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The relationship between cement fatigue damage and implant surface finish in proximal femoral prostheses A. B. Lennona, B. A. O. McCormackb, and P. J. Prendergasta,* a Centre for Bioengineering, Department of Mechanical Engineering, Trinity College,

Dublin, Ireland. b School of Engineering, Institute of Technology, Sligo, Ballinode, Co. Sligo, Ireland.

First submitted February, 2003 Revised version, June 2003. *Corresponding Author Patrick J. Prendergast, Ph.D. Centre for Bioengineering Department of Mechanical Engineering, Trinity College, Dublin, Ireland Tel: +353 (0)1 608 1383 Fax: +353 (0)1 679 5554 E-mail: pprender@tcd.ie www.biomechanics.ie

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Abstract

The majority of cemented femoral hip replacements fail as a consequence of

loosening. One design feature that may affect loosening rates is implant surface finish.

To determine whether or not surface finish affects fatigue damage accumulation in a

bone cement mantle, we developed an experimental model of the implanted proximal

femur that allows visualization of damage growth in the cement layer. Five matt

surface and five polished surface stems were tested. Pre-load damage and damage

after two million cycles was measured. Levels of pre-load (shrinkage) damage were

the same for both matt and polished stems; furthermore damage for matt vs. polished

stems was not significantly different after two million cycles. This was due to the

large variability in damage accumulation rates. Finite element analysis showed that

the stress is higher for the polished (assumed debonded) stem, and therefore we must

conclude that either the magnitude of the stress increase is not enough to appreciably

increase the damage accumulation rate or, alternatively, the polished stem does not

debond immediately from the cement. Significantly (p=0.05) more damage was

initiated in the lateral cement compared to the medial cement for both kinds of surface

finish. It was concluded that, despite the higher cement stresses with debonded stems,

polished prostheses do not provoke the damage accumulation failure scenario.

Keywords: Bone cement, hip replacement, Exeter prosthesis, porosity, damage

accumulation, arthroplasty

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Nomenclature σi ith principal stress component

σi max maximum of ith principal stress around a pore

σ max maximum stress around a pore

ν Poisson’s ratio

A, B, C constants used in the expressions for evaluating stress around a pore

FI interface failure index

St interface tensile strength

Sc interface compressive strength

Ss interface shear strength

σ interface normal stress

τ interface shear stress

1

1 Introduction

The success or otherwise of a total hip replacement operation is influenced by the

surgeon’s choice of hip prosthesis1. One design feature that differs considerably between

prostheses is surface finish2,3,4. Ling4 observed that a polished surface of a particular

geometry (i.e., the Exeter prosthesis) subsided within the cement mantle. Therefore,

subsidence of polished implants allows “self-tightening”5; this phenomenon is now taken

to be the basis of how implants with polished surfaces can achieve greater longevity

compared to implants with a matt surface. Huiskes et al.6 have proposed that polished

hip prosthesis stems may be termed “force-closed designs” because they achieve stability

when the load applied is balanced by the frictional force on the debonded stem, and that

matt surface prostheses may be termed “shape-closed designs” because they aim to

remain bonded with the cement mantle.

It is not a simple matter to say what event begins the loosening process of an

orthopaedic implant prosthesis. If debonding of the stem/cement interface begins the

process then the force-closed (polished) designs should commence the loosening process

more rapidly than shape-closed (matt) designs and it would follow that polished stems

should fail faster – however this does not accord with clinical findings. For example,

follow-up studies reported by the Swedish hip register1 show that the Exeter polished

stem outperforms the Exeter Matt as well as many other matt stems. The retrievals of

Jasty et al.7 of 16 specimens found that some debonding was present in every case but

only one case showed radiographic loosening. Similarly, Fornasier and Cameron8 found

all five stems of an autopsy retrieval study to be debonded at the cement/bone interface

but none to be clinically loose. Therefore, it would seem that mechanical loosening by

damage accumulation is not provoked by debonding. In fact, the evidence of the superior

2

performance of the Exeter polished to the Exeter matt prosthesis points to the opposite

conclusion9. Investigations using both physical and numerical models led Verdonschot

and Huiskes10 to conclude that increased roughness for straight-tapered stem designs

could reduce subsidence but would inevitably lead to increased cement damage and wear.

