Environmental effects on thermally induced multistability in unsymmetric composite laminates

Composites: Part A 40 (2009) 1240–1247

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Environmental effects on thermally induced multistability in unsymmetric composite laminates Julie Etches *, Kevin Potter, Paul Weaver, Ian Bond Advanced Composites Centre for Innovation and Science, University of Bristol, University Walk, Bristol BS8 1TR, UK

a r t i c l e

i n f o

Article history: Received 11 November 2008 Received in revised form 20 May 2009 Accepted 20 May 2009

Keywords: A. PMCs B. Residual/internal stress B. Environmental degradation

a b s t r a c t The principles involved in the generation of thermal induced multistability in carbon fibre epoxy laminates have received much interest in the published literature. This work examines the effects of moisture absorption on the mechanical properties of these plates focussing on geometry and ‘snap-through’ loadings. Samples were monitored from a dry state until moisture equilibrium was achieved. It was observed that substantial changes in geometry and snap-through performance occurred as moisture content increased. As part of this work, a first order strain energy analysis was modified to incorporate a hygrothermal strain term to enable prediction of the laminate shape due to moisture content. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Morphing structures are currently receiving widespread attention in the academic and industrial communities as a means of facilitating structural shape tailoring. One of the common examples for an application that would greatly benefit from morphing structures is that of substantial planform, camber or control surface geometric change in aeroplane wings [1]. One method of achieving a morphing capability is by the use of multistable laminated fibre reinforced polymer composites to create components that can undergo significant shape change [2–4]. Previous work in this field has included research into the understanding of the shapes formed [5–7] and energy required to transform between stable states [8], as well as investigations into methods of actuation including shape memory wires [9] and piezoceramic patches [10–13]. The principal mechanism as to how multistability is bestowed on a laminated composite is via thermally induced residual stresses created during the high temperature curing process. However, a potential problem then arises in that these materials have a susceptibility to moisture absorption from the surrounding environment which relieves some of the residual stress, thereby altering the geometry of the laminate. Fibre reinforced composites are known to absorb moisture from their environments, with maximum moisture uptakes of around 1.8 wt% depending on the particular resin–fibre combination [14]. Choi et al. [15] investigated the effects of the hygroscopic behaviour of carbon fibre reinforced plastic (CFRP) as utilised in the aerospace industry. It was found * Corresponding author. Tel.: +44 117 331 7914. E-mail address: [email protected] (J. Etches). 1359-835X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2009.05.018

that glass transition temperatures are affected by moisture ingress and that laminate thickness or lay-up does not significantly affect the diffusion rate or equilibrium water uptake. The moisture can also affect the mechanical properties of composites, Abdel-Magid et al. [16] investigated the combined effects of load, moisture and temperature on glass based epoxy composites. It was found that strength and stiffness can be reduced due to the influence of the moisture, causing matrix plasticization and degradation of the fibre/matrix interface. Jana and Bhunia [17] demonstrated that, for woven carbon fibre/epoxy composites, the interlaminar shear strength dropped from 55 MPa dry to 30 MPa after hygrothermal cycling for a moisture uptake of 1.3 wt%. These works demonstrate the dramatic effects relatively small quantities of moisture can impose on fibre reinforced composites. Bistable composites will also be affected by the absorption of moisture. Analysis by Portela et al. [12] attempted to account for this moisture effect on the behaviour of a multistable laminate, however, an arbitrary value for moisture content within the laminate was chosen due to a lack of available data. The finite element analysis showed that moisture has a significant effect on the load required to cause change between stable states, but due to the limitations of the analysis approach used different moisture levels were not investigated. Similar work by Hufenbach et al. [18] acknowledges the effect of hygrothermal properties on the curvature of the laminates but no experimental work has been carried out to validate the extent. Choi et al. [15] experimentally examined the moisture effect on the curvature of an unsymmetrical composite lay-up and reported that curvature decreases with increasing moisture content. However, no investigation into the effect on snap-through loadings was carried out nor was there any indica-

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as an aerodynamic component would typically be designed to sustain a particular load prior to transforming between states, and the initial and final shapes of the stable states would need to be well defined. If these are likely to change with respect to the environment it could substantially alter both the load response and the initial and final geometries. Therefore, the aim of this study has been to quantify the change in curvature due to moisture absorption for a thin (0.25 mm) unsymmetrical bistable CFRP laminate and the related effect on the bistable nature of the laminate. As part of this work a simple model has been used to investigate the effect of moisture on the residual thermal strain energy. Also, experiments were performed to establish the relationship between the relative humidity of the environment and the moisture uptake of the CFRP laminate.

