IMP....Shape Memory Mechanics of an Elastic Memory Composite Resin

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Journal of Intelligent Material Systems and

http://jim.sagepub.com/content/14/10/623The online version of this article can be found at:

DOI: 10.1177/104538903036213

2003 14: 623Journal of Intelligent Material Systems and StructuresErik R. Abrahamson, Mark S. Lake, Naseem A. Munshi and Ken Gall

Shape Memory Mechanics of an Elastic Memory Composite Resin

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Shape Memory Mechanics of an Elastic Memory Composite Resin

ERIK R. ABRAHAMSON,1,* MARK S. LAKE,1

NASEEM A. MUNSHI1 AND KEN GALL2

1Composite Technology Development, Inc., 2600 Campus Drive, Suite D, Lafayette, Colorado, 80026, USA2University of Colorado, Boulder, Colorado, 80303, USA

ABSTRACT: Substantially more attention has been given in the past to shape memory alloysand shape memory ceramics than to shape memory polymers because unreinforced shapememory polymers have much lower stiffness and recovery force potential than shape memoryalloys and shape memory ceramics. However, when incorporated into a fiber-reinforcedcomposite, both the stiffness and the recovery force of a shape memory polymer can bedramatically improved. This paper presents recent advances in characterizing the shapememory mechanics of a thermoset shape memory polymer resin for Elastic MemoryComposite (EMC) materials. In particular, heretofore undocumented response behavior ischaracterized through a series of thermo-mechanical tests of a commercially available EMCresin, and a lumped parameter model is adapted to accurately correlate this behavior. Throughapplication of this model, it appears that the molecular transition associated with the shapememory effect occurs at a temperature other than the glass transition temperature of the resin.

Key Words: shape memory polymer, elastic memory composite, glass transition, shaperecovery

BACKGROUND

SHAPE memory polymers are a subset of the broad

class of smart materials known as shape memory

materials (Otsuka and Wayman, 1998). Substantially

more attention has been given in the past to shape

memory alloys and shape memory ceramics than to

shape memory polymers because unreinforced shape

memory polymers have much lower stiffness and

recovery force potential than shape memory alloys andshape memory ceramics. However, when incorporated

into a fiber-reinforced composite, both the stiffness and

the recovery force of a shape memory polymer can be

dramatically improved (Liang et al., 1997; Gall et al.,

2000; Ni et al., 2000). The key advantages of fiber-

reinforced shape memory polymer materials (i.e. elastic

memory composites) over shape memory alloys and

shape memory ceramics are the substantially lower

densities and higher strain capacities, and potentially

lower processing costs that are achievable with elastic

memory composites (EMC). The key advantage of

EMC materials over traditional composite materials is

that the shape memory polymer resin has a high elastic-

strain capacity and the ability to store, and subsequently

recover, mechanically induced strain when subjected to

a specific thermo-mechanical cycle.

Recent studies have identified several interaction

phenomena between the reinforcement fibers and the

shape memory polymer resin in an EMC laminate that

enable the laminate to be bent to relatively small radii of

curvature without inducing damage in the fibers. For

example, it has been shown that fiber microbuckling

allows high compressive strains to occur in uni-axially

reinforced EMC laminates, see Figure 1. (Gall et al.

2001; Murphey et al., 2001; Lake and Beavers, 2002). In

cross-ply laminates, inter- and intra-laminar resin

shearing can be significant. In all laminates, relatively

high strains must develop in the shape memory polymerresin in order to avoid fiber breakage.

The present study is focused on the shape memory

behavior of the bulk resin rather than the behavior of

the fiber-reinforced resin. This approach is taken

because the strains induced in the resin within a fiber-

reinforced laminate vary dramatically throughout the

laminate, and the shape memory behavior of the resin

can vary with the magnitude of induced strain (Lake and

Beavers, 2002). In addition, the present study is focused

on the shape memory characteristics of a commercially

available thermoset resin. Nearly all past work that has

been cited in the literature on shape memory polymers

is limited to thermoplastic chemistries as opposed to

thermoset chemistries (Liang et al., 1997; Tobushi et al.

