Relationship Between Morphology

and Mechanical Properties of

Ultra High Molecular Weight

Polyethylene

Third Annual Report for the Period

October 1, 1981 - September 30, 1982

Task 80-01, NBS-Bureau of Medical Devices Interagency Agreement

March 1 983

issued May 1 983

U.5. DEPARTMENT OP COMMERCE

NATIONAL 3UREAU OF STANOARCS

V

06^

U3

NBSIR 83-2696 (FDA)

RELATIONSHIP BETWEEN MORPHOLOGY

AND MECHANICAL PROPERTIES OF

ULTRA HIGH MOLECULAR WEIGHT

POLYETHYLENE

tiAT,°NAL bui?eao OF STANDARDS

LIBRARY JUl 21 1983

noV ate

J. M. Crissman

Principal Investigator

L. J. Zapas

Project Leader

F. A. Khoury

Project Leader

Third Annual Report for the Period

October 1, 1981 - September 30, 1982

Task 80-01, NBS-EMD Interagency Agreement

NBS-Bureau of Medical Devices Interagency Agreement

March 1 983

Issued May 1 983

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

Table of Contents

1 • Abstract * i

2. List of Figures ii

3. Introduction 1

4. Structural Changes Associated with the Uniaxial

Stretching of Ultra High Molecular Weight

Polyethylene (UHMWPE) 1

5. 2.1 Background 1

6. 2.2 Structural Changes in Samples Stretched and

Held at Strains in the Range 0.1 to 1.0 3

7. Mechanical Behavior Studies 11

8. 3.1 Two Step Creep and Recovery 12

9. 3.2 Multistep in Stress Creep and Recovery 19

10 . 3.3 Influence of Thermal History on the Creep

and Recovery of UHMWPE at Small Deformations. 24

11). Summary 29

12 . Work Plan for FY 1983 31

13 . References 33

%

- i -

Abstract

, This report describes work done during FY 1982 under task 80-01,

NBS-FDA/BMD (Bureau of Medical Devices) Interagency agreement. The

report covers the third year of a four year project concerned with the

study of the morphology and mechanical properties of ultra high molecular

weight polyethylene (UHMWPE) . During FY 1982, the two principle areas of

investigation were (1) the examination by x-ray diffraction of morphological

changes occurring in UHMWPE while under strain, and (2) the creep and

recovery behavior of UHMWPE at small deformations. A new one dimensional

constitutive equation is presented which describes very well the creep and

recovery behavior of this material at small deformations.
ii

List of Figures

Figure 1 Wide angle x-ray diffraction patterns. (a) Unstretched compression

molded sample of UH-C; H denotes amorphous ring. (b-h) Same

sample after it was stretched and kept taut at strains of (b) 0.1,

(c) 0.15, (d) 0.23, (e) 0.3, (f) 0.48, (g) 0.64 and (h) 1.0.

Figure 2 Same sample as Fig. 1 after it was released and had contracted

from a strain of 1.0 (Fig. 1(h)) to a strain of 0.4.

Figure 3 Creep strain (—0—) and strain during recovery (-> ) versus time

(log-log coordinates) from experiments carried out at constant

t-^ but varied applied stress a^. The dashed lines represent the

recovery predicted using equation lb.

Figure 4 Strain during recovery (log-log coordinates) from experiments

done at constant applied stress but varied t^. The dashed

lines represent the recovery predicted using equation lb.

Figure 5 Values of (t^;t-^) versus t^ on log-log coordinates.

Figure 6 Superposition of the recovery data shown in Figure 4 onto a master curve.

Figure 7 Comparison of the recovery data shown in Figure 3 (solid lines)

and the values of recovery (circles) predicted using equation 2.

Figure 8 Multistep creep and recovery data for the stress histories

indicated. The creep data are represented by the curves labelled

1 and 3, and the recovery data by the curves labelled 2 and 4.

The triangles and circles are the predicted values of the creep

and recovery calculated using equation 2.

Figure 9 Multistep creep and recovery data for the stress history

indicated. The labelling is the same as in Figure 8.

Figure 10 Multistep creep and recovery data for experiments done in which

the extensometer was rezeroed just prior to the application of

the third step. The labelling is the same as in Figure 8.

Figure 11 Creep strain versus time (log-log coordinates) for UHMWPE

quenched from the melt (Q) , slowly cooled from the melt (SC),

and slowly cooled from the melt followed by annealing at a temperature near the melting point (A). Applied stress 4MPa.

Figure 12 Superposition of recovery data for UHMWPE prepared under varied

thermal histories. In each case the applied stress during the

creep step was 4MPa.
1. Introduction

This report describes work done during FY 1982 under task 80-01,

NBS-BMD (Bureau of Medical Devices) Interagency Agreement. Background

information relevent to this work, as well as a summary of the work done

during FY 1980 and FY 1981, can be found in references [1] and [2] .