Fig. 1. Schematic of bistable samples showing geometric dimensions.

2. Experimental work

Fig. 2. Test fixture for transformation loading measurements.

tion given as to utilising the moisture content in predicting geometrical changes. Other work involving the assessment of changes in moisture on curved unsymmetric laminates has included Wu et al. [19], who investigated the hygrothermal performance through the use of a transient simulated laminate methodology; Gendron et al. [20] developed two non-linear models to study the deformation of unsymmetrical cardboard sheets subject to moisture changes; and Gigliotti et al. [21] modelled and simulated hygrothermoelastic stresses in composite plates in order to understand the effect of transient and cyclical environmental conditions. An alternative method to overcome the moisture effects in a bistable composite laminate has been developed by Daynes et al. [22]. This laminate does not rely on thermal residual stresses to generate the multiple states, but utilises the application of fibre prestress to manipulate the residual stresses within the laminate. The quantitative assessment of environmental effects on the bistable nature of CFRP unsymmetrical laminates is important, particularly if these structures are to be applied as a morphing or actuated component. For example, a bistable CFRP laminate deployed

As the amount of water moisture absorbed by a component is a relatively slow diffusion controlled process, it was decided to investigate thin CFRP laminates as these would respond most rapidly to the environmental conditions. Panels of 200 mm  200 mm were laid up by hand using Hexcel 8552-AS4 unidirectional carbon fibre/epoxy prepreg with a nominal ply thickness of 0.125 mm. The lay-up sequence chosen was 0°/90° with two plies being utilised to generate panels with a nominal thickness of 0.25 mm. The samples were processed in an autoclave according to the manufacturer’s recommended cycle of 1 h at 120 °C, followed by 2 h at 180 °C at a pressure of 700 kPa (7 bar). Once the samples were removed from the autoclave the precise weight and geometry of the samples was monitored over a period of two months. Fig. 1 shows the depth (d) and chord (c) that were the dimensions used to assess geometric changes in the bistable samples over the test period. The samples were kept at 20 ± 1 °C and 65 ± 2% RH (relative humidity) for the duration of the testing. As described above, water absorption is likely to have a significant effect on the residual curvature of the laminate. This, in turn, will have a significant effect on the transformation or ‘snap through’ loading associated with the laminate. Snap-through loading was measured using a method previously described by Potter et al. [23]. A schematic of the test fixture is shown in Fig. 2. A flat 5 mm thick aluminium plate is rigidly mounted to the base of an Instron 3343 test machine. The bistable panel is simply supported on this plate. A rounded indenter (diameter 10 mm) is attached to the crosshead of the machine, centred over the CFRP specimen and

70

2.0 1.8

60

1.4 1.2

40

1.0 30

0.8

20

Sample B % Chord change Sample A % Chord change Sample B % weight gain Sample A % weight gain

10 0 0

10000

20000

30000

40000

50000

60000

70000

Time (mins) Fig. 3. Geometric changes and weight gain for the bistable CFRP panels.

0.6 0.4 0.2

0.0 80000

% Weight gain

% Chord change

1.6 50

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terise their performance; the ability to maintain two stable nonplanar states, the geometry of these stable states, and the load required to transform or ‘snap’ between these stable states. 3.1. Effect on residual curvature Results from the periodic monitoring of the bistable CFRP panels are shown in Fig. 3. It can be seen that there is a substantial change in geometry that relates to the environmental conditions. The initial chord length for sample A was 127 mm and at equilibrium conditions the chord length increased to 193 mm. This difference is visible on comparing the images within Figs. 4 and 5, which show the shapes of a dry laminate and the same sample after 48 h at 20 °C and 65% RH. Such a large difference (>50%) will have a marked effect on any component designed to utilise the bistable nature of the composite as the geometry and load response for transformation between states will have significantly changed. However, it must be noted that these panels were thin (0.25 mm) and chosen to demonstrate a rapid response to the moisture in the environment. Real components are likely to be much more substantial than those considered herein with a resulting slower time to reach a saturated state for any given environmental conditions.

