CHAPTER 9:
MECHANICAL FAILURE
ISSUES TO ADDRESS...
• How do flaws in a material initiate failure?
• How is fracture resistance quantified; how do different
material classes compare?
• How do we estimate the stress to fracture?
• How do loading rate, loading history, and temperature
affect the failure stress?
Ship-cyclic loading
from waves.
Computer chip-cyclic
thermal loading.
Hip implant-cyclic
loading from walking.
1
MODERATELY DUCTILE FAILURE
• Evolution to failure:
necking

• Resulting
fracture
surfaces
(steel)
particles
serve as void
nucleation
sites.
void
nucleation
void growth
and linkage
shearing
at surface
fracture
50
50mm
mm
100 mm
4
BRITTLE FRACTURE SURFACES
• Intragranular
• Intergranular
(between grains) 304 S. Steel
(metal)
(within grains)
316 S. Steel
(metal)
160mm
4 mm
Polypropylene
(polymer)
Al Oxide
(ceramic)
3mm
1 mm
5
IDEAL VS REAL MATERIALS
• Stress-strain behavior (Room T):
TSengineering<< TSperfect
materials
materials
• DaVinci (500 yrs ago!) observed...
--the longer the wire, the
smaller the load to fail it.
• Reasons:
--flaws cause premature failure.
--Larger samples are more flawed!
6
FLAWS ARE STRESS
CONCENTRATORS!
• Elliptical hole in
a plate:
• Stress distrib. in front of a hole:
• Stress conc. factor:
• Large Kt promotes failure:
7
ENGINEERING FRACTURE DESIGN
• Avoid sharp corners!
Stress Conc. Factor,
K t=
2.5
2.0

max

o
increasing w/h
1.5
1.0
0
0.5
1.0
sharper fillet radius
r/h
8
WHEN DOES A CRACK PROPAGATE?
• rt at a crack
tip is very
small!
• Result: crack tip
stress is very large.
 tip
• Crack propagates when:
 tip 
K
2 x
increasing K
the tip stress is large
enough to make:
K ≥ Kc
distance, x,
from crack tip
9
GEOMETRY, LOAD, & MATERIAL
• Condition for crack propagation:
K ≥ Kc
Stress Intensity Factor:
--Depends on load &
geometry.
Fracture Toughness:
--Depends on the material,
temperature, environment, &
rate of loading.
• Values of K for some standard loads & geometries:

units of K :
MPa m
or ksi in
K   a
a
K  1.1 a
10
DESIGN AGAINST CRACK GROWTH
• Crack growth condition: K ≥ Kc
Y a
• Largest, most stressed cracks grow first!
--Result 1: Max flaw size
--Result 2: Design stress
dictates design stress.
dictates max. flaw size.
2


1
Kc


a max  
 Ydesign 

design 
Kc
Y a max
12
DESIGN EX: AIRCRAFT WING
• Material has Kc = 26 MPa-m0.5
• Two designs to consider...
Design B
Design A
--largest flaw is 9 mm
--failure stress = 112 MPa
• Use...
c 
Kc
--use same material
--largest flaw is 4 mm
--failure stress = ?
Y a max
• Key point: Y and Kc are the same in both designs.
--Result:
112 MPa 9 mm
c
a max
A  c
4 mm
a max
B
Answer:
• Reducing flaw size pays off!
c B  168MPa
13
LOADING RATE
• Increased loading rate...
--increases y and TS
--decreases %EL
• Why? An increased rate
gives less time for disl. to
move past obstacles.
• Impact loading:
sample
--severe testing case
--more brittle
--smaller toughness
final height
initial height
14
TEMPERATURE
• Increasing temperature...
--increases %EL and Kc
• Ductile-to-brittle transition temperature (DBTT)...
15
DESIGN STRATEGY:
STAY ABOVE THE DBTT!
• Pre-WWII: The Titanic
• WWII: Liberty ships
• Problem: Used a type of steel with a DBTT ~ Room temp.
16
FATIGUE
• Fatigue = failure under cyclic stress.
specimen
bearing
compression on top
bearing
motor
counter
flex coupling
tension on bottom
• Stress varies with time.
--key parameters are S and m
• Key points: Fatigue...
--can cause part failure, even though max < c.
--causes ~ 90% of mechanical engineering failures.
17
FATIGUE DESIGN PARAMETERS
• Fatigue limit, Sfat:
--no fatigue if S < Sfat
• Sometimes, the
fatigue limit is zero!
S = stress amplitude
unsafe
case for
Al (typ.)
safe
103
105
107
109
N = Cycles to failure
18
FATIGUE MECHANISM
• Crack grows incrementally
 
typ. 1 to 6
da
m
 K
dN
~ 
 a
increase in crack length per loading cycle
crack origin
• Failed rotating shaft
--crack grew even though
Kmax < Kc
--crack grows faster if
•  increases
• crack gets longer
• loading freq. increases.
19
IMPROVING FATIGUE LIFE
1. Impose a compressive
surface stress
(to suppress surface
cracks from growing)
--Method 1: shot peening
--Method 2: carburizing
shot
put
surface
into
compression
2. Remove stress
concentrators.
C-rich gas
bad
better
bad
better
20
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  and T < 0.4Tm, failure stress decreases with:
increased maximum flaw size,
decreased T,
increased rate of loading.
-for cyclic :
cycles to fail decreases as  increases.
-for higher T (T > 0.4Tm):
time to fail decreases as  or T increases.
26