During FY 1982, the two principal areas of investigation were

(1) the examination by x-ray diffraction of morphological changes

occurring in UHMWPE while under strain, and (2) the creep and recovery

behavior of UHMWPE at small deformations. A comparison of the creep and

recovery behavior of specimens prepared under different thermal histories

is also presented.

2. Structural Changes Associated with the Uniaxial Stretching of Ultra High

Molecular Weight Polyethylene (UHMWPE)

2.1 Background

As indicated in previous reports [1,2] compression molded samples

of the UH-A and UH-C ultra high molecular weight polyethylenes do not

exhibit macroscopic necking when stretched uniaxially. Furthermore

they undergo large recoveries from deformation (even from large strains)

when they are released under zero stress. For example, samples which

were stretched to a strain of 3.0 at a rate of 0.02 /min exhibited

residual strains in the range 172% - 192% twenty four hours after they

were released (see Table 6, ref. [2]).

Our previous studies of the structure and orientation changes

resulting from uniaxial stretching at room temperature and at 37 °C

have been limited to an examination of the wide angle [1,2] and small

angle [1] x-ray diffraction patterns exhibited by the stretched samples

after they had been allowed to contract under zero tension for

periods in excess of twenty four hours. The residual strains in the

t Numbers in brackets indicate references found at the end of this report.
2

released samples were of course larger the higher the initially

imposed strain, and ranged from 0.2 to 3.0. Among the features

which were observed in all these samples [1,2] was the presence of

a small proportion of crystallites exhibiting wide angle x-ray

reflections characteristic of the metastable crystalline form of

polyethylene [3,4], The structure of the remaining majority of the

crystallites was the normal orthorhombic structure [5].

The metastable crystalline form of polyethylene usually

occurs in small proportions and is quite common in variously deformed

lower molecular weight polyethylene samples. It is characterized in

particular by three wide angle x-ray reflections corresponding to

interplanar spacings of 0.455nm, 0.38gnm, and 0.35^nm. These

spacings differ significantly from those of the prominent orthorhombic

110 and 200 reflections which are 0.41nm and 0.37nm respectively.

Two different but related unit cells have been proposed for the

metastable crystalline form of polyethylene. The cell proposed by

Turner-Jones [3] is triclinic with a=0.4285nm, b=0.4820nm, c=0.254nm,

a=90°, 8=110.25°, y=108°, whereas that proposed by Seto, Hara, and

Tanaka [4] is monoclinic with a=0.809nm, b=0.253nm, c=0.479nm and

8=107.9°. The indices of the 0.45^, 0.38q, and 0.35^ reflections

based on the triclinic cell [3] are 010, 100 and 110 respectively.

The corresponding indices based on the monoclinic cell [4] are 001,

200 and 201. As we have done previously in our discussions of the

wide angle x-ray diffraction patterns exhibited by strained samples

after they were allowed to contract, we shall identify the

three above mentioned reflections associated with the
- 3 -

metastable crystalline form of polyethylene in terms of their

indices based on the triclinic cell [3]. A subscript t will be

' appended to the indices of the reflections to distinguish them

from the orthorhombic reflections.

The exploratory experiments described below represent

additional steps in an effort aimed at determining the structural

changes associated with the deformation, and the partial recovery

from deformation, of compression molded UHMWPE.

2.2 Structural Changes in Samples Stretched and Held at Strains in the

Range of 0.1 to 1.0.

Evidently, determination of the nature of the processes which

underlie the partially reversible deformation behavior exhibited

by compression molded UHMWPE requires knowledge of the structure of

the strained samples before and after they are released. The experiments

described below represent a first step in establishing a basis for

comparing our earlier observations on the structures of stretched

samples after they are released, with the structures exhibited by

the samples prior to being released.

The wide angle x-ray diffraction (WAXD) patterns shown in Fig.l

were all obtained from the same dumbbell shaped sample of compression

molded UH-C polymer. The density of the sample was 0.941 g/cm~. The

pattern in Fig. la represents the unstretched sample. This sample was

stretched to progressively larger strains in a stepwise manner

up to a strain of 1.0. Stretching was carried out in a simple hand

operated stretching frame. After each of seven increases in clamp

separation the corresponding strain in the gauge section of the specimen

was determined, following which a WAXD pattern was recorded
photographically using a flat plate camera and Ni filtered CuKa x-ray radiation [Figs. 1, b-h]. At least ten minutes were allowed to

lapse after each increase in imposed strain before the corresponding

pattern was recorded using an exposure time of ten minutes. The

sample was held taut throughout these experiments.

The following features and trends exhibited in Figs. (l,a-h) may

be noted:

(i) As pointed out in previous reports the WAXD pattern of the

unstretched specimen (Fig. la) exhibits a very diffuse inner ring (H)

which is attributable to the amorphous regions in the sample, as well

as the two intense 110 and 200 diffraction rings characteristic of

orthorhombic polyethylene.