1997, 1998; Ni et al., 2000) Of course, most structural-

grade composite components for spacecraft applications

incorporate thermoset resins rather than thermoplastic

resins, due to the better mechanical performance

ease of fabrication, and environmental durability

inherent in thermoset resins.*Author to whom correspondence should be addressed.E-mail: [email protected]

JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, Vol. 14October 2003 623

1045-389X/03/10 062310 $10.00/0 DOI: 10.1177/104538903036213 2003 Sage Publications

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MECHANICS OF SHAPE MEMORY POLYMERS

The shape memory effect in materials is essentially the

capacity to recover mechanically induced and frozen

strain upon application of heat, magnetic field, or

electric field. The shape memory effect has been

demonstrated in ceramics, metals, and polymers, and

the molecular mechanisms responsible for the effect

have been found to be different for each of these three

materials (Otsuka and Wayman, 1998). In metals and

ceramics, the shape memory effect is related to a well-

defined crystalline phase change in the material, whichoccurs at a specific temperature and/or stress level. In

polymers, the shape memory effect is related to a variety

of molecular interactions, which have less well-defined

activation temperatures and/or stresses.

Tobushi and others have postulated that the shape

memory effect in polymers is related to the phase change

that occurs through the glass transition (Tobushi et al.,

1997, 1998). This postulate leads to an apparent analogy

between the martensiteaustenite transformation tem-

peratures in shape memory alloys and the glass

transition temperature in shape memory polymers.

Indeed, the accepted thermo-mechanical cycles for

affecting shape memory response in shape memory

polymers and alloys are both defined with respect to

these transition temperatures. The commonly accepted

thermo-mechanical cycle for testing shape memory

polymers is given in Table 1.

The present paper includes the results of recent studies

that have uncovered an additional similarity between the

shape memory behavior of an EMC resin and shape

memory alloys. Specifically, it has been found that the

phase change, associated with the shape memory

effect in this EMC resin, can be excited either under

combined thermal and mechanical loading (i.e., using

the loading cycle listed above), or under pure mechanical

loading. In other words, it has been found that

mechanically induced strain can be either frozen in

this EMC resin at temperatures well below the Tg of the

resin, and recovered by subsequent thermal cycling

above the Tg of the resin, or recovered without further

heating when strained well above Tg of the resin.

This discovery is significant because it has led to the

identification of a lumped-parameter viscoelastic model

that accurately represents the shape memory mechanics

of the EMC resin. Furthermore, through application of

this model, it appears that the molecular transitionassociated with the shape memory effect occurs at a

temperature other than the Tg of the resin. Ultimately, it

is hoped that this model will lead to better predictions of

the shape memory mechanics of fiber-reinforced EMC

materials that are made with the resin. The next section

of this paper summarizes the experimental procedures

and results from testing of the CTD-DP-5.1 resin.

Subsequently, the analytical model that describes EMC

shape memory behavior is presented and correlated with

the experimental results.

Figure 1. Microbuckling of fibers in EMC rods: (a) Lateral bending test of 6.35 mm (1/4-in.) dia. EMC rod; (b) Fiber microbuckles in 6.35 mm(1/4-in.) and 1.59 mm (1/16-in.) rods.

Table 1. Typical thermo-mechanical cycle for shapememory polymers (SMP) testing.

Step Procedure

1 Mechanically induce strain while the SMP

is heated above its Tg2 Freeze the induced strain by holding the

mechanical load and cooling below Tg3 Remove load and lightly constrain in packaged shape

4 Recover frozen strain by reheating the SMP above Tg

624 E. R. ABRAHAMSON ET AL.

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EXPERIMENTAL INVESTIGATION OF

THE SHAPE MEMORY MECHANICS OF

AN EMC RESIN

In the present program, several specimens of CTD-

DP-5.1 EMC resin were subjected to a variety of

thermo-mechanical loading conditions, and the shapememory behavior of the material was characterized. All

testing was done in tension, and all specimens were

fabricated using an ASTM standard tensile test speci-

men design (Anon, 1997). New testing procedures were

developed and applied, and these procedures are

described below.

