ti alloys as biomaterials - biotinet

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%

• extraordinarily high energy absorption

Schaeder et al. Science, 334 (2011) 962-965.

http://www.bbc.co.uk/news/technology-15788735




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.


AL Greer, Damage tolerance at a price, Nature Mater. 10 (2011) 88-89.

contour of

constant syKc



typical trade-off

between sy and Kc



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


―The mechanical


materials‖


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


―The mechanical


materials‖


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

containing bulk amorphous alloys, Acta Mater. 54 (2006) 349.

Uniaxial compression

plastic

brittle

CA Angell: Science 267 (1995) 1924.

gTTg TTd

dm

))/(

log( 10

Fragility

GP Johari: Philos. Mag. 86 (2006) 1567.

gTTg TTd

dm

))/(

log( 10Angell‘s ―fragility‖ of liquid:

plasticity

―strength‖ brittleness

―fragility‖

better

glass-forming

ability

The better the glass-forming ability, the more likely to be brittle!

Compilation of all relevant and available data on as-cast

(unannealed) metallic glasses (mostly, but not all BMGs)



or G/B

For plasticity, we want

high values of B/G

A Damage-Tolerant Glass MD Demetriou, ME Launey, G Garrett, JP Schramm, DC Hofmann,

WL Johnson, RO Ritchie: Nature Materials 10 (2011) 123-128.

Define: f =

(probability of shear activation event)/(probability of cavitation event)

Then derive: logf = (Tg/T)[(B/G) − 1]

Study the BMG Pd79Ag3.5P6Si9.5Ge2 (rods, critical diameter = 6 mm)

n= 0.42 plastic zone size = 6 mm

Comparison:

sy (MPa) Kc (MPa m1/2)

low-C steel < 500 > 200

silicates up to 3000 < 1

MGs in general 500−5000 1−100

Pd79Ag3.5P6Si9.5Ge2 1490 200

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



highest known

product of sy

and Kc



highest known

product of sy

and Kc

anisotropy?

M.F. Ashby & A.L. Greer: Scripta Materialia 54 (2006) 321.

(in Viewpoint Set on Mechanical Behavior of Metallic Glasses, edited by T.C. Hufnagel)

Fracture toughness and elastic limit for metals, alloys, ceramic,

glasses, polymers and metallic glasses. The contours show the

process-zone size d in mm. BMG foams may be attractive

because of small strut cross-sections.

J.H. Tregilgas, ―Amorphous titanium

aluminide hinge‖

Adv. Mater. Proc. 162 (Oct. 2004) 40.

MEMS Applications of Metallic Glasses

The Texas Instruments Digital

Light Processor (DLP) data

projector technology is based on

mirrors supported by amorphous

Ti-Al hinges. DLP devices with

>1.3 x 106 addressable mirrors

are in production, and the hinges

still show no fatigue failures after

1012 cycles.

plasticity

―strength‖ brittleness

―fragility‖

better

glass-forming

ability

The better the glass-forming ability, the more likely to be brittle!

Spray-coating of femural head

Matching of thermal expansion coefficients

Hydroxyapatite coatings

can be applied to Ti-

based components by

plasma spraying. As the

hot coating cools, it may

spall off:)

aTi ≈ 0.6 aHA

Alloying with Mn may be

useful:

Ti: a = 8.4 × 10–6 K–1

Mn: a = 22 × 10-6 K–1

(2) must be biocompatible

— not toxic

— not allergenic

— not carcinogenic

Metals in general are corroded in the body and can have adverse effects:

Ni, Cr, Co are allergenic

Ti, Nb, Ta are essentially inert.

(3) must be low-cost and easy to manufacture

— Ti parts can be made by forging and machining.

Ti-Based Metallic Glasses

— belong mainly in two families:

• early transition metal ‒ metalloid

for example Ti100‒xSix (x = 15‒20)

[A Inoue & T Masumoto, Sci. Rep. Res. Inst. Tohoku Univ. 28A (1980) 165]

• early transition metal ‒ late transition metal

for example Ti-Co

such transition metal systems are the basis of the most-studied BMGs

unfortunately, late transition metals (Co, Cr, Cu, Fe, Ni) tend to be

problematic!

AL Greer, ―Metallic Glasses‖ Science 267 (1995) 1947-1953.

S Vitta, AL Greer & RE Somekh, ―Rapid solidification of cobalt-titanium alloys

induced by nanosecond laser pulses‖ Mater. Sci. Eng. A179/A180 (1994) 243-248

Problem Elements

Sensitisation

About 10% of the general population have allergic reactions to:

Be, Co, Cr, Ni

Oxidation stress

Some metal ions, when not chelated, lead to an excess of oxidising

free radicals. Problem cases include: Co, Cr, Cu, V. In principle, Fe is

on this list, but the associated cytotoxicity is very low.

Carcinogenicity

Many mechanisms. Problem cases include: Be, Co, Cr

Cytotoxicity

Depends on corrosion rate: Al, Be, Cu, Ni

Acceptable Elements

Ti

Nb, Ta, Zr

Au, Pd, Pt

B, C, P, Si

Sc, Sn, Y

Fe

Base system for Ti-based glasses in BioTiNet: Ti-Zr-Si

From: Laura Martin, PhD Thesis, University of Cambridge 2012

Existing studies of Ti-based glassy alloys for biomedical applications:

Corrosion Resistance

Metallic glasses should be chemically uniform, and can contain high

concentrations of protective species (e.g. Cr). They can be highly

corrosion-resistant, but this is not guaranteed.

Other glass-forming systems

—that may be promising for non-degradable biomedical applications:

Zr-based

Fe-based?

Conclusions

Metallic glasses extend the range of properties obtainable with alloys.

Their relatively low Young‘s modulus is attractive for orthopaedics.

Optimization of multi-component compositions is likely to involve

compromises, in particular between glass-forming ability and mechanical

properties.

Metallic glasses are likely to have good strength, surface finish (&

patternability) wear resistance, corrosion resistance, formability.

Metallic glasses can be made into foams.

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)



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


All the data superposed, together with data on oxide glasses for

comparison. Overall, (m/B)crit = 0.41-0.43



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.



ti alloys as biomaterials - biotinet

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