Transcript MSE536 Mechanical Properties

MECHANICAL PROPERTIES
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 do dislocations
cause permanent deformation? What materials are
most resistant to permanent deformation?
• Toughness and ductility: What are they and how
do we measure them?
• Ceramic Materials: What special provisions/tests are
made for ceramic materials?
1
ELASTIC DEFORMATION
1. Initial
2. Small load
3. Unload
bonds
stretch
return to
initial

F
Elastic means reversible!
2
PLASTIC DEFORMATION
(METALS)
1. Initial
2. Small load
3. Unload
F
Plastic means permanent!
linear
elastic
linear
elastic
plastic

3
ENGINEERING STRESS
• Tensile stress, s:
• Shear stress, t:
Ft
s
Ao
original area
before loading
Stress has units:
N/m2 or lb/in2
4
ENGINEERING STRAIN
• Tensile strain:
• Lateral strain:
/2
wo
• Shear strain:
L/2
Lo
/2
L/2
/2
 = tan 
/2 - 
/2
Strain is always
dimensionless.
/2
8
STRESS-STRAIN TESTING
• Typical tensile specimen
• Typical tensile
test machine
• Other types of tests:
--compression: brittle
materials (e.g., concrete)
--torsion: cylindrical tubes,
shafts.
9
LINEAR ELASTIC PROPERTIES
• Modulus of Elasticity, E:
(also known as Young's modulus)
• Hooke's Law:
s=Ee
• Poisson's ratio, n:
metals: n ~ 0.33
ceramics: ~0.25
polymers: ~0.40
Units:
E: [GPa] or [psi]
n: dimensionless
10
OTHER ELASTIC PROPERTIES
• Elastic Shear
modulus, G:
t=G
M
t
G
1
simple
torsion
test

M
• Elastic Bulk
modulus, K:
P
P
• Special relations for isotropic materials:
E
E
G
K
2(1  n)
3(1  2n)
P
pressure
test: Init.
vol =Vo.
Vol chg.
= DV
12
YOUNG’S MODULI:
COMPARISON
Metals
Alloys
1200
1000
800
600
400
E(GPa)
200
100
80
60
40
109 Pa
Graphite
Composites
Ceramics Polymers
/fibers
Semicond
Diamond
Tungsten
Molybdenum
Steel, Ni
Tantalum
Platinum
Cu alloys
Zinc, Ti
Silver, Gold
Aluminum
Magnesium,
Tin
Si carbide
Al oxide
Si nitride
Carbon fibers only
CFRE(|| fibers)*
<111>
Si crystal
Aramid fibers only
<100>
AFRE(|| fibers)*
Glass-soda
Glass fibers only
GFRE(|| fibers)*
Concrete
GFRE*
20
10
8
6
4
2
1
0.8
0.6
0.4
0.2
CFRE*
GFRE( fibers)*
Graphite
Polyester
PET
PS
PC
CFRE( fibers)*
AFRE( fibers)*
Epoxy only
PP
HDPE
PTFE
LDPE
Wood( grain)
13
PLASTIC (PERMANENT)
DEFORMATION
(at lower temperatures, T < Tmelt/3)
• Simple tension test:
15
YIELD STRENGTH, sy
• Stress at which noticeable plastic deformation has
occurred.
when ep = 0.002
tensile stress, s
sy
engineering strain, e
ep = 0.002
16
YIELD STRENGTH: COMPARISON
sy(ceramics)
>>sy(metals)
>> sy(polymers)
Room T values
Based on data in Table B4,
Callister 6e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
17
TENSILE STRENGTH, TS
• Maximum possible engineering stress in tension.
• Metals: occurs when noticeable necking starts.
• Ceramics: occurs when crack propagation starts.
• Polymers: occurs when polymer backbones are
aligned and about to break.
18
TENSILE STRENGTH:
COMPARISON
TS(ceram)
~TS(met)
~ TS(comp)
>> TS(poly)
Room T values
Based on data in Table B4,
Callister 6e.
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.
19
DUCTILITY, %EL
L f  Lo
x100
• Plastic tensile strain at failure: %EL 
Lo
Adapted from Fig. 6.13,
Callister 6e.
Ao  A f
• Another ductility measure: %AR 
x100
Ao
• Note: %AR and %EL are often comparable.
--Reason: crystal slip does not change material volume.
--%AR > %EL possible if internal voids form in neck.
20
TOUGHNESS
• Energy to break a unit volume of material
• Approximate by the area under the stress-strain
curve.
Engineering
tensile
stress, s
smaller toughness (ceramics)
larger toughness
(metals, PMCs)
smaller toughnessunreinforced
polymers
Engineering tensile strain, e
21
HARDENING
• An increase in sy due to plastic deformation.
• Curve fit to the stress-strain response:
22
MEASURING ELASTIC MODULUS
• Room T behavior is usually elastic, with brittle failure.
• 3-Point Bend Testing often used.
--tensile tests are difficult for brittle materials.
• Determine elastic modulus according to:
E
F
L3

4bd3
rect.
cross
section

F
L3
 12R 4
circ.
cross
section
23
MEASURING STRENGTH
• 3-point bend test to measure room T strength.
cross section
d
b
rect.
L/2
F
L/2
R
circ.
location of max tension
• Typ. values:
• Flexural strength:
fail
s fs  s m

1.5FmaxL
bd2
rect.

