44 A. Pai et al.
(a) (b)
(c) (d)
Fig. 3.1 Typical stress-strain curves for martensite and austenite: monotonic loading (plots a and
b), cyclical loading (plots c and d) [32]
Fig. 3.2 General
characteristic of SMA
stress-strain behaviour
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 45
the detwinned martensite is elatically deformed until plasticity (not shown) sets in.
For a test conducted above Af (100 % austenite), in segment a − b, the austenite is
elastically deformed. In segment c − d, austenite to stress-induced-martensite (SIM)
transformation proceeds up to 2. Then, for the rest of e − f , 100 % martensite is elas-
tically deformed until plastic deformation starts.
The basis of the model is a closed form mathematical description of this ‘s-
shaped’ curve in a single step, without the use of conditional statements but including
parameters to describe the curvatures present. The curve is described by the ‘base
equation’, bq, in Eq. (3.4) where 1, 2 and 3, calculated in Eqs. (3.1), (3.2) and
(3.3) respectively, describe the function, roughly speaking, in segments a − c, c − d
and d − f , respectively. Here, E1, E2 and E3 are the slopes of the curve (moduli) in
segments a − b, c − d and e − f , respectively, k1 and k2 describe the curvatures of
the function in segments b − c and d − e, respectively, 1 and 2 are the strains at
the ‘knees’ and ( p, p) are the coordinates of any point on the curve. In the model,
they are the end coordinates of the function, but this is mathematically not required.
An extra coordinate ( pp, pp) is used to represent the start coordinates of the func-
tion. Note that the vast majority of existing stress-strain models use the dash-dotted
straight line segments in Fig. 3.2 as an approximation. The implementation in this
case requires a series of conditional statements to distinguish between the three seg-
ments ≤ 1, 1 < < 2 and ≥ 2 and the curvatures at the knees in the −
function are replaced by sharp corners (k1 and k2 are ∞).
Analysis of the experimental data has shown that the unloading and reloading
behaviour of martensite follow a parabolic locus, as shown exemplary by the green
dash-dotted curve in Fig. 3.1 (plot (b) and (c)). The parabolic shape can be explained
based on the microstructural condition of the Ni-Ti SMA wires. For improved shape
memory behaviour, wires are strongly textured to allow for high transformation
strains. However, minor volume fractions of grains of all possible orientations can
be expected to be found within these wires. Grain orientation corresponds to critical
stress levels for phase transformation of single grains [3, 4, 33]. Thus, small volume
fractions of the wire might show a premature and others sluggish phase transforma-
tion. As a consequence, unloading and reloading in martensite is characterized by
the smooth curvatures depicted. Particularly in the case where twinned martensite is
present in the material, the parabolic nature of the stress-strain curve can be further
attributed to internal stresses present in the deformed microstructure providing the
driving forces for a minor backward or forward movement of the twin boundaries.
Further micro-structural analysis to confirm this is planned.
To model this behaviour, Eq. (3.4) is augmented with q in Eq. (3.5) for a parabola
in segment 2 − f (see the red dashed line in Fig. 3.2) or with q in Eq. (3.6) for a
parabola in segment a − 1 to model the green dotted line in Fig. 3.2. The parame-
ter q is the parabolic constant. Consequently, the final base equation is given by
Eq. (3.7). Note that should a parabolic locus be absent, then q = 0, rendering q = 0
and Eq. (3.7) is identical to Eq. (3.4).
46 A. Pai et al.
1 = (E1 − [ − p + 1 ln ( 1 + ek1( p− 1) )] (3.1)
E2) k1 1 + ek1( − 1) (3.2)
(3.3)
2 = E2( − p[) + p 1 ln ( 1 + e−k2( p− 2) )] (3.4)
3 = (E3 − E2) − p − k2 1 + e−k2( − 2)
bq(E1,2,3, 1,2, k1,2, ( p, p), ) = 1 + 2 + 3
For unloading:
[ e−k2( − 2))]
q = q( − 2) − 2 + 1 ln ( +
− k2 1
[ 1
q( p − 2) p − 2 + k2 ln ( + e−k2 ( p − 2 ) )] (3.5)
1
(3.6)
For loading: (3.7)
[ e−k1( 1− ))]
q = q( − 1) − 1 − 1 ln ( +
− k1 1
[ 1
q( p − 1) p − 1 − k1 ln ( + e−k1 ( 1 − p ) )]
1
bq(E1,2,3, 1,2, k1,2, ( p, p), q, ) = 1 + 2 + 3 + q
The ubiquitous s-shaped curves in SMAs can herewith be described mathemati-
cally with one closed-form equation. With the base equation in Eq. (3.7), the entire
SMA model algorithm is described in the following section.
3.3 SMA Model Algorithm
The complete model to describe SMA constitutive behaviour is characterised by the
following steps, as shown graphically in Fig. 3.3:
1. Model initialisation: The model is initialised once, with 7 parameters, E1, E2, E3,
1, 2, k1, k2 from an identification process (Sect. 3.4) using data from a simple
monotonic experiment, as in the plots (a) and (b) of Fig. 3.1. All other parameters,
q, ( pp, pp), ( p, p) are set to 0.
2. Model update: The parameters set by the initialisation process in step 1 are
updated by an update process (Sects. 3.5 and 3.6), that is triggered each time
the input strain changes direction (from loading to unloading or vice versa). The
update process includes the update of ( pp, pp) and ( p, p) to the start and end
coordinates of the previous loading sequence in order to track the stress-strain
history of the material and to ensure continuity of the calculated stress.
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 47
Fig. 3.3 Model algorithm
Consider, for example, an input strain as in Fig. 3.4a, where initial loading to 4 %
strain is followed by unloading to 2 % and reloading to 8 % strain. Initially, at the
start of loading, ( p, p) and ( pp, pp) are set to the starting coordinate (0, 0), q = 0
and the model is initialised with the identified parameters. Using exemplary para-
meters, the red dashed curve in Fig. 3.4b is generated using Eq. (3.7). The SMA,
however is loaded only upto 4 % and at this point, the input strain changes direction
(unloading). Here, ( pp, pp) and ( p, p) are updated to the start and end point of
the loading curve, (0, 0) and (4, 475), respectively and the model is updated with
new parameters, which are calculated using the parameter update algorithm (see
Sects. 3.5 and 3.6) yielding the green dash dotted curve in Fig. 3.4. Unloading pro-
ceeds until 2 % strain, where once again the input strain changes direction (reload-
ing). Then ( pp, pp) and ( p, p) are set to the start and end points of the unloading
curve, (4, 475) and (2, 190), the model is once again updated with new parameters
and reloading proceeds until 8 % strain. The complete stress-strain curve correspond-
48 A. Pai et al.
(a) (b)
Fig. 3.4 Modelling algorithm sequence: a input strain, b stress versus strain
ing to the input strain is the bold blue curve in Fig. 3.4b. Note that for every cycle,
the parameters E1, E2, E3, 1, 2, k1, k2, q, ( pp, pp), ( p, p) are sufficient to describe
the s-shaped stress-strain behaviour. The following sections present the initialization
and update process in detail.
3.4 Model Initialization: Parameter Identification
In the model initialization process, the parabolic coefficient q is set to 0 due to the
fact that the initial loading curves don’t have any parabolic components. Further, the
values ( p, p) and ( pp, pp) are set to the initial strain and stress in the SMA. As
typical experiments start with 0 MPa stress and 0 % strain, ( p, p) and ( pp, pp) are
commonly (0, 0). The remaining parameters are extracted with an automatic para-
meter identification algorithm that accepts the stress-strain data from a monotonic
experiment as an input and produces parameters E1, E2, E3, 1, 2, k1, k2 as an output.
This occurs in the following steps:
1. Selection of any two points in the segments a − b, c − d, e − f (see Fig. 3.2):
These are called ( 1ab, a1b), ( a2b, a2b); ( 1cd , c1d ), ( 2cd , c2d ); ( 1ef e1f ), ( 2ef , e2f ).
2. Identification of slopes E1, E2, E3 using Eq. (3.8), where n is either 1, 2 or 3 and
xy is either ab, cd or ef .
3. Calculation of 1, 2 as the intersection of the lines through the points in step
1 with slopes in step 2 using Eqs. (3.9) and (3.10) (see the dash-dotted lines in
Fig. 3.2).
4. Calculation of k1, k2 with Eqs. (3.11) and (3.12), where 1 and 2 are the stresses
at 1 and 2 (extracted from the data).
5. Optimization of all parameters to minimize the mean square error between the
data and the model using an unconstrained, gradient-based, nonlinear optimiza-
tion algorithm, e.g. fminsearch from MATLAB®, with the values calculated in
steps 2–4 above as the initial values.
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 49
The steps above are used for the loading curve in the monotonic experiment. From
the unloading curve, only two values are required: u1ld, the strain at the first unload-
ing knee and E2uld, the slope of the unloading plateau, with which the ‘width’ of the
hysteresis loop is calculated. Both values are easy to extract from the experimen-
tal data. Note that when the material is martensitic at the start of the experiment,
unloading is characterised by the presence of residual strain and no hysteresis loop
is present. Therefore for martensite, 1uld and E2uld are both set to 0. The next two
sections present the Model Parameter Update process.
En = x2y − x1y (3.8)
2xy − 1xy (3.9)
(3.10)
1 = ( c1d − E2 1cd ) − ( a1b − E1 a1b) (3.11)
E1 − E2 (3.12)
2 = ( c1d − E2 c1d ) − ( e2f − E3 2ef )
k1 =
( E3 − E2 − a1b − E2 1 + E1 a1b )−1
− 1 + 1 E1 − E2
−ln(2)
( 2 − e2f − E2( 1 − e2f ) )−1
ln(2) − 2 E3 − E2
k2 = +
3.5 Model Parameter Update: Parameter Calculation
for Austenite
The model parameter update process is triggered by a change in direction of the input
strain. This direction change is detected by using the signum (sgn) function to ascer-
tain a zero crossing of the derivative of the input strain. The parameters ( pp, pp) and
( p, p) are updated first to the starting and end coordinates of the previous sequence.
The rest of the parameters are calculated based on whether the material is in the
martensitic or austenitic state at 0 stress, as shown in the following sections. In this
section, the update process for austenite will be presented. Martensite follows in
Sect. 3.6 below. In order to differentiate between the identified and calculated para-
meters, the calculated parameter names have the superscript ∗. For clarity, the model
update calculations are presented in the following sections for austenite unloading
and reloading separately and Fig. 3.4 will be used for explanation. A summary of the
parameter update is given in Fig. 3.9.
