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Conceptos Elementales de Propiedades Mecanicas
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Chapter 6 - 1
ISSUES TO ADDRESS...
Stress and strain: What are they and why are they used instead of load and deformation?
Elastic behavior: When loads are small, how much deformation occurs? What materials deform least?
Plastic behavior: At what point does permanent deformation occur? What materials are most
resistant to permanent deformation?
Toughness and ductility: What are they and how do we measure them?
Chapter 6:
Mechanical Properties
Chapter 6 - 2
Elastic means reversible!
Elastic Deformation
1. Initial 2. Small load 3. Unload
F
bonds
stretch
return to
initial
F
Linear- elastic
Non-Linear- elastic
Chapter 6 - 3
Plastic means permanent!
Plastic Deformation (Metals)
F
linear elastic
linear elastic
plastic
1. Initial 2. Small load 3. Unload
p lanes still sheared
F
elastic + plastic
bonds stretch & planes shear
plastic
Chapter 6 - 4
Stress has units:
N/m2 or lbf/in2
Engineering Stress
Shear stress, :
Area, A
F t
F t
F s
F
F
F s
= F s
A o
Tensile stress, :
original area
before loading
Area, A
F t
F t
= F t
A o 2
f
2 m
N or
in
lb =
Chapter 6 - 5
Simple tension: cable
Note: = M/AcR here.
Common States of Stress
A o = cross sectional
area (when unloaded)
F F
o
F
A
o
F s
A
M
M A o
2R
F s A c
Torsion (a form of shear): drive shaft Ski lift (photo courtesy P.M. Anderson)
Chapter 6 - 6
(photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM
o
F
A
Simple compression:
Note: compressive
structure member
( < 0 here). (photo courtesy P.M. Anderson)
OTHER COMMON STRESS STATES (1)
A o
Balanced Rock, Arches National Park
Chapter 6 - 7
Bi-axial tension: Hydrostatic compression:
Pressurized tank
< 0h
(photo courtesy
P.M. Anderson)
(photo courtesy
P.M. Anderson)
OTHER COMMON STRESS STATES (2)
Fish under water
z > 0
> 0
Chapter 6 - 8
Tensile strain: Lateral strain:
Shear strain:
Strain is always
dimensionless.
Engineering Strain
90
90 - y
x = x/y = tan
L o
L
L
w o
Adapted from Fig. 6.1 (a) and (c), Callister 7e.
/2
L /2
L o w o
Chapter 6 - 9
Stress-Strain Testing
Typical tensile test machine
Adapted from Fig. 6.3, Callister 7e. (Fig. 6.3 is taken from H.W.
Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of
Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons,
New York, 1965.)
specimen extensometer
Typical tensile specimen
Adapted from
Fig. 6.2,
Callister 7e.
gauge length
Chapter 6 - 10
Linear Elastic Properties
Modulus of Elasticity, E: (also known as Young's modulus)
Hooke's Law:
= E
Linear-
elastic
E
F
F simple tension test
Chapter 6 - 11
Poisson's ratio,
Poisson's ratio, :
Units:
E: [GPa] or [psi]
: dimensionless
> 0.50 density increases
< 0.50 density decreases (voids form)
L
-
L
metals: ~ 0.33
ceramics: ~ 0.25
polymers: ~ 0.40
Chapter 6 - 12
Mechanical Properties
Slope of stress strain plot (which is proportional to the elastic modulus) depends
on bond strength of metal
Adapted from Fig. 6.7,
Callister 7e.
Chapter 6 - 13
Elastic Shear modulus, G:
G
= G
Other Elastic Properties
simple
torsion
test
M
M
Special relations for isotropic materials:
2(1 )
E G
3(1 2 )
E K
Elastic Bulk modulus, K:
pressure
test: Init.
vol =Vo.
Vol chg.
= V
P
P P P = - K
V V o
P
V
K V o
Chapter 6 - 14
Metals
Alloys
Graphite
Ceramics
Semicond
Polymers Composites
/fibers
E(GPa)
Based on data in Table B2,
Callister 7e.
Composite data based on
reinforced epoxy with 60 vol%
of aligned
carbon (CFRE),
aramid (AFRE), or
glass (GFRE)
fibers.