(ii) At strains of 0.1 to 1.0 (Figs.l, b-h) the stretched sample

exhibits the normal orthorhombic reflections, as well as the 'extra'

reflections characteristic of the metastable crystalline form of

polyethylene. The intrinsically most intense among the latter reflections,

namely the 101 can be readily seen even at a strain of 0.1. The

weaker 100

t and 110t which are barely visible at low strains tend to

become all the more evident the higher the strain indicating that the

proportion of metastable triclinic crystallites increases with increasing

strain.

(iii) As can be seen in Figs. 1 (b-c) the azimuthally broad

(arced) 010 t reflections centered on the meridian (which corresponds

to the stretching direction) and the much less intense 110

t arcs

centered on the equator are characteristic features of the WAXD

patterns obtained at small strains in the range 0.1-0. 2. At higher
5

strains, the 110^ arcs remain centered on the equator indicating

that among the planes which are parallel to the c-axis (and hence

the chain axis direction) in the triclinic crystallites, the (110) t

planes are the first to become oriented preferentially parallel to

the stretching direction. The 010^ arcs seen in Figs.l(b-c)

split progressively at higher strains (Fig. d-h) into two

broad arcs. The azimuthal angle _ between the most intense nortions of OlOt

these arcs and the stretching direction increases with increasing strain.

At a strain of 1 . 0, ^Q^Q t is about 60° and ^OOt is ~65°. On the

basis of these azimuthal dispositions of the 010 t and 100

t arcs,

as well as the preferential equatorial disposition of the 110

t arcs,

it can be estimated (see e.g. Ref. 6) that whereas the triclinic

crystallites are oriented with the (110) t planes preferentially parallel

to the stretching direction, the distribution in the angle of

inclination of the c-axis (and hence the chains) in the crystallites

relative to the stretching direction is peaked at about an angle of ~30°.

(iv) The effect of increasing strain on the orientation of the

orthorhombic crystallites is qualitatively similar to the trends

exhibited in the lower molecular weight polyethylenes [6,7], as well

as those observed in our earlier examination of samples of UHMWPE

which had been allowed to contract freely after being stretched to

various strains [1,2]. Typically the (200) planes are the first to

orient themselves preferentially parallel to the stretching direction.

The manifestation of this feature is evidenced at small strains by the

progressive increase in the intensity of the 200 diffraction ring in

the equatorial region relative to that in the meridional region

(Fig.l, b-d) . At higher strains (e.g. >0.3, Figs . 1 , e-h) the 200
6

Figure 1 Wide angle x-ray diffraction patterns. (a) Unstretched compression

molded sample of UH-C; H denotes amorphous ring. (b-h) Same

sample after it was stretched and kept taut at strains of (b) 0.1,

(c) 0.15, (d) 0.23, (e) 0.3, (f) 0.48, (g) 0.64 and (h) 1.0. Stretching

direction vertical. is azimuthal angle.
7

110

110

200

110

110

Figure 1 (contd)
8

reflections occur as arcs centered on the equator. The orientation

of the (110) planes with increasing strain is characterized by the

progressive splitting of the 110 diffraction ring into two pairs of

broad arcs. The azimuthal angle 'I'hq between the most intense portion

of these arcs and the stretching direction increases progressively

with increasing strain, and, correspondingly, the overlap between

the arcs increases in the equatorial region. This trend reflects the

increasing tendency for the orthorhombic crystallites to orient

themselves with the c-axis (and hence the chains) more closely parallel

to the stretching direction with increasing strain. At a strain of 1.0

^110 ~ 60° • Using this value for anc* t *ie equatorial orientation of

the 200 reflections as a basis, it may be estimated that the

distribution in the angle of inclination of the c-axis (and hence the

chains) of the orthorhombic crystallites relative to the stretching

direction is peaked about an angle of =36°.

In summary, the following qualitative features emerge from the experiment

described above concerning the effect of strain on the manifestation of

polymorphism and the changes in crystallite orientation resulting from

uniaxial stretching:

(a) The occurrence of metastable (triclinic) crystallites manifests

itself at all strains in the range 0.1 to 1.0. The proportion of triclinic

crystallites apparently increases with increasing strain in that range.

(b) The triclinic and orthorhombic crystallites start to align themselves

respectively with the (010)

t planes and the (200) planes preferentially

parallel to the stretching direction from the early stages in deformation.

(c) The distributions in the angle of inclination of the c-axis in the

triclinic and orthorhombic crystallites relative to the stretching direction

at a strain of 1.0 are peaked at inclinations of roughly 30° and 36°

respectively.
- 9 -

The sample used in the experiment described above was released

under zero stress. The WAXD pattern shown in Fig. 2 was taken after it

had contracted from an initial strain of 1.0 to a strain of 0.4. It is

evident from a comparison of Fig. 2 with Fig. lh (strain 0.1, sample

taught) that one of the main changes which occurred when the sample

contracted was a substantial decrease in the proportion of triclinic

crystallites. Thus, in contrast with Fig.lh, the 110 t and 100

t reflections

are barely if at all visible in Fig. 2. Furthermore the intensity of the

010

t arcs relative to 110 orthorhombic arcs appears to be considerably

diminished in Fig. 2 as compared to Fig.lh. Indeed, comparison of Fig.

with the WAXD patterns of the stretched-unreleased sample at comparable

strains, i.e. Fig.le (strain 0.3) and Fig. If (strain 0.475), indicates

that the proportion of triclinic crystallites is higher in the latter two

cases than in the released sample.