Fig. 4. Dry laminate.

Fig. 5. Laminate after 48 h at 20 °C and 65% RH.

3.2. Effect on transformation load The effects of the moisture absorption on the loads required to generate snap-through are shown in Fig. 6, along with the chord and height changes recorded at the time of testing. All samples retained their bistable nature for the duration of the testing. It can be seen that as the chord lengthens and the height decreases due to moisture absorption, the load to generate a ‘snap-through’ event reduces markedly. On comparing the load–displacements traces obtained as part of this work to those obtained by Potter et al. [23] a significant difference was observed. In the previous work, a plateau in the load– displacement data was reached, followed by a reduction in load until bifurcation and snap-through occurred. The load–displacement data from the current work can be seen in Fig. 7 and it is noticeable that after the plateau the load increases prior to bifurcation and snap-through of the plate. On inspection of the sample during this secondary load increase it was noticed that the plate undergoes local distortion due to the indenter. This can be seen in Fig. 8 which shows the surface profile

lowered to impart an actuation to the bistable panel. Samples were tested at a crosshead speed of 10 mm/min, and the load/displacement data was recorded. The ‘snap-through’ load performance of each panel was measured over several days. Prior to the commencement of testing the samples were placed at 130 °C overnight to ensure no moisture was present. The first test happened as soon as practical from when the samples reached room temperature on removal from the oven. For the duration of the testing the samples were maintained at 20 ± 1 °C and 65 ± 2% RH, apart from the brief excursions to uncontrolled room conditions for the duration of the testing, which was no more than 10 min. 3. Results When bistable CFRP laminates are considered for use in morphing structures, there are several important features that charac-

200

3.5

180

Length (mm)

140

Chord Length (mm)

120

Height (mm)

2.5 2

Snap through loading (N)

100

1.5

80 60

1

40 0.5

20 0

0

0

1

2

3

4

5

6

7

Time (Days) Fig. 6. Change in snap-through load with exposure to 20 °C and 65% RH.

8

Snap through load (N)

3

160

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3.5

3

Day 0 Plateau

Load (N)

2.5

2 Day 1 1.5 Day 2 1 Day 4 0.5 Day 7 Day 3

0 0

10

20

30

40

50

60

70

Displacement (mm) Fig. 7. Load–displacement traces for bistable plate over several days exposure to 20 °C and 65% RH.

of half the plate during this loading phase. The spot height measurements were taken on a 10  10 mm grid using a linear potentiometric displacement transducer. This profile also shows that while the global deformation is reasonably symmetric, near the indenter, a significant asymmetry is generated towards the edge of the plate. It is believed that this distortion has not been previously observed, probably because thicker plates which have been used, would have sufficient stiffness to resist this local deformation. In the case reported here, the laminate is only 0.25 mm in thickness and appears to have insufficient stiffness to resist the localised deformation. It is also evident that as the moisture content in the sample increases over time, this effect becomes less apparent as

20

the load required to cause snap-through is reduced and, therefore, the localised deformation is also reduced. 4. Analytical modelling To make use of this data and provide a prognostic capability, an analytical model was required that linked residual strain energy to the level of moisture within the CFRP panel. Potter et al. [23] used a first order estimate of the strain energy within a bistable CFRP laminate to demonstrate that a small portion of the locked in thermal strain is relieved by the development of curvature within the plate.

Indenter

18 16 14 12

Distance 10 (mm)

8 6 4 2 0

Mid plane of sample

Free edge of sample Fig. 8. Profile of plate due to local deformation.

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The expression used to calculate the strain energy within the bistable laminate is given in Eq. (1), where S is the strain energy/ area, E is the Young’s modulus, e is the linear distribution of strain and eth is the thermal strain within the 90° ply, and z is the distance from the mid-plane.

