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?. - PowerPoint PPT Presentation
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? 1 • Toughness and ductility: What are they and how do we measure them? MECHANICAL PROPERTIES • Ceramic Materials: What special provisions/tests are made for ceramic materials?
Transcript
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?
1
• Toughness and ductility: What are they and how do we measure them?
MECHANICAL PROPERTIES
• Ceramic Materials: What special provisions/tests aremade for ceramic materials?
F
bonds stretch
return to initial
2
1. Initial 2. Small load 3. Unload
Elastic means reversible!
F
Linear- elastic
Non-Linear-elastic
ELASTIC DEFORMATION
3
1. Initial 2. Small load 3. Unload
Plastic means permanent!
F
linear elastic
linear elastic
plastic
planes still sheared
F
elastic + plastic
bonds stretch & planes shear
plastic
PLASTIC DEFORMATION (METALS)
4
• Tensile stress, : • Shear stress, :
Area, A
Ft
Ft
FtAo
original area before loading
Area, A
Ft
Ft
Fs
F
F
Fs
FsAo
Stress has units:N/m2 or lb/in2
ENGINEERING STRESS
8
• Tensile strain: • Lateral strain:
• Shear strain:/2
/2
/2 -
/2
/2
/2
L/2L/2
Lowo
Lo
L L
wo
= tan Strain is alwaysdimensionless.
ENGINEERING STRAIN
• Typical tensile specimen
9
• Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts.
gauge length
(portion of sample with reduced cross section)=
• Typical tensile test machine
load cell
extensometerspecimen
moving cross head
STRESS-STRAIN TESTING
• Modulus of Elasticity, E: (also known as Young's modulus)
10
• Hooke's Law:
= E • Poisson's ratio, :
metals: ~ 0.33 ceramics: ~0.25 polymers: ~0.40
L
L
1-
F
Fsimple tension test
Linear- elastic
1E
Units:E: [GPa] or [psi]: dimensionless
LINEAR ELASTIC PROPERTIES
• Elastic Shear modulus, G:
12
1G
= G
• Elastic Bulk modulus, K:
P= -KVVo
P
V
1-K Vo
• Special relations for isotropic materials:
P
P P
M
M
G
E2(1 )
K E
3(1 2)
simpletorsiontest
pressuretest: Init.vol =Vo. Vol chg. = V
OTHER ELASTIC PROPERTIES
130.2
8
0.6
1
Magnesium,Aluminum
Platinum
Silver, Gold
Tantalum
Zinc, Ti
Steel, NiMolybdenum
Graphite
Si crystal
Glass -soda
Concrete
Si nitrideAl oxide
PC
Wood( grain)
AFRE( fibers)*
CFRE *
GFRE*
Glass fibers only
Carbon fibers only
Aramid fibers only
Epoxy only
0.4
0.8
2
46
10
20
406080
100
200
600800
10001200
400
Tin
Cu alloys
Tungsten
<100>
<111>
Si carbide
Diamond
PTF E
HDPE
LDPE
PP
Polyester
PSPET
CFRE( fibers)*
GFRE( fibers)*
GFRE(|| fibers)*
AFRE(|| fibers)*
CFRE(|| fibers)*
MetalsAlloys
GraphiteCeramicsSemicond
PolymersComposites
/fibers
E(GPa)
Eceramics > Emetals >> Epolymers
109 Pa
YOUNG’S MODULI: COMPARISON
15
• Simple tension test:
(at lower temperatures, T < Tmelt/3)
tensile stress,
engineering strain,
Elastic initially
Elastic+Plastic at larger stress
permanent (plastic) after load is removed
pplastic strain
PLASTIC (PERMANENT) DEFORMATION
16
• Stress at which noticeable plastic deformation has occurred.
when p = 0.002 tensile stress,
engineering strain,
y
p = 0.002
YIELD STRENGTH, y
17
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibersPolymers
Yield
str
en
gth
, y (M
Pa)
PVC
Ha
rd t
o m
ea
sure,
si
nce in
ten
sion
, fr
actu
re u
sually
occu
rs b
efo
re y
ield
.
