Strain Induced Anisotropic Properties of Shape Memory Polymer

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IOP PUBLISHING SMART MATERIALS AND STRUCTURES

Smart Mater. Struct. 17 (2008) 055021 (7pp) doi:10.1088/0964-1726/17/5/055021

Strain induced anisotropic properties ofshape memory polymer

Richard Beblo and Lisa Mauck Weiland1

Department of Mechanical Engineering and Material Science, University of Pittsburgh,

660 Benedum Hall, Pittsburgh, PA 15261, USA

E-mail: [email protected] and [email protected]

Received 17 March 2008, in final form 30 June 2008

Published 10 September 2008

Online at stacks.iop.org/SMS/17/055021

AbstractHeat activated shape memory polymers (SMPs) are increasingly being utilized in ambitious,

large deformation designs. These designs may display unexpected or even undesirable

performance if the evolution of the SMPs mechanical properties as a function of deformation is

neglected. Yet, despite the broadening use of SMPs in complex load bearing structures, there

has been little research completed to characterize how the material properties change upon

application of large strain. The following is an experimental investigation into the strain

induced anisotropic properties of the SMP Veriflex. It is found that under large uniaxial strain

the SMPs stiffness in the transverse direction can be reduced as much as 86%, while the

toughness in the axial direction may increase by an order of magnitude in some cases.

A generalized analysis suggests that this trend should be expected for any SMP.

1. Introduction

Since their development in the late 1960s and early 1970s,

engineered polymers such as shape memory polymers (SMPs)

have been widely researched for their capability to recover

from large amounts of strain as well as their ability to switch

between relatively low and high moduli [13]. Their unique

characteristics have made them attractive for several design

concepts which rely on the polymers ability to soften, be

deformed by relatively low force, and then harden as a

new shape capable of carrying loads, possibly over several

cycles. Such characteristics are possible through the use of an

elastic segment and a transitioning segment. Above the glasstransition temperature Tg, the elastic segment dominates the

material response, while below Tg, the transitioning segment

crystallizes, dominating the material response.

In the biomedical field, SMPs have been proposed

as stents for the treatment of cardiovascular disease and

aneurysms [4, 5]. Biodegradable formulations have also

been developed for use as internal sutures, aiding in

minimally invasive surgeries [6]. The automotive industry

is implementing designs using SMPs in active air dams and

aerodynamic control actuators for improved fuel economy

and performance [7]. Further, SMPs are being considered

in the aeronautical and astronautical fields in morphing1 Author to whom any correspondence should be addressed.

aircraft wing structures as a skin allowing large in-plane

deformations of the wing. The design goals of the latter

are to create a class of military aircraft capable of multi-

mission roles [8, 9]. In efforts to augment such designs, novel

heating and cooling schemes have been developed, including

magnetic nanoparticles [10, 11], both reducing the need for

large and complex heating and cooling systems and improving

the response time of the polymer.

Heat activated SMPs are divided into categories based

on their chemical makeup, the most common of which are

polystyrene, polyurethane, and epoxy based polymers [12].

The constitutive response of SMPs is best described by

considering four discrete temperature regions as illustrated by

figure 1. In the lowest temperature regime, or the glassy state,

the small strain approximation is reasonable; hence a constant

elastic modulus is typically assumed, such as in the generalized

form of Hookes law,

i =1

E

i

j + k

, i j =

i j

G, (1)

where is the strain, E is the Youngs modulus, is the

stress, is Poissons ratio, G is the shear modulus, is the

shear stress, is the shear strain, and i , j , and k are any even

perturbation of an orthonormal basis. In the two transition

regions, time dependent temperature equations are deriveddescribing the assumed isotropic moduli of the polymer. For

0964-1726/08/055021+07$30.00 2008 IOP Publishing Ltd Printed in the UK1
http://dx.doi.org/10.1088/0964-1726/17/5/055021mailto:[email protected]:[email protected]://stacks.iop.org/SMS/17/055021http://stacks.iop.org/SMS/17/055021mailto:[email protected]:[email protected]://dx.doi.org/10.1088/0964-1726/17/5/055021