The issue of subsidence and surface finish was again addressed by Speirs et al.11 who

demonstrated that a matt stem could exhibit greater cyclic motion than a polished stem in

spite of lower overall migration. However, their matt and polished stems had different

geometries so the effect of surface finish alone could not be separated from other factors.

In this paper, we aim to find out whether or not a matt stem (i.e. one that tends to

stay bonded) reduces damage accumulation in the cement mantle relative to polished

stems. Since computational approaches have been tried before, it was decided to take an

experimental approach by using a physical model of the implanted proximal femur. The

physical model is a development of the one used by McCormack and Prendergast12 which

allows exposure of the cement so that quantitative measurements of damage

accumulation can be made.

2 Methods

The physical model of the femoral-side of T.H.R.

The physical model consists of a curved implant fixated into the space formed between two

aluminium ‘covers’ (side plates). The resulting rectangular structure has a second moment of area

of 19,026 mm4 at the mid section of the stem, which compares to a value of 25,591 mm4

estimated from cross sectional data of Noble et al. 13 for the isthmus of the femur. The inside of

the covers are layered with cancellous bone strips; cancellous bone margins have been predicted

3

to affect prosthesis subsidence rates14. These were formed from bovine rib bone, cut and pressed

to conform to the curved inside walls of the aluminium, and were fixed using epoxy resin once

they had conformed. ‘Windows’ in the side allowed direct observation of microdamage

accumulation in the cement. Physiological features include interdigitated cement-bone interfaces

(achieved due to the cancellous bone strips) and a trochanteric process enabling the attachment of

an abductor load through a lever (Fig. 1a). Polyethylene inserts were used to prevent cement

escaping during preparation and to keep the cement surface continuous with the exposed stem and

bone surfaces. This also allowed pressure to build up in the specimen ensuring cement

interdigitation with the cancellous bone strips. Simplex Rapid cement was hand mixed for

approximately 60 s at 1 beat/s and then introduced into the cavity. This cement has the same

chemical composition as Simplex P without radio-opaque filler or antibiotics to give a translucent

cement that is suitable for damage visualisation by light transmission. Cement flowed around the

stem and ~5 mm beneath the tip where it was occluded by a plug. The specimen was allowed to

cure for 24 h. Specimens were stored for at least 1 week after preparation. Five polished and five

matt surface stems, i.e. 10 stems in total, were tested (Fig. 1b). The surface fabrication of the

stems was: (i) grit blasted, with mean Ra = 2.12 µm and (ii) polished, with mean Ra = 0.04 µm.

The surface finish was measured using a white light interferometer.

Crack measurement procedure

Dye penetrant was applied to the cement layers of each specimen before testing. An optical

comparator with a ×20 lens was used to project a magnified image of the cement surface onto a

screen. All observed cracks were traced onto acetate transparencies; these had markings placed on

them to allow referral to the comparator measurement system. If a crack was seen to extend

below the surface the focus was changed to assess the full projected length of the crack. The

transparencies were scanned and thresholded to remove any background greyscale from the

4

scanning operation. Image analysis was used to calculate the position, length, and slope of each

crack for each physical model specimen.

2.3 Fatigue testing

Specimens were clamped in 12° adduction and a load was applied to the lever. The load

applied produced a joint reaction force of 2.9 kN through the implant head-centre at 20°

to the long axis of the stem and an abductor load of 1.6 kN at 15° to vertical (Fig. 1a). The

joint load corresponds to 4.2 BW, assuming a 70 kg body mass. The abductor load (55%

of joint load) is similar to that used by Burke et al.15 in a rig designed to simulate single

leg stance. Specimens were tested at 5 Hz for 2×106 cycles in air at room temperature;

higher frequencies of loading were not used to avoid the possibility of cement heating. In

addition, cyclic actuator displacements were recorded.

2.4 Finite element stress analysis

Only half the specimen was modelled because it has mirror symmetry about the frontal

plane (Fig. 1c). Eight-node hexahedral finite elements were used (ANSYS type

SOLID45). Nodes corresponding to the clamped surfaces of the specimen (as shown in

the loading schematic, Fig. 1b) were restrained normal to each clamped surface. Linear

elastic material properties were used (Table 1). Loads were applied to the centres of the

head and muscle attachment, which were attached to the mesh using truss elements

(ANSYS type LINK8). Two interfacial conditions were simulated:

(i) a bonded interface modelled by coupling degrees of freedom for coincident

nodes and

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(ii) debonding with a low coefficient of friction (µ = 0.25) modelled using

surface-surface contact elements (ANSYS types CONTA173 and

TARGE170).

