1. MASE 542/CHEM 442 BIOMATERIALS
Spring 2012
H. Funda Yagci Acar
Koç University
İstanbul

2. Metals

3. Metals Metallic Bond Crystalline Alloy: Mixtures Close packed
Unit cell
Alloy: Mixtures .
FCC Structure
HCP Structure

4. fig_01_03
density
fig_01_03

5. Metallic Crystal Structures
Reasons for dense packing:
Typically, only one element is present, so all atomic radii are the same.
Metallic bonding is not directional.
Nearest neighbor distances tend to be small in order to lower bond energy.
Electron cloud shields cores from each other

6. Crystal structure

7. Body Centered Cubic Structure (BCC)
Atoms touch each other along cube diagonals
ex: Cr, W, Fe (), Tantalum, Molybdenum
Coordination # = 8
2 atoms/unit cell: 1 center + 8 corners x 1/8
Adapted from Fig. 3.2, Callister & Rethwisch 8e.

8. Atomic Packing Factor: BCC3 a a 2
length = 4R =
Close-packed directions:
3 a
Volume of atoms/unit cell in volume of unit cell
APF = 4 3 p (
a/4 ) 2
atoms
unit cell
atom
volume a
APF = 0.68
Adapted from
Fig. 3.2(a), Callister & Rethwisch 8e.

9. Hexagonal Close-Packed Structure (HCP)
• ABAB... Stacking Sequence
• 3D Projection
• 2D Projection c a
A sites B
sites
Bottom layer
Middle layer
Top
layer
Atomic packing number
6 atoms/unit cell
• Coordination # = 12
APF = 0.74
ex: Cd, Mg, Ti, Zn
• c/a = 1.633
Adapted from Fig. 3.3(a),
Callister & Rethwisch 8e.

10. Theoretical Density, r Density =  = Cell Unit of Volume Total in
Atoms
Mass
Density =  =
VC NA
n A
 =
where n = number of atoms/unit cell
A = atomic weight
VC = Volume of unit cell = a3 for cubic
NA = Avogadro’s number
= x 1023 atoms/mol

11. Theoretical Density, r  = Ex: Cr (BCC) A = 52.00 g/mol R = 0.125 nm
n = 2 atoms/unit cell a R
a = 4R/ 3 = nm
 = a3
52.00 2
atoms
unit cell
mol g
volume
6.022 x 1023
theoretical
= 7.18 g/cm3
ractual
= 7.19 g/cm3
Adapted from
Fig. 3.2(a), Callister & Rethwisch 8e.

12. Densities of Material Classes
In general: r
metals r
ceramics r
polymers
>
>
Why?
Metals have...
• close-packing
(metallic bonding)
• often large atomic masses
Ceramics have...
• less dense packing
• often lighter elements
Composites have...
• intermediate values
Polymers have...
• low packing density
(often amorphous)
• lighter elements (C,H,O)

14. Crystals as Building Blocks
• Some engineering applications require single crystals:
-- diamond single
crystals for abrasives
(Courtesy Martin Deakins,
GE Superabrasives, Worthington, OH. Used with permission.)
• Properties of crystalline materials
often related to crystal structure.
-- Ex: Quartz fractures more easily along some crystal planes than others.

15. Single vs Polycrystals
E (diagonal) = 273 GPa
E (edge) = 125 GPa
• Single Crystals
-Properties vary with
direction: anisotropic.
Data from Table 3.3, Callister & Rethwisch 8e. (Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.)
-Example: the modulus
of elasticity (E) in BCC iron:
• Polycrystals
-Properties may/may not
vary with direction.
-If grains are randomly
oriented: isotropic.
(Epoly iron = 210 GPa)
-If grains are textured,
anisotropic.
200 mm
Adapted from Fig. 4.14(b), Callister & Rethwisch 8e.
(Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)

16. Polycrystals overall component properties are not directional.
Anisotropic
• Most engineering materials are polycrystals.
Adapted from Fig. K, color inset pages of Callister 5e.
(Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany)
1 mm
Isotropic
• Nb-Hf-W plate with an electron beam weld.
• Each "grain" is a single crystal.
• If grains are randomly oriented,
overall component properties are not directional.
• Grain sizes typically range from 1 nm to 2 cm
(i.e., from a few to millions of atomic layers).