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Smart Mater. Struct. 17 (2008) 055021 R Beblo and L M Weiland

Figure 1. Heat activated shape memory polymer cycle.

instance, from conservation of energy theory, the internal

energy can be expressed as [13]

u

t =

mnD

mn +r

q

m,m, (2)

which can then be related to the Youngs modulus, where

is the density, u is the internal energy, t is time, D is a

deformation rate tensor, r represents internal heat generation

per unit mass, q represents the heat flux across the boundary,

and m and n are indicial indices. The first term on the right-

hand side of the equation is referred to as the stress power, and

it accounts for the mechanical work done to the polymer. In the

highest operating temperature regime, or the elastic region, the

material response is viscoelastic, for which there are several

accepted models including Maxwells model,

Totalt

= Dt

+ St

= + 1

Eddt

, (3)

where is the viscosity, and the subscripts D and S

indicate damper and spring related quantities, respectively.

Moreover, several mathematical models of varying complexity

and accuracy have been proposed. There are two basic

methodologies utilized in the development of constitutive

models describing SMPs. The first employs the use of

piecewise functions, breaking up the response of the polymer

into the four distinct regimes illustrated by figure 1 and

outlined in equations (1)(3). Such methods have been used

by Barot et al, and have proven accurate under most loading

conditions with the exception of being ill-suited to modelplastic strain below Tg [14]. Bhattacharyya et al have also

proposed a model paralleling this methodology [15]. The

second approach used to model SMPs makes assumptions such

as the polymer being isotropic under all conditions in order to

derive a single constitutive equation, for example the model

proposed by Tobushi et al [16]:

=

E+ m

y

k

m1

k+

+ 1

b

c 1

n

s

+ , T (4)where the dot denotes a time derivative, m, b, and kare material

parameters, the subscripts y and c represent yield and creeplimits respectively, s denotes unrecoverable quantities, T is

temperature, and , and are the viscosity, retardation time,

and the coefficient of thermal expansion respectively. Strictly

speaking, the assumption of isotropy is not true; however,

the resulting single thermoviscoplastic constitutive equation

is useful for many applications where 3D modeling is not

required. Such models as those developed by Tobushi et al

[15, 16] are useful for unidirectional loading environments andmultiple-cycle modeling. Diani et al have also proposed a

single equation constitutive model capable of 3D predictions;

however, the model assumes the polymer to be isotropic below

Tg and that all strain is elastic, and is thus incapable of

modeling plastic deformation in the glassy state [17]. Other

models proposing single equation constitutive relations include

those by Liu et al [18] and Lin et al [19].

Extensive experimental studies have also been performed

characterizing the thermomechanical properties of SMPs,

including changes in stiffness with respect to temperature and

strain recovery capabilities [2022]. Gall et al have reported

the storage and release of internal stress through a typical

shape memory cycle of a composite of epoxy based SMP and

dispersed SiC particles [23]. An SMPs ability to recover from

nearly any amount of applied strain has been quantified as well

as its creep characteristics under continuous loading [24, 25].

Tobushi et al have conducted experiments indicating that

the shape recovery characteristics of a polyurethane SMP

foam are time and temperature dependent [25]. Yang et al,

studying an ether based polyurethane SMP, have reported the

effect of prolonged moisture exposure on the glass transition

temperature [26, 27]. Applications and material characteristics

of thin film SMP have also been reported [28, 29]. Poilane

et al, for example, have confirmed macroscale test results of

thin films of SMP using nanoindentation, bulge, and membranepoint deflection test techniques [28], while Tobushi et al

have proposed using such thin film SMPs as passive choke

devices for engines and customizable utensils for disabled

patients [29].