To investigate the possible effect of porosity on stress, an approximation for the

maximum stress occurring around a pore was made. The analytical solution for stress at

the pole and equator of a pore due to a remote uniaxial stress16 can be superposed to give

the stress components at the pole and equator with respect to each principal stress of a

multiaxial stress state. The maximum of these superposed stresses can then be found

according to Eqn. 1:

�������

�

�

�������

�

�

��

���

�

��

���

�

��

���

�

321

3213max

321

3212max

321

3211max

max

Max =

Max =

Max =

Max =

+ Bσ + AσCσ + Bσ + CσAσ + Aσ + BσCσ + Cσ + BσAσ + Aσ + CσBσ + Cσ + AσBσ

σ

σ

σ

σ , (1)

where

( )( ) ( ) ( ) ,

572315,

5721527,

572153

ν-ν- = C

ν-ν-= B

ν-ν+-= A

and ν is Poisson's ratio. This was done for the centroid of every cement finite element in

order that regions that were more susceptible to damage from pores could be identified.

To assess the likelihood of debonding, a failure index was calculated at the

cement-metal interface using a Hoffman criterion17 with constants taken from

Verdonschot and Huiskes18,

22sct

2

ct

1111 τσσSSSSS

FI +���

����

�−+= (2)

6

where σ and τ are interface normal and shear stress respectively, St = 8 MPa is the tensile

strength of the interface, Sc = 70 MPa is the compressive strength, and Ss = 6 MPa is the

shear strength. Higher positive values imply greater tendency for failure and failure is

assumed to occur at FI = 1.

3 Results

Examination of the specimens before loading identified pre-load cracks in both medial

and lateral cement layers of both matt and polished stems, see Fig. 2. If damage is

quantified as the sum-of-crack-lengths (i.e., �=

n

ia

1i where ia is the length of the ith crack

and there are n cracks) then, as expected, there is no significant difference in the amount

of pre-load (shrinkage) damage for the matt versus polished stems. The polished stems

tended to have more damage than the matt stems after 2 m cycles of loading, see Fig. 2

and Table 2, but this was not statistically significant.

Some considerable variation was found in both quantity of damage (Table 2) and

spatial distribution of damage (Fig. 2). Accumulation of damage in the lateral cement was

higher in the polished specimens compared with their matt counterparts (p = 0.05, Table

2). This can be explained by noting that debonding raised the tensile stress level and

caused a significant change in the stress transfer pattern, with relief of stress in the distal-

lateral and mid-medial regions and elevation of the stress in the mid-lateral, proximo-

lateral, and disto-medial regions (Fig. 3). Inclusion of porosity according to Eqn. (1)

raised the stresses to failure levels for both bonded and debonded stems over much larger

regions (Fig. 3). Calculation of volumes of cement stressed to different tensile stress

ranges illustrates, quantitatively, how debonding influences the stress distribution in the

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cement layers (Fig. 4) — only a small region on the lateral side of the bonded model

experienced stress above 3 MPa while both lateral and medial sides of the debonded

model had a relatively large proportion of the cement volume raised to higher stresses.

Specimens with high amounts of pre-load (shrinkage) damage had highest

accumulated damage after two million cycles (Fig. 5). However, one of the specimens for

both the matt and polished groups still did not fit the observed trend and a good

correlation could only be achieved by excluding one specimen from each group, see Fig.

5. We propose that an explanation for this might be that the polished stem outlier (P3)

had not debonded and that the matt stem outlier (M5) had debonded.

Cyclic actuator displacement (or “inducible displacement”) was of a similar

magnitude for both matt and polished stems (Fig. 6). A regression analysis was

performed to determine if inducible displacement was correlated with total damage. It

was found that much of the increase in the measured inducible displacement could be

attributed to an increase in the total damage present (Fig. 6). In contrast to this, a similar

analysis for the displacement under peak or minimum load (i.e., migration) showed poor

correlation with damage (R2=0.11 and R2=0.19, respectively).

