BioTiNet Summer School: ‗Titanium in Medicine‘ Caldes d‘Estrach (Barcelona) Spain, 3‒7 June 2012 Ti alloys as biomaterials: ― focus on metallic glasses — BioTiNet: balancing reduced Young‘s modulus and resistance to deformation, to relieve problems with stress shielding in orthopaedic implants. A. L. Greer Dept. of Materials Science & Metallurgy University of Cambridge (with thanks to Laura Martin)
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BioTiNet Summer School: ‗Titanium in Medicine‘
Caldes d‘Estrach (Barcelona) Spain, 3‒7 June 2012
Ti alloys as biomaterials:
― focus on metallic glasses
— BioTiNet: balancing reduced Young‘s modulus and
resistance to deformation, to relieve problems with
stress shielding in orthopaedic implants.
A. L. Greer
Dept. of Materials Science & Metallurgy University of Cambridge (with thanks to Laura Martin)
A history of materials usage
Mapping materials properties
Progress in engineering materials since 1945
―Holes‖ in property space
— and a possible vector for materials development
Ultralight metallic microlattices
Material with 99.99% open volume
The solid (only 0.01%!) is designed on nm, mm and mm scales
Interconnected hollow tubes
with 100 nm wall thickness
Unprecedented mechanical properties for a metal:
• complete recovery from compression strain of >50%
AL Greer: Damage tolerance at a price, Nature Mater. 10 (2011) 88-89.
Photo
: M
axim
ilien E
. Launey
At a notch, cracks of several 100 mm are stable. The shear
bands are very finely spaced.
Pd79Ag3.5P6Si9.5Ge2 BMG
MD Demetriou et al., A damage-tolerant glass, Nature Mater. 10 (2011) 123-128.
MD Demetriou et al., A damage-tolerant glass, Nature Mater. 10 (2011) 123-128.
AL Greer, Damage tolerance at a price, Nature Mater. 10 (2011) 88-89.
contour of
constant syKc
MD Demetriou et al., A damage-tolerant glass, Nature Mater. 10 (2011) 123-128.
AL Greer, Damage tolerance at a price, Nature Mater. 10 (2011) 88-89.
typical trade-off
between sy and Kc
MD Demetriou et al., A damage-tolerant glass, Nature Mater. 10 (2011) 123-128.
AL Greer, Damage tolerance at a price, Nature Mater. 10 (2011) 88-89.
highest known
product of sy
and Kc
Some applications of synthetic materials in medicine
Structure and Properties of Bone
— a composite of ceramic crystals in a polymer matrix.
Dry bone:
• 70 wt% calcium phosphate, approximately hydroxyapatite
Ca10(PO4)6(OH)2
typical ceramic: linear elastic, stiff, brittle
• 30 wt% collagen (the most common protein in the body)
and other organics
elasticity is strongly non-linear:
In the body, bone also contains ~10 wt% water
cortical or compact bone
cancellous or spongy bone
Bone structure: hierarchy and anisotropy
Stress lines (tension and compression) in the
head of the human femur.
from D‘Arcy Thompson: On Growth and Form
Cancellous (or spongy) bone
much lower Young‘s modulus than cortical bone
good for graded modulus match to cartilage
Section through the head of a human femur
showing the trabeculae within the spongy
(cancellous) bone. The bony trabeculae
follow the major force lines.
UGK Wegst & MF Ashby
―The mechanical
efficiency of natural
materials‖
Philosophical Magazine
84 (2004) 2167-2181.
Elastic limit of
cortical bone
≈ 0.4% cortical
cancellous
called rutting, as a mating ritual to prove to females that they are the stronges t stag and
hence will produce the healthiest offspring. Antlers are shed and re-grown each year, and
so can be used to make furniture and artwork.
Stags fighting
UGK Wegst & MF Ashby
―The mechanical
efficiency of natural
materials‖
Philosophical Magazine
84 (2004) 2167-2181.
Impact toughness of
cortical bone
≈1.5 kJ m‒2
— compared to
~0.01 kJ m‒2
for monolithic HA
Hip-joint replacement
Replacement of the head of the femur: Materials requirements
1) must meet basic mechanical requirements
— needs to be strong and reliable
Of the possible material types:
• ceramics are generally too brittle
• polymers suffer badly from creep and fatigue
• metals are foreign in living systems, but:
— good combination of strength and toughness
— metals are almost always chosen.