Youngs Moduli: Comparison
109 Pa
0.2
8
0.6
1
Magnesium,
Aluminum
Platinum
Silver, Gold
Tantalum
Zinc, Ti
Steel, Ni
Molybdenum
G raphite
Si crystal
Glass - soda
Concrete
Si nitride Al oxide
PC
Wood( grain)
AFRE( fibers) *
CFRE *
GFRE*
Glass fibers only
Carbon fibers only
A ramid fibers only
Epoxy only
0.4
0.8
2
4
6
10
2 0
4 0
6 0 8 0
10 0
2 00
6 00 8 00
10 00 1200
4 00
Tin
Cu alloys
Tungsten
Si carbide
Diamond
PTF E
HDP E
LDPE
PP
Polyester
PS PET
C FRE( fibers) *
G FRE( fibers)*
G FRE(|| fibers)*
A FRE(|| fibers)*
C FRE(|| fibers)*
Chapter 6 - 15
Simple tension:
FL o
E A o
L
Fw o
E A o
Material, geometric, and loading parameters all contribute to deflection.
Larger elastic moduli minimize elastic deflection.
Useful Linear Elastic Relationships
F
A o /2
L /2
Lo w o
Simple torsion:
2 ML o
r o 4 G
M = moment = angle of twist
2ro
Lo
Chapter 6 - 16
(at lower temperatures, i.e. T < Tmelt/3)
Plastic (Permanent) Deformation
Simple tension test:
engineering stress,
engineering strain,
Elastic+Plastic at larger stress
permanent (plastic) after load is removed
p
plastic strain
Elastic initially
Adapted from Fig. 6.10 (a),
Callister 7e.
Chapter 6 - 17
Stress at which noticeable plastic deformation has occurred.
when p = 0.002
Yield Strength, y
y = yield strength
Note: for 2 inch sample
= 0.002 = z/z
z = 0.004 in
Adapted from Fig. 6.10 (a),
Callister 7e.
tensile stress,
engineering strain,
y
p = 0.002
Chapter 6 - 18
Room T values
Based on data in Table B4,
Callister 7e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
Yield Strength : Comparison Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
Yie
ld s
tre
ng
th,
y
(MP
a)
PVC
Ha
rd to
me
asu
re
,
sin
ce
in t
en
sio
n, fr
actu
re u
su
ally
occu
rs b
efo
re y
ield
.
Nylon 6,6
LDPE
70
20
40
60 50
100
10
30
2 00
3 00
4 00
5 00 6 00 7 00
10 00
2 0 00
Tin (pure)
Al (6061) a
Al (6061) ag
Cu (71500) hr Ta (pure) Ti (pure) a Steel (1020) hr
Steel (1020) cd Steel (4140) a
Steel (4140) qt
Ti (5Al-2.5Sn) a W (pure)
Mo (pure) Cu (71500) cw
Ha
rd to
me
asu
re,
in c
era
mic
ma
trix
an
d e
po
xy m
atr
ix c
om
po
site
s, sin
ce
in
te
nsio
n, fr
actu
re u
su
ally
occu
rs b
efo
re y
ield
.
H DPE PP
humid
dry
PC
PET
Chapter 6 - 19
Tensile Strength, TS
Metals: occurs when noticeable necking starts. Polymers: occurs when polymer backbone chains are aligned and about to break.
Adapted from Fig. 6.11,
Callister 7e.
y
strain
Typical response of a metal
F = fracture or
ultimate
strength
Neck acts as stress
concentrator
en
gin
eering
TS s
tress
engineering strain
Maximum stress on engineering stress-strain curve.
Chapter 6 - 20
Tensile Strength : Comparison
Si crystal
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
Ten
sile
str
eng
th,
TS
(M
Pa
)
PVC
Nylon 6,6
10
100
200
300
1000
Al (6061) a
Al (6061) ag
Cu (71500) hr
Ta (pure) Ti (pure) a
Steel (1020)
Steel (4140) a
Steel (4140) qt
Ti (5Al-2.5Sn) a W (pure)
Cu (71500) cw
L DPE
PP
PC PET
20
30 40
2000
3000
5000
Graphite
Al oxide
Concrete
Diamond
Glass-soda
Si nitride
H DPE
wood ( fiber)
wood(|| fiber)
1
GFRE (|| fiber)
GFRE ( fiber)
C FRE (|| fiber)
C FRE ( fiber)
A FRE (|| fiber)
A FRE( fiber)
E-glass fib
C fibers Aramid fib
Room Temp. values Based on data in Table B4,
Callister 7e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
AFRE, GFRE, & CFRE =
aramid, glass, & carbon
fiber-reinforced epoxy
composites, with 60 vol%
fibers.