FmaxL
R3
sfs(MPa)
Si nitride
700-1000
Si carbide
550-860
Al oxide
275-550
glass (soda)
69
Material
E(GPa)
300
430
390
69
24
TENSILE RESPONSE: ELASTOMER
CASE
• Compare to responses of other polymers:
--brittle response (aligned, cross linked & networked case)
--plastic response (semi-crystalline case)
25
T AND STRAIN RATE:
THERMOPLASTICS
• Decreasing T...
--increases E
--increases TS
--decreases %EL
• Increasing
strain rate...
--same effects
as decreasing T.
26
TIME DEPENDENT DEFORMATION: CREEP
• Stress relaxation test:
--strain to eo and hold.
--observe decrease in
stress with time.
• Relaxation modulus:
s(t )
Er (t ) 
eo
• Data: Large drop in Er
for T > Tg.
(amorphous
polystyrene)
• Sample Tg(C) values:
PE (low Mw)
PE (high Mw)
PVC
PS
PC
-110
- 90
+ 87
+100
+150
27
HARDNESS
• Resistance to permanently indenting the surface.
• Large hardness means:
--resistance to plastic deformation or cracking in
compression.
--better wear properties.
28
DESIGN OR SAFETY FACTORS
• Design uncertainties mean we do not push the limit.
• Factor of safety, N
Often N is
between
sy
s working 
1.2 and 4
N
• Ex: 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.
s working 
220,000N


2

 d / 4 


sy
N
5
29
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
s
• 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!
2.5
s max
Stress Conc. Factor, Kt = s
o
2.0
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.
s tip
• Crack propagates when:
s 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:
s
units of K :
MPa m
or ksi in
K  s a
a
K  1.1s a
10
DESIGN AGAINST CRACK GROWTH
• Crack growth condition: K ≥ Kc
Ys 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  K c

a max  
 Ysdesign 

sdesign 
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...
sc 
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
sc
a max
A  sc
4 mm
a max
B
Answer:
• Reducing flaw size pays off!
sc B  168MPa
13
LOADING RATE
• Increased loading rate...
--increases sy 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 sm
• Key points: Fatigue...
--can cause part failure, even though smax < sc.
--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
 DK
dN
~ Ds
 a
increase in crack length per loading cycle
crack origin
• Failed rotating shaft
--crack grew even though
Kmax < Kc
--crack grows faster if
• Ds 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 s and T < 0.4Tm, failure stress decreases with:
increased maximum flaw size,
decreased T,
increased rate of loading.
-for cyclic s:
cycles to fail decreases as Ds increases.
-for higher T (T > 0.4Tm):
time to fail decreases as s or T increases.
26
Joint Replacement: Materials, Properties
and Implications
This diagrams shows seven locations
where total joint arthroplasties (TJAs)
are currently used to replace poorly
functioning joints.
The history of total hip
arthroplasty ins
particularly to biomaterials
science because it is one of
the best illustrations of
how an implant first used
over a century ago has
evolved into the highly
successful status it has,
primarily because of
advances in biomaterials.
Table of most common orthopedic biomaterials
Examples of the
three types of
bearing couples
used in modern
TJA. From top to
bottom: metal-onpolymer, ceramic0n-ceramic, and
metal-on-metal.
Mechanical properties of dominant orthopedic
biomaterials
Approximate weight percent of different metals within popular
orthopedic alloys
Electrochemical properties of implant metals (corrosion
resistance) in 0.1 M NaCl at pH 7.
Examples of new THA and TKA oxidized
zirconium components currently gaining
popularity because of enhanced mechanical and
biocompatibility properties.
Examples of currently used surface coatings on
stems of THA to enhance both short- and longterm fixation
Schematic of the interface of
a passivating alloy surface in
contact with a biological
environment
Modular junction taper connection of a
total hip arthroplasty showing corrosion
of the taper connections. Macrograph of
deposits of CrPO4 corrosion particle
products on the rim of a modular Co-Cr
femoral head.
A schematic showing examples of
the most common cytokines
produced by cells reacting to
implant debris acting through a
variety of pathways to negatively
affect bone turnover.
Cytokines are a category of signaling proteins
and glycoproteins that, like hormones and
neurotransmitters, are used extensively in
cellular communication. Cytokines are critical
to the development and functioning of both
the innate and adaptive immune response.
They are often secreted by immune cells that
have encountered a pathogen, thereby
activating and recruiting further immune cells
to increase the system's response to the
pathogen.
TEM images of (a) macrophage
containing phagocytized titanium
particles and (b) endothelial cell lining
with embedded titanium debris.
development of a granuloma emanating
from an unfilled screw hole.
Photomicrograph (5x) of a section
through an acetabular section of a
femoral stem retrieved at autopsy, 89
months after implantation. Note that the
periprosthetic cavity surrounded
development of a granuloma emanating
from an unfilled screw hole.
Approximate average concentrations (ng/ml or ppb) of metal in
human body fluids with and without TJA.
Concentrations of metal in body tissue of humans
with and without TJA
Polarized light micrograph (190x) of
paraaortic lymph node demonstrates the
abundance and morphology of birefringent
particles within macrophages. The large
filamentous particles were identified by IR
spectroscopy to be polyethylene.
Epithelioid granulomas (A) within the portal
tract of the liver (40x) and (B) within the
splenic parenchyma (15X) in a patient with a
failed Ti-alloy THA and symptomatic
hepatitis. (C) Backscattered SEM image of a
granuloma in the spleen (3000x)
demonstrating Ti-alloy particles.
A compilation of investigations showing the averaged percentages of metal
sensitivity among the general population for NI, Co and Cr, among patients
after receiving a metal containing implant, and among patient populations
with failed implants.
The LINK SB Charite III artificial disk showing the range of standard
sizes available. This design consists of an UHMWPE sliding core, which
articulates unconstrained between two highly polished metal endplates,
simulating the movement of the spine.