50 A. Pai et al.
3.5.1 Austenite Unloading
In order to model austenite unloading behaviour, a number of known phenomena
have to be considered. One of these is the formation of residual strain, r. Due
to several reasons, e.g. plastic deformation of the martensite and micro-yielding
effects, degradation of SMAs can be present, manifesting itself in the accumulation
of irrecoverable portions of strain in the reverse transformation [2, 3]. The amount
of residual strain saturates after about 50 cycles according to a negative exponent
(c.f. Eq. (3.13),1 where n is the number of cycles) due to strain hardening (training
effect). This is consistent with findings available in literature, e.g. in [29].
r = (0.37)(1 − e−0.035(n−2)) + 0.05 (3.13)
For austenite unloading, the values of E1∗, E2∗ and k1∗ remain the same as the val-
E1∗ = E1, E2∗ = E2uld and k1∗ = k1. The rest
ues identified in the initialization step i.e. need to be updated (see Fig. 3.6a where
of the parameters E3∗, ∗1, 2∗, k2∗ and q∗
the green dash dotted unloading curve is considered) and their respective calcula-
tions are shown below, considering that ( p, p) are the already updated values (the
∗ values) i.e. the value at which the previous loading ended and where this current
unloading sequence begins. The calculation of the parameters are highly dependant
on the volume fraction of martensite, , which with increasing strain is hypothe-
sised to progress according to the curve shown in Fig. 3.5 i.e. when ≤ 1, then the
material is fully austenitic and = 0. Conversely, when ≥ 2, the material is fully
martensitic (SIM) and = 1. Between the knees i.e. 1 < < 2, the formation of
martensite progresses linearly. is mathematically described by Eq. (3.16), where n
in Eq. (3.14) is proportional to the slope of the curve at m (Eq. (3.15)), the midpoint
between the knees. The selection of such a phase fraction profile is based on the
hypothesis that the evolution of the volume fraction of martensite is directly related
to the input strain. When the input strain is below 1, it causes elastic deformation
of the austenite present, but is not sufficient to cause propagation of the martensite
Fig. 3.5 Evolution of
martensite fraction as
function of strain
1The values 0.37, −0.035 and 0.05 are found empirically from experimental data.
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 51
fraction. Conversely, when the input strain is above 2, where the material has fully
been transformed to martensite, additional strain does not contribute to the evolution
of more martensite but rather to elastic deformation. The propagation of martensite
occurs mainly when the input strain is in between the knees (the plateau), moreover,
this propagation is linearly dependant on the input strain.
n = 2 4 1 (3.14)
− (3.15)
(3.16)
m = 2 + 1
2
= 1
1 + e−n( − m)
The calculation of the required parameters is as follows:
∙ E3∗: The calculation of E3∗ is highly dependant on the volume fraction of martensite
present in the material at p, the strain where unloading occurs. It is calculated with
Eq. (3.17) where p is evaluated at = p in Eq. (3.16).
E3∗ = (1 − p)E1 + pE3 (3.17)
Equation (3.17) implies that should unloading occur when p = 0 (100 % austen-
ite), then E3∗ = E1 i.e. elastic unloading with the austenitic modulus E1. Should
unloading occur when p = 1 (100 % martensite), then unloading is also elastic
but with the martensitic modulus E3. Therefore, E3∗ = E3. If however, unloading
occurs between the knees i.e. 0 < p < 1, then the microscopic composition of
the SMA is a mixture of austenite and martensite and the unloading slope E3∗ is a
weighted linear combination of the slopes E1 and E3.
∙ ∗2: This parameter describes the start of the reverse transformation of marten-
site to austenite and is also highly dependant on p. It is updated using (3.18) by
considering the width of the hysteresis loop, calculated with u1ld and E2uld. r is
the residual strain, calculated with Eq. (3.13). The dependence on p is achieved
through E3∗, which itself is highly dependant on p.
2∗ = E3∗ p − E1 r + (E1 − E2uld ) u1ld − p + r (3.18)
E3∗ − E2uld
∙ q∗ and k2∗: In addition to the unloading moduli calculated above, the experimental
data shows a parabolic locus. As mentioned earlier, this parabolic locus occurs due
to sluggish behaviour of individual grains. The material unloads elastically until
r e∗2v,ecraslecutrlaantesdfoarmboavtieo,nwshtreerses,th e ∗2rei.vee.rsstereSssIMat- a 2∗us(tseeneitFeigtr.a3n.s6fao)rims actailocnulsattaerdtsu. sTinhge
Eq. (3.19). The calculation of the parabolic coefficient q to represent grain slug-
gishness then proceeds with the quadratic formula in Eq. (3.20). k2∗ is subsequently
52 A. Pai et al.
(a) (b)
Fig. 3.6 Parameter update for unloading (a) and reloading (b) in austenite
calculated with Eq. (3.21) to ensure a smooth transition between the parabola and
the rest of the curve.
∗2 = E3∗( 2∗ − p) + p (3.19)
a = ( p − √ 2∗)2; b = ∗2 − p − E3∗( 2∗ − p); c = ln(2)(E3∗ − E2∗)2
q∗ = −b − b2 − 4ac
2a (3.20)
k2∗ = 4q (3.21)
E3∗ − E2∗
∙ 1∗: With all the other values, 1∗ is then calculated with by solving for 1 in Eq. (3.7)
yielding Eq. (3.22) where 2, 3 and q are calculated with Eqs. (3.2), (3.3) and
(3.5), evaluated at = r and r = 0. The calculation shows the dependency of
on ∗1,
the hysteresis loop width, which is based clearly on p (through a dependance
on ( p, p) and E3∗), a phenomenon that is observed in experiments (see
Sect. 3.7). ( )
k1 + p
r − 3 − 2− q
E1 −E2
= 1 ln ⎛⎜ e − e ⎞⎟∗k1 p (3.22)
1 ( )
k1
k ⎜⎝ e − 1 ⎟⎠1
r − 3 − 2− q + p − r
E1 −E2
A summary of the parameter calculation is given in Fig. 3.9.
3.5.2 Austenite Reloading
FEo2∗raanudst e∗1nhitaevreetlooabdeinugp,dtahteedv,aalsuesshoowf nE3∗in, q∗, k1∗ and k2∗ remain the same. Only E1∗,
Fig. 3.6b, where, this time, the blue solid
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 53
reloading curve is considered. E1∗ is calculated exactly as in Eq. (3.17) and is repeated
here for clarity.
E1∗ = (1 − p)E1 + pE3 (3.23)
In reloading, a distinction is made between partial or complete reloading, depending
on the end point of the previous unloading cycle (and therefore the reloading start
point). Should the unloading end point be less than 1uld, then complete reloading
is considered, as the material composition is 100 % austenite. Conversely, partial
reloading is considered when the unloading end point is greater than 1uld, where the
material is a mixture of austenite and SIM, as is the case in Fig. 3.6 for the solid blue
reloading curve.
1∗ and E2∗ are updated only when the previous unloading step was partial. 1∗ is
calculated with the hypothesis that formation of SIM starts at a critical stress value,
that is given by the initial yield strength, 1 (see Figs. 3.2 and 3.6b). Using E1∗,
calculated in Eq. (3.23), 1∗ is given by Eq. (3.24) and E2∗ is consequently calculated
with Eq. (3.25).
∗1 = 1 − p + p (3.24)
E1∗ (3.25)
2 − 1
E2∗ = 2 − 1∗
A phenomenon that is exclusive to austenite reloading is the formation of ‘steps’
in the austenite plateau and a decrease of the plateau stress when reloading follows
periods of partial unloading (partial in this case meaning unloading before the 2nd
knee). These effects are shown in Fig. 3.7a, and were also presented, among oth-
ers, in the experimental data of [34], who attribute these phenomena to functional
fatigue with the following explanation: Deformation of the austenite beyond the 1st
knee is characterised by the formation and propagation of SIM bands. Outside these
(a) (b)
Fig. 3.7 Partial loading cycles in austenite showing ‘steps’ (a), modelling of last step (b)
54 A. Pai et al.
bands, the material is still austenitic. When the material undergoes cyclical partial
unloading, then the band interfaces
first traverse previously cycled regions. These regions are associated with a lower criti-
cal stress of interface propagation. For the interface to pass into the uncycled region, the
macrosopic stress must increase. When the interfaces have completely passed into the uncy-
cled region, the macroscopic stress reaches the level of the upper plateau [34],
therefore causing the formation of ‘steps’ macroscopically. Should the SMA be
exposed to several partial loading cycles as in Fig. 3.7a, then a step occurs at each
unloading point as though the material has ‘memory’ of the unloading positions. The
most pronounced step is at the last unloading cycle (or at the absolute strain maxi-
mum of the previous loading cycles) as shown by the red dotted circles in Fig. 3.7a.
To avoid unnecessary complexity, only this pronounced step is considered.
The algorithm is as follows:
∙ A step of height sn, for n = 1, signifying that only one step is considered, is cal-
culated as the stress difference between the red dotted plateau and the solid blue
plateau in Fig. 3.6b at pp using Eq. (3.26). Here, np and pnp are calculated with
Eq. (3.4) using ∗ parameters, input = pnp, p = np for np and p = npp for npp
(See inset in Fig. 3.6b). Note that for n = 1, pn = p and npp = pp.
∙ is calculated with Eq. (3.4) using ∗ parameters and as the input strain.
∙ sn calculated in Eq. (3.27) for n = 1 is then added to . The result is shown by the
solid blue line in Fig. 3.7b, where a ‘step’ at pp is visible (compare to Fig. 3.4b,
where no step is present).
sn = pnp − np (3.26)
(3.27)
sn = sn
1 + e−ks( − pnp)
Note that if there is a need to consider 2 or more steps, n = 2, 3, 4, … can also
be calculated in the manner above and added to , thereby easily allowing for the
model to be extended as required. A summary of the calculations in this section are
also given in Fig. 3.9.
3.6 Model Parameter Update: Parameter Calculation
for Martensite
In this section, the model parameter update for martensite is presented separately for
loading and reloading using Fig. 3.1c for explanation (see Fig. 3.8). The calculations
are summarised in Fig. 3.9.
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 55
(a) (b)
Fig. 3.8 Modelling martensite unloading (left) and reloading (right)
3.6.1 Martensite Unloading
Martenite unloading is characterised by the presence of residual strain. The mod-
elling of martensite unloading is quite simple in that only q∗ and E3∗ need to be
calculated as shown in Fig. 3.8. The parameters E1∗, E2∗ are set to 0 because these
portions of the curve do not exist, 1uld is also set to 0 because loading and unload-
ing in martensite displays no hysteresis. All other parameters remain unchanged (see
Fig. 3.8a). The calculation of q∗ and E3∗ use exactly the same Eqs. (3.20) and (3.17)
respectively, as for austenite, where in this case p refers to the fraction of detwinned
martensite present in the material at the point of unloading.