4 Discussion

This study attempted to quantitatively assess the effect of implant surface finish on

cement damage accumulation. There were several limitations in the experimental

approach. The main one was that there are no hoop stresses since a layered cement

mantle, and not an annular one, was formed; hoop stresses are known to be significant in

supporting polished prostheses19. This simplification of the real in vivo structure was

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necessary to facilitate visualization and counting of the microcracks. Other limitations of

the model were

(i) Only cracks that intersect the surface can be stained and therefore cracks

wholly within the mantle were not counted. This leads to an underestimate of

the number of cracks. Furthermore, the measurement is based on an

orthogonal projection of each crack and this will cause an underestimation of

crack length for those cracks which have their longest axis at an angle to the

viewing plane.

(ii) Blood and fat inclusions have been shown to reduce properties of both the

cement-metal interface as well as the bulk cement itself20. Damage

accumulation could therefore be higher for in vivo reconstructions.

(iii) Only an abductor muscle load was included in the model. In support of this

simplification, a recent study has shown that inclusion of more muscles does

not greatly affect cement stresses during walking21. Also stumbling loads are

not included and therefore damage accumulation rates measured are likely to

be conservative. A further simplification with respect to loading is that

frictional torques generated at the head are neglected; a complex mechanical

system such as that recently published by Lui et al.22 would be required to

implement this.

(iv) The solution for the stress in a porous cement assumes an isolated pore,

without any nearby boundaries or neighbouring pores, and a remotely applied

stress. However, the stress raising effect of the pore is very localised (for a

uniaxial case the stress drops back to within 5% of the remote value at twice

9

the radius from the pore centre16), so we believe this is an acceptable

simplification.

(v) To more accurately test a force-closed concept for the polished stems, it

would be better to remove cement distal to the stem tip. However, the intent of

the study was to keep as many factors as possible common between the two

groups. Future work could investigate this issue more fully.

(vi) Due to the load controlled nature of the test, creep of the cement would

therefore be expected in the experimental model; however viscoelasticity was

not included in the finite element analysis.

Despite these limitations with respect to the physical model, it does succeed in allowing a

view of damage accumulation in the cement mantle. Visualization of crack growth would

not be possible with anything other than a layered system, although more complex

methods using acoustic emission could have been used; if used in combination with some

form of internal strain measurement, such as that developed by Cristofolini and

Viceconti23, a system for monitoring both damage accumulation and strain redistribution

due to debonding could be envisaged for a physiological reconstruction.

We did not confirm the hypothesis that a matt stem reduces damage accumulation

in the cement mantle compared to a polished stem. Even if the clear trend was that the

polished stem had more damage accumulation, the difference was not significant for the

cement mantle taken as a whole; this was because the variation in damage accumulation

between specimens was considerable. Since it is likely that an even greater variation

exists clinically, the conclusion of indistinguishable damage accumulation for matt and

polished stems is likely to hold in the clinical setting.

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Taking the lateral cement mantle on its own, there was significantly less damage

for the matt stem compared to the polished stem. An increase in volumes of highly

stressed cement for the case of complete debonding (Fig. 4) offered evidence that high

stress causes the trend towards higher damage accumulation observed in the polished

group. However, when comparing contour stresses for both models with the observed

spatial distributions of cracking (compare Fig. 3 with Fig. 2), cracks appeared in regions

where stress was predicted to be low, or even compressive. This could be explained by

including porosity in the stress calculation (Fig. 3), which showed that tensile stress could

be experienced over the entire exposed cement layers.

The main result of our research on this topic is that damage accumulation is so

variable that the damage accumulation failure scenario is not easily controlled by

prosthesis design parameters. The variability is both spatial (Fig. 2) and in terms of the

total quantity of damage (Table 2). Similar variability has been found under fatigue

loading of standard specimens in uniaxial tension24,25; therefore it may be concluded that

the variability is not primarily due to features of this physical model but rather is a

characteristic of the cement itself — most probably porosity and the random nature of

pre-load damage.

Pre-load cracking was one feature common to both matt and polished stems.

Lennon and Prendergast26 have previously predicted that residual stress due to

polymerisation-induced shrinkage can be sufficient to cause cracking in the presence of

pores. The lack of a significant difference in the levels of pre-load damage between matt

and polished stems suggests that the polished stems did not debond before testing, i.e. did

not debond because of shrinkage.