While each of the above models and experimental studies

is well suited for its intended purpose, none appropriately

addresses the anisotropies that occur at high strains in

SMPs. Moreover, the anisotropies that arise in polymers

in general when subjected to large strain have been well

documented. For instance, refer to the classic works of

Treloar et al [30] and Flory et al [31] involving rubber

elasticity. More recent experimental studies continue tosupport this expectation. For instance, Arruda et al [32] have

conducted experiments similar to those presented below on

polycarbonate and polymethylmethacrylate specimens. Strain

induced orientated crystallization has also been studied and

modeled, and has been found to cause similar anisotropies in

polyethylene terephthalate (PET) by Rao et al [33]. Below

Tg, strain hardening in polycarbonate has been observed by

Govaert et al, revealing a sinusoidal-like relationship between

the yield stress and the angle between the investigated direction

and the direction of alignment [34]. HAPEX, a substitute

for bone having an isotropic tensile strength of 18 MPa,

after being oriented through an extrusion process, has been

found to become anisotropic, with tensile strengths of 80 and9 MPa in the direction of and perpendicular to the direction

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of extrusion, respectively, by Bonner et al [35]. Experiments

proving strain induced alignment of microdomain structures

in polystyrene-block-polybutadiene-block-polystyrene (SBS)

triblock copolymers have been conducted with the use of x-

ray scattering techniques and transmission electron microscopy

by Aida et al [36]. While the phenomenon of polymer chain

alignment due to strain and its effect on mechanical propertieshas been well researched, differences between polymer

systems substantiate the need for the direct experimental

investigation of this effect in shape memory polymers. At

least as significant is the need to ensure that end users of

SMPs become alert to this generalized phenomenon, as this

discussion is relatively absent from current SMP literature.

The following work is an experimental investigation

into the effect large strains have on the styrene based SMP

Veriflex (a product of Cornerstone Research Group, LLC)

above and below the glass transition temperature Tg. The

experiments outlined in this work explicitly aim to quantify

these anisotropies to aid in the design of structures requiring

both morphing capabilities and multi-directional loading.

Following the experimental results, a generalized modeling

construct for anticipating the observed anisotropies is offered

to further reinforce the expectation that similar anisotropies

should be expected to evolve in other SMP (or any polymer)

formulations.

2. Experimental procedures

Veriflex is a cross-linked thermoset copolymer manufactured

in two parts: a resin and a hardener. Once mixed, the polymer

can be cast into any shape as well as machined after curing.

The manufacturer reports a glass transition temperature Tg of62 C.

2.1. Sample preparation

The resin and hardener are mixed per the manufacturers

specifications. A medium vacuum, approximately 27 Hg, ispulled on the sample until there are no remaining air bubbles

from mixing, while avoiding excess vacuum as this will remove

styrene from the mixture. The uncured polymer is then poured

into a steel mold conforming to the ASTM D638-03 type IV

specimen standard. The mold, treated with a manufacturer

supplied mold release, is then placed in a laboratory ovenat 75 C for 39 14

h. The extended 314

h as compared to

the manufacturers specifications compensates for the thermal

capacity of the mold.

In the creation of the samples for characterizing axial

response, the resulting 25 mm thick molded polymer is cut into

4 mm thick specimens for the standard isotropic tensile tests.

Each specimen is sanded with 200 then 600 grit sandpaper to

remove all tool marks and ensure a flaw free test sample.

In the creation of samples that are preconditioned with

axial strain, the 25 mm thick molded polymer is heated well

above Tg to 80C, strained, and cooled to below Tg prior

to slicing. Each specimen is then sliced and sanded per the

method above. Some of these samples are tested in thiscondition to characterize any changes in axial response as a

result of preconditioning; the remainder are further conditioned

for transverse characterization.

Samples for characterizing transverse response are sliced

from the preconditioned dog-bones such that only the

traditional gage length remains. This results in rectangular

specimens, as opposed to the preferred dog-bone style;

however, use of a video extensometer to monitor deformationonly in the central portion of the sample minimizes the edge-

effect error associated with this sample type.