3.6.2 Martensite Reloading
As mentioned earlier, martensite reloading is also characterised by a parabolic locus
(see Fig. 3.1) and is attributed to the presence of internal stresses in the material. The
value of q and 1 are the only parameters that need updating as shown in Fig. 3.8b. 1∗
is simply set to the value of pp, the point at which the previous unloading took place
because detwinned martensite formation will start again when the plateau stress is
reached and this occurs at pp. The value of q is calculated using Eq. (3.28), where
q = 1∗
uated at = pp and 1, 2 and 3 are calculated with Eqs. (3.1), (3.2) and (3.3) eval-
= q and using the updated values (the ∗ values) for the other parameters
i.e. E1 = E1∗ and E1 = E2∗. All other parameters remain unchanged.
q∗ = 1 + 2 + 3 (3.28)
( q − p)2
56 A. Pai et al.
Fig. 3.9 Parameter update summary for austenite and martensite. Numbers in brackets are equation
numbers
3.7 Experimental Validation and Discussion
In order validate the model, a number of tensile stress-strain experiments were car-
ried out using a servo hydraulic testing rig. The experiments were performed at
room temperature with two sets of 0.5 mm diameter poly-crystalline Ni-Ti SMA
wires, differing only in their Af temperatures (95 ◦C and −25 ◦C). Consequently,
both a 100 % martensitic and a 100 % austenitic initial condition at room tempera-
ture were established. The martensite wires were placed in a furnace at 400 ◦C for
1 min and allowed to cool to room temperature before the experiment. This ensured
that all residual strains in the wire were eliminated prior to testing. The wire speci-
mens were mounted in the testing machine using custom built fixing grips featuring
grooves of appropriate diameter to facilitate installation and alignment. All geomet-
rical dimensions were measured to enable for correct stress and strain calculation.
The wire lengths were about 60 mm. The tensile experiments were conducted under
constant cross-head displacement velocity of 2 mm/min. Loading-unloading exper-
iments were performed using the same set-up. For loading, the machine was run
in displacement control up to the given displacement value, while unloading was
conducted in displacement control up to a minimum force level of 5 N (approxi-
mately 25 MPa). All experiments were carried out on wires from the same batch.
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 57
The monotonic experiments were carried out on a wire sample, A1, for austenite and
M1, for martensite. The corresponding data was used to extract the model parameters
(see Sect. 3.7.1). Wire sample A1 was subsequently used for both austenite complete
and partial cyclic loading experiments (see Sects. 3.7.2 and 3.7.3). The results for
the experiments for martensite cyclic loading with wire sample M1 are shown in
Sect. 3.7.4 and the results with other wire samples are shown in Sect. 3.7.5. Further,
the tic, toc commands in MATLAB® were used to give a ball park value for the com-
putational time of the model. The model was run 20 times each on a computer with
an Intel Core i3-M330 processor with a CPU clock speed of 2.13 GHz and 4 GB of
RAM and the average value was then documented as the computational time.
3.7.1 Monotonic Loading and Unloading and Parameter
Identification
In these experiments, the wire samples were loaded up to a maximum displacement
of 5 mm (approx. 8.5 % strain) followed by an unloading ramp to a minimum force
of 5 N. The results are plotted as solid black curves in Fig. 3.10 for both austenite
(Fig. 3.10a) and martensite (Fig. 3.10b). The model parameters deduced from the
experimental data are shown in Table 3.1. With all the required parameters identi-
fied, the model produces the results depicted by the red dashed line in Fig. 3.10. The
results are in good agreement with experimental data especially at the knees where
(a) (b)
Fig. 3.10 Austenite (a), Martensite (b): Monotonic loading, unloading—experiment and model
Table 3.1 Model parameters identified from monotonic experiments
E1 E2 E3 1 (%) 2 (%) k1 (–) k2 (–) u1ld E2uld
(GPa) (GPa) (GPa) (%)
0.3 0
Austenite 40 0.7 25 1.13 7.45 3.5e3 1.4e3 0 0
Martensite 29 0.39 15.8 0.58 6.43 580 170
58 A. Pai et al.
most other models are not accurate enough. The computational time was 29 ms for
martensite and 30 ms for austenite. Note that for the sake of simplicity, the model
does not account for the ‘peaks’ at strains of about 0.5 and 5.5 % for austenite unload-
ing in Fig. 3.10. These peaks can be related to the phase transformation behaviour in
SMAs. In the case of pseudoelastic behaviour, the austenite reverse transformation
from the fully martensitic state can be separated into two parts: initiation of initial
austenite followed by movement of band like phase fronts. Such kind of local trans-
formation behaviour is naturally accompanied by a sudden change in stress-strain
response [4, 35], i.e. a load increase as seen in Fig. 3.10. This effect is not mod-
elled in order to avoid complexity and thereby maintain the model’s computational
efficiency.
3.7.2 Austenite Complete Cyclic Loading
In these experiments, the Ni-Ti wires having an Af of −25 ◦C were loaded in displace-
ment control with the input displacement as shown in Fig. 3.11. In the first cycle, the
wire is loaded up to 0.2 mm followed by an unloading ramp down to 5 N. This was
repeated for 25 cycles in a single test run, whereby the maximum displacement of
the loading portion for each cycle was increased by 0.2 mm with respect to the pre-
vious cycle, i.e. the maximum displacements of cycles 2, 3 … 25 were 0.4, 0.6 … 5
mm, respectively. The results are plotted by the solid black curve in Fig. 3.12. With
the parameters in Table 3.1, the model uses Eq. (3.7) multiple times, updating the
required parameters, as presented in Sect. 3.5, each cycle. The model predictions are
in Fig. 3.12 (red dash-dot line) and they show good overall correlation with experi-
mental data with a root-mean-square-error of 7.2 MPa. The computational time for
Fig. 3.11 Input
displacement versus time for
cyclical experiments
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 59
Fig. 3.12 Austenite
complete cyclical
loading—experiment (solid)
and model (dashed)
the model is 120 ms. When considering the model predictions in Fig. 3.12, the most
important observations are as follows:
∙ Inclusion of the build up of residual strain in the model automatically causes
‘shifts’ of the pseudoelastic loop each cycle, a phenomenon that is clearly observed
in the experiments.
∙ In the experiments, a further observed phenomena is the consecutive decrease
of the onset of forward transformation (the critical stress for SIM formation),
which is induced by micro-plasticity in the SMA [2, 3]. Micro-plasticity leads
to a slight increase in dislocation density, and thus, introduces local stress fields
in the microstructure. These stress fields assist martensitic phase transformation.
With respect to the Clausius-Clapeyron equation, phase transformation of SMAs
at constant test temperature is described by a constant stress value needed for trans-
formation to SIM [4]. Thus, internal stress fields lower the external stress needed,
as the sum of both stress values has to be considered. However, micro-plasticity
and slip are characterized by irreversibility, leading to the aforementioned evolu-
tion of residual strain [3]. This consecutive reduction of the critical stress is also
automatically predicted by the model.
∙ In addition to modelling fatigue effects such as the formation of residual strain, the
model also includes load history memory i.e. steps in the austenite plateau. In the
model, only 1 step is considered, although the addition of as many (or as few) steps
as required is allowed for. The root-mean-square error when using 2 or 3 steps are
both around 7.2 MPa, the same RMS-error as when 1 step is used. Therefore,
1 step seems to be sufficient for predicting this behaviour without unnecessarily
complicating the model.
∙ The model predicts increase of the hysteresis loop widths with increasing strain.
60 A. Pai et al.
3.7.3 Austenite Partial Cyclic Loading
In these experiments, two variations were performed. In the first, the Ni-Ti wires
were subjected to 25 load–unload cycles, whereby the loading strain was increased
by 0.4 % each cycle and the wire was then partially unloaded until 3 % strain recovery
was achieved as shown in Fig. 3.13. The results are plotted in Fig. 3.14 with the model
as the red dash-dotted line, an RMS-error of 20.3 MPa and computational time of 97
ms. In the second experiment, the wire was subjected to an input strain as shown in
Fig. 3.15, with the model results plotted with the red dotted line in Fig. 3.16, an RMS-
error of 14 MPa and computational time of 75 ms. As a basis for the development of
the model, the authors made the hypothesis that the unloading behaviour of austenite
Fig. 3.13 Input strain 9
versus time for austenite
partial cyclical loading—25 8
cycles
7
Fig. 3.14 Austenite partial
cyclical loading for 25 Strain [%] 6
cycles—experiment (solid)
and model (dashed) 5
4
3
2
1
00 500 1000 1500 2000
Time [sec]
Stress [MPa] 1000 Experiment
800 Model
600 8 10
400 246
200 Strain [%]
0
0
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 61
Fig. 3.15 Input strain 8
versus time for austenite 7
partial cyclical loading 6
5
Strain [%] 4
3
2
1
0 0 100 200 300 400 500
Time [sec]
Fig. 3.16 Austenite partial Experiment
cyclical 700 Model
loading—experiment (solid) 600
and model (dashed) 500
400
Stress [MPa] 300
200
100
00 1 2 3 4 5 6 7 8
or martensite is based on the volume fraction of either SIM or detwinned martensite,
respectively, present in the SMA at the time of unloading. Using this hypothesis,
the model and experiments have good correlation lending weight to its accuracy.
Microstructure analysis to confirm this is planned.
3.7.4 Martensite Cyclic Loading
The experiments evaluating the behaviour of the fully martensitic SMA were con-
ducted in the same fashion as the experiments detailed in Sect. 3.7.2 above for the
austenitic condition. The results are plotted in Fig. 3.17 showing experimental data
62 A. Pai et al.
Fig. 3.17 Martensite cyclical loading—expt. (solid) and model (dashed)
(solid black curve) and the model (red dash-dotted curve). The RMS-error is 6.0
MPa and the computational speed is 94 ms. Note that the model can also reproduce
the minor hysteresis loops present with each unloading–reloading cycle (see inset in
Fig. 3.17). As in the austenite case above, the hypothesis that the unloading behav-
iour of martensite is based on the volume fraction of detwinned martensite present
in the SMA at the time of unloading produces good correlation between the model
and experiments. Microstructure analysis to confirm this is likewise planned.
3.7.5 Experimental Validation on Different Wire Samples
The results above show extremely good correlation between experimental data and
the model for wire samples A1 and M1. In order to further test the robustness of
the model, the cyclical experiments were carried out for wire samples A2 and A3
in the austenitic state and for wire sample M2 in the martensitic state. The model
is calculated using the parameters extracted from the monotonic experiments on A1
and M1. The root-mean-square errors in MPa for the experiments are summarised
in Table 3.2 and the results are plotted in the figures below.
The results for complete cyclical loading in austenite are shown in Fig. 3.18. The
plots show the model plotted with the parameters in Table 3.1. The model and exper-
iment correlation is acceptable except when the strains are higher than 2. Changing
the value of 2 to 7.8 (from 7.45) produces better RMS-error values of 12.8 and 10.8
MPa, respectively (as opposed to 13.6 and 12.2 MPa). This could imply that the A1
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 63
Table 3.2 Root-mean-square error between experimental data and model (cc: complete cycles,
pc-25: 25 partial cycles, pc: partial cycles)
A1 A2 A3 M1 M2
cc (MPa) 7.2 13.6 12.2 6.0 6.1
(fig no.) (3.12) (3.18a) (3.18b) (3.17) (3.21)
pc-25 (MPa) 20.3 16.8 23.5 – –
(3.19a) (3.19b)
(fig no.) (3.14)
pc (MPa) 14 11.9 18.6 – –
(fig no.) (3.16) (3.20a) (3.20b)
(a) 800 Experiment (b) 800 Experiment
Model Model
700 700
Stress [MPa] 600 Stress [MPa] 600
500 500
400 400
300 300
200 200
100 100
0 0
012345678 012345678
Strain [%] Strain [%]
Fig. 3.18 Austenite complete cyclical loading: A2 (a), A3 (b)
(a) Experiment (b) Experiment
Model Model
1000 1000
800 246 246
Stress [MPa] 600 Stress [MPa] 800
400 Strain [%] Strain [%]
200 600
00
400
200
8 10 0 8 10
0
Fig. 3.19 Austenite partial cyclical loading 25 cycles: A2 (a), A3 (Monotonic loading, unloading)
was already partly detwinned before the experiment, resulting in a lower value for
2. Figures 3.19 and 3.20 show the model and experimental data for partial cycli-
cal loading in austenite. The model parameters used here were also the same as in
Table 3.1.