The exploratory experiments described above clearly indicate that the

characterization of the partially reversible deformation behavior of

UHMWPE must involve not only the quantitative determination of the changes

in crystallite orientation in the samples, but also quantitative determination

of the relative amounts of the different crystalline forms.

With regard to the recent interest (see Section 3) in the behavior of

UHMWPE under the influence of low stresses (and hence small strains) , we have

examined the WAXD patterns exhibited by samples stretched up to a strain

of 0.05 in an attempt to determine the lower limit of deformation at which

the occurrence of triclinic crystallites manifests itself. This limit

remains to be explored quantitatively using densitometry to examine the

diffraction patterns. One complication which should be noted is that the
Figure 2 Same sample as Fig. 1 after it was released and had contracted

from a strain of 1.0 (Fig. 1(h)) to a strain of 0.4. Original

stretching direction vertical.
- 11 -

intrinsically most intense of the triclinic reflections, i.e. the 010

t

,

corresponds closely with that of the amorphous halo (H) in the samples.

However, the occurrence of weak and azimuthally broad meridional 010^

arcs was visually evident in the diffraction patterns of samples stretched

and kept taut at a strain of 0.05.

3. Mechanical Behavior Studies

In reference [2] a set of experiments was described in which cylinders,

of UHMMPE were subjected to creep in compression at a constant applied load

followed by recovery at zero load. The recovery data were presented in

Figure 15 of reference [2]. Also shown in the same figure was the strain

during recovery predicted assuming a superposition principle [3] of the form

eR(t) = e c (t + t x ) - e c (t) (1)

where c R

(t) is the strain during recovery at a time t after a creep

experiment of duration t-]_, and e c (t + t^) and £

c (t) are the strain in a creep

experiment at time t+t-^ and t. In the experiments described in reference [2]

the duration of both the creep step and the recovery step was fixed at

3300 seconds and the magnitude of the applied stress was varied. It was

found that the recovery at the early times agreed well with the predicted

values, but at the longer recovery times approaching t-^ the actual recovery

was significantly less than was the predicted recovery.

Since the ability of UHMWPE to recover after deformation represents

an important aspect of durability and lifetime, we have examined in some

detail the creep and recovery behavior of UHMWPE at small deformations for

widely different creep histories and preparation conditions. In sections

3.1 and 3.2 we shall describe two step and multistep creep and recovery

experiments done on the material designated as slowly cooled UH-A in

reference [2]. The results of these experiments led us to formulate a new
- 12 -

one dimensional constitutive equation which describes plasto-viscoelastic

behavior. In the new derivation the assumption is made that the undeformed

state of the material depends upon the prior stress history. In Section

3.3 the creep and recovery behavior of the slowly cooled UH-A will then be

compared to that of quenched UH-A and annealed UH-A.

3.1 Two Step Creep and Recovery

The present experiments were done in uniaxial extension rather than

in uniaxial compression which was the case in reference [2]. Provided

that the maximum creep strains are sufficiently small, the creep experiment

can be considered a constant true stress experiment* It is anticipated

that in this range of deformations the behavior in extension will not be

significantly different from that in compression. Moreover, it is

possible to cut several tensile bars from each sheet of material thereby

minimizing specimen to specimen variability, whereas each cylinder must

be prepared individually.

In a two step creep and recovery experiment the specimen is

subjected to a constant applied stress, a^, for a time t]_, after which

the applied stress is removed and the specimen is maintained at

zero load thereafter. The specimen strain is determined as a function

of time during both the creep and recovery portion of the experiment.

For each experiment a fresh specimen was used (no prior deformation

history) and care was taken in handling the specimen prior to and

during mounting of the specimen in the test machine.

The first set of experiments to be described involves creep for

3 4

10 seconds followed by recovery for times of up to 10 seconds. The

data are presented in Figure 3 for experiments carried out at applied

stresses in the range from 1 to 8 MPa. This range of applied stresses
13

01 j2 B *-> •h q

J_l

*-> CJ 4J u q

ui c

ai

q

q CO

co o a)

