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Chapter 9 - 1
ISSUES TO ADDRESS...
• How do cracks that lead to failure form?
• How is fracture resistance quantified? How do the fracture resistances of the different material classes compare?
• How do we estimate the stress to fracture?
• How do loading rate, loading history, and temperatureaffect the failure behavior of materials?
Chapter 9: Mechanical Failure
Chapter 9 - 3
Fracture mechanisms
An oil tanker fractured in a brittle manner by crack propagation around its girth(cyclic loading from waves).
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Chapter 9 - 4
Ductile failure:•Significant plastic deformation •Often one piece
Example: Pipe Failures
Brittle failure:
• Little or no plastic deformation
• Catastrophic
• Often many pieces
• Ductility is a function of temperature, strain rate and stress state.
Chapter 9 - 5
Ductile vs Brittle Failure
Large Moderate%AR or %EL Small
• Ductile fracture is
usually more desirable
than brittle fracture!
• Classification:
Ductile:
• Warning before fracture
•Needs more strain energy
Brittle:
•No warning
• Pure gold and lead at room
temperature
• Other metals, polymers, and
glasses at high temperatures
Very Ductile
ModeratelyDuctile
BrittleFracturebehavior:
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Chapter 9 - 7
• Evolution to failure:
10 mm
Moderately Ductile Failure
neckingvoid growth and linkage
Cup-and-cone fracture
void nucleation
shearing at surface
fracture
• A steel fracture surfaces
Particles/defects serve as voidnucleation sites
Chapter 9 - 9
Ductile vs. Brittle Failure
Cup-and-cone fracture Brittle fracture
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Chapter 9 - 10
Ductile Failure
Chapter 9 - 12
Brittle Fracture Surfaces
Intergranular Intragranular
Difference?
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Chapter 9 - 13
Brittle Fracture Surfaces
• Intergranular (between grains)
A transgranular fracture surface: SEM
fractograph of ductile cast iron
• For most brittle crystalline materials
Crack propagation = Cleavage: successive and repeated breaking
of atomic bonds along specific crystallographic planes
Chapter 9 - 15
Brittle Fracture Surfaces
• Intragranular (within grains)
• Occurrence of processes that weaken or embrittle grain
boundary regions.
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Chapter 9 - 17
• Stress-strain behavior (Room Temp.)
Ideal vs Real Materials
σ
ε0.1
perfect materials- no flaws
carefully produced glass fiber
typical ceramic typical strengthened metaltypical polymer
• Presence of very small, microscopic flaws or cracks at the
surface and within the interior of a body of material.
TS << TSengineeringmaterials
perfectmaterials
Chapter 9 - 18
Ideal vs Real Materials
Reprinted w/
permission from R.W.
Hertzberg,
"Deformation and
Fracture Mechanics
of Engineering
Materials", (4th ed.)
Fig. 7.4. John Wiley
and Sons, Inc., 1996.
• DaVinci (500 yrs ago!) observed...- the longer the wire,
the smaller the load for failure.
• Reasons:• Flaws cause premature failure
• An applied stress may be amplified or concentrated at the tip of the flaws
• Larger samples contain more flaws!
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Chapter 9 - 19
• Flaws:
�reduce cross section area
�are stress concentrators!
(stress raiser)
Chapter 9 - 20
ρt
Concentration of Stress at Crack Tip
where•σo = applied stress•σm = stress at crack tip•a = length of a surface crack or half of the length of an internal crack.
•ρt = radius of curvature
•Kt= stress concentration factor
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Chapter 9 - 21
Engineering Fracture Design
r/h
sharper fillet radius
increasing w/h
0 0.5 1.01.0
1.5
2.0
2.5
Kt
�Avoid sharp corners!�Avoid sudden change in dimensions!
σ
r , fillet
radius
w
h
o
σmax