Chapter 6 - 21
Plastic tensile strain at failure:
Adapted from Fig. 6.13,
Callister 7e.
Ductility
Another ductility measure: 100 x A
A A RA %
o
f o -
=
x 100 L
L L EL %
o
o f
Engineering tensile strain,
E ngineering
tensile
stress,
smaller %EL
larger %EL Lf
Ao Af Lo
Chapter 6 - 22
Energy to break a unit volume of material Approximate by the area under the stress-strain curve.
Toughness
Brittle fracture: elastic energy
Ductile fracture: elastic + plastic energy
very small toughness (unreinforced polymers)
Engineering tensile strain,
E ngineering
tensile
stress,
small toughness (ceramics)
large toughness (metals)
Adapted from Fig. 6.13,
Callister 7e.
Chapter 6 - 23
Resilience, Ur
Ability of a material to store energy
Energy stored best in elastic region
If we assume a linear
stress-strain curve this
simplifies to
Adapted from Fig. 6.15,
Callister 7e.
y y r 2
1 U
ydUr 0
Chapter 6 - 24
Elastic Strain Recovery
Adapted from Fig. 6.17,
Callister 7e.
Chapter 6 - 25
Hardness
Resistance to permanently indenting the surface. Large hardness means: --resistance to plastic deformation or cracking in
compression.
--better wear properties.
e.g., 10 mm sphere
apply known force measure size of indent after removing load
d D Smaller indents mean larger hardness.
increasing hardness
most plastics
brasses Al alloys
easy to machine steels file hard
cutting tools
nitrided steels diamond
Chapter 6 - 26
Hardness: Measurement
Rockwell
No major sample damage
Each scale runs to 130 but only useful in range 20-100.
Minor load 10 kg
Major load 60 (A), 100 (B) & 150 (C) kg
A = diamond, B = 1/16 in. ball, C = diamond
HB = Brinell Hardness
TS (psia) = 500 x HB
TS (MPa) = 3.45 x HB
Chapter 6 - 27
Hardness: Measurement Table 6.5
Chapter 6 - 28
True Stress & Strain
Note: S.A. changes when sample stretched
True stress
True Strain
iT AF
oiT ln 1ln1
T
T
Adapted from Fig. 6.16,
Callister 7e.
Chapter 6 - 29
Hardening
Curve fit to the stress-strain response:
T K T
n
true stress (F/A) true strain: ln(L/Lo)
hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers)
An increase in y due to plastic deformation.
large hardening
small hardening y 0
y 1
Chapter 6 - 30
Variability in Material Properties
Elastic modulus is material property
Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability.
Statistics
Mean
Standard Deviation
2
1
2
1n
xxs i
n
n
xx n
n
where n is the number of data points
Chapter 6 - 31
Design uncertainties mean we do not push the limit. Factor of safety, N
N
y
working
Often N is
between
1.2 and 4
Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a
factor of safety of 5.
Design or Safety Factors
4
0002202 /d
N,5
N
y
working1045 plain carbon steel:
y = 310 MPa
TS = 565 MPa
F = 220,000N
d
L o
d = 0.067 m = 6.7 cm
Chapter 6 - 32
Stress and strain: These are size-independent measures of load and displacement, respectively.
Elastic behavior: This reversible behavior often shows a linear relation between stress and strain.
To minimize deformation, select a material with a
large elastic modulus (E or G).
Toughness: The energy needed to break a unit volume of material.
Ductility: The plastic strain at failure.
Summary
Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive)
uniaxial stress reaches y.
Chapter 6 - 33
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. Adapted from Fig. 22.30(b), Callister 7e.
(Fig. 22.30(b) is courtesy of National
Semiconductor Corporation.)
Adapted from Fig. 22.26(b),
Callister 7e.