Because the trend in damage accumulation is different for matt versus polished

stems, it can be surmised that similar interfacial conditions did not persist after cyclic

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loading commenced. Two specimens exhibited aberrant behaviour; to attempt to explain

this we calculated a Hoffmann failure index for the bone-cement/metal interface. It is

highest on the medial side (Fig. 7) and indicating that a weak matt interface would

debond on that side first. Similarly it is lowest on the lateral side (Fig. 7) and, therefore, if

a polished stem had not debonded on one of its interfaces it is likely to be the lateral one

— and it is on the lateral side that one of the polished specimens (P3) behaves as part of

the matt group. Therefore it is concluded that, at two million cycles, some polished

specimens may not debond much whereas some matt specimens may debond

significantly. Similar variability in debonding may also occur in vivo with cemented hip

prostheses, although polished stems such as the Exeter are more likely to debond more

completely and rapidly due to the lack of distal support from the cement.

Cyclic displacement (often referred to as 'inducible' displacement27) showed a

good correlation with damage (see Fig. 6 and section 4). This supports the use of

inducible displacement as a measure for discriminating between different prosthesis

designs27. The lack of correlation between permanent migration and damage suggest that

other phenomena determine migration, such as cement creep and debonding of the stem.

It should also be noted that residual stresses normal to the stem-cement interface may

affect the load-displacement behaviour, as shown by Mann et al28 in tapered and straight

stem models.

5 Conclusions

1) Analysis of cement cracking in an experimental model of the femoral side of a

total hip replacement has shown that, despite generally higher stresses in cement

mantles of polished stems, the microdamage does not apparently accumulate at a

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faster rate for those stems. Therefore the hypothesis that overall damage

accumulation was greater around polished stems than around matt stems was not

confirmed (p>0.05).

2) The reason seemed to be that the variability in the strength of the bone cement

due to (a) porosity and (b) pre-load (shrinkage) damage masks the effect of the

increase in stress that occurs with a polished surface finish.

3) A consequence of damage accumulation is increased “inducible displacement” of

the stem relative to the bone. Therefore inducible displacements may be a

measure of the extent of damage accumulation in a cemented joint replacement,

and could be used in a pre-clinical test.

Acknowledgements

The MediLink project of the PRTLI programme provided financial support of one of us

(Dr A.B. Lennon) for the computational part of this research. Further financial support

was provided by the Standards Measurements and Testing Program of the European

Commission (Contract No. SMT4-CT96-2076). Sulzer Medica, Winterthur, Switzerland,

are thanked for stem polishing and the Department of Mechanical Engineering,

University College Dublin for use of their optical comparator.

13

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List of Captions Tables:

Table 1: Material properties used in the finite element model.

Table 2: Mean sum-of-crack-lengths for pre-test, post-test, and growth during testing

for medial and lateral observable cement for each group. Significance values are

for a one tail Student’s t-test at 95% confidence.

Figures:

Figure 1: (a) Schematic of assembled model, including lever used to apply joint

reaction force and muscle loading and clamp for attachment to material testing

machine, (b), photograph of assembled rig mounted on materials testing

machine, and (c) mesh used for finite element analysis.

Figure 2: Spatial distribution of observed cracks for all specimens and mean sum-of-

crack-lengths (95% confidence) for each specimen type before and after testing.

Figure 3: Maximum principal stress for cement exposed by windows in bonded and

debonded models for cases of completely poreless cement and cement with a

uniform distribution of pores (i.e. a pore at the centroid of each cement element).

Figure 4: Distribution of volume of observable cement experiencing discrete stress

ranges. Black indicates volumes stressed to above 5 MPa while the total height

of each bar indicates the total volume experiencing tensile stress—note that there

is a decrease in the overall volume experiencing tensile stress for the medial side

in spite of the increase in volumes experiencing higher stresses.

Figure 5: Growth in summed crack length vs pre- test summed crack length for (a)

lateral and (b) medial cement layers. Data labels refer to specimen no. within a

population sample (e. g. M1 = matt specimen no. 1). Two trend lines (lateral

polished and medial matt datasets) each correspond to the best fit with an outlier

removed (P3 and M5 respectively).

Figure 6: Inducible displacement of actuator head at end of test vs summed crack

length at end of test.