Tests were performed over a range of temperatures

through the glass-transition regime of the CTD-DP-5.1

resin. Figure 2 presents data from DMA testing (under

torsional loading) of the resin. Plotted in Figure 2 are

the shear modulus, G, complex shear modulus (i.e., loss

modulus), G*, and the ratio of G*/G. The peak in the

G*/G curve is defined as the Tg of the resin, and is at71C. It can be seen that most of the variation in

modulus for CTD-DP-5.1 occurs between 20 and 80C.

All tests in the present program were conducted with the

specimen at temperatures between these two extremes.

Description of Test Procedures

Shape memory polymers have not received as much

attention in the literature as shape memory alloys and

shape memory ceramics. Hence, there does not currently

exist a standard test procedure for investigating their

shape memory behavior. One procedure that is com-

monly applied incorporates the thermo-mechanical cycle

outlined in Table 1 (Ni et al., 2000).In the present

program, a new test procedure was developed and

applied. The test procedure is based on applying the

thermo-mechanical cycle described in Table 2. Unlike

the cycle described in Table 1, the new cycle involves

straining the EMC resin at temperatures below its Tgand determining whether strain that is frozen at these

temperatures is recoverable with subsequent heating

above Tg. A matrix of tension tests were performed to

specified strain levels and at specified temperatures. As

mentioned previously, the range of test temperature

covered most of the glass-transition regime.

The test specimens were fabricated with the ASTM

standard geometry shown in Figure 3 (Anon, 1997). The

cross section in the necked region of the specimenmeasured 6.35mm (1/4in.) wide by 3.18 mm (1/8in.

thick. The specimens were machined from 3.18 mm

(1/8 in.) thick flat plates of resin, which were cured in a

15.24 cm (6 in.) by 20.3 cm (8in.) rectangular mold

The final machining of the specimens to the dog bone

profile shown in Figure 3 was performed using an

end-mill. Note, the left-hand specimen in Figure 3

has been painted black to facilitate videometric strain

measurement (to be discussed later), and the right-hand

specimen is unpainted.

TEST APPARATUS AND VIDEOMETRY SYSTEM

Testing was performed using a servo-hydraulic MTSload frame, with a maximum load capacity of 490kN

(110,000 lbf) and a 4 kN (1000 lbf) load cell installed for

adequate load resolution (see Figure 4). Elevated

temperature tests were performed using an electrically

heated thermal shroud (see Figure 4(b)), and room

temperature tests did not necessitate the thermal shroud

(see Figure 4(a)). While performing room-temperature

tests, strain within the necked region of the specimen

was measured directly using a videometry system

Figure 3. Test specimens.Figure 2. CTD-DP-5.1DMA data.

Table 2. New thermo-mechanical cycle for EMC resin

testing.Step Procedure

1 Mechanically strain the EMC resin to high strain values

while it is below its Tg2 Remove the mechanical load and observe residual

frozen strain

3 Recover the frozen strain by reheating the EMC resin

back above Tg

Shape Memory Mechanics of an EMC Resin 625



5/11

(note cameras in Figure 4(a) and reflective targets on

specimens in Figure 3). The videometry system was

designed to accurately measure high values of induced

strain (i.e., 10%


6/11

After each test was complete, the specimen was

removed from the load frame and its length (i.e.,

distance between videometry targets) was again mea-

sured and recorded. The specimen was then heated,

above its glass transition temperature, to 120C and held

at that temperature for approximately 30 min. The

specimen was then cooled to room temperature, andthe distance between videometry targets was again

measured and recorded. This heat cycle allowed for

recovery of any stored strain. Each specimen was tested

only once (i.e., one load cycle and subsequent heat cycle)

in order to eliminate any variations in behavior due

to multiple load cycles.

During elevated-temperature tests, a thermal shroud

was fitted around the specimen as discussed earlier

(see Figure 4(b)). The thermal shroud incorporated

electrical heating elements capable of heating the

specimen to the desired test temperatures. Prior to an

elevated-temperature test, the load frame and hardware

were first brought up to the test temperature, then thespecimen was placed into the heated load frame and

brought to temperature. With the specimen at tempera-

ture, the test protocol described previously was

executed. The complete matrix of tests performed

during the present program is presented in Table 3

(note an X in Table 3 indicates a test that was

performed). Tests were conducted up to three maximum

strain values (i.e., 10, 20, and 30%), and at six average

temperatures (i.e., 25, 35, 45, 55, 65, and 85C). In

general, the specimen was a few degrees cooler than the

average test temperature at the beginning of the test, and

a few degrees warmer than the average test temperatureat the end, due to buildup of strain energy during

loading.