Vi o Vi

O)

a > w CU nj 1

,J CO 4» q <u T o q v-x •H

>. <U U -H T3

01

q G) > M ,2 G cfl CO a u q

cuu «

T3

u CU to q t q <u

•r-i £ c

-1 i—1

Vi -H

q

q

u • c

'a

a C‘H D -U

C

X

q

•H QJ co

q

C3 co cr

V; fi <u cu

+-i

O

r-^ w q 4) tO

4-1 CO

q

T3 •H q ra 00 q co cu q

aj •H

'T'

w i—i T3 1 q q- Oi Q q a u 1 -h q cj -H

!-< qJ q)

q

O 01 01 •H O -H u q cj q Q

Vc

q

OJ W3 > >>

CO

O

u

rH j-> CU

a ! q > q &o _q 0 q o o

V. r-i I—! CJ CJ +J

C")O

V4q

CO •H

p4

NlVdlS
14

includes those which are likely to be experienced by the UHMWPE

component of a prosthesis in actual use. We note that an applied

stress of 1 MPa corresponds to a load of less than 1 kg (for our

specimens) . Thus it is important in setting up the experiment

that care is taken in handling the specimens. By inspection of

Figure 3 it can be seen that at an applied stress of 8 MPa the

3 maximum strain attained at 10 seconds was 0.025, whereas at t=l

second the strain was about 0.009, so that the applied stress during

the creep step was constant within 1.5 percent. For smaller values of

2 t^, even up to t^ = 10 seconds, the change in stress during the

creep step was less than 0.5 percent.

Also shown in Figure 3 (dashed lines) is the behavior predicted

by equation 1. At early times the observed values and the

predicted values of the recovery coincide, whereas at the longer

recovery times approaching t-^ the two curves deviate significantly.

This behavior is equivalent to that noted earlier for the slowly

cooled UH-C in compression (Figure 15, reference [2]).

A second set of experiments was done in which the applied stress

was held constant and the time of creep, t^, was varied from 1 second

to 10^ seconds. In each case the recovery was monitored for up to 10^

seconds. These results are shoxm in Figure 4. Again, the dashed

lines correspond to the recovery predicted by equation 1. In Figure 4

it can be seen that the strain during recovery tends to plateau to a

finite value. This behavior has been found to be true also for

experiments carried out at much smaller applied stresses where the

maximum creep strain was of the order of 0.001 and less. This behavior

cannot be described by the various non-linear viscoelastic theories

of simple materials.
15

NIV&1S

Figure

4

Strain

during

recovery

(log-log

coordinates)

from

experiments

done

at

constant

applied

stress

but

varied

t-^.

The

dashed

lines

represent

the

recovery

predicted

using

equation

1*
-16

We now introduce the following one dimensional constitutive

equation. At small deformations.

e(t )=/ "/ J*(a(O f t-?)dC+J(a(t),o) + 1 )

g(a(C))dC (/ g(a(C))d^. ( 2 )

In equation 2, e(t) is the strain observed at time t, c(£) is the

applied stress at time £,, <j) f g (a(C))d^^ is a functional which

\ *^o / depends on the stress history, and J(a,t) is in the manner of a non-linear

compliance multiplied by o. J* (*,*) denotes the derivative of J (*,*)

with respect to the second argument, and J(o,t)=J*(o,t)=g(o)=0.

For the two step creep and recovery experiment just described, it can

be shown that

eR

(t1;t) = e c (a;t+t

1 )-e

c (a;t) - <j>(g(a) (t+t

1

) + <j>(g(a)t)

+4>(g(a)t1 ), (3)

where e R

(t-^;t) is the strain during recovery at a time t after creep

for a time tp and e^Cajt) is the strain during the creep at a stress

a and time t. If we now define.

e R (ti;t) - e c (a;t+t 1

) + e c (a;t) = AeRC

(t

1

;t), (4)

then for the case where t=t n ,

AeRc( t

l

;tl) = 2<+

) (g( a ) t i) " <p(g(a)2t1

. (5)

In equation 5 Ae

R(

_,(t-^; t-^) represents the deviation of the actual

recovery from that calculated using equation 1 (at a time t-^ after

creep for a duration t^). If it is now assumed that in its simplest form

<f> (g (<?) t^) can be represented by

KgCcO^) = g(o)t

1 a

. ( 6 )
- 17

A £ where g(a) = (g (a)) , then from equation 5 it follows that

= §( CT ) ( 2_2 1//3

) tl 06 = (constant) t]_ a

. (7)

For constant a a plot of log Ae (t^t^ versus log t should then

yield a straight line with slope a. Such a plot is shown in

Figure 5 for six experiments in which t^ was varied from 1 second

O to 10 seconds. (Four of the curves are shown in Figure 4.) To a

very good approximation the data can be represented by s straight

line having a slope of one third. Equation 7 can then be rewritten

as

Ae

RC ( ti

; ti) = 0.74 g(a)tx

1

(8)

from which g(a) can be determined.

It was also found that the creep curves can be represented rather

well by the following relation:

s c (a;t) = fL (a) + f

2 (a)t

1//3

. (9)

In the case where both the function <j> and J have the same

exponential dependence on time, as is the case in the present work, it

can easily be shown that recovery data, obtained from creep experiments

having different durations t-^ (at constant a), can be superposed onto

a master curve with predetermined shift factors. For example, in the

present work the recovery at time t after a creep for time t^ is given by

e R

(tl5 t) = e(o)[(t+t1

) 1/3 - t 1/3

] + gCcOtj

173

, (10)

where 8(a) = f£(a) " g(a). Then the recovery e R

(t;t i ), where t i

= a

i t^

xs

eR

(t;t i ) = 9(a) )l/3_£

l/ 3 . ,

v 1/3. 1/3 +g(a)ai

t]_

For values of t = a^t.