Figure 3.21 shows the results for a martensite cyclical experiment conducted on
M2. The model is calculated using the parameters extracted from the monotonic
64 A. Pai et al.
(a) Experiment (b) Experiment
Model Model
700 700
600 600
Stress [MPa]500 500
Stress [MPa]
400 400
300 300
200 200
100 100
0 0
012345678 012345678
Strain [%] Strain [%]
Fig. 3.20 Austenite partial cyclical loading: A2 (a), A3 (b)
Fig. 3.21 Martensite 600
cyclical loading with M2 Experiment
Model
500
Stress [MPa] 400
300
200
100
0
012345678
Strain [%]
experiments conducted on M1 and shows a similar RMS-error of 6.1 MPa between
the model and experiment.
Both the austenite data and the martensite data in this Section show reasonable
correlation between the model and experiments, except for the sensitivity in 2 for
the austenite complete cyclical model. This correlation is sufficient for future devel-
opment of SMA controllers. Further experiments to test the model parameters on
wires from other batches will be conducted in future work.
3.8 Conclusion
This paper presents a novel phenomenological constitutive model that can be used to
predict the behaviour of either martensite or austenite subjected to arbitrary loading
and unloading cycles. The model is continuous and differentiable, with parameters
3 Modelling the Constitutive Behaviour of Martensite and Austenite . . . 65
that are few, physical and easy to identify and the parameter identification process
has to be carried out only once for the same batch of wires. Further, the use of opti-
mization algorithms guarantees that the identified parameters produce a minimum
mean-square-error between the data and the monotonic experiments. In addition to
accurately modelling the curvature at the knees, the model includes experimentally
observed phenomena such as quadratic loci for major and minor loops in both phases,
the variation of the unloading slopes based on the volume fraction of the phases
present and load history effects such as the build up of residual strain and ‘steps’
in the austenite plateau. The model’s simplicity guarantees computational efficiency
without compromising accuracy in predicting observed behaviour, as was verified
with monotonic and cyclic loading-unloading experiments, including wires different
than those used to extract the model parameters. The model can therefore form the
basis for the development of real-time control algorithms for SMA actuators. Further,
although the experimental verification was carried out using NiTi wires, the phenom-
ena that are modelled are universal for all other SMAs such as iron based, copper
based alloys etc. To model the behaviour of these alternative SMAs, only the para-
meter identification step is required. Future work will concentrate on microstructure
analyses and extension of the model to intermediate temperatures where the 0 stress
SMA composition is a mixture of martensite and austenite. Further, effects such
as nucleation and the propagation of martensite will be evaluated to a greater extent
with techniques such as in situ scanning electron microscopy (SEM), combined with
digital image correlation. Thereby, it will be possible to correlate martensite for-
mation and propagation with the underlying model assumptions and, if necessary,
refine the calculations, e.g. for the evolution of the martensite fraction as shown in
Eq. (3.16), in order to include observed phenomena.
Acknowledgements The authors would like to acknowledge the assistance of Jens Broeker and
Christian Lauhoff with the experiments.
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Chapter 4
Experimental Investigations of Actuators
Based on Carbon Nanotube Architectures
Sebastian Geier, Thorsten Mahrholz, Peter Wierach
and Michael Sinapius
Abstract Commercially successful actuators typically meet a mechanical profile
which combines high flexibility and stiffness. Current smart materials used as electro-
mechanical actuators suffer from low or unstable mechanical properties. This is the
reason why these actuators are additionally fixed on structures. This kind of actu-
ators represents an additional weight when they are switched off. A new class of
carbon nanotube actuators shows promising electromechanical properties combin-
ing low density, high Young’s modulus and comparatively high free strains up to
1%. Paper-like architectures made of carbon nanotubes are tested in capacitor mode—
two electrodes are immersed into an electrolyte. As a result an in-plane deflection
of the electrodes can be detected. The actuation-mechanism is still subject of con-
troversy. Different experiments indicate different physical effects. A comparison of
the results reveals a possible dependency on the specimen-composition. Actuated
tensile tests are carried out addressing the dependencies between specimen com-
position and possible physical effects. Two architectures are tested and compared:
papers made of randomly oriented single-walled carbon nanotubes and multi-walled
carbon nanotube-arrays, which feature single, continuous carbon nanotubes in one
dimension of the specimen. The tests are conducted in dry, wet and wet/actuated
condition to determine further effects of swelling and mechanical weakening. Dif-
ferent actuation potentials and electrolytes are tested. The mechanical performance
of the carbon nanotube paper strongly depends on the conditions, which is demon-
strated by a significant reduction of the Young’s modulus. Additionally, electrical
S. Geier (✉) ⋅ T. Mahrholz ⋅ P. Wierach 67
German Aerospace Center (DLR), Lilienthalplatz 7, 38108 Braunschweig, Germany
e-mail: [email protected]
T. Mahrholz
e-mail: [email protected]
P. Wierach
e-mail: [email protected]
M. Sinapius
Technical University of Braunschweig, Langer Kamp 6, 38106 Braunschweig, Germany
e-mail: [email protected]
© Springer International Publishing Switzerland 2017
A.L. Araujo and C.A. Mota Soares (eds.), Smart Structures and Materials,
Computational Methods in Applied Sciences 43,
DOI 10.1007/978-3-319-44507-6_4
68 S. Geier et al.
charging seems to start an irreversible mechanical degradation. A general statement
for CNT-arrays cannot be easily given because of the variation in the results. If the
best results are considered to be the ideal results, no condition dependency can be
detected. According to the experimental set-up, the sample composition and the test-
ing method a quantum-mechanical effect might be most likely the reason for the
array-actuation.
4.1 Introduction
In 1999 active behaviour in carbon nanotube-based materials was detected for the
first time. Since then a lot of research has been done to understand the driving mech-
anism and to qualify the material for applications. Its low density and low activation
voltage as well as comparatively high free strain provide a motive for its use as a
structural actuator. In this context the actuation mechanism was analysed to deter-
mine whether it is a change in the length of the carbon bonds or if it is the result of an
electrostatic repulsion between charged carbon tubes. However, there are a couple
of other physical explanations. Where CNT-based actuation is considered, there is
still no clear, general opinion. The experience so far is based on experiments with
paper-like carbon nanotube mats. According to scientific opinion, the most common
reason for the actuation of CNT-papers is ion-induced swelling.
Iijima’s paper in 1991 [9] about rolled up graphitic sheets, also referred to be car-
bon nanotubes, marks the start of the great scientific attention paid to this special
carbon allotrope. Excellent electromechanical properties such as stiffness, strength,
electrical and thermal conductivity seem to open up an almost endless number of
applications [4, 29]. Beyond theoretical and applied scientific publications the use
in commercial applications appears to be extremely challenging. One main reason
might be the performance gap between nano-scale and macroscopic structures. How-
ever, the rise of graphene since 2004 and unsolved quality problems at the CNT-
synthesis [7] has resulted in dwindling scientific interest although CNTs remain a
prime candidate as nano-transistors for future super-fast computers [11].
Besides the already mentioned excellent material-specific properties the use of
CNTs as electromechanical transducers generating free strain up to 0.2% is also
observed [3]. The experimental set-up can be described as follows: CNT-papers are
tested like a capacitor with a working electrode and counter electrode based on sheets
of CNTs within an electrolyte. From the reproducibility point of view the CNT-
based counter electrode can be replaced by a solid platinum-electrode. The paper of
the working electrode is analysed using an optical device which reveals an increas-
ing deflection with increasing charge irrespective of the polarity. Considering the
mechanical properties this material seems to be a promising candidate for a smart
and structural material. In contrast the latest active materials like piezo ceramics
(PZT), shape memory alloys (SMA), shape memory polymers (PMA) or electroac-
tive polymers (EAP) are either too brittle or too weak to transform forces or are sim-
4 Experimental Investigations of Actuators Based . . . 69
Fig. 4.1 Overview of the electromechanical properties of common smart materials
ply too heavy for lightweight applications. In Fig. 4.1 an overview of the mechanical
and active properties of the most common active materials is given.
However, results like free strain or actuation force of CNT-based actuators must
be treated with circumspection because they depend on the analysed architecture
made up of CNTs as well as on the analysis method used. In this context the term
architectures represents structures of macroscale dimensions formed of individual,
nano-scale or micro-scale CNTs. The dimensions of CNTs are too small to extend
from one side to the other side of the architecture on their own. Generally, the archi-
tecture is based on carbon tubes entangled with each other or linked by van der
Waals forces. Thus, results found by testing CNT-based architectures can only par-
tially represent the active behaviour of single tubes. Furthermore using out of-plane
set-ups to analyse CNT-papers in bending mode [3] also gives rather qualitative
results because secondary effects like thermal- or diffusion-induced volume change
can extensively influence the findings. To reduce these effects, the measurements
are performed in a pre-stressed mode at the in-plane test set-up [19]. Prerequisite
for these tests is that the composition of the tested material is considered to be sym-
metrical or homogeneous. Various macroscale tests confirm the detected deflections
but a general satisfactory explanation for the effect cannot be given. A similar pic-
ture emerges for nano-scale investigation such as the atomic force microscopy of
single tubes conducted by Minett [14], Fraysse [5] and Sippel-Oakley [20]. Raman-
spectroscopy as a different method for analysis is conducted by Gupta [8]. In this
70 S. Geier et al.
paper charged CNT-papers are analysed but because of the superimposing signals
of several tubes no significant evidence about the mechanism type can be provided.
Suppiger [24] concluded from in-plane tests of CNT-papers an electrostatic actua-
tion mechanism is the result of an inverse correlation between Young’s modulus and
free strain. In addition Whitten [27] revealed a strong dependence between the active
performance and the condition (dry or wet) under which the CNT-papers are tested.
Furthermore it can be shown that the type of electrolyte also affects the mechani-
cal properties, whether comparably small water-soluble ions or long ionised mole-
cules of an ionic liquid form the double layers. Spinks [21] explains the measured
deflections of CNT-papers as being due to their honeycomb type composition, which
swells by gas evolution as result of irreversible chemical reactions. All the mentioned
features lead to the assumption that actuated CNT-papers seem to be considerably
influenced by the linking between the individual tubes instead of being able to trans-
fer the properties of the durable hexagonal carbon structure. By contrast CNT-arrays
readily attain microscale dimensions (tube length) which greatly improve testing of
the atomic structure of the material. A comparable approach is taken by Yun [30].