Test Results

COMPARISON OF VIDEOMETRY

AND CROSSHEAD STRAIN MEASUREMENTS

As discussed previously, the videometry system was

only used during room temperature tests, so strain

measurements during elevated-temperature tests werebased on crosshead displacement. Of course, deriving

strain from crosshead displacement implicitly assumes

that the crosshead and specimen mounting hardware are

rigid, and all deformation occurs in the specimen. A key

parameter that is needed to estimate strain from

crosshead displacement is the effective gauge length on

the specimen (i.e., the length across which the deforma

tion is assumed to occur). An empirical value of 3.94 cm

(1.55 in.) was determined for this gauge length by

correlating the crosshead displacement data and the

videometry strain data.

To illustrate this correlation, Figure 5 present

the stressstrain response for a specimen tested to30% strain at room temperature. LVDT strain plotted

in Figure 5 was produced by dividing crosshead

displacement by the gauge length of 3.94 cm (1.55 in.)

and the other value of strain was produced using

the videometry system. Note that the crosshead

measured strain and videometry-measured strain

match reasonably well across the range of strain up to

30%. The two strain values differ the most at low strains

due to mechanical settling of the load frame, which is

sensed by the crosshead-motion measurement. However

the present tests are mainly concerned with high

strain response, so the strain estimates based oncrosshead motion were deemed acceptable for al

subsequent tests.

HIGH-STRAIN RESPONSE

AT ROOM TEMPERATURE

Figure 6 shows the stressstrain response from room

temperature tests (i.e., average specimen temperature

Figure 5. Crosshead and videometry strains at 25C.

Table 4. Numerically derived values for CTD-DP-5.1constitutive parameters.

Temperature (C) Eo (MPa) Et (MPa) cr (MPa)

25 470 3.7 20 0.85

35 410 7.7 13 0.65

45 76 5.5 10 0.15

55 4.8 4.4 0.69 0.10

65 6.2 5.2 0.69 0.05

85 5.4 5.4

Table 3. Test matrix.

Average Temperature (C*)

"max (%) 25 35 45 55 65 85

10 X

20 X

30 X X X X X X

*Note the specimen temperature varied by 34C during each test, so thisis an approximate average temperature during the tests.




7/11

equal to 25C) to maximum strains of approximately 10,

20, and 30%, respectively. All three tests show the

same trend. At the onset of loading, the materialexhibits high stiffness (i.e., E% 690 MPa) up to an

induced strain of approximately 3% and an induced

stress of approximately 20 MPa (3000 psi). Within a

few percent of additional strain, the stiffness of the

material drops by approximately two orders of mag-

nitude and remains relatively constant up to the

predetermined maximum induced strain. Once max-

imum strain was reached, crosshead motion was

reversed and the load was removed at the same rate it

was applied. The stiffness of the specimen during

unloading was close to that measured at the onset of

loading (i.e., E% 690 MPa).

It should be apparent from the data presented inFigure 7 that the specimens exhibited a net (i.e.,

residual) strain at the end of each room-temperature

test. After each test was complete and residual strain

was recorded, the specimen was heated well above its Tg(i.e., to 120C) for a period of 30 min, and then cooled

back to room temperature. Once cooled, the remaining

residual strain was measured. As mentioned previously,

the residual strain after load cycling and heat cycling

was determined by measuring the distance between

videometry targets on the specimen. Targets were

initially spaced at a distance of about 2.54 cm (1 in.)

and this distance was measured to an accuracy of

approximately 0.0254mm (0.001 in.) using hand

calipers, so the accuracy of the residual strain measure-

ment was approximately 0.1%.