2.2. Experimental setup

All tests are conducted with a screw driven MTI universal

load frame under displacement control. Characterization of

axial response is performed at a strain rate of 2 mm per

minute to avoid viscous effects, resulting in a maximum

starting strain rate of 4.5% per minute for unconditioned

samples. Characterization of transverse response is performed

at a rate of 0.25 mm per minute, resulting in a maximum

starting strain rate of 3.5% per minute for conditioned samples.Ambient tests are conducted at room temperature, 23 C, usinga 2 kN Transducer Techniques load cell. Tests above Tg(reported to be 62 C) are conducted at 80 C using a 1 kNTransducer Techniques load cell. A Bemco FTU3.0-100x600

UTM temperature/humidity chamber is used for environmental

control. A Messphysik ME46-450 video extensometer is used

to monitor axial and transverse deformation, with contrast

lines drawn directly on the samples. Specimen dimensions

are recorded with digital calipers, accurate to 0.01 mm.

Experimental results are reported as true stress/strain values.

3. Experimental results

Tables 13 and figure 2 summarize the experimental results

and include statistical errors as calculated using Students

t-distribution; per ASTM D638-03, at least five tests are

performed per reported measurement. Figure 2 is presented

using representative true strain values measured from the

original isotropic state before testing or any preconditioned

strain is applied. This method results in the curves for the 40%

and 70% preconditioned cases being offset (figure 2). This

reporting strategy allows a direct comparison of the total strain

applied to the sample beginning from the isotropic state. For

the characterization of transverse response in preconditionedsamples, this strategy results in an initial offset to a negative

strain due to the Poisson effect.

While offsetting for preconditioning in the figures enables

a convenient visual of the total linear deformation away from

the isotropic state, this strategy may obscure the meaning

of in-service performance. All tabulated results correspond

with zeroed initial conditions for all tested samples. Table 1

provides a summary of the measured material properties as

functions of preconditioning, temperature, and direction. Here,

the Youngs modulus of the specimens tested below Tg is

defined as the slope of the linear portion of the stress/strain

curve as seen in the top left and top right graphs in figure 2;

the slope is measured between the strains of 0.25% and 1.0%.The Youngs modulus above Tg is reported as the initial slope

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Figure 2. Representative stressstrain curves with offsets to illustrate preconditioning: axial testing below Tg (top left); transverse testingbelow Tg (top right); axial testing above Tg (bottom left); transverse testing above Tg (bottom right).

Table 1. Experimentally determined Youngs modulus, yield stress, and Poissons ratio.

Youngs modulus (MPa) Yield (MPa)Below Tg (23

C) Below Tg (23 C) Poisson ratioPreconditioned

strain (%) Axial Transverse Axial Transverse Axial

0 1140 71 13.0 1.2 0.4840 1300 50 190 15 15.6 1.1 11.3 2.0 0.4770 1270 120 160 51 14.6 1.2 9.5 0.4 0.38

Above Tg (80C) Above Tg (80 C)

Preconditionedstrain (%) Axial Transverse Axial Transverse Transverse

0 0.44 0.046 NA 0.4840 0.96 0.08 0.51 0.04 NA NA 0.4770 1.56 0.03 0.10 0.01 NA NA 0.38

of the stress/strain graph at the beginning of the test, as seen in

the bottom left and bottom right graphs in figure 2; the slope

is measured between the strains of 0% and 25%. Poissons

ratio is defined as the ratio of transverse strain to axial strain

in the same stress/strain region as that used to calculate the

Youngs modulus, where the video extensometer employed

tracks the response in both directions throughout any given test.

There is only modest variation in the Youngs modulus in the

axial direction, with all experimentally determined values in

the range of the manufacturers reported value of 1241 MPa.

Similarly the yield stress, taken as the onset of the non-linear

response, is relatively insensitive to preconditioning in the

axial direction.

However, the Youngs modulus in the transverse directionis seen to decrease by as much as 86%, falling from 1140 MPa

initially to 160 MPa with 70% strain preconditioning. The

yield stress is also observed to fall off by 30% in this case.

No yield stresses are reported above Tg because, although the

response is not linear to failure, there is no onset of plastic

deformation; this is consistent with the polymers rubber-like

behavior in the soft state and its ability to recover from nearly

any applied strain up to failure.