Nylon 6,6
LDPE
70
20
40
6050
100
10
30
200
300
400500600700
1000
2000
Tin (pure)
Al (6061)a
Al (6061)ag
Cu (71500)hrTa (pure)Ti (pure)aSteel (1020)hr
Steel (1020)cdSteel (4140)a
Steel (4140)qt
Ti (5Al-2.5Sn)aW (pure)
Mo (pure)Cu (71500)cw
Ha
rd t
o m
ea
sure
, in
cera
mic
matr
ix a
nd
ep
oxy m
atr
ix c
om
posi
tes,
sin
ce
in
ten
sion
, fr
actu
re u
sually
occu
rs b
efo
re y
ield
.HDPEPP
humid
dryPC
PET
¨
Room T values
y(ceramics) >>y(metals) >> y(polymers)
Based on data in Table B4,Callister 6e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & tempered
YIELD STRENGTH: COMPARISON
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• 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.
TENSILE STRENGTH, TS
strain
en
gin
eeri
ng
s
tress
TS
Typical response of a metal
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Room T valuesSi crystal
<100>
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibersPolymers
Ten
sile
str
en
gth
, TS
(MPa
)
PVC
Nylon 6,6
10
100
200300
1000
Al (6061)a
Al (6061)agCu (71500)hr
Ta (pure)Ti (pure)aSteel (1020)
Steel (4140)a
Steel (4140)qt
Ti (5Al-2.5Sn)aW (pure)
Cu (71500)cw
LDPE
PP
PC PET
20
3040
20003000
5000
Graphite
Al oxide
Concrete
Diamond
Glass-soda
Si nitride
HDPE
wood( fiber)
wood(|| fiber)
1
GFRE(|| fiber)
GFRE( fiber)
CFRE(|| fiber)
CFRE( fiber)
AFRE(|| fiber)
AFRE( fiber)
E-glass fib
C fibersAramid fib TS(ceram)
~TS(met)
~ TS(comp) >> TS(poly)
Based on data in Table B4,Callister 6e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & temperedAFRE, GFRE, & CFRE =aramid, glass, & carbonfiber-reinforced epoxycomposites, with 60 vol%fibers.
TENSILE STRENGTH: COMPARISON
• Plastic tensile strain at failure:
20
Engineering tensile strain,
Engineering tensile stress,
smaller %EL (brittle if %EL<5%)
larger %EL (ductile if %EL>5%)
• Another ductility measure: %AR
Ao A fAo
x100
• Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck.
Lo LfAo Af
%EL
L f LoLo
x100
Adapted from Fig. 6.13, Callister 6e.
DUCTILITY, %EL
• Energy to break a unit volume of material• Approximate by the area under the stress-strain curve.
21
smaller toughness- unreinforced polymers
Engineering tensile strain,
Engineering tensile stress,
smaller toughness (ceramics)
larger toughness (metals, PMCs)
TOUGHNESS
• An increase in y due to plastic deformation.
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• Curve fit to the stress-strain response:
large hardening
small hardeningunlo
ad
relo
ad
y 0
y 1
T C T n“true” stress (F/A) “true” strain: ln(L/Lo)
hardening exponent: n=0.15 (some steels) to n=0.5 (some copper)
HARDENING
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• Room T behavior is usually elastic, with brittle failure.• 3-Point Bend Testing often used. --tensile tests are difficult for brittle materials.
FL/2 L/2
= midpoint deflection
cross section
R
b
d
rect. circ.