Figure 7 shows the recovered strain (i.e., the

maximum induced strain minus residual strain),

postload and postheat cycling, for the three room-

temperature tests. Six data points are plotted in Figure 7;

the x data points correspond to the postload-cycle

recovered strain, and data points correspond to the

postheat-cycle recovered strain. The amount of strain

recovered immediately after load cycling was found to

increase with induced strain in approximately the

following proportion:

"r % 3:03 0:16"i 1

where "i is the maximum induced strain, and "r is the

recovered strain. The relationship in Equation (1) is a

near perfect fit to the experimental data, as shown by the

dashed line passing though the postload cycle points in

Figure 7.

The dashed line passing through the postheat-cycle

data points has a slope of one, and corresponds to fully

recovered strain (i.e., zero residual strain). It is

particularly important to note that, for induced strainsup to 30% at room temperature, the CTD-DP-5.1 resin

exhibits complete strain recovery upon heat cycling

above Tg. This result suggests that the significant

reduction in stiffness observed in the material for induced

strains above 3%, is NOT the result of plastic (i.e.,

unrecoverable) strain in the material, but rather it is the

result of a transition between two different elastic states

within the material.

HIGH-STRAIN RESPONSE THROUGHOUT

THE GLASS TRANSITION REGIME

Specimens were strained to approximately 30%, andsubsequently unloaded, while held at approximately 35,

45, 55, 65, and 85C, respectively. This range of

specimen temperatures allowed strain recovery to be

characterized throughout the glass transition regime of

the resin, determined by DMA testing (see Figure 2).

Figure 8 shows the stressstrain response measured

during elevated-temperature tests. Figure 8(a) presents

data from testing at 25, 35, and 45C, Figure 8(b)

presents data from testing at 55 and 65C, and both

plots include data from testing at 85C. Note that there

Figure 7. Strain recovery of specimens tested at 25C.

Figure 6. Comparison of test results at 25C for three maximuminduced strains.




8/11

is an order of magnitude difference in the scale of the

stress axis in these plots.

By comparing the results presented in Figure 8(a),

several key aspects of the material behavior becomeapparent. First, compare the response of the material

under increasing load at 25, 35, and 85C. At the onset

of loading, the material then exhibits a high stiffness

(i.e., E% 690 MPa) up to strains of about 3% and

for temperatures below 45C. The material exhibits a

substantially reduced stiffness (i.e., E% 6.9 MPa) for

higher strains and/or temperatures. Now, compare

the response of the material under decreasing load at

25, 35, and 45C. After achieving maximum strain

and as the load is being reduced, the material again

exhibits a high stiffness (i.e., E% 690 MPa), which

gradually decreases as the load is removed. In general,

the slope of the unloading curve decreases as the stress

approaches zero.

By comparing the slopes of the stressstrain curves in

several key regions, additional patterns in the material

behavior emerge. At the onset of loading and for strains

up to about 3%, the material exhibits approximately the

same stiffness at both 25 and 35C. Similarly, as

the strain is increased above 5%, the material exhibits

the same dramatically reduced stiffness at 25 and 35C.

Furthermore, the material exhibits essentially the same

reduced stiffness at all strain levels when heated to 85 C.

It appears from these data, that the material exhibit

two different stiffnesses depending on temperature

and induced strain level. It is logical to assume tha

these different stiffnesses are associated with differen

intrinsic phases or states within the material

Furthermore, transition from the high-stiffness to the

low-stiffness state appears to be affected by eitheelevating the temperature sufficiently or inducing

sufficient mechanical strain. In general, transition

from the high-stiffness state to the low-stiffness

state occurs within a fairly narrow range of induced

strain, except for the case of loading at 45C. At 45C

the material exhibits a gradual reduction of stiffnes

with increasing strain, for the entire range of strain up

to 30%.

Consider now the results presented in Figure 8(b)

from testing at 55, 65, and 85C. First, note the apparent

deadband in response (i.e., region of zero stiffness)

between approximately 5 and 9% induced strain is an

artifact of compliance in the load frame and not a trueresponse of the material (recall that the strain measure

ments in these tests are based on crosshead motion)

Neglecting this artifact in the data, a key feature to note

is that the slope of the stressstrain curve, on the portion

of the curve corresponding to increasing load, is

essentially the same at these three test temperatures

Conversely, the slope of the stressstrain curve, on the

portion of the curve corresponding to decreasing load

decreases with increasing temperature. In the limit, at a

temperature of 85C, the slope of the loading and

unloading portions of the stressstrain curve are nearly

equal and the hysteresis is minimal. This effect at 85C is

exactly the same as the pseudoelastic effect in shapememory alloys whereby the metals are stressed above

their phase transition temperature and show complete

recovery upon unloading. No documented work on

shape memory polymers was found showing the same

effect.