Towers of CNTs, a term for arrays, are actuated to measure their free strain using an
optical device on the top of the arrays. Unfortunately, the weak mechanical linking
between the tubes and the silicon substrate as well as the curly shape of the individual
tubes reduces the significance of the results in respect of clarifying the mechanism
of the observed actuation. Further research [6] compares different types of arrays
according to their morphology and degree of orientation. As expected the degree
of orientation is an important parameter for an accurate description of the actuation
and its mechanism. In the presented paper two types of samples are compared in
tests to clarify their electromechanical dependencies. Firstly mentioned CNT-papers
of randomly oriented single-walled CNTs (SWCNTs) are further analysed to define
decisive parameters for their actuation. Then secondly arrays of multi-walled CNTs
(MWCNTs) are tested in the same set-up. It is expected that a comparison of the
electromechanical results of both sample types (CNT-paper vs. CNT-arrays) will
reveal their individual condition-related behaviour and differences in terms of com-
position and charge-induced active behaviour giving an insight into their different
actuation mechanisms.
4.2 Experimental Set-Up
In the following section the test set-up, the testing procedure, the specimen prepara-
tion and the calculations used are presented.
4 Experimental Investigations of Actuators Based . . . 71
4.2.1 Set-Up of the Actuated Tensile Test and Test Procedure
A standard tensile test serves as the basis for the experiment and is combined with
the in-plane deflection-measurement facility. In this approach the tested specimen
simultaneously acts as the working electrode. The two other electrodes are positioned
next to it within a reservoir containing an electrolyte. The samples are tested under
three different conditions: dry condition as a reference, wetted by the electrolyte but
uncharged and in actuated condition within the electrolyte. One specimen is tested
in its elastic regime repeating the measurements at least six times for each condition
to obtain improved statistical reliability. Furthermore several electrolytes are tested.
To avoid contamination by ions remaining from earlier experiments each electrolyte
has its own individual CNT-sample which is cut from the same master-paper.
The main part of the actuated tensile testing facility is a standard tensile testing
device (Z005, Zwick GmbH & Co. KG) which is supplemented by two clamping
jaws and a cylindrical reservoir made of polytetraflurethylene (PTFE). The reser-
voir filled with electrolyte ensures the wetting and ionic interconnection of the sam-
ples/working electrode, the reference electrode and the platinum counter electrode
during the experiment. PTFE remains electrochemically inert during charging of the
samples which avoids contamination as a result of chemical reactions between the
corrosive, salty electrolyte and parts made of base materials such as metal or steel. It
is well known that PTFE is a comparatively soft material and thus CNTs cannot be
tested to their extremum. The aim of these experiments is a qualitative comparison of
samples made of two different materials based on carbon tubes: randomly oriented
single-walled nanotube-based architectures versus multi-walled carbon nanotubes of
macroscopic length. A schematic picture and a detailed view of the test set-up are
shown in Fig. 4.2. The tests are conducted at a speed of 0.03 mm/min to avoid prior
mechanical damage. To obtain sufficient resolution a 10 N load cell (KAP-Z, Zwick
GmbH & Co. KG) is used. Experiences of the accuracy of the two available testing
modes (deflection- and load-controlled) delivered by the testing device result in the
selection of deflection controlled tests. Consequently the results are recorded with
the force as the dependent variable. The load- and deflection-data is recorded by the
software TestExpert II V3.31, also provided by Zwick.
The CNT-samples are arranged similarly to an in-plane strain test set-up which
can be considered as the standard test set-up and is described elsewhere [19]. Within
the three electrode cell the CNT-sheet represents the working electrode. For reasons
of reproducibility a Pt-wire acts as counter electrode. A calomel electrode (KE 10,
Sensortechnik Meinsberg GmbH) acts as the reference electrode. The working and
the counter electrode are arranged like a capacitor with the reference electrode in
between, positioned closer to the working electrode. All electrodes are immersed
in a specimen-specific electrolyte which is described later. The cell is controlled by
a potentiostat (1030 PC.T., IPS Elektroniklabor GmbH & Co. KG) and is charged
via a function generator (FG 300, Yokogawa Deutschland GmbH). The results are
recorded via a data acquisition system (SCM05, LMS International). Both clamp-
ing jaws are equipped with electrodes for measuring the electrical resistivity of the
72 S. Geier et al.
Fig. 4.2 Schematic sectional sketch, overview and detail view on the real test set-up of the actuated
tensile test
sample and indicating damage to the specimen caused during mounting or inaccurate
clamping.
Previously published tests are conducted under varying conditions until mechan-
ical failure. The measurement of mechanical strength is critical for the use of brit-
tle CNT-papers. However, testing until mechanical failure does not represent the
design operating principle of a commercial actuator. For this reason only one speci-
men (per electrolyte) is tested within its elastic range. All deviations resulting from
material inhomogeneities in the master-paper can be avoided. The relative differ-
ences between the different conditions are analysed. The absolute results are only
of secondary interest. In the presented test series the specimens are immersed in
their individual electrolyte for at least 30 min so that they become saturated with
ions and to avoid material swelling during the test. A swelling of a porous material
such as the CNT-papers can also be misinterpreted as active behaviour. Actually as
swelling occurs, it is detected as a slowly drifting signal. Furthermore as a result
of slight shifting and deformation of the clamps during the installation of a sample,
tensile or compression stresses can occur. Therefore the clamping length is individ-
ually adjusted in order to start all tests in unloaded condition. As an additional test
a preloaded condition of 0.015 N is tested. The specimens are charged constantly
throughout the test using voltage steps of ± 0.5 V and ± 0.9 V according to their
redox-window of ±1 V and loaded up to an uncritical force of 0.03 N until the test
is stopped. This procedure is repeated at least six times using the same voltage step.
Afterwards the specimen is tested in uncharged condition to enable relaxation of the
material. The campaign continues using higher voltage steps within the range of the
redox-window for negative and positive potentials around the zero potential of 0.1
V. The Young’s moduli of the different steps are compared afterwards and are calcu-
lated between 0.04 N and 0.14 N. In the case of preloaded conditions the calculation
was carried out at 0.019 N and 0.029 N. The average CNT-paper sample geometry
is 1.5 mm in width with a free length between the clamping jaws of 5 mm.
4 Experimental Investigations of Actuators Based . . . 73
4.2.2 Quality Assessment and Sample Preparation
The quality of the supplied CNT-based components is crosschecked using several
analysis methods. After passing these tests master-papers with a diameter of 40 mm
are manufactured from the CNT powder using a high-pressure filtration-process. For
better reproducibility all tested specimens are cut out of one master-paper. In contrast
the array samples are taken from a CNT-forest grown on a silicon wafer. In several
process steps samples of 2.8 mm length are prepared. Furthermore three different
aqueous electrolytes are tested experimentally in order to detect the influence of the
ion-radius. Due to their highly hydrophobic character, CNT-arrays can only be tested
using ionic liquids. In this study the results of only one ionic liquid are presented.
In preparation for the filtration process, the supplied CNT-powder is selectively
analysed using scanning electron microscopy (LEO 1550, Zeiss Jena AG, work-
ing distance of 7 mm, operating voltage of 5 kV). Ideas about the composition of
the material and how to handle it are in particular derived from the morphology
of the CNT-agglomerates, the evidence of the type of CNTs (single or bundled
single-walled CNTs vs. MWCNTs) and a chemical element analysis performed using
energy dispersive X-ray spectroscopy. Thermogravimetric analyses are carried out
to determine the thermal stability of the carbon material and the amount of metal-
lic particles. A CNT-paper is produced by completing the following five steps. The
first step is the preparation of an aqueous solution containing 99 g deionized water,
one gram surfactant (sodium dodecyl sulfate, SDS, with a purity of 99% supplied by
Sigma-Aldrich Co. LCC.) and 0.1 g SWCNT-powder (Elicarb 0925, Thomas Swan
Ltd.). The CNTs are homogenized in an ultrasonic bath at maximum power (Sonorex
Digital 10P, Bandelin Electronic GmbH & Co. KG) for 180 min. In a second step the
prepared suspension is filtered under a pressure of 6 bar and deposited on a polycar-
bonate (PC) membrane with 400 nm pores (Track-Etche polycarbonate membrane
23006-47, supplied by Satorius AG). Then the sheet is rinsed with 600 ml deionized
water to remove the surfactant that coats the CNTs which would electrically insulate
them. In the most critical fourth step the paper must be peeled off the membrane and
is pressed between two PTFE-based blocks by 1.87 Pa in an oven at 80 ◦C (UFP 500
M1 T 300C, Memmert GmbH & Co. KG) for at least 4 h in the final process step.
The upper and lower surfaces of the sheets are analysed selectively using scanning
electron microscopy. To detect a swelling as a result of ion intercalation, ions of dif-
ferent diameters are analysed. It is expected that their geometry has an influence on
the mechanical behavior of the paper. To reveal the different behaviour an unimolar
sodium chloride solution, an unimolar potassium chloride solution and an unimolare
sodium nitrate solution are tested and the measured Young’s moduli are compared.
The crystalline and hydrated ion radii of sodium (Na), potassium (K), chloride (Cl)
and nitrate (NO3) are reported by Nightingale [16] and reproduced in Table 4.1. By
using the same ion such as Cl− (or Na+) the influence of different ion radii of Na+ and
K+ (Cl− vs. NO3−) should be obviously. Although the ions are saturated in water it
74 S. Geier et al.
Table 4.1 Overview of Ion Crystalline radius Hydrated radius
crystalline and hydrated ion (pm) (pm)
radii used for aqueous Cl−
electrolytes NO−3 181 332
K+ 264 335
Na+ 133 331
358
95
is unclear whether the hydrated radius or the crystalline radius is the dominant influ-
ence. Due to the water basis, the redox-window should not exceed the range −0.9 to
+0.9 V.
The MWCNT-arrays are supplied by the Technical University of Hamburg-
Harburg (TUHH, Germany) on a silicon wafer. These arrays are grown in 5.5 hours
using a standard thermal chemical vapor deposition process (CVD). The degree of
tube orientation and variation in tube diameter is analysed by SEM. However, an
excellent paper about similar tubes and their specific geometrical parameters was
published by Vainio [25]. In this paper the MWCNT-arrays are selectively analysed
using SEM to reproduce some of the values given in [25]. By contrast the SWCNTs
are too small for a SEM-approach. Their geometrical parameters such as length,
diameter and number of walls are analysed and published by the supplier Thomas
Swan Ltd. (Elicarb 0925, Thomas Swan Ltd.) and are not further investigated by
methods such as transmission electron microscopy. Both times the chirality was not
determined. Dependent on the dimensions of the CNT-arrays a special preparation
process must be applied (see Fig. 4.3).