-1/3

s R (ti;t) = a ± £ R

( aiti; a

± t).

(ID

( 12 )
18

(h rL

;)

Da 9v

Figure

5

Values

of

At;

pr

, (

t, ;

t

-, )

versus

t,

on

jog-log

coordinates.
.19 _

Starting from an experiment for which the recovery is e (t, ,t), we

R -L can then superpose any other recovery data e R

(t;t^) by first dividing

1/3 by (the ratio of t^/t^), and then shifting along the time axis by

a^. This procedure was carried out for the data shown in Figure 4, and

the results are presented in Figure 6, where t^ was taken to be 10 s.

From Figure 6 it is evident that the material will stop recovering

after a time greater than about 10 s, or a time three orders of

magnitude greater than the step time t-^.

The functions f^(a) and f 2

( a ) can be determined from the data

shown in Figure 3 where the time t-^ was held constant, but the magnitude

of the applied stress was varied from 1 to 8 MPa. By using values

of these functions and value of g(o) determined with equation 8 we

were able to reproduce all of the recovery data to within two percent

or better. Examples of the calculated values of the recovery are shown

in Figure 7, where the solid lines represent the actual data and the

open circles the calculated values. It can be seen that there is

excellent agreement between the two sets of results.

3.2 Multistep in Stress Creep and Recovery Experiments

We have also considered more complicated stress histories involving

multistep creep and recovery. In one set of experiments the material,

having been at rest up until time t=0, was subjected to the multistep

stress histories indicated in Figures 8 and 9. For these experiments the

extensometer was not reset to zero throughout the course of the

experiment. The observed responses for the creep and recovery steps are

shown in Figures 8 and 9 as sets of curves labelled 1-4. The time at

the onset of each step is taken to be the time t=0. The points (circles

and triangles) are the values of the strain calculated using equation 2.

The agreement is indeed very good. At the early times the creep strain
20

!

Figure

6

Superposition

of

the

recovery

data

shown

in

Figure

A

onto

master

curve.
21

C\J'o

00'o

if)

LlI

I—

Nivyis

Figure

7

Comparison

of

the.

recovery

data

shown

in

Figure

3

(solid

lines)

and

the

values

of

recovery

(circles)

predicted

using

equation

2
22

NlVdlS

Figure

8

Multistep

creep

and

recovery

data

for

the

stress

histories

indicated.

The

creep

data

are

represented

by

the

curves

labelled

1

and

3,

and

the

recovery

data

by

the

curves

labelled

2

and

4.

J

he

triangles

and

circles

are

the

predicted

values

of

the

creep

and

recovery

calculated

using

equation

2.
23

NIV&1S

Figure

9

Multistep

creep

and

recovery

data

for

the

stress

history

indicated.

The

labelling

is

the

same

as

in

Figure

8.
- 24

during the third step (second creep step) is significantly larger

than during the first step, although at the very long time the two

curves appear to be approaching one another asymptotically. For

the recovery it is found that the strain during the fourth step

(second recovery step) remains larger than that for the second step

and as time increases the ratio of the two becomes larger. From

similar experiments, where the recovery period was extended to much

longer times, the agreement between the observed response and the

calculated values was found to be equally good.

A second set of experiments was performed in which the stress

histories were similar to those just described except that the

extensometer in each case was reset to zero just prior to the

application of the third step (at the end of the first recovery step).

These results are presented in Figure 10. In this case the creep at

the early times is now the same for both the first and third steps,

but at the longer times the strain during the second creep step (third

step in stress) is somewhat less than that of the first step. This

behavior provides an indication that mechanical preconditioning is

occurring in the material. Also, it can be seen from Figure 10 that

the recovery during the fourth step occurs much more rapidly than during

the second step. In fact the recovery is even more rapid than that

predicted by equation 1.

3.3 Influence of Thermal History on the Creep and Recovery of UHMUPE at

Small Deformations

We now compare the creep and recovery behavior of the slowlv

cooled UH-A (density = 0.934 g/cm^) to that of the UH-A processed under

different conditions. Specimens of the UH-A polymer were prepared either
2

MPa

2

MPa

- 25 -

C\J

‘o

CO

'o

NlVdlS

CO

O

C\J

O

CO

L±J 2

ho

oO

i o

Figure

10

Multistep

creep

and

recovery

data

for

experiments

done

in

which

the

extensometer

was

rezeroed

just

prior

to

the

application

of

the

third

step.