(2) must be biocompatible
— not toxic
— not allergenic
— not carcinogenic
Metals in general are corroded in the body and can have adverse effects.
(3) must be low-cost and easy to manufacture
— Ti parts can be made by forging and machining.
Mapping materials properties
Cortical bone
Cortical bone
Mechanical properties of materials relevant for bone and bone replacement
closed-cell Al foam
open-cell Al foam
components made from foamed aluminium
shaped filters made from foamed nickel
Young's modulus of various synthetic
biomaterials as a function of porosity
Metallic Glasses
• metals and alloys are naturally crystalline
• pure metals cannot form glasses — their simple structure
crystallizes too easily on cooling the liquid
• liquid metals have a low viscosity, very similar to that of water
• alloying can stabilize the liquid, and aids glass
formation (―confusion principle‖)
• for a binary alloy such as Fe80B20 (atomic %), the critical cooling
rate for glass formation is
105 to 106 K s–1
Bulk Metallic Glasses
• multicomponent compositions aid glass formation
• the critical cooling rate is low (~1 K s–1)
• glasses can be formed in bulk
(maximum diameters mm up to a few cm)
Bulk metallic glasses ― at the cutting edge of metals research
AL Greer and E Ma,
MRS Bulletin 32 (2007) 611-615.
Elastic limit sy plotted against density r for 1507 metals, alloys, metal-matrix composites and metallic glasses. The contours show the specific strength sy/r.
Metallic glasses for structural applications
MF Ashby & AL Greer: Scripta Materialia 54 (2006) 321.
(in Viewpoint Set on Mechanical Behavior of Metallic Glasses, edited by TC Hufnagel)
Wear resistance of BMGs
AL Greer, KL Rutherford & IM Hutchings, ―Wear resistance of amorphous alloys
and related materials‖ Int. Mater. Rev. 47 (2002) 87-112.
SV Madge, DV Louzguine-Luzgin, JJ Lewandowski & AL Greer,―Toughness,
extrinsic effects and Poisson‘s ratio of bulk metallic glasses‖ Acta Mater, accepted
for publication.
J Schroers et al., Scripta Mater. (2007) 57, 341
Unachievable shapes for metals?
Hollow, thin, seamless, complex parts ―
[courtesy: Jan Schroers, Yale]
Surface Replication with BMGs
J. Schroers, Advanced Materials, 21 (2010)
from Materials Selection in Mechanical Design (2nd ed.)
M. F. Ashby, Butterworth-Heinemann, 1999
metallic glasses
— compared to metals
and alloys in general,
the glasses have high
strength s and low
stiffness E, that is,
unusually high elastic
strain —
s/E
UGK Wegst & MF Ashby
―The mechanical
efficiency of natural
materials‖
Philosophical Magazine
84 (2004) 2167-2181.
Elastic limit of
cortical bone
≈ 0.4%
2% for metallic
glasses
cortical
cancellous
Fracture toughness and Young’s modulus for metals, alloys,
ceramic, glasses, polymers and metallic glasses. The contours
show the impact toughness Gc in kJ m–2.
MF Ashby & AL Greer: Scripta Materialia 54 (2006) 321.
(in Viewpoint Set on Mechanical Behavior of Metallic Glasses, edited by TC Hufnagel)
The same data presented in terms of Poisson‘s ratio. The critical
value corresponding to (m/B)crit = 0.41-0.43 is ncrit = 0.31-0.32.
JJ Lewandowski, WH Wang & AL Greer, ―Intrinsic plasticity or brittleness of
metallic glasses‖, Philos. Mag. Lett. 85 (2005) 77.
Alloy design To avoid intrinsic brittleness and to have greater resistance to annealing-induced embrittlement — • we need to choose component elements with small m/B or, equivalently, high n (ideally n should tend towards 0.5, which is the value for liquids)
Au
Nb
Pd
Pt
Hf
Al
Cu
Zr
Ti
Ni
Ca
Co
Fe
Mg
Nd
La
Pr
Y
Tb
Gd
Ce
Be
m/B
0.12
0.22
0.24
0.27
0.27
0.35
0.35
0.39
0.42
0.43
0.44
0.45
0.48
0.49
0.50
0.52
0.52
0.54
0.57
0.58
0.61
1.02
n
0.44
0.40
0.39
0.38
0.37
0.34
0.34
0.33
0.32
0.31
0.31
0.30
0.29
0.29
0.28
0.28
0.28
0.26
0.26
0.26
0.25
0.03
plastic brittle
m/B
n
Compression tests on
Fe65Mo14C15B6 show improved
plasticity on doping with Er or Dy.