It should be apparent from the data presented in

Figure 8 that the material retains residual strain a

the end of each elevated-temperature load-cycle test

except for the test at 85C. After completion of each

of the elevated temperature tests, the residual strain

was recorded, the specimen was heated to 120C for

30min and cooled back to room temperature, and

the remaining residual strain was measured. As men

tioned previously, the residual strain after load

cycling and heat cycling was determined by measuring

the distance between the videometry targets on the

specimen.

Figure 9 compares the maximum induced strain with

the residual strains measured postload and posthea

cycling, for the six elevated-temperature tests com

pared in Figure 8. The amount of strain recovered

immediately upon removal of the load generally

increases with increasing temperature. As mentioned

Figure 8. Comparison of stressstrain response at elevated tem-peratures: (a) Data from moderate-temperature tests; (b) Data fromhigh-temperature tests.




9/11

previously, essentially all of the induced strain is

instantaneously recovered upon removal of load

with the material at 85C, which is 14C above Tg.

The residual strain after heat cycling is essentially zero

for all test temperatures. Hence, the CTD-DP-5.1 resin

exhibits essentially complete strain recovery for all test

conditions considered.

MODELING OF SHAPE MEMORY

MECHANICS OF AN EMC RESIN

The data presented in the last section indicate that the

CTD-DP-5.1 resin does not exhibit plastic yielding at

strains up to 30%, and within the temperature range of

2585C. Furthermore, it was deduced that the sig-

nificant drop in stiffness at an induced strain between 3

and 5% (below 45C) is the result of a transition

between two different elastic states within the material

as opposed to plastic deformation. This section presents

a lumped-parameter model of the resin that exhibits two

elastic states and predicts all of the key response effects

seen in the CTD-DP-5.1 resin.

Figure 10(a) presents a sketch of the model. It

incorporates four elements: two elastic springs, a

viscous damper, and a friction slider. The friction

slider, which can be stuck or free to slide, represents

the two elastic-response states seen in the experimental

data. The model is an adaptation of the Valanis

Model from viscoplasticity (Valanis, 1971). A key

feature is that the friction slider progresses from

fully stuck to fully free over a finite range of strain.

The primary difference between the present application

of the Valanis Model and its traditional application

in plasticity theory, is that the values for the four

empirical parameters vary with temperature. In parti-

cular, the stick-slip threshold of the friction slider, cr,

decreases with increasing temperature and vanishes at

temperatures approaching Tg. This temperature variation

is essential to analytically capture the shape memory

behavior of the material.The Valanis Model is governed by the following

nonlinear first order constitutive equation:

_ t Eo _"" t 1 sgn _"" t =cr Et" t t

1 sgn _"" t =cr Et" t t

C"" t

2

The stiffnesses, Eo and Et, damping, C, and the stick-slip

stress, cr, in Equation (2) are defined in Figure 10.

The parameter, , in Equation (2) controls the rate at

which the friction slider progresses from fully stuck

to fully slipping. The value of is restricted to be withinthe range of 0 1, and high values of correspond

to sudden transition from sticking to slipping, whereas

small values of correspond to gradual transition

from sticking to slipping. Figure 10(b) presents a

sketch of a typical stressstrain response predicted

using Equation (2), and illustrates the effect of on

the response.

Consider now the solution of Equation (2). In

general, solving Equation (2) requires knowledge of

the strain history, "(t), strain-rate history, _""(t), and

Figure 10. Viscoelastic model of EMC resin: (a) Lumped-parametermodel; (b) Typical stressstrain response.

Figure 9. Strain recovery of specimens tested at elevated tempera-

tures.