Chapter 8: Mechanical Failure
Adapted from chapter-opening
photograph, Chapter 8, Callister 7e. (by
Neil Boenzi, The New York Times.)
Chapter 6 - 34
Fracture mechanisms
Ductile fracture
Occurs with plastic deformation
Brittle fracture
Little or no plastic deformation
Catastrophic
Chapter 6 - 35
Ductile vs Brittle Failure
Very
Ductile
Moderately
Ductile Brittle
Fracture
behavior:
Large Moderate %AR or %EL Small
Ductile fracture is usually
desirable!
Adapted from Fig. 8.1,
Callister 7e.
Classification:
Ductile:
warning before
fracture
Brittle:
No
warning
Chapter 6 - 36
Ductile failure: --one piece
--large deformation
Figures from V.J. Colangelo and F.A.
Heiser, Analysis of Metallurgical Failures
(2nd ed.), Fig. 4.1(a) and (b), p. 66 John
Wiley and Sons, Inc., 1987. Used with
permission.
Example: Failure of a Pipe
Brittle failure: --many pieces
--small deformation
Chapter 6 - 37
Evolution to failure:
Resulting fracture
surfaces
(steel)
50 mm
particles
serve as void
nucleation
sites.
50 mm
From V.J. Colangelo and F.A. Heiser,
Analysis of Metallurgical Failures (2nd
ed.), Fig. 11.28, p. 294, John Wiley and
Sons, Inc., 1987. (Orig. source: P.
Thornton, J. Mater. Sci., Vol. 6, 1971, pp.
347-56.)
100 mm
Fracture surface of tire cord wire
loaded in tension. Courtesy of F.
Roehrig, CC Technologies, Dublin,
OH. Used with permission.
Moderately Ductile Failure
necking
void nucleation
void growth and linkage
shearing at surface
fracture
Chapter 6 - 38
Ductile vs. Brittle Failure
Adapted from Fig. 8.3, Callister 7e.
cup-and-cone fracture brittle fracture
Chapter 6 - 39
Brittle Failure
Arrows indicate pt at which failure originated
Adapted from Fig. 8.5(a), Callister 7e.
Chapter 6 - 40
Intergranular (between grains)
Intragranular (within grains)
Al Oxide
(ceramic) Reprinted w/ permission
from "Failure Analysis of
Brittle Materials", p. 78.
Copyright 1990, The
American Ceramic
Society, Westerville, OH.
(Micrograph by R.M.
Gruver and H. Kirchner.)
316 S. Steel
(metal) Reprinted w/ permission
from "Metals Handbook",
9th ed, Fig. 650, p. 357.
Copyright 1985, ASM
International, Materials
Park, OH. (Micrograph by
D.R. Diercks, Argonne
National Lab.)
304 S. Steel
(metal) Reprinted w/permission
from "Metals Handbook",
9th ed, Fig. 633, p. 650.
Copyright 1985, ASM
International, Materials
Park, OH. (Micrograph by
J.R. Keiser and A.R.
Olsen, Oak Ridge
National Lab.)
Polypropylene
(polymer) Reprinted w/ permission
from R.W. Hertzberg,
"Defor-mation and
Fracture Mechanics of
Engineering Materials",
(4th ed.) Fig. 7.35(d), p.
303, John Wiley and
Sons, Inc., 1996. 3 mm
4 mm 160 mm
1 mm (Orig. source: K. Friedrick, Fracture 1977, Vol.
3, ICF4, Waterloo, CA, 1977, p. 1119.)
Brittle Fracture Surfaces
Chapter 6 - 41
Stress-strain behavior (Room T):
Ideal vs Real Materials
TS
Chapter 6 - 42
Flaws are Stress Concentrators!
Results from crack propagation
Griffith Crack
where
t = radius of curvature
o = applied stress
m = stress at crack tip
ot
/
t
om Ka
21
2
t
Adapted from Fig. 8.8(a), Callister 7e.
Chapter 6 - 43
Concentration of Stress at Crack Tip
Adapted from Fig. 8.8(b), Callister 7e.
Chapter 6 - 44
Engineering Fracture Design
r/h
sharper fillet radius
increasing w/h
0 0.5 1.0 1.0
1.5
2.0
2.5
Stress Conc. Factor, K t max
o
=
Avoid sharp corners!