Use of doping to improve plasticity
XJ Guo, AG McDermott, SJ Poon & GJ Shiflet, Appl. Phys. Lett. 88 (2006) 211905.
Compression tests on
Fe65Mo14C15B6 show improved
plasticity on doping with Er or Dy.
Use of doping to improve plasticity
XJ. Guo, AG McDermott, SJ Poon & GJ Shiflet, Appl. Phys. Lett. 88 (2006) 211905.
Fe65–xMo14C15B6Erx (circles)
Fe65–xMo14C15B6Dyx (triangles)
The critical n is again ~0.32
S.W. Lee, M.Y. Huh, E. Fleury & J.C. Lee, Crystallization-induced plasticity of Cu-Zr
It is likely that Ti-based BMGs can be developed that are fully
biocompatible.
Fatigue resistance and compatibility with coatings remain to be
adequately tested.
• the plastic flow stress in shear is proportional to the elastic shear
modulus — thus the shear modulus is a measure of the difficulty of
plastic flow
• similarly the bulk modulus is a measure of the difficulty of cracking
• thus high values of the shear-to-bulk modulus ratio m/B should favour
brittleness and vice versa
• proposed by Pugh in 1954, and developed by others —
S.F. Pugh, Philos. Mag. 45 823 (1954).
A. Kelly, W.R. Tyson and A.H. Cottrell, Philos. Mag. 15 567 (1967).
J.R. Rice and R. Thomson, Philos. Mag. 29 73 (1974).
A.H. Cottrell, in Advances in Physical Metallurgy, edited by J.A. Charles and
G.C. Smith (Institute of Metals, London, 1990), pp. 181–187.
Metals: Plasticity or Brittleness?
• For polycrystalline metals there is a scale from ductile, low m/B (Ag,
Au, Cd, Cu) to brittle, high m/B (Be, Ir)
• for fcc metals (m/B)crit = 0.43-0.56 or 0.32-0.57
• for hcp metals (m/B)crit = 0.60-0.63
• for bcc metals (m/B)crit = 0.35-0.68
• thus critical modulus ratio (m/B)crit is not very well defined even for
one structure type
• (m/B)crit is affected by anisotropy
• most detailed theory for (m/B)crit concerns dislocation emission from a
crack tip
What will happen for metallic glasses?
— no anisotropy
— no dislocations
— no clearly different structures
With BMGs, good data are now available
Fracture data are presented in terms of the energy of fracture
G = K2/E(1 – n2)
where K is the toughness (stress intensity at fracture) and n is Poisson‘s ratio
Compilation of all relevant and available data on as-cast
(unannealed) metallic glasses (mostly, but not all BMGs)
JJ Lewandowski, WH Wang & AL Greer, ―Intrinsic plasticity or brittleness of
metallic glasses‖, Philos. Mag. Lett. 85 (2005) 77.
The inset shows the decrease in toughness as a function of annealing time for Vitreloy 1. The main figure shows a good correlation of embrittlement with the changing m/B. JJ Lewandowski, WH Wang & AL Greer, ―Intrinsic plasticity or brittleness of
metallic glasses‖, Philos. Mag. Lett. 85 (2005) 77.
All the data superposed, together with data on oxide glasses for
comparison. Overall, (m/B)crit = 0.41-0.43
JJ Lewandowski, WH Wang & AL Greer, ―Intrinsic plasticity or brittleness of
metallic glasses‖, Philos. Mag. Lett. 85 (2005) 77.
The same data presented in terms of Poisson‘s ratio. The critical
value corresponding to (m/B)crit = 0.41-0.43 is ncrit = 0.31-0.32.
JJ Lewandowski, WH Wang & AL Greer, ―Intrinsic plasticity or brittleness of
metallic glasses‖, Philos. Mag. Lett. 85 (2005) 77.