In a first step a complete cross-section of the array is cut off using a sharp razor
blade. The as-produced specimen thickness is about 1 mm. In a subsequent step the
cross-section is divided into a set of specimens with almost the same width. These
samples must be carefully removed from the razor blade using tweezers. To com-
press the sample in order to increase its bulk-density it is positioned between two
microscope slides. The manual compression already achieves a 80–97% reduction
of the thickness. Further compacting can be conducted using a manual hydraulic
press (Atlas manual 25 tons hydraulic press GS25011, Specac Limited) by applying
a load of 10 tonnes which implies an average pressure of 10895 MPa. The results are
also analysed via SEM.
A digital microscope (VHX-1000, Keyence Corporation) is used to measure the
exact length and width of the sample geometry. The thickness is measured using a
micrometer screw (IP 54, Mitutoyo Europe GmbH). To avoid structural damage the
samples are positioned between two glass-slides during the thickness-measurement.
Contact angle measurements reveal the array’s super-hydrophobic character (Con-
tact Angle System OCA 20, DataPhysics Instruments GmbH) which is the reason
for using an ionic liquid as a nonpolar electrolyte. Further measurements show high
capacitive potentials for 1-ethyle-3-methylimidazolium bis(trifluormethyl-
sulfonyl)imide (EMImTFSA, IoLiTec GmbH) and a comparable large redox window
with a range of ±2 V. Here voltage steps of ± 1 V and ± 1.5 V are used. During
4 Experimental Investigations of Actuators Based . . . 75
Fig. 4.3 Schematic manufacturing process of CNT-array samples
activation the array samples are preloaded with 0.45 N. This specific value derives
from the load needed to align the curly arrays. During several tests it was found to
be a very reproducible load. The specimen geometry ranges between 4 and 5 µm
in thickness and 4–4.6 mm in width with a clear length between the clamping jaws
of 1 mm. The electrical conductivity is tested in a four-point measuring set-up. Two
set-ups are tested in respect of the sample geometries. While CNT-papers are tested
in a set-up featuring a gap l0con of 5 mm between the clamping jaws the arrays are
76 S. Geier et al.
(a)
(b)
Fig. 4.4 a Overview of the set-up. b Detailed view of the gap between the two measuring elec-
trodes of the small sample device
tested using a distance-range l0con of 1–0.5 mm. The set-up for testing CNT-arrays is
shown in Fig. 4.4. The three results applying the specific current values of 1, 5 and
10 mA are then averaged.
4.2.3 Mathematical Formulae for Calculating Experimental
Results
The following section explains the formulae used for calculating the presented
results. Firstly the formula for the volumetric conductivity measurements is given.
Secondly the formulae to calculate the mechanical properties such as Young’s mod-
ulus are given in detail. Here the values of force and deflection recorded by the ten-
sile testing machine are the two input parameters used as the basis for all calculated
results. All other results are directly measured or calculated by the integrated soft-
ware of the analysis set-up.
The volumetric electrical conductivity is tested using a four-point measuring
facility. The specific conductance is calculated based on the sample’s geometry, the
thickness tsp, width wsp and the distance between the measuring electrodes l0con (see
Eq. 4.1, [13]).
= I ⋅ l0con [ S ] (4.1)
U ⋅ tsp ⋅ wsp ⋅ 100 cm
4 Experimental Investigations of Actuators Based . . . 77
[]
S conductance
cm
tsp [mm] thickness of sample
wsp [mm] width of sample
l0con [mm] distance between electrodes
I [mA] current between electrodes
U [V] voltage between electrodes
The Young’s modulus E of the material is calculated from the stress n using the
measured force Fn and the specimen’s cross section geometry calculated from wsp
and tsp (compare Eq. 4.2 [28]). As second parameter the relative strain n, is calcu-
lated using the detected displacement lsp, see Eq. 4.3 [28]. Finally E is calculated
from Eq. 4.4 as the mean value of all points of the graph. At least five additional
experiments with similar results should confirm that the experiments are only con-
ducted in the linear-elastic region of the CNT-sheets.
n = Fn = Fn [MPa] (4.2)
Asp wsp ⋅ tsp
n = lsp [%] (4.3)
l0
E= [MPa] (4.4)
Asp [m2] specimen’s cross-section area
E [Pa] Young’s modulus
n [[Pa]] mechanical stress
n % relative strain
Fn [N] force during test
l0 [m] free distance between clamp jaws
wsp [m] width of sample
tsp [m] thickness of sample
4.3 Results and Discussion
The quality assessment of CNT-papers and CNT-arrays is presented followed by the
results of the actuated tensile tests of CNT-papers on the one hand and the results of
the CNT-arrays on the other hand.
78 S. Geier et al.
Fig. 4.5 a Sectional SEM image of a CNT-paper fracture line revealing a build-up of three main
layers (SE-detector). b Plan view on aligned, individual SWCNTs at the fracture line as a conse-
quence of pulled apart SWCNTs of a bundle (in-lens-detector)
4.3.1 Quality Assessment of CNT-Based Architectures
Focusing on the specimens which will be tested later this section deals with the SEM-
assisted characterisation of their morphology. At first the CNT-paper architectures
are analysed revealing a layered like build-up as result of the particle sedimenta-
tion during filtration. Their mechanical properties result from the friction between
individual single-walled CNTs of a bundle and the entanglement of several bundles.
The mechanical failure of a CNT-paper seems rather to be a failure of the SWCNT-
interlinking than a structural failure of the single SWCNTs. SEM-images as well
as conductivity measurements confirm the anisotropic character of the multi-walled
tubes containing array samples.
SEM-images of the CNT-paper surface reveal no detailed information about the
paper composition because due to the filtration process the surface areas consist of
highly compacted material. Thus, only SEM-images of the CNT-paper fracture line,
as it is presented in Fig. 4.5a, can give an insight into the paper’s structure and com-
position. Similar findings are documented by Spinks [21, 22] and Mechrez [12].
The cross-section reveals a layer-like build-up rather than a homogeneous, mono-
lithic structure. However, contrary to what might appear to be the case in Fig. 4.5a
the layers are not completely separated but connected by individual tubes. The lay-
ers may result from mass induced sedimentation of the homogenized CNT powder
during the filtration process which indicates that the paper composition cannot be
considered as symmetrical. While single CNTs are almost not evident on the top and
bottom side of the paper, only a plan view onto the fracture line in Fig. 4.5b shows
bundles of SWCNT which are aligned in the direction of the tensile load.
SEM-analyses of the tested samples in comparison of the dry, untested samples
indicate an irreversible swelling of the paper as is shown in Fig. 4.6.
4 Experimental Investigations of Actuators Based . . . 79
Fig. 4.6 a SEM image of the dry paper (in-lens-detector). b SEM image of the CNT-paper after
actuated testing in an electrolyte (in-lens-detector)
Analyses of the thickness before and after testing reveal a swelling of 12.5% as
result of charging and ion diffusion. SEM-analyses (compare Fig. 4.7a) of CNT-
arrays reveal an mean length lcnt of 2200 µm with slightly varying average diameters
of 20 nm as is apparent in Fig. 4.7. The CNT-curvature varies along the array length
and width (compare Fig. 4.7c). For the following tensile tests the waviness provides
an opportunity to align the sample by preloading it before a sliding of the sample
within the mounting occurs. A careful in-situ check of the stress-strain behaviour
indicates the preload under which an alignment of the MWCNTs can be presumed.
The following SEM-images Fig. 4.8a, b show the results for CNT-arrays com-
pacted by the hydraulic press. Obviously the space between the as-produced MWC-
NTs of the array in a are reduced while the orientation is mainly preserved. However,
tested specimens show areas of structural failure as it can be seen in Fig. 4.8c. Pro-
vided that the multi-walled CNTs consist of a continuous carbon structure along the
whole length, the detected tube failure perpendicular to their axis implies structural
damage to the carbon structure itself. Reasons for this failure are extreme, selective,
external impacts which probably appear in or near to the clamping jaws where the
CNTs are fixed.
The average specific conductivity of 169 S∕cm on the top side (compacted by
water) indicates a high level of entanglement of the SWCNTs. The rear side fea-
tures a slightly lower averaged specific conductivity of 167 S∕cm which might be a
result of the fabrication. During the filtration very small particles and scattered SWC-
NTs diffuse into the pores of the membrane. During the detachment of a CNT-paper
from the polycarbonate membrane a very thin layer of strongly adhesive particles
remains on the membrane leaving a rough lower paper-surface behind. The surface
roughness might be the reason for the slightly lower specific conductivity. The con-
ductivity varies across the whole paper in the range of 203-145 S/cm which could
be an effect of electronic conduction by a compact composition (see Fig. 4.9a). The
results found for the conductivity are in good agreement with other specific measure-
80 S. Geier et al.
Fig. 4.7 a SEM-image of the overall array length (in-lens-detector). b Image with higher resolution
for a better view on the waviness (in-lens-detector). c Detailed view of curly CNTs (in-lens-detector)
Fig. 4.8 a Detailed SEM image of as produced CNT-arrays bundles (in-lens-detector). b Detailed
image of arrays compacted by the hydraulic press (in-lens-detector). c View on a fracture line of a
failed array sample (in-lens-detector)
4 Experimental Investigations of Actuators Based . . . 81
Fig. 4.9 a Thickness distribution of a CNT-paper. b Conductivity distribution of the tested CNT-
paper
ments of SWCNT-papers (150–170 S/cm [17]). However, the thickness varies with
the degree of compaction between 193–115 µm as shown in Fig. 4.9b, but the com-
pletely different distributions indicate no correlation between the two parameters.
Another aspect affecting the electrical conductivity could be the homogeneity of the
paper composition. Apart from the layer-like build-up, no agglomerates as leftovers
of the sonification process are found in the SEM-analyses. Due to the fact that the
SEM-analysis is a very selective method and possibly the agglomerates may be flat-
tened during the filtration process, it is possible that there still compacted areas of
agglomerates. These agglomerates feature a few SWCNTs as interconnections which
are merely touching each other. This might be an explanation for the varying results
of the local conductivity.
In comparison to the papers containing randomly oriented single-walled tubes,
CNT-arrays feature a clear anisotropic electrical character as result of their align-
ment. Along the tubes an electrical conductivity of 145.3 ± 18.6 S/cm with a max-
imum electrical conductivity of 460 S/cm is measured, while perpendicular to the
tubes only 6.2 ± 2 S/cm is measured. In other literature results for the specific con-
ductivity of papers containing randomly oriented multi-walled CNTs vary between
6.53 S/cm [23] and 45 S/cm [12] depending on the chemical treatment. For aligned
multi-walled papers Wang [26] reports results of 200 S/cm along the MWCNT-
orientation. However, the measured high values along the tubes indicate a better
conductivity resulting from a electron transport along the carbon structure that tends
towards ballistic transport. Due to a higher resistance as a consequence of the gaps
and weak Van der Waals-linking between the tubes the results found in the perpen-
dicular direction are comprehensible.