The

labelling

is

the

same

as

in

Figure

8.
26

by quenching the material from the melt into ice water, or by

annealing the slowly cooled material at a temperature near the

melting point according to procedure (iv) described in Table 1 of

reference [2]. The respective densities of the two preparations

were 0.923 g/cm^ and 0.940 g/cm . Such a range in density very

nearly corresponds to the extremes in density which we have achieved

for the UH-A polymer by varying the thermal history during processing.

Densities in this range are also representative of those found for

pieces cut from unused commercial prosthesis components (see

reference [2]).

As was the case in Section 3.1, the deformations were kept

sufficiently small so that the experiment can be considered one at

constant true stress. In order to keep the maximum strain below

about 2 percent, all the experiments were carried out at an applied

stress of 4 MPa. For each of the three preparations a series of two

step creep and recovery experiments was done in which the applied

stress was kept constant (4MPa) and the duration of the creep step,

t, was varied. A comparison of the creep behavior is shown in

Figure 11 for the case in which t^=10 seconds. The creep behavior

of the slowly cooled and annealed materials is rather similar. At

3

1 second the creep strain is the same for both, whereas at 10 seconds

the annealed material has actually crept more by about 19 percent.

This particular annealing treatment appears to have had only a modest

influence on the creep of the UH-A. Quenching, on the other hand, has

a significant effect on the creep. For example, at 1 second the

quenched polymer has crept nearly twice as much as has either the

slowly cooled or annealed polymer.
27

NIV&1S

Figure

11

Creep

strain

versus

time

(log-log

coordinates)

for

UHMWPE

quenched

from

the

melt

(Q)

,

slowly

cooled

from

the

melt

(SC),

and

slowly

cooled

from

the

melt

followed

by

annealing

at

a

temperature

near

the

melting

point

(A).

Applied

stress

4MPa.
28

NlVdlS

Figure

12

Superposition

of

recovery

data

for

U1IMWPE

prepared

under

varied

thermal

histories.

In

each

case

the

applied

stress

during

the

creep

step

was

4MPa.
29

In order to compare the recovery data for the three different

preparations, we have followed the same procedures described in

Section 3.1 and have superposed onto a master curve the individual

recovery curves for each preparations. The results are shown in

Figure 12. All three curves show a tendency to plateau to a finite

value of strain at long times. It can be observed that at any

recovery time, t, the quenched material has recovered much less than

either the slowly cooled or annealed material. The results shown in

Figure 12 indicate that for a given recovery time, t, applied stress,

a^, and duration of creep, t-| , the slowly cooled UH-A experienced the

least amount of creep and the greatest amount of recovery.

Summary

From wide angle x-ray diffraction (WAXD) studies the following

qualitative features emerge concerning the effect of strain on the

manifestation of polymorphism and the changes in crystallite orientation

resulting from uniaxial stretching:

(1) The occurrence of metastable (triclinic) crystallites manifests

itself at all strains in the range 0.1 to 1.0. The proportion of triclinic

crystallites apparently increases with increasing strain in that range.

(2) From the early stages of deformation the triclinic and

orthorhombic crystallites start to orient themselves with respect to the

stretching direction.

(3) The distributions in the angle of inclination of the C-Axis in the

triclinic and orthorhombic crystallites relative to the stretching direction at

a strain of 1.0 are peaked at inclinations of about 30° and 36° respectively.

(4) Upon release from stress, one of the principle changes which

occurs when the sample contracts is a substantial decrease in the proportion

of triclinic crystallites.
30 -

(5) Explanatory experiments clearly indicate that the characterization

of the partially reversible uniaxial deformation behavior of UHMWPE will

involve not only the quantitative determination of the changes in

crystallite orientation, but also quantitative determinations of the

relative amounts of the different crystalline forms.

(6) In an attempt to determine the lower limit of deformation at

which the occurrence of triclinic crystallites manifests itself, the WAXD

of samples stretched to strains as small as 0.05 has been examined. At

this junction it can be reported that in samples stretched and held taut

at a strain of 0.05 visual evidence of the triclinic form was observed.

Since the ability of UHMWPE to recover after deformation represents

an important aspect of durability and lifetime, the creep and recovery

behavior of the UHMWPE polymer was examined in the region of small

uniaxial deformations. Both two step and multistep experiments were done

(T=23°C) in which either the duration of creep step was held constant and

the applied stress was varied, or the applied stress was held constant

and the duration of creep step was varied. In all cases the deformations

were kept sufficiently small that the creep portion of the experiment

could be considered as one at constant true stress. An important finding

from this work is that even after very small deformations the material only

partially recovers back toward the initial undeformed state. That is, the

strain during recovery tends to plateau to a finite value of strain.

The results of these experiments led us to formulate a new one

dimensional constitutive equation which describes plasto-viscoelastic

behavior. Using the proposed new equation, and the results from the two

step and multistep creep and recovery experiments, we were able to

reproduce all of the recovery data to within two percent or better.
31

The influence of thermal history on the creep and recovery

behavior of UHMWPE has also been examined at small deformations.