10/11

strain-acceleration history, ""(t). In the present program,

all testing was conducted at a constant strain rate,

_""test, hence:

"" t 0

_"" t _""test

" t _""testt

With these functions defined, Equation (2) can be

integrated numerically using a variety of integration

techniques (Burden, 1985). In the present study, Eulers

Method was applied to convert the differential equation

in Equation (2) to the following difference equation.

n 1 n Eo _""testt1 sgn _"" =cr Et _""testnt n

1 sgn _"" =cr Et _""testnt n

4

where

t is the numerical integration time step, n is thenumber of the time step, and n is the stress at the nth

time step.

For a given set of data, best-fit values for the

stiffnesses, Eo and Et, and the stick-slip stress, cr, can

be determined by least-squares fitting of straight lines

to the appropriate regions of the data as sketched in

Figure 10(b). A best-fit value for must be determined

iteratively by solving Equation (4) forselected values of,

and comparing the results to the test data. The best-fit

values for these constitutive parameters are presented in

Table 4 and Figure 11 for the range of test temperatures

considered in the present program. Figure 12 presents

a comparison of the test data (presented originally inFigure 8), and the numerical solutions of Equation (4).

In general, the numerical model captures all significant

trends in the observed behavior, and the numerical and

experimental results agree well for all test temperatures.

Consider now the variation of the constitutive

parameters as a function of temperature shown in

Figure 11. For comparison, the shear modulus, G, of

the CTD-DP-5.1 resin (from DMA test data presented

in Figure 2) is also plotted in Figure 11. Note that the

computed values for Eo, cr, and all decrease with

increasing temperature, similar to the trend observed for

G during DMA testing. On the other hand, the value for

Et remains relatively unchanged with temperature.

The most notable difference between the trendobserved in the DMA data and those observed in the

numerically derived constitutive parameters, is that the

drop in Eo, cr, and occurs at a lower temperature

than the drop in G observed in DMA testing. This

difference in temperatures, which is between 20 and

25C, indicates that the molecular transition associated

with the shape memory effect in CTD-DP-5.1 occur

below the glass transition temperature, Tg. In particular

it appears that the peak in the shape memory phase

transition occurs in the range of 4550C, rather than at

the Tg, which is 71C.

This result implies that the traditional approach of

basing the thermo-mechanical cycle for shape memorypolymers (e.g., Table 2) on Tg might be inappropriate

It might be more appropriate to define a shape memory

transition temperature, on which thermo-mechanica

cycles can be based.

Figure 12. Comparison of test data with model predictions: (aModerate-temperature test results; (b) High-temperature test results

Figure 11. Numerically derived values for CTD-DP-5.1 constitutiveparameters.




11/11

One final point must be reiterated regarding the

variation in constitutive parameters with temperature,

and the resulting ability of the Valanis Model

(i.e., Figure 10(b)) to predict shape memory behavior.

As mentioned previously, the original application of the

Valanis Model for predicting viscoplastic behavior did

not require the parameters of the model to vary withtemperature. In the present application for predicting

shape memory response in EMC resins, the variation of

the parameters with temperature is critical to capturing

all aspects of the material behavior. Clearly, the

variation of the parameters with temperature is neces-

sary to accurately capture the loadcycle response

behavior observed at different temperatures. Of equal

importance (but possibly less obvious), the stick-slip

threshold of the friction slider, cr, must decrease with

increasing temperature and must vanish at temperatures

approaching Tg, if the model is to predict the recovery of

residual strain described in Figures 7 and 9.

CONCLUSIONS

The present paper was focused on a shape memory

polymer resin for Elastic Memory Composite (EMC)

materials. Heretofore undocumented response behavior

was characterized through a series of thermo-mechan-

ical tests of an EMC resin. Specifically, it was found that

the phase change, associated with the shape memory

effect in EMC resins, can be excited either under

combined thermal and mechanical loading (i.e., using

the loading cycle listed above), or under pure mechanical

loading. In other words, it was found that largemechanically induced strains can be induced and

recovered due solely to mechanical loads. Shape

memory alloys exhibit behavior similar to this.