82 S. Geier et al.
4.3.2 Results of CNT-Papers Tested in Actuated-Tensile Mode
The focus of the actuated tensile tests is the identification of influencing parameters
on the structural integrity of carbon nanotube-based papers. Beside different condi-
tions, the diameter of the charged ions and prestressing the samples before testing
are also analysed. The literature states that the mechanical integrity reacts inversely
to the active behaviour. In this context the results point out a small influence of the
ion-type but a dominating influence of the sample-condition itself, whether it pro-
vides access for ions to intercalate into the paper-structure or if it is a rather closed
structure featuring only the outer surfaces as areas for docking of the ions.
Prior test results already document a reduction of 44% in the Young’s modulus
merely by wetting a CNT-paper which is in good agreement with the experimental
data of Whitten [27] (38%). However, these tests which are up to the point of paper
failure feature high standard deviations especially when actuated. It is nearly impos-
sible to reach a significant conclusion on the influence of charging and ion radius.
Therefore the test procedure was adapted to improve reproducibility and reduce stan-
dard deviations. In the presented experiments CNT-papers are tested within their
elastic range so that way a reversible experiment with reproducible results can be
expected. Figure 4.10a–c presents the average mechanical results of CNT-papers
immersed in unimolar solutions of NaCl, KCl and NaNO3. The specific results are
given in Table 4.2. The presented graphs are shown zoomed because the differences
between the charged states are very small. The given graphs represent the mean
results of six tests.
It can be seen from Table 4.2 that Young’s modulus reduces with charge inde-
pendent of the electrolyte. The negative charged anions Cl− and NO3− have a bigger
impact on the modulus than the positive cations at the same potential. It is found
that the modulus reduction is proportional to the increasing voltage. Interestingly
the effect of the same negative ion (Cl−) is different using the two electrolytes, NaCl
and KCl. While the negative Cl−ions of the NaCl-solution cause a loss of 1.4% at
a voltage of +0.6 V and a further loss of 53% at +1 V, this extreme trend is not
found in the results of KCl. Here the Cl−-ions cause almost no loss at +0.6 V and
only 0.9% at +1 V. aInt +c1onVtr.aAstcttuhaellNyOth3−e-ieoffnescctaoufsNe Oa 3−lo-siosnosfi1s7e.x6p%ecatted+t0o.6beVbaigngdear
further loss of 38%
due to its comparatively similar or larger geometry (see Table 4.1). Probably more
Cl−-ions are attracted to intercalate into the paper. Reasons for the different results
for the same ion (Cl−), although the same counter and reference electrode, molar
concentration and charge are being used, can either be unknown interactions with
the positive counter-ion or different geometries and specific surfaces of the work-
ing electrode. However, these inconsistent results reveal the need to conduct more
experiments. The impact of the cations is comparatively small so no conclusion in
4 Experimental Investigations of Actuators Based . . . 83
Fig. 4.10 a Mechanical properties during charging in NaCl-based electrolyte. b Mechanical prop-
erties during charging in a KCl-solution. c Mechanical properties during charging in NaNO3
84 S. Geier et al.
Table 4.2 Overview of results of the CNT-paper test
Volts (V) NaCl-solution average KCl-solution average NaNO3-solution average
Young’s modulus (MPa)
Young’s modulus (MPa) Young’s modulus (MPa)
376 ± 1.6
0 529 ± 1.6 571 ± 6.3 352 ± 1.5
284 ± 34.5
−0.4 531 ± 3.7 559 ± 5 234 ± 29.6
155 ± 4.9
−0.8 515 ± 7.2 558 ± 8.9
+0.6 508 ± 5.6 559 ± 6.7
+1 276 ± 0 554 ± 7.8
respect of the crystal or hydrated radius of the two different positive ions, Na+ or K+
can be reached (Table 4.2).
The reduction in the Young’s modulus caused by charging the sample irrespective
of the electrolyte can be identified as a general trend. Furthermore the reduction
in the modulus correlates with the increasing voltage difference. The effect of the
charged KCl-ions is comparatively low. In contrast in the sodium chloride solution
the effect of the Cl−-ions is more dominant while for NaNO3 the negative ion NO−3
causes a loss of almost 51% and the positive Na+-ion causes an overall loss of 19%
(calculated in comparison to the previous result). Probably only higher voltages are
able to activate enough ions to highlight the impact of different ion-radii.
The results demonstrated that a CNT-paper can be tested with reproducible results
in its elastic range. However, using electrical charging the structure is irreversibly
shifted towards lower mechanical stiffness. In spite of intermediate steps of zero
charge for recover of the mechanical behaviour the initially properties can never
be regained. Figure 4.11 presents the calculated stiffness of the specimen at every
voltage-step.
The tests are carried out using the NaCl- and the KCl-based electrolyte (blue
graph vs. orange graph). The linear fitting (continuous orange line vs. dashed and
pointed line) reveals a slightly higher degradation for the NaCl-solution. This trend
increases dramatically when NaCl is used at 1 V (dashed and pointed line vs. dashed
line). The results remain at the level of the previous, charged test with only slight
mechanical recovery. It seems that the charging causes an irreversible softening.
However, within this state (under constant conditions such as constant stress) the
sample shows no further degradation (see low standard deviations in Fig. 4.11. The
stress-strain graphs feature the same gradient in Fig. 4.12b during mechanical cycling
of the specimen) and the reduced mechanical properties can be reproducibly mea-
sured. A tensile test at the end of the campaign can still be carried out revealing a
notable mechanical residual strength, as it can be seen in Fig. 4.12a.
In total the effect of the Cl−-ion seems to be most effective when compared with
its positive counterparts and the other tested negative ion NO3−. Considering the radii
of Table 4.1, the crystalline radius appears to be the decisive parameter but in com-
parison to the other tested radii a clear correlation is not demonstrated here. However,
more tests need to be carried out to prove if the radius might be the explanation for
4 Experimental Investigations of Actuators Based . . . 85
Fig. 4.11 Overview of the decreasing mechanical stiffness during the tests using the NaCl-solution
(blue) and KCl-solution (orange) at different voltages
Fig. 4.12 a Seven overlapping stress-strain graphs with a test until failure as the seventh cycle.
b Detailed view on the stress-strain graphs of the seven mechanical cycles. For better visual dis-
tinction every individual graph exhibits an offset of 0.0001% to the preceding graph
86 S. Geier et al.
the actuation of CNT-papers. Furthermore ions with a grater difference between the
hydrated and crystalline radii would yield clearer results.
The inconsistent results can be explained by the test parameters. Using the PTFE
clamping induces small loads on the samples which have to be taken into consid-
eration. The direction of the load, whether if it is a compression or a tensile load,
cannot be controlled but by adjusting the tensile machine a load-free situation can
be achieved before every experiment. For better comparison and reproducibility this
operation is conducted before each test. Similar results for tensile-tested SWCNT-
papers have not be found in literature until now. However, cyclic voltammetry tests
with different electrolytes were conducted by Barisci [1, 2] to investigate their redox-
windows for irreversible chemical reactions. Riemenschneider [18] measured the
effect of six different anions on the active performance of a CNT-paper. No clear
correlation between the ion size and the measured deflections was found. It was indi-
cated that this result might be caused by ion-contamination during the tests or very
slow diffusion processes of the ions which interfere with each other. Mirfakhrai [15]
analysed the effect of different ions (ions of one aqueous electrolyte compared with
ions of one ionic liquid) on the actuation of CNT-yarns. Here a linear correlation
between the generated strain and the volume of the unsolvated ions, respectively the
number of ions was revealed. Only the results of Whitten [27] point out a possible
effect of ion radius on the mechanical properties by comparing an ionic liquid and
aqueous electrolyte. It can be demonstrated that the ionic liquid reduces the elastic
modulus by 39% which might be the result of the large dimensions of their ions.
Unfortunately further experiments during charging to address the effect of the indi-
vidual ions were not carried out. However, detailed experiments carried out using the
NaNO3-solution revealed that the mechanical stress within the paper has a decisive
influence on the results. Figure 4.13a presents this influence at negative voltages and
Fig. 4.13b shows it for positive potentials. The specific data is given in Table 4.3.
It is found that a preloading of 0.2 N causes a 23% higher Young’s modulus. The
mentioned trend of paper degradation during charging can be observed with both
conditions but under the prestressed condition it is reduced by 12.7% which is only
half as much as for the unloaded condition (24%) with negative charging. Interest-
ingly, with positive voltages the paper exhibits a mechanical degradation of 45%
independent of the load condition. The reduction close to 1 V must be treated with
circumspection because this potential is very near to the redox window of water
(±1 V). Possibly chemical effects influence these results which is the reason for a
reduction in the maximum potential to ±0.7 V. Here once again the unloaded condi-
tion reveals a comparatively higher reduced stiffness of 37.7% while the preloaded
condition features a slightly lower loss of 32.1%.
To explain this effect the paper must be considered as a porous structure which can
be opened and closed by preloading (see Fig. 4.14a, b). Figure 4.5a already shows a
clear coincidence because here the paper reveals several layers. If the layers are com-
pressed or unloaded longitundinally the flexible structure of the paper opens gaps
greatly increasing the specific surface area across which the ions can diffuse (see
Fig. 4.14a). This process causes the structure to swell and become softer because the
ions are not able to transmit forces. During the test the ions are forced outside the
4 Experimental Investigations of Actuators Based . . . 87
Fig. 4.13 a Comparison of the stiffness at negative potentials with (blue curve) and without (red
curve) preloading of the paper (NaNO3). b Comparison of the stiffness at positive potentials with
(blue curve) and without (red curve) preloading of the paper (NaNO3)
paper by the constricting structure of the paper. Probably the ions tend to reduce the
adhesion between CNTs within the paper so that it becomes more and more flexible.
If the paper is preloaded the gaps remain closed as it is shown in Fig. 4.14b and so
fewer ions can diffuse into the structure to soften it. Similar findings caused by gas-
bubbles instead of ions were published by Spinks [21]. Here the CNT-papers feature
several layers which are working like a pneumatic actuator driven by electrochemi-
cally produced gas.
88 S. Geier et al.
Table 4.3 Overview of CNT-paper stiffness results with and without preloading using NaNO3 as
electrolyte
Volts (V) Unloaded Preloaded with 0.2 N
Mean Young’s Standard deviation Mean Young’s Standard deviation
modulus (MPa) (%) modulus (MPa) (%)
0 376 0.4 489 2.5
−0.4 352 0.4 477 1.7
−0.6 335 6.4 462 1.8
−0.8 284 12.1 427 2.9
+0.6 234 12.6 381 3.1
+0.8 177 18.1 290 3.9
+1 155 3.2 234 6.7
Fig. 4.14 a Unloaded
condition enabling ions to
diffuse into the layers of the
paper. b Loaded condition
with more or less closed
layers
4.3.3 Results of CNT-Arrays Tested by Actuated Tensile
Testing
Multi-walled carbon nanotube-arrays of a microscopic length are tested as the second
tested CNT-based architecture. In contrast to the randomly oriented papers, these
samples consist of continuous tubes which are tested along their length. Therefore a
qualitative mechanical test of the carbon structure is more appropriate. If the same
test procedure is performed as is described for SWCNT-papers, the MWCNT-arrays
reveal almost no influence of the test-condition. As it has already been mentioned in
the section dealing with the quality assessment of the arrays these structures have a
4 Experimental Investigations of Actuators Based . . . 89
curly shape. In contrast to the papers preloading is needed here to ensure a further
alignment. Active behaviour of almost the same value can be detected using negative
and positive voltages and by increasing the voltage to the limits of the allowed redox-
window of the ionic liquid.