17. Polymorphism
Two or more distinct crystal structures for the same material (allotropy/polymorphism)     titanium
  , -Ti
carbon
diamond, graphite
BCC
FCC
1538ºC
1394ºC
912ºC
-Fe
-Fe
-Fe
liquid
iron system

18. Tin: allotropic transformation
figun_03_p53a
Tin: allotropic transformation
Body-centered tetragonal
Dimond cubic
figun_03_p53a
Slow process
Volume increase 27%
Disintegration into coarse powder
Density decrease
7.3 to 5.77 g/cm3
1850 winter in russia.
Very cold winter.
Solders had white tin buttons
At cold weather they crumbelled
Tin disease
Callister: figun_03_p53b

19. Composition

20. Composition Metal/element – generally pure
Alloys – combination of different elements
Amalgams – alloys of metals in mercury

21. Metal Alloys
Impurity atoms are added intentionally to impart specific characteristics
Usually to increase mechanical strength and corrosion resistance

22. Ti alloys a b transformation temp depends on impurity!
V, Niobium, Molybdenum :decrease the temp (b- phase stabilizer)
Four types of alloys
Alpha: Al, tin ( superior creep, satisfactory stregth and thoughness
Beta: V, Mo (Highly forgeable, high fracture thoughness)
Alpha+beta (formable)
Near alpha
High temp reactivity
RT: inert to aq, marine, air environment

23. Callister: page 413

24. Metals High tensile, fatigue and yield strengths
load bearing implants
internal fixation devices used for orthopedic applications
dental implants
Low reactivity and good ductility
Good for stems of hip implant devices
Their properties depend on the processing method and purity of the metal
The selection of the material must be made appropriate to its intended use.
Metals

25. MECHANICAL PROPERTIES
Strength
Modulus
Thoughness
Ductility
....

26. Strength = Maximum load / Area
Strength: this is the maximum load that a material can withstand without breaking and is derived by dividing the maximum force by the cross sectional area of the material.
Strength = Maximum load / Area

27. Strength
Tensile strength is important for a material that is going to be stretched or under tension.
Fibers need good tensile strength.
Concrete is an example of a material with good compressional strength.
flexural strength: Strength upon bending
torsional strength: if it is strong when one tries to twist it.
impact strength. A sample has impact strength if it is strong when one hits it sharply and suddenly, as with a hammer.
Yield Strength - The stress a material can withstand without permanent deformation.

28. Strength Shear : Force parallel to the area
megapascals (MPa) OR gigapascals (GPa).
1 MPa = 100 N/cm2,
1 GPa = 100,000 N/cm2,
1 GPa = 1,000 MPa.
1 N/cm2 = 1.45 psi.

29. Modulus = Stress / Strain (N/m2 )
“stiffness or resistance to deformation” when exposed to stress
Modulus = Stress / Strain (N/m2 )
1GPa =103MPa=109N/m2
Modulus of elasticity (E: GPa)
(Young`s modulus)

30. What happens under stress?
Bonds stretcth (small changes in the interatomic distance)
Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal

31. Modulus of different materials
Due to different types of bonding

32. Young’s Moduli: Comparison
Graphite
Ceramics
Semicond
Metals
Alloys
Composites
/fibers
Polymers
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 00
1200
Tin
Cu alloys
Tungsten
<100>
<111>
Si carbide
Diamond
PTF E
HDP
LDPE PP
Polyester PS
PET C
FRE( fibers)
FRE( fibers)*
FRE(|| fibers)*
E(GPa)
Based on data in Table B.2,
Callister & Rethwisch 8e.
Composite data based on
reinforced epoxy with 60 vol%
of aligned
carbon (CFRE),
aramid (AFRE), or
glass (GFRE)
fibers.
109 Pa

33. Modulus of Metals

34. Elastic Deformation d F F Elastic means reversible! d bonds stretch
1. Initial
2. Small load F d
bonds
stretch
3. Unload
return to
initial F
Linear-
elastic
Elastic means reversible!
Non-Linear-
elastic d

35. Temp dependence of modulus

36. Plastic (Permanent) Deformation
• Simple tension test:
Elastic+Plastic
at larger stress
engineering stress, s
Elastic
initially
permanent (plastic)
after load is removed ep
plastic strain
engineering strain, e
Adapted from Fig. 6.10(a),
Callister & Rethwisch 8e.
(at lower temperatures, i.e. T < Tmelt/3)

37. Plastic deformation
stress is not proportional to strain and non-recovarable!
Perminent deformation
Atomic perspective
Bonds break and form again with new neighbours
CRYSTALLINE: slip
NONCRYSTALLINE: viscous flow

38. Yield Strength, sy y = yield strength sy tensile stress, s
• Stress at which noticeable plastic deformation has
occurred.
when ep = 0.002
tensile stress, s
engineering strain, e sy ep
= 0.002
y = yield strength
Note: for 2 inch sample
 = = z/z
 z = in
Adapted from Fig. 6.10(a),
Callister & Rethwisch 8e.