The discovery of this intrinsic behavior has led to the

identification of a simple lumped-parameter model

that accurately represents the thermo-mechanical and

shape memory response of EMC resins. The so-called

Valanis Model has been shown to correlate very well

with measured stressstrain response over a range of

temperatures encompassing the glass transition regime

of the resin. Through application of this model, it

appears that the molecular transition associated with the

shape memory effect occurs at a temperature other than

the glass transition temperature, Tg. This result implies

that the traditional approach of basing the thermo-

mechanical cycle for shape memory polymers on Tgmight be inappropriate. It might be more appropriate to

define a shape memory transition temperature, on

which thermo-mechanical cycles can be based.

Ultimately, it is hoped that the present work will

improve the ability to model and predict the shape

memory mechanics of fiber-reinforced EMC materials

that are made with these shape memory resins.

NOMENCLATURE

C material damping (Pa s).

Eo effective modulus at low strain (Pa)

Et effective modulus at high strain (Pa)

Tg resin glass transition temperature (C)

"i induced strain"r recovered strain

_"" constant strain rate during tests (s1)

applied stress (Pa)

n stress at the nth time step (Pa)

cr stick-slip stress of friction slider (Pa)

microslip parameter

REFERENCES

Anon. 1987. ASTM Designation D638-86 Standard Test Methodfor Tensile Properties of Plastics, Annual Book of ASTM

Standards, Section 8 Plastics, Vol. 8.01, pp. 218, Plastics(I)C117D1600.

Burden, R.L. and Faires, J.D. 1985. Numerical Analysis, pp. 205206,PWS-Kent Publishing Company, Boston, MA.

Gall, K., Mikulas, M.M., Munshi, N.A., Beavers, F.L. and Tupper,M.L. Nov 2000. Carbon Fiber Reinforced Shape MemoryPolymer Composites, Journal of Intelligent Material Systems andStructures, 11:877886.

Gall, K., Tupper, M.L., Munshi, N.A. and Mikulas, M.M. 2001.Micro-Mechanisms of Deformation in Fiber ReinforcedPolymer Matrix Elastic Memory Composites, Presented at the42nd AIAA/ASME/ASCE/AHS/ASC SDM Conference, April1619, Seattle, WA, AIAA Paper No. 2001-1419.

Lake, M.S. and Beavers, F.L. 2002. The Fundamentals ofDesigning Deployable Structures with Elastic MemoryComposites, Presented at the 43rd AIAA/ ASME/ASCE/AHS/

ASC SDM Conference, April 2225, Denver, CO, AIAA Paper No.2002-1454.

Liang, C., Rogers, C.A. and Malafeew, E. April 1997. Investigationof Shape Memory Polymers and Their Hybrid Composites,Journal of Intelligent Material Systems and Structures, 8:380386.

Murphey, T.W., Meink, T. and Mikulas, M.M. 2001. SomeMicromechanics Considerations in the Folding of RigidizableComposite Materials, Presented at the 42nd AIAA/ASME/ASCE/AHS/ASC SDM Conference, April 1619, Seattle, WA, AIAAPaper No. 2001-1418.

Ni, Q-Q. et al., 2000. Development of Smart Composites Based onShape Memory Polymer, Presented at the InternationalSymposium on Smart Structures and Microsystems, Oct. 1921,Hong Kong.

Otsuka, K. and Wayman, C.M. (eds), 1998. Shape Memory Materials,Cambridge University Press, Cambridge, UK.

Pappa, R.S., Jones, T.W., Robson, S. and Shortis, M.R. 2002.Photogrammetry Methodology Development for GossamerSpacecraft Structures, to be presented at the 43rd AIAA/ASME/ASCE/AHS/ASC SDM Conference, 2225 April, Denver, CO.

Tobushi, H., Hashimoto, T., Hayashi, S. and Yamada, E. August1997. Thermomechanical Constitutive Modeling in ShapeMemory Polymer of Polyurethane Series, Journal of IntelligentMaterial Systems and Structures, 8:711718.

Tobushi, H., Hashimoto, T., Ito, N., Hayashi, S. and Yamada, E.1998. Shape Fixity and Shape Recovery in a Film of ShapeMemory Polymer of Polyurethane Series, Journal of IntelligentMaterial Systems and Structures, 9:127136.

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