In contrast to randomly oriented architectures such as CNT-papers, arrays feature
an anisotropic material because of CNTs of microscopic scale. All measurements
are carried out along the axis of these CNTs. The curly shape of the tubes and the
semiconducting substrate on which the arrays are usually grown are challenges to
be overcome before accurate analyses can be achieved. By cutting the tubes off the
substrate and preparing samples of unaffected CNTs a high electrical resistance as
well as a weak mechanical linking can be avoided. Furthermore the wavy shape
works like a micro-scale spring providing a mechanical backup to avoid premature
failure of the sample. Once the spring is stretched to the maximum, almost perfect
alignment can be expected. The active measurements are carried out in this condi-
tion. Figure 4.15a reveals a very brittle but comparatively stiff mechanical behav-
ior of CNT-sheets. In contrast CNT-arrays only reach a maximum Young’s modu-
lus of 20–40 MPa but as a result of their shape they are much more flexible. Their
comparatively low Young’s modulus and tensile strength is caused by the clamping.
The nano-scale CNT-structures begin to slide out of the mounting before a struc-
tural failure of the carbon bonds can take place. The CNT-sheets consist of highly
compacted and entangled SWCNTs with comparatively large specimen geometries
(length of 15 mm, width of 1.9 mm and a thickness of 0.2 mm). In contrast the array
specimens are much smaller (length of 2.8 mm, 4 mm in width and a thickness less
than 0.04 mm) consisting of individual, continuous MWCNTs which are as long as
the entire sample-length. Due to their lower curvature, multi-walled tubes are not
as reactive as single-walled CNTs so that they are not bundled. Therefore friction
or Van der Waals forces as mechanisms dominating the mechanical integrity or as a
possible actuation-effect can be ignored.
The clamping cannot provide a material test of the tubes. The dimensions of sin-
gle MWCNTs as well as bundles of MWCNTs are too small and flexible to be fixed
so they are immobile. In terms of sliding between sample and mounting and creep-
ing of the material itself the macroscale mounting is inadequate for material testing
of untreated nano-scale materials. However, until now this approach represents the
only means of electrically conductive clamping and prevention of polymeric con-
tamination at the same time. The results are compared qualitatively. Furthermore
the specimen geometry is not as perfect as assumed theoretically. At the beginning
of the tensile test the array is macroscopically aligned (compare Fig. 4.15a (A)-1
to (A)-2)). In the second phase the tube-waviness is to be aligned which depends
on the order of individual array-waviness and overall orientation. As a result this
phase differs not only from sample to sample but also from cycle to cycle (see
Fig. 4.15b). While phase (A)-2 can be considered as a rather material dominated
test of a stretched macroscopic spring, phase (A)-3 represents a more mechanical
behavior of almost waveless MWCNT bundles until single tubes slip off the mount-
ing in phase (A)-4 and cause the following mechanical breakdown in phase (A)-5.
The modulus varies between 18–68 MPa which cannot be attributed to the single
90 S. Geier et al.
Fig. 4.15 a Typical (a)
stress-strain curve with
predicted behavior of the
array-architecture.
b Stress-strain curves of the
CNT-array under tensile
testing and under different
conditions
(b)
MWCNTs. Their individual modulus of about 1 TPa [29] is several magnitudes
higher but as mentioned a material characterisation is not the aim of this research.
However, the mechanical behavior of the tubes as well as the reproducibility dur-
ing load cycling (under dry conditions) is presented in Fig. 4.15b and shows a sta-
ble, reproducible mechanical behavior. Phase (A)-3. Figure 4.16a reveals no negative
effect on the mechanical behavior caused by wetting as is reported for CNT-papers.
In this test the Youngs modulus remains at 16 MPa regardless of the condition. How-
ever, the active measurements are carried out in constant, preloaded condition (0.45
N) in order to align the wavy tubes of the array. The so aligned CNTs can be consid-
ered as highly anisotropic material for more efficient strain and force generation.
The ionic liquid EMImTFSA provides a redox window of −2 V to 2 V (see
Fig. 4.16b). To avoid irreversible chemical reactions as a result of the cyclovoltam-
metry the voltage range is reduced to ±1.5 V. Asymmetric current peaks, especially
at high positive potentials using voltage cycles of ±1.7, ±1.9 and ±2 V are evidence
4 Experimental Investigations of Actuators Based . . . 91
of dominant oxidation reactions at the electrode. It can be presumed that the elec-
trode materials, carbon and platinum, are electrochemically stable. The electrolyte
degrades by electrolysis into a gas-phase which is not desirable for a long lifetime of
constant performance and the structural integrity of a nano-actuator. Visual inspec-
tions during the tests are carried out to detect bubbles caused by gassing. Further-
more the colour of the ionic liquid (see Fig. 4.16b, small image) is visually compared
before and after the experiments. Both tests reveal no evidence of degradation or
contamination by oxidised materials.
The load generated is recorded because the load cell has higher resolution than
the crosshead displacement sensor. In Fig. 4.17 all results of the array-actuator acti-
vated by −1.5 and 1.5 V are presented. All tests are carried out using a frequency of
10 mHz. Graphs of both the current and the charge confirm the actuator set-up to be
capacitive with only a tiny amount of current leakage. It can be seen, that both poten-
tials generate forces but with different shapes. While the negative potential generates
a very quick force reaction with sharp edges and almost constant values, the force
response of the positive potential shows rising and falling gradients. This reaction
might be a result of a slow, diffusion dominated process which might be accompa-
nied by electrochemical reactions which need more time to take place. The shape
also indicates that the chemical processes are not finished and higher forces would
be achieved by reducing the frequency. Due to the fact that the molecular structure
of the ions is more complex than the aqueous electrolytes, the ion radius can hardly
be considered as an explanation for this reaction. Although the molecular structures
of the ions are similarly long and complex their effect is very different.
If the arrays can be considered as aligned tubes generating an elongation during
charging the ion radius should have no impact. However, the shapes of the generated
forces are very different but the values of the forces corresponding to the different
(a) (b)
Fig. 4.16 a Stress-strain curve of the tested CNT-array under different conditions. b Cyclovoltam-
metry graph using a scan rate of 40 mV/s revealing the redox-window of EMImTFSA. The small
picture shows the ionic liquid before (left) and after (right) the tests
92 S. Geier et al.
current [A] 2 current [A] 2
voltage [V] voltage [V]
0 0
−2 50 100 150 −2 50 100 150
0 150 0 150
150 150
0.01 150 0.01 150
0 0
−0.01 50 100 −0.01 50 100
0
0
x 10−3 x 10−3
charge [C] 5 charge [C] 5
0 0
−5 100 −5 100
force [N] 0 50 force [N] 0 50
x 10−3 x 10−3
2 2
0 0
−2 −2
0 50 100 0 50 100
time [s] time [s]
Fig. 4.17 Voltage step, current, charge and force graphs at −1.5 and +1.5 V
potentials −1.5 and at 1.5 V are the same: 0.0015 N. Possibly the ions feature differ-
ent flexibility in their molecular structure which provides different accessibility to
the carbon surface or into the array-sample. It is difficult to find comparable results in
the literature because either the tests are performed in nano-scale on scattered MWC-
NTs or even SWCNTs using Raman-spectroscopy [10] or atomic force microscopy
[5, 20] or comparable macro-scale experiments measured the deflections. Yun [30]
conducted these latter mentioned experiments by measuring on the top of a multi-
wall carbon nanotube tower. He measured a mean free strain of 0.15% using a two
molar sodium chloride electrolyte, at a frequency of 10 Hz and a voltage step of 4 V.
The analysed MWCNTs are almost straight but featuring a curly shape comparable
to the arrays of this paper.
The results of the presented experiments—an elongation instead of a
contraction—as well as the sample composition—aligned, pre-loaded MWCNTs—
and the experimental set-up—measurements within the redox-window and with an
appropriate electrical conductivity—point rather to a quantum mechanical reason for
the measured actuation.
4 Experimental Investigations of Actuators Based . . . 93
4.4 Conclusion
This paper presents an actuated tensile test of two different types of carbon nanotube-
based architectures. Both kinds of specimens, CNT-papers with randomly oriented
SWCNTs and arrays containing highly aligned MWCNTs, reveal different mor-
phologies and show rather contradictory trends in their mechanical behaviour under
wet conditions. While the measurements of the CNT-paper are focused on their
charged induced stiffness reduction through their testing within the elastic range,
the CNT-arrays are analysed in respect of the exhibition of active behaviour. With
very low standard deviations it can be demonstrated that CNT-papers react sensi-
tively on wet conditions, charging and preloading. It can be detected that higher
potentials cause an increasing mechanical degradation. Moreover the experiments
indicate a stronger effect for the negative charged anion which might be attributed to
their comparatively larger crystalline radius. An ion-induced degradation obtained
using different anion- or cation-radii cannot be verified or disproved until now and
requires additional testing under similar mechanical (preloaded) conditions. The pre-
load of the paper has a decisive influence on the degree of degradation. The preload
seems to control the accessibility of the ions through the paper-porosity and com-
position and fits furthermore the evidence of the inverse proportionality of Young’s
modulus to the active strain. The MWCNT-arrays reveal stable mechanical behaviour
independent of the condition. During the actuated tensile tests an active performance
at negative and positive voltages is found. Nonetheless the test set-up, the specimen
composition and the results, force degradation during charging can be considered
as elongation of the sample, strongly indicate a quantum mechanical effect as the
reason for actuation.
Acknowledgements This work is part of the basic research on future smart materials at the DLR—
Institute of Composite Structure and Adaptive Systems. It was supported by the German Research
Council (DFG) within the framework of the DFG PAK 355—‘Basics for CNT-based Actuators’ and
the German Federal Ministry of Education and Research (BMBF) project ‘Aktu_Komp’. Tribute
must also be paid to colleagues at the Institute of Composite Polymers at the Technical Univer-
sity Hamburg-Harburg for their contribution in the fields of CNT-materials and the Institute of
Mechanical Process Engineering, department of Interface Chemistry at the Technical University of
Clausthal-Zellerfeld for their expertise/support in respect of ionic liquids.
References
1. Barisci JN, Wallace GG, Baughman RH (2000) Electrochemical characterization of single-
walled carbon nanotube electrodes. J Electrochem Soc 147(12):4580–4583
2. Barisci JN, Wallace GG, Baughman RH (2000) Electrochemical quartz crystal microbalance
studies of single-wall carbon nanotubes in aqueous solutions. Electrochem. Acta 46, 509–517
3. Baughman RH et al (1999) Carbon nanotube actuators. Science 284:1340–1344
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