Also evident from figure 2, and summarized in table 2,

is the sometimes substantial increase in failure strain upon

application of strain preconditioning. Below Tg there is a

significant increase in the failure strain in the axial direction. In

fact, with preconditioning, the SMP is capable of withstanding

nearly as much strain below Tg as it is above Tg. Accounting

for the preconditioned strain, the maximum strains at failurein the axial direction below Tg for the 40% and 70%

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Table 2. Failure strain as a function of preconditioned strain (zero offset).

Axial TransversePreconditionedstrain (%) Minimum (%) Maximum (%) Minimum (%) Maximum (%)

0 5.2 31.2 5.2 31.2Below Tg (23

C) 40 67.7 82.3 36.6 47.6

70 11.4 61.2 23.5 32.30 110.9 119.1 110.9 119.1

Above Tg (80C) 40 58.3 138.4 78.0 85.8

70 29.1 40.2 168.1 176.4

Table 3. Modulus of toughness as a function of preconditioned strain.

Axial (MJ m3) Transverse (MJ m3)Preconditionedstrain (%) Minimum Maximum Minimum Maximum

0 0.9 4.6 0.9 4.6Below Tg (23

C) 40 15.1 20.0 2.7 5.070 1.8 13.9 1.0 2.0

Above Tg (80C) 0 0.47 0.57 0.47 0.57

40 0.18 1.27 0.20 0.2870 0.04 0.15 0.08 0.12

preconditioned cases become 123% and 130%, respectively,

which is comparable to the isotropic above Tg case having a

maximum failure strain of 120%.

Directly related to the amount of strain the polymer

is capable of withstanding before failure is the modulus of

toughness, presented in table 3. As is evident, below Tg the

modulus of toughness in the axial direction is increased by

more than an order of magnitude with strain preconditioning.

4. Discussion

An SMP is frequently employed for its ability to sustain large

strain. More specifically, an SMP is often considered desirable

for design because it may be warmed, subjected to substantial

deformation with low forces, and then locked into the new,

load carrying configuration at a lower temperature. This shape

may be expected to support complex loads. The foregoing

experimental procedure employs strain preconditioning as a

means to explore the load carrying capability of the newly

locked-in shape.

Based on the experimental results of the previous section,for simple uniaxial design strategies it is appropriate to treat

the Youngs modulus as a constant below Tg. Further, while

the stiffness above Tg increases by a factor of three over the

range of preconditioning considered, as compared to the cold

state stiffness it may be appropriate to also treat this value of

Youngs modulus as a constant for uniaxial loading. However,

in SMP based designs carrying complex loads, the foregoing

clearly illustrates that assuming constant, isotropic stiffness

values above and below Tg would be ill-advised. Similarly, any

design that relies on SMP toughness may display unexpected

performance; in fact, in the case of toughness the material may

be under-utilized.

The following explanation is offered for the observedanisotropic response. It is proposed that during the

preconditioning above Tg the energy required for shear

between two adjacent polymer chains is greatly reduced,

allowing them to slide relative to one another and partially

align. This proposition is consistent with the partial polymer

chain alignment reported for other polymer systems at large

strains [20]. Once cooled, the response of the polymer in the

axial (aligned) direction will be dominated by the deformation

of the polymer chain covalent bonds. This is expected to

correspond with an increase in stiffness, but more importantly,the amount of energy required to break these aligned covalent

bonds will become significant.

Consider next the response in the transverse direction. It

can be argued intuitively that, if partial alignment results in

a stronger material in the aligned direction, then the cross-

links that enabled this alignment are necessarily less able to

support load. However, this intuitive argument alone fails to

adequately address the substantial degradation in transverse

stiffness. In addition, however, this point may also be argued

from Boltzmann statistical thermodynamics first principles.

If it is assumed that rotation about a given polymeric bond

is unrestricted, then the Helmholtz free energy is strictly a

function of the entropy, where the entropy is given as

S(r) = c + kln P(r), (5)

where c is a constant of integration, k is Boltzmanns constant,

and P(r) is the probability density function defining the

distance between polymer chain cross-links. One relatively

simple way to explore this is via the three-chain rule, which

essentially assumes that in the virgin state the polymer chains

will tend to align with each of the Cartesian axes [30],

S= 3

S(ro) + 2S(ro1/2) 3S(ro)

, (6)

where S is the change in entropy associated with an applieddistortion, is the number density of network chains, r0 is the

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root mean square of the distance between cross-links and =L/L i is the relative length of the sample upon deformation.