• Determine elastic modulus according to:
E
F
L3
4bd3
F
L3
12R4
rect. cross
section
circ. cross
section
Fx
linear-elastic behavior
F
slope =
MEASURING ELASTIC MODULUS
24
• 3-point bend test to measure room T strength.F
L/2 L/2cross section
R
b
d
rect. circ.
location of max tension
• Flexural strength:
rect. fs m
fail 1.5FmaxL
bd2
FmaxL
R3
xF
Fmax
max
• Typ. values:Material fs(MPa) E(GPa)
Si nitrideSi carbideAl oxideglass (soda)
700-1000550-860275-550
69
30043039069
MEASURING STRENGTH
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• Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case)
TENSILE RESPONSE: ELASTOMER CASE
initial: amorphous chains are kinked, heavily cross-linked.
final: chains are straight,
still cross-linked
0
20
40
60
0 2 4 6
(MPa)
8
x
x
x
elastomer
plastic failure
brittle failure
Deformation is reversible!
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• Decreasing T... --increases E --increases TS --decreases %EL
• Increasing strain rate... --same effects as decreasing T.
20
40
60
80
00 0.1 0.2 0.3
4°C
20°C
40°C
60°Cto 1.3
(MPa)
Data for the semicrystalline polymer: PMMA (Plexiglas)
T AND STRAIN RATE: THERMOPLASTICS
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• Stress relaxation test:
Er(t)
(t)o
--strain to and hold.--observe decrease in stress with time.
• Relaxation modulus:
• Data: Large drop in Er
for T > Tg.(amorphouspolystyrene)
• Sample Tg(C) values:PE (low Mw)
PE (high Mw)PVCPSPC
-110- 90+ 87+100+150
103
101
10-1
10-3
105
60 100 140 180
rigid solid (small relax)
viscous liquid (large relax)
transition region
T(°C)Tg
Er(10s) in MPa
TIME DEPENDENT DEFORMATION: CREEP
time
strain
tensile test
o
t( )
• Resistance to permanently indenting the surface.• Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties.
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e.g., 10mm sphere
apply known force (1 to 1000g)
measure size of indent after removing load
dDSmaller indents mean larger hardness.
increasing hardness
most plastics
brasses Al alloys
easy to machine steels file hard
cutting tools
nitrided steels diamond
HARDNESS
• Design uncertainties mean we do not push the limit.• Factor of safety, N
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working
y
N
Often N isbetween1.2 and 4
• 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.
1045 plain carbon steel: y=310MPa TS=565MPa
F = 220,000N
d
Lo working
y
N
220,000N
d2 /4
5
DESIGN OR SAFETY FACTORS
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?
1
• How do loading rate, loading history, and temperature affect the failure stress?
• 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!
IDEAL VS REAL MATERIALS
7
• Elliptical hole in a plate:
• Stress distrib. in front of a hole:
• Stress conc. factor:
BAD! Kt>>3NOT SO BAD
Kt=3
max
t
2o
a 1
t
o
2a
Kt max /o
• Large Kt promotes failure:
FLAWS ARE STRESS CONCENTRATORS!
8
• Avoid sharp corners!
r/h
sharper fillet radius
increasing w/h
0 0.5 1.01.0
1.5
2.0
2.5
Stress Conc. Factor, Ktmaxo
=
ENGINEERING FRACTURE DESIGN
r , fillet
radius
w
h
o
max
• t at a cracktip is verysmall!
9
• Result: crack tip stress is very large.
• Crack propagates when: the tip stress is large enough to make: distance, x,
from crack tip
tip K2x
tip
increasing K
K ≥ Kc
WHEN DOES A CRACK PROPAGATE?
10
• Condition for crack propagation:
• Values of K for some standard loads & geometries:
2a2a
aa
K a K 1.1 a
K ≥ KcStress Intensity Factor:--Depends on load & geometry.
Fracture Toughness:--Depends on the material, temperature, environment, & rate of loading.
• 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
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-on-polymer, ceramic-0n-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.
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.
Approximate weight percent of different metals within popular orthopedic alloys
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 long-term 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.
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.
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.
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.
