Introduction to Fracture Mechanics
Ashraf -F. Bastawros
Aerospace and Engineering Mechanics
Iowa State University
bastaw@iastate.edu, X4-3039
Howe Hall Rm. 2347
Spring 2005
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
Utilization of Fracture Concepts
• Pharos utilized fracture in cutting huge lime stone.
Carve a starter wedge
Fill it with wood, and add water
• Everyday practice:
- Cutting glass sheets
- Cracks around drainage holes
- Cracks around window frames
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
1
Design Concepts
• Applied stresses < Tensile strength
• Applied stresses < Endurance limit (S-N curve)
¾ 20th Century Disasters
Titanic (1912)
*Chemistry: low residual nitrogen and manganese content,
and higher levels of sulfur, phosphorus, and oxygen
*Microstructure: very large grains
*Service temperature: —2°C on the night the ship collided with the iceberg
The ductile-brittle transition temperature (using 20 lbs.-ft. for the test)
was found to be 20°C in one direction and 30°C in the other
*Processing: Rivet holes were cold-punched
http://www.memagazine.org/backissues/aug98/features/titanic/testing.html
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
Design Concepts
Believing that the Titanic was invincible, many passengers were
willing to board lifeboats only after the bow began to sink below
below
the water's surface.
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
2
Design Concepts
• Applied stresses < Tensile strength
• Applied stresses < Endurance limit (S-N curve)
¾ 20th Century Disasters
- Titanic (1912) Large grains, Sulfur contents, high GTT
- Boston Molasses Tank (1912)
- Liberty ships (1940’s) temperatures
- Aloha Airline (1988) corrosive environment
- United—Sioux city crash (1989) hard phase inclusion
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
Fatigue Failure
Aloha Airlines, 4/28/1988. The aircraft lost 1/3 of its roof
due to a stress fracture while cruising at 24,000 feet.
From: http://www.airdisaster.com/
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
3
Inception of fracture mechanics
• Griffith energy criterion (1920)
Change of strain energy, G = Gain in surface energy
G = Gc at the moment of fracture
Gc Critical energy release rate
Measure of material fracture toughness
• Irwin (1956)
G=
πσ 2a
E
σ f ∝1 a
Iowa State University
Gc =
πσ 2f ac
E
, Gc = constant
Fracture Mechanics, Spring 2006
Ashraf Bastawros
Design Concepts for Fracture
1. Applied stresses (service)
2. Minimum flaw size (material microstructure)
3. Material fracture toughness
σ
B
da
= f (loading)
dN
a
Crack length, a
4. Crack growth rate,
σ 2 > σ1
FG da IJ
H dN K
σ
Iowa State University
Fracture Mechanics, Spring 2006
a1 ,σ 2
FG da IJ
H dN K
a1 ,σ 1
Cycle N
Ashraf Bastawros
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Fracture
• Proceeds in two stages
– crack formation and crack growth
• Ductile fracture
– extensive plastic deformation
– slow crack growth - called “stable”
• Brittle fracture
– almost no plastic deformation
– very rapid crack growth - called “unstable”
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
Classify Materials from Toughness Mechanisms
Brittle
Semi-Brittle
Ductile
Ceramics
BCC-HCP
Metals
Inter metallic
LiF, MgO
Polymers
Brittle
Polymers
Rock Salt
Temperature
Focus on microstructure point of view
Sub µm
µm
Macro
0.1µm
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
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Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
Basics for fracture
1. Size effects (plastic zone, annular J or K dominance relative to
microstructure size scale).
2. Microscopic deformation mechanisms
control fracture toughness
3. Microstructure surprises.
4. Environmental surprises (chemical or thermal)
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
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