Specimens of the higher molecular weight UHMWPE (UH-A) were

prepared by quenching the material from the melt into ice water,

by slowly cooling it from the melt, and by annealing the slowly

cooled polymer at a temperature near the melting point. The

9 3 3 respective densities were 0.923 g/cm2

, 0.935 g/cm , and 0.940 g/cm .

Under an applied stress of 4MPa the slowly cooled and annealed

materials were found to have rather similar creep behavior, the

annealed material showing a somewhat more rapid creep subsequent to the

initial loading. The quenched material, on the other hand, exhibited

nearly twice the amount of creep, under the same applied stress, as

that observed for either the slowly cooled or annealed material.

Correspondingly, the quenched polymer recovered significantly less

than either of the other two preparations. It can be concluded that

fora given recovery time, applied stress, and duration of creep,

the slowly cooled UH-A exhibited the least amount of creep and

greatest amount of recovery.

5. Work Plan for FY 1983

(1) Work started in FY 1982 on the multistep creep and recovery behavior

of UHMWPE at small deformations will be extended to include cyclic loading

histories (a^ = 2.5 - 4MPa) . Histories involving short time loading and

3 f) unloading over many cycles (10 -10°) will be examined in order to determine

whether the creep and recovery can be described by a scheme similar to

that developed in sections 3.1 and 3.2.

(2) The influence of temperature on the creep and recovery behavior of

UHMWPE at small deformations will be studied in the temperature ranee from

23°C to 50°C.
32 -

(3) The effect of irradiation on the creep and recovery behavior of

UHMWPE at small deformations will be investigated at 23°C and 37°C for

dosages in the range from 1-5 Mrad.

(4) Aspects of the fine structure of undeformed samples which are

relevant to their mechanical behavior when subjected to small strains will

be examined. In addition when deemed necessary attempts will be made to

detect and determine aspects of the fine structural changes resulting from

small deformations.
33

References

[1] G. B. McKenna, F. Khoury, and J. M. Crissman, "Relationship Between

Morphology and Mechanical Properties of Ultra High Molecular Weight

Polyethylene", First Annual Report to the Bureau of Medical Devices,

Task 80-01, NBS-BMD Interagency Agreement, October, 1980. (NBSIR

81-

2209 FDA).

[2] J. M. Crissman, F. Khoury, and G. B. McKenna, "Relationships Between

Morphology and Mechanical Properties of Ultra High Molecular Weight

Polyethylene", Second Annual Report to the Bureau of Medical Devices,

Task 80-01, NBS-BMD Interagency Agreement, December, 1981. (NBSIR

82-

2493 FDA).

[3] A Turner-Jones, "The Triclinic Crystal Form of Polymethylenes and

Polyethylene", J. Polymer Sci. , 62_, 533 (1962).

[4] T. Seto, T. Hara, and K. Tanaka, "Phase Transformation and Deformation

Processes in Oriented Polyethylene", Japanese J. Appl. Physics, 7_, 31

(1968).

[5] C. W. Bunn, "The Crystal Structure of Long-Chain Paraffin Hydrocarbons.

The Shape of the -C^- group, "Trans. Faraday Soc., 39_, 482 (1939).

[6] A. Keller, "Unusual Orientation Phenomena in Polyethylene Interpreted in

Terms of the Morphology", J. Polymer Sci., 15_, 31 (1955).

[7] I. L. Hay and A. Keller, "Polymer Deformation in Terms of Spherulites"

,

Kolloid Z.U.Z. Polymere, 204, 43 (1965).

J. D. Ferry, Viscoelastic Properties of Polymers , John

New York, 1961, page 15.

[ 8 ] Wiley & Sons, Inc.,

NBS-114A (rev. 2-ac) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

1. PUBLICATION OR 2 REPORT NO.

NBSIR 83-2696

. Performing Organ. Report NoJ 3. Publication Date May 1983

NBS-BMD Interagency Agreement, Task 80-01, Third Annual Report

Relationship Between Morphology and Mechanical Properties of Ultra High

Molecular Weight Polyethylene

5. AUTHOR(S)

,j

^ Crissman, L.J. Zapas, F.A. Khoury

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234 Annual Report

10/1/81 - 9/30/82

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Food and Drug Administration

Bureau of Medical Devices

3257 Georgia Ave.

Silver Spring, Md. 20910

10. SUPPLEMENTARY NOTES

| Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

This report describes work done during FY 1982 under task 80-01, NBS-FDA/BMD

(Bureau of Medical Devices) Interagency agreement. The report covers the third

year of a four year project concerned with the study of the morphology and mechanical

properties of ultra high molecular weight polyethylene (UHMWPE) . During FY 1982, the

two principle areas of investigation were (1) the examination by x-ray diffraction of

morphological changes occurring in UHMWPE while under strain, and (2) the creep and

recovery behavior of UHMWPE at small deformations. A new one dimensional

constitutive equation is presented which describes very well the creep and recovery

behavior of this material at small deformations.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Creep, morphology, polyethylene, recovery, ultra high molecular weight, x-ray

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