action
• Hatch Openings
• Broke in Two

3
Fracture Mechanics

• No load transfer across
• crack/hole.
• Stress higher than ??
• Water analogy

4

• Crack is sharp discontinuity

5

• Crack is sharp discontinuity
• Crack grows under action of stress
• Controlling Factor
• Available energy gt required work to create new
  surface

6
Flaws are Stress Concentrators!

• Griffith Crack
• where ?t radius of curvature
• so applied stress
• sm stress at crack tip

?t
Adapted from Fig. 8.8(a), Callister 7e.
7
Concentration of Stress at Crack Tip
Adapted from Fig. 8.8(b), Callister 7e.
8
Engineering Fracture Design
Avoid sharp corners!
s
Adapted from Fig. 8.2W(c), Callister 6e. (Fig.
8.2W(c) is from G.H. Neugebauer, Prod. Eng.
(NY), Vol. 14, pp. 82-87 1943.)
9
Crack Propagation

• Crack propagation depends on sharpness of crack
  tip
• A plastic material deforms at the tip, blunting
  the crack.
• deformed region
• brittle
• Blunting has two effects reduces stress
  concentration, absorbs energy in plastic work.

plastic
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Flow of Energy/Work in Fracture
Plastic Work
WORK of External Force, Pd
Elastic Energy
Crack Surface Energy
As a crack grows, the stress behind the tip falls
to zero, releasing the stored elastic energy in
the material, this energy can be used to do the
plastic or surface work of fracture
11
When Does a Crack Propagate?

• Crack propagates if above critical stress
• where
• E modulus of elasticity
• ?s specific surface energy
• a one half length of internal crack
• For ductile gt replace gs by gs gp
• where gp is plastic deformation energy

i.e., sm gt sc
12
Mode I Westegaard Solution
13
Stress Intensity Factor

• Let ? 0 and we get
• K /?2?r
• where K Y???a

14
What is K?

• Stress Intensity Factor
• Represents Intensity of ? Field At Tip
• Shape of ? Distribution Given by 1/ ?2?r
• Represents the energy available in the near field
  to do the work of fracture!

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Crack Growth Criteria

• If KAPPLIED gt KC
• A Crack Will Grow

16

• Mathematically, what happens to
• ? yy k/ ? 2?r as r ? 0?
• 2. Actual stress distribution

17
Plastic Zone at Crack Tip
18
3. Rearranging the Westegard solution and setting
the stress equal to the yield strength In
front of crack
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Question

• If increasing the loading rate increases the
  yield (flow) stress of most materials, what will
  happen to the plastic zone at a crack tip as the
  rate is increased?
• Zone decreases in size
• Zone increases in size
• Zone doesnt change

20
Effect of Strength on Toughness
Sourcebook on Industrial Alloy and Engineering
Data, ASM International
21
Effect of Test Variables

• Temperature

FCC
K
C
BCC HCP
Temperature
22
Effect of Test Variables

• Temperature
• Crack Tip Radius (?)

23
Effect of Test Variables

• Temperature
• Crack Tip Radius
• Specimen Thickness

24
Effect of Test Variables

• Temperature
• Crack Tip Radius
• Specimen Thickness
• Strain Rate
• d?/dt

25
Loading Rate
Increased loading rate... -- increases sy
and UTS -- decreases EL
Why? An increased rate gives less time
for dislocations to move past obstacles.
s
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Critical Stress Intensity Factor- KIC

• This is the value of K at crack advance for
• -Mode I (opening mode)
• -Plain strain (thick specimens)
• -Sharp crack
• You will need to have KIC values for the
  particular strain rate, temperature, and
  environment for which you are engineering.
• There is a similar KIIC for Mode II fracture.

27
Fracture Toughness
Based on data in Table B5, Callister
7e. 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.
28

• I. Approaches To Fracture
• Fracture Mechanics
• Linear Elastic F.M.
• Elastic Plastic F.M.
• Transition Temperature (older)
• Charpy
• Drop weight tear
• Dynamic tear

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II. Methods of Testing 1. LEFM ASTM E399 2.
E-P ASTM E-813 3. Charpy ASTM E-23
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III. Transition Temperature Approach A.
Standard Charpy V- Notch Result
Total Energy of Fracture
31
Charpy Testing
Impact loading -- severe testing case
-- makes material more brittle -- decreases
toughness
Adapted from Fig. 8.12(b), Callister 7e. (Fig.
8.12(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.)
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III. Transition Temperature Approach Plot
Impact E versus Temperature
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Temperature
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 lt 914C)
polymers

Impact Energy
More Ductile

Brittle

s

High strength materials (
gt E/150)
y
Temperature
Adapted from Fig. 8.15, Callister 7e.
Ductile-to-brittle
transition temperature
34
III. Transition Temperature Approach Define
DBTT 1. 50 Fracture Appearance Temperature
(FATT) 2. Midpoint in Energy 3. Lateral
contraction method
35

• III. Transition Temperature Approach
• Problem Service experience doesnt
  necessarily match experiment.
• 1. Specimens are thin structures may not be
  
• --- lack of constraint
• 2. Specimen tip is blunt --- real cracks are
  usually sharp
• Charpy may yield Non-Conservative estimates of
  DBTT!!!

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DBTT Design

• Allowable Stress -Usually - Sy / F.S.
• (F.S. Factor of Safety)
• DBTT 40?C use Sallowable
• DBTT 30?C to 40?C use .90 Sallowable
• DBTT 20?C to 30?C use .75 Sallowable
• DBTT 10?C to 20?C use .5 Sallowable
• less than DBTT 10 Not Allowed