39. Yield strength : resistance to plastic deformation
35MPa: low strength Al
Over 1400MPa for high stregth-steel
yielding
Yielding= where plastic deformation starts: important to know for function
P: onset of plastic deformation in microscopic level
Typical metal

40. Yield Strength : Comparison
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Yield strength, s y
(MPa)
PVC
Hard to measure ,
since in tension, fracture usually occurs before yield.
Nylon 6,6
LDPE 70 20 40 60 50
100 10 30
200
300
400
500
600
700
1000
2000
Tin (pure) Al
(6061) a ag Cu
(71500) hr Ta
(pure) Ti
Steel
(1020) cd
(4140) qt
(5Al-2.5Sn) W
Mo (pure) cw
Hard to measure,
in ceramic matrix and epoxy matrix composites, since
in tension, fracture usually occurs before yield. H
DPE PP
humid
dry PC
PET
Room temperature values
Based on data in Table B.4,
Callister & Rethwisch 8e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered

41. Tensile strength aligned and about to break. 50MPa: Al
3000 MPa : high stregth-steel
Tensile strength
Plastic
Max plastic deformation
fracture
Elastic
After M: it is useless
necking
• Metals: occurs when noticeable necking starts.
• Polymers: occurs when polymer backbone chains are
aligned and about to break.
M: Max stress sustained under tension
If you apply this much of stress it will fracture

42. Tensile Strength: Comparison
Si crystal
<100>
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Tensile
strength, TS
(MPa)
PVC
Nylon 6,6 10
100
200
300
1000 Al
(6061) a ag Cu
(71500) hr Ta
(pure) Ti
Steel
(1020)
(4140) qt
(5Al-2.5Sn) W cw L
DPE PP PC
PET 20 30 40
2000
3000
5000
Graphite
Al oxide
Concrete
Diamond
Glass-soda
Si nitride H
wood
( fiber)
wood(|| fiber) 1
GFRE
(|| fiber)
( fiber) C
FRE A
FRE( fiber)
E-glass fib
Aramid
fib
Room temperature values
Based on data in Table B.4,
Callister & Rethwisch 8e.
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.

43. brass

44. Ductility
Degree of plastic deformation that has been sustained at fracture
the ability of a material to deform before breaking
Expressed quantitatively as % elongation or % area reduction
Little or no plastic deformation: Brittle: 5% or less fracture strain

45. Ductility 100 x A RA % - = Engineering tensile strain, e E ngineering
• Plastic tensile strain at failure:
x 100 L EL % o f - =
Adapted from Fig. 6.13, Callister & Rethwisch 8e.
Engineering tensile strain, e E
ngineering
tensile
stress, s
smaller %EL
larger %EL Lf Ao Af Lo
• Another ductility measure:
100 x A RA % o f - =

46. fig_06_14
Ductility usally increases with temperature
IRON
fig_06_14

48. Resilience
Capacity to absorb Energy when it is deformed elastically and then, upon unloading, to have this energy recovered.
Energy/unit volume (J/m3)
If resilient:
High yield strength
Low moduli of elasticity

49. fig_06_15 Thoughness Resistance to fracture when there is a crack
Ability to absorb energy and plastically deform before fracture
Energy/unit3

50. Toughness Engineering tensile strain, e E ngineering tensile stress, s
• Energy to break a unit volume of material
• Approximate by the area under the stress-strain curve.
very small toughness
(unreinforced polymers)
Engineering tensile strain, e E
ngineering
tensile
stress, s
small toughness (ceramics)
large toughness (metals)
Adapted from Fig. 6.13, Callister & Rethwisch 8e.
Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy

51. Strength vs Toughness
strength :how much force is needed to break a sample
toughness : how much energy is needed to break a sample.
Blue: takes lots of force to break it and it breaks
Red: deformation cause E dissipation. Elongates and takes more E before breaking
BRITTLE

52. Modulus
“stiffness or resistance to deformation” when exposed to stress
Modulus = Stress / Strain (N/m2 ).
fibers
plastics
elastomers
1GPa =103MPa=109N/m2

53. Elongation
ultimate elongation: amount you can stretch the sample before it breaks
elastic elongation : percent elongation you can reach without permanently deforming your sample (snap back to its original length once you release the stress on it. )
Elastomers: 500 to 1000 % elongation

54. Elongation
ultimate elongation: amount you can stretch the sample before it breaks
elastic elongation : percent elongation you can reach without permanently deforming your sample (snap back to its original length once you release the stress on it. )
Elastomers: 500 to 1000 % elongation

55. Others
Fatigue: A material failing at a lower stress value than the ultimate strength value due cyclic loading
Hardness: the resistance of a material to surface abrasion.

56. fig_01_03
fig_01_03

57. fig_01_04
fig_01_04

58. fig_01_05
fig_01_05

59. fig_01_06
fig_01_06

60. fig_01_07
fig_01_07

62. Summary • 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).
• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches sy.
• Toughness: The energy needed to break a unit
volume of material.
• Ductility: The plastic strain at failure.