Figure 7: Failure index for medial and lateral cement-metal interfaces. The lateral

interface is longer and so extends farther on the graph.

Table 1: Material properties used in the finite element model.

Material E (GPa) ν Cement 2.4 0.33

Stem 210.0 0.33 Cancellous Bone 2.0 0.30

Aluminium 73.0 0.33

Table 2: Mean sum-of-crack-lengths for pre-test, post-test, and growth during testing

for medial and lateral observable cement for each group. Significance values are for a

one tail Student’s t-test at 95% confidence.

Matt Polished (mm)� ia (mm)� ia

p

Pre 9.933 ± 11.025 5.500 ± 2.330 0.24 Medial Post 23.459 ± 15.993 24.149 ± 12.266 0.47 Growth 13.527 ± 8.725 18.649 ± 9.958 0.24 Pre 17.841 ± 9.224 16.316 ± 16.229 0.44 Lateral Post 35.626 ± 16.769 61.537 ± 32.186 0.11 Growth 17.785 ± 8.370 45.221 ± 25.871 0.05

Lever

Clamp

12 o

15 o 55.9 mm

M J

A

20.2 o

(a) (b) (c)

Figure 1: (a) Schematic of assembled model, including lever used to apply joint

reaction force and muscle loading and clamp for attachment to material testing

machine, (b), photograph of assembled rig mounted on materials testing machine, and

(c) mesh used for finite element analysis.

Figure 2: Spatial distribution of observed cracks for all specimens and mean sum-of-

crack-lengths (95% confidence) for each specimen type before and after testing.

0 2.5 5 7.5 10 +< 0(MPa)

Porous Porous

No Pores No Pores

Bonded Debonded

Figure 3: Maximum principal stress for cement exposed by windows in bonded and

debonded models for cases of completely poreless cement and cement with a uniform

distribution of pores (i.e. a pore at the centroid of each cement element).

0

1000

2000

3000

4000

MedialBonded

MedialDebonded

LateralBonded

LateralDebonded

>3 MPa0-3 MPa

Figure 4: Distribution of volume of observable cement experiencing discrete stress

ranges. Black indicates volumes stressed to above 5 MPa while the total height of

each bar indicates the total volume experiencing tensile stress—note that there is a

decrease in the overall volume experiencing tensile stress for the medial side in spite

of the increase in volumes experiencing higher stresses.

.

20406080100

1020

3040

50Pr

e-te

st c

rack

leng

th (m

m)

Growth (mm)

Mat

t (de

note

d M

1-M

5)

Polis

hed

(den

oted

P1-

P5)

P1

P2P3

P4

P5

M1

M4

M3

M2

M5

00

(a) L

ater

al

20406080100

Growth (mm)

Mat

t (de

note

d M

1-M

5)

Polis

hed

(den

oted

P1-

P5)

P1

P2P3

P4P5

M1

M4

M3

M2

M5

00

1020

3040

50Pr

e-te

st c

rack

leng

th (m

m)

(b) M

edia

l

Figu

re 5

: Gro

wth

in su

mm

ed c

rack

leng

th v

s pre

- tes

t sum

med

cra

ck le

ngth

for (

a) la

tera

l and

(b) m

edia

l cem

ent l

ayer

s. D

ata

labe

ls re

fer t

o

spec

imen

no.

with

in a

pop

ulat

ion

sam

ple

(e. g

. M1

= m

att s

peci

men

no.

1).

Two

trend

line

s (la

tera

l pol

ishe

d an

d m

edia

l mat

t dat

aset

s) e

ach

corr

espo

nd to

the

best

fit w

ith a

n ou

tlier

rem

oved

(P3

and

M5

resp

ectiv

ely)

.

R2 =

0.7

2

R2 =

0.6

7R

2 = 0

.98

R2 =

0.9

4

R2 = 0.7375

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 50 100 150 200Damage (mm)

Indu

cibl

e di

spla

cem

ent (

mm

)

Figure 6: Inducible displacement of actuator head at end of test vs summed crack

length at end of test.

0

0.1

0.2

0.3

0.4

0.5

0 25 50 75 100 125Proximal to Distal (mm)

Failu

re In

dex

MedialLateral

Figure 7: Failure index for medial and lateral cement-metal interfaces. The lateral

interface is longer and so extends farther on the graph.