The first parenthetical term of equation (6) corresponds with

the axial response; the second parenthetical term corresponds

with the transverse response; the final parenthetical term

corresponds with the virgin state. The nominal stress f and

corresponding modulus [ f] of the system are then expressedas [37]

f = T

S

T

f= f

2 , (7)

where T is the temperature. For the general case presented

here, a normal distribution function, such as equation (8), is

utilized for P(r), the chain length probability density function.

P (r) = 1

2exp

(x )

2

22

, (8)

where is the standard deviation, is the expected value,

and x becomes r0 in the axial direction and r01/2in the transverse direction, as indicated in equation (6).

Substituting equation (8) into equation (5) and subsequently

into equation (6) yields

Saxial

= kr0

2(r0 ) (9)

Stransverse

= kr0

22

r0

1/2

, 3/2 (10)

where the entropic response with respect to distortion is

considered for the respective axial and transverse directions. In

this form, it is relatively easy to envision that the magnitude of

the axial term will increase with increasing axial deformation as all other terms in the expression are positive constants.

Further manipulation of equations (9) and (10) via equation (6)

only serves to multiply the expressions by terms that will

cancel in the resulting ratio of interest,

faxial =

2

r03 2

r0 1/2

ftransverse . (11)

Because r0 and are necessarily positive and is greater

than 1 for our tensile preconditioning, the numerator will

be larger than the denominator, yielding a coefficient greater

than 1. This supports the experimental observation that themodulus in the transverse direction is smaller than in the axial

direction with increasing strain. Further, because the terms in

the numerator are of higher order than the denominator, the

transverse properties decrease relative to the axial properties at

a correspondingly increased rate.

The details of the above discussion may be easily

manipulated. For instance, considerable detail could

be introduced to accommodate the multiphased nature of

Veriflex in comparison to the rubber elasticity basis of this

development; the Johnson family of distributions might have

been employed [38]; or more formally developed orthotropic

constitutive equations may have been offered [39]. In

addition, it should be noted that the above theory is knownto have increasingly significant errors above extension ratios

between 2 and 2.5, depending upon the polymer system [30].

However, despite the simplistic application of statistical

thermodynamics, the characteristic qualities of the analysis are

fixed. Thus first principles support the observed, substantial

degradation in transverse stiffness with the introduction of

preconditioning. The significance of choosing this highly

generalized construct is that it may be reasonably argued thatthe experimentally observed anisotropic trends in Veriflex

should be expected in any SMP, and for that matter, any

polymer employed in large strain applications.

5. Conclusions

With shape memory polymers being aggressively considered

for high strain applications, it is becoming increasingly

important that their three-dimensional characteristics be

quantified. When first partially aligning the polymer chains

with strain preconditioning above Tg, such as is likely tooccur in high strain applications, substantial variations in the

fundamental material properties are observed. These include

substantially decreased transverse stiffness and substantially

increased axial toughness (in some cases an order ofmagnitude). While the above results may necessitate the

use of somewhat more complex material models during the

material design process, the ability to manipulate directional

material stiffness and toughness could also become a powerful

design tool in itself. The foregoing offers insight into how the

property variation will manifest itself. Moreover, because the

physical mechanisms proposed for the observed response are

argued from principles applicable to any polymer material, theexperimental trends presented in this report are not expected to

be limited to the specific case of Veriflex.

Acknowledgments

The authors would like to acknowledge Dr Clark, for

his assistance and expertise; HRL Laboratories, LLC, for

their knowledge of shape memory polystyrenes and aid in

sample preparation techniques, and CRG Industries, LLC, for

supplying Veriflex and counsel.

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Strain Induced Anisotropic Properties of Shape Memory Polymer

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