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.)
r , fillet
radius
w
h
o
max
Chapter 6 - 45
Crack Propagation
Cracks propagate due to sharpness of crack tip
A plastic material deforms at the tip, blunting the crack.
deformed
region
brittle
Energy balance on the crack
Elastic strain energy-
energy stored in material as it is elastically deformed
this energy is released when the crack propagates
creation of new surfaces requires energy
plastic
Chapter 6 - 46
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
Kc = c/ 0
For ductile => replace s by s + p
where p is plastic deformation energy
212
/
sc
a
Ei.e., m > c
or Kt > Kc
Chapter 6 - 47
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.
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
5
K Ic
(MP
a
m 0.
5 )
1
Mg alloys
Al alloys
Ti alloys
Steels
Si crystal
Glass - soda
Concrete
Si carbide
PC
Glass 6
0.5
0.7
2
4
3
10
2 0
3 0
Diamond
PVC
PP
Polyester
PS
PET
C-C (|| fibers) 1
0.6
6 7
4 0
5 0 6 0 7 0
100
Al oxide Si nitride
C/C ( fibers) 1
Al/Al oxide(sf) 2
Al oxid/SiC(w) 3
Al oxid/ZrO 2 (p) 4 Si nitr/SiC(w) 5
Glass/SiC(w) 6
Y 2 O 3 /ZrO 2 (p) 4
Chapter 6 - 48
Crack growth condition:
Largest, most stressed cracks grow first!
Design Against Crack Growth
K Kc = aY
--Result 1: Max. flaw size dictates design stress.
max
cdesign
aY
K
amax no fracture
fracture
--Result 2: Design stress dictates max. flaw size.
2
1
design
cmax
Y
Ka
amax
no fracture
fracture
Chapter 6 - 49
Two designs to consider...
Design A --largest flaw is 9 mm
--failure stress = 112 MPa
Design B --use same material
--largest flaw is 4 mm
--failure stress = ?
Key point: Y and Kc are the same in both designs.
Answer: MPa 168)( Bc Reducing flaw size pays off!
Material has Kc = 26 MPa-m0.5
Design Example: Aircraft Wing
Use... max
cc
aY
K
c amax
Ac amax
B
9 mm 112 MPa 4 mm --Result:
Chapter 6 - 50
Loading Rate
Increased loading rate... -- increases y and TS
-- decreases %EL
Why? An increased rate gives less time for
dislocations to move past
obstacles.
y
y
TS
TS
larger
smaller
Chapter 6 - 51
Impact Testing
final height initial height
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.)
(Charpy)
Chapter 6 - 52
Increasing temperature... --increases %EL and Kc
Ductile-to-Brittle Transition Temperature (DBTT)...
Temperature
BCC metals (e.g., iron at T < 914C)
Imp
act E
ne
rgy
Temperature
High strength materials ( y > E/150)
polymers
More Ductile Brittle
Ductile-to-brittle transition temperature
FCC metals (e.g., Cu, Ni)
Adapted from Fig. 8.15,
Callister 7e.
Chapter 6 - 53
Pre-WWII: The Titanic WWII: Liberty ships
Problem: Used a type of steel with a DBTT ~ Room temp.
Reprinted w/ permission from R.W. Hertzberg,
"Deformation and Fracture Mechanics of Engineering
Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and
Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard,
The Discovery of the Titanic.)
Reprinted w/ permission from R.W. Hertzberg,
"Deformation and Fracture Mechanics of Engineering
Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and
Sons, Inc., 1996. (Orig. source: Earl R. Parker,
"Behavior of Engineering Structures", Nat. Acad. Sci.,
Nat. Res. Council, John Wiley and Sons, Inc., NY,
1957.)
Design Strategy:
Stay Above The DBTT!
Chapter 6 - 54
Fatigue
Fatigue = failure under cyclic stress.
Stress varies with time. -- key parameters are S, m, and
frequency
max
min
time
m S
Key points: Fatigue... --can cause part failure, even though max < c.
--causes ~ 90% of mechanical engineering failures.
Adapted from Fig. 8.18,
Callister 7e. (Fig. 8.18 is
from Materials Science in
Engineering, 4/E by Carl.
A. Keyser, Pearson
Education, Inc., Upper
Saddle River, NJ.) tension on bottom
compression on top
counter motor
flex coupling
specimen
bearing bearing
Chapter 6 - 55
Fatigue limit, Sfat: --no fatigue if S < Sfat
Adapted from Fig.
8.19(a), Callister 7e.
Fatigue Design Parameters
Sfat
case for steel (typ.)
N = Cycles to failure 10
3 10
5 10
7 10
9
unsafe
safe
S = stress amplitude
Sometimes, the fatigue limit is zero!
Adapted from Fig.
8.19(b), Callister 7e.
case for Al (typ.)
N = Cycles to failure 10
3 10
5 10
7 10
9
unsafe
safe
S = stress amplitude
Chapter 6 - 56
Crack grows incrementally
typ. 1 to 6
a~
increase in crack length per loading cycle
Failed rotating shaft --crack grew even though
Kmax < Kc --crack grows faster as increases crack gets longer loading freq. increases.
crack origin
Adapted from
Fig. 8.21, Callister 7e.
(Fig. 8.21 is from D.J.
Wulpi, Understanding
How Components Fail,
American Society for
Metals, Materials Park,
OH, 1985.)
Fatigue Mechanism
mK
dN
da
Chapter 6 - 57
Improving Fatigue Life
1. Impose a compressive
surface stress (to suppress surface
cracks from growing)
N = Cycles to failure
moderate tensile m Larger tensile m
S = stress amplitude
near zero or compressive m Increasing
m
--Method 1: shot peening
put surface
into compression
shot --Method 2: carburizing
C-rich gas
2. Remove stress
concentrators. Adapted from Fig. 8.25, Callister 7e.
bad
bad
better
better
Adapted from
Fig. 8.24, Callister 7e.
Chapter 6 - 58
Creep
Sample deformation at a constant stress ( ) vs. time
Adapted from
Fig. 8.28, Callister 7e.
Primary Creep: slope (creep rate)
decreases with time.
Secondary Creep: steady-state
i.e., constant slope.
Tertiary Creep: slope (creep rate)
increases with time, i.e. acceleration of rate.
0 t
Chapter 6 - 59
Occurs at elevated temperature, T > 0.4 Tm
Adapted from Figs. 8.29,
Callister 7e.
Creep
elastic
primary secondary
tertiary
Chapter 6 - 60
Strain rate is constant at a given T, -- strain hardening is balanced by recovery
stress exponent (material parameter)
strain rate
activation energy for creep
(material parameter)
applied stress material const.
Strain rate increases
for higher T,
10
2 0
4 0
10 0
2 0 0
10 -2 10 -1 1 Steady state creep rate (%/1000hr) s
Stress (MPa) 427 C
538 C
649 C
Adapted from
Fig. 8.31, Callister 7e.
(Fig. 8.31 is from Metals
Handbook: Properties
and Selection:
Stainless Steels, Tool
Materials, and Special
Purpose Metals, Vol. 3,
9th ed., D. Benjamin
(Senior Ed.), American
Society for Metals,
1980, p. 131.)
RT
QK cns exp2
Secondary Creep
Chapter 6 - 61
Creep Failure Estimate rupture time S-590 Iron, T = 800 C, = 20 ksi
Failure: along grain boundaries.
time to failure (rupture)
function of
applied stress
temperature
L)t(T rlog20
applied
stress
g.b. cavities
Time to rupture, tr
From V.J. Colangelo and F.A. Heiser, Analysis of
Metallurgical Failures (2nd ed.), Fig. 4.32, p. 87, John
Wiley and Sons, Inc., 1987. (Orig. source: Pergamon
Press, Inc.)
L)t(T rlog20
1073K
Ans: tr = 233 hr
24x103 K-log hr
Adapted from
Fig. 8.32, Callister 7e.
(Fig. 8.32 is from F.R.
Larson and J. Miller,
Trans. ASME, 74, 765
(1952).)
L(10 3 K-log hr)
Str
ess, ksi
100
10
1 12 20 24 28 16
data for S-590 Iron
20
Chapter 6 - 62
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.
SUMMARY
Recommended