Sð0 Þ þ Sð90 Þ ¼

1 2

Z

h

E11 e2 dz þ

0

1 2

Z

0

E22 ðe þ eth Þ2 dz

ð1Þ

h

For both the 0° and 90° ply the linear strain can be determined from Eqs. (2) and (3):

e¼

ðz  z0 Þ R

ð2Þ

where

z0 ¼

ðE11  E22 Þ h ðE11 þ E22 Þ 2

ð3Þ

and R is radius of curvature and h is half the plate thickness. For the 90° ply, the thermal strain is obtained from the thermal expansion coefficient with a temperature change of 160 °C, cool down from 180 °C to 20 °C (Eq. (4)). In this case, the thermal strain is 0.0048 reflecting the value of coefficient of thermal expansion (30  106 °C1[24]). It is assumed that there is no thermal strain in the 0° ply due to the low value of longitudinal thermal expansion coefficient and is taken as zero [23].

eth ¼ a  DT

ð4Þ

The hygrothermal effects can be accounted for in a similar manner to the thermal strain, Eq. (5).

eh ¼ b  m

ð5Þ

where eh is hygrothermal strain, b is coefficient of moisture expansion and m is equilibrium moisture content of the laminate. For a unidirectional composite, b11 = 0 [25] and

b22 ¼

qc ð1 þ tm Þ 3 qw

ð6Þ

where qc is density of composite, qw is density of water and tm is Poisson’s ratio of matrix and the values were obtained from [24,26]. Incorporating Eq. (5) in Eq. (1) gives Eq. (7):

1 2

Z

h

E11 e2 dz þ

0

1 2

Z

0

E22 ðe þ eth  eh Þ2 dz

ð7Þ

h

0° ply 90° ply 90° ply with moisture

0.5 0.45

5. Estimate of moisture content within a laminate The results so far indicate that the radius of curvature of an unsymmetrical CFRP (AS4/8552) panel can be predicted for a known moisture content. However, it is not always practical to directly obtain the moisture content within a component. It would be far more useful to be able to predict the moisture content and, thereby, the radius of curvature, from a more measurable quantity such as relative humidity of the surrounding environment. Shen and Springer [14] postulated that maximum moisture content, Mm, within a composite material is related to the relative humidity, /, of the surrounding environment according to Eq. (8), where a and b are determined experimentally.

Mm ¼ a/b

ð8Þ

Total Total with 0.5% moisture

Energy minimum at R=58.1mm

0.4

Strain energy (J)

Sð0 Þ þ Sð90 Þ ¼

It is possible that the value of E22 could be affected by a variable moisture content, however, with the samples being held at room temperature it is likely to be minimal compared to the changes in the residual strains [27]. The effect of the incorporation of the hygrothermal strain component into the overall residual strain can be seen in Fig. 9, which shows the strain plots for the 0° and 90° plies and the total strain when the laminate is dry and when it has a moisture content of 0.5 wt%. The 0° ply is unaffected by the moisture as its coefficient of moisture expansion is zero. However, it can be seen that the strain energy within the 90° ply is substantially reduced with the addition of the moisture term. Fig. 9 allows the prediction of the radius of curvature expected for a bistable laminate at the point where the overall strain energy is at a minimum. It can be seen that for a dry laminate the predicted radius of curvature in a 200 mm  200 mm panel is 58.1 mm and in the case of 0.5 wt% moisture content a predicted radius of curvature of 90.9 mm is given. The predicted curvatures for various moisture contents can be compared to the data collected from experimentation, Fig. 10. The experimental R values were calculated from height and chord lengths of the samples under investigation. It can be seen that the predicted values closely match the experimental data. There is likely to be some variation due to slight differences in panel thickness caused by irregularities within the prepregs [28].

0.35 0.3 0.25

Energy minimum at R=90.9mm

0.2 0.15 0.1 0.05 0 40

60

80

100

120

Radius of curvature (mm) Fig. 9. Predicted effect of moisture on residual strain energy.

140

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J. Etches et al. / Composites: Part A 40 (2009) 1240–1247

Radius of curvature (mm)

250

200

150

100

50

Predicited Radius of Curvature Sample B Sample A

0 0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

Moisture Content (wt%) Fig. 10. Comparison of predicted and measured radius of curvature for a range of moisture contents.

To obtain a and b the mass of thin (0.125 mm) composite panels (single ply samples, 50  20 mm) was monitored after exposure to different relative humidities and 20 °C for 20 days. The panels were placed in enclosed chambers either directly above saturated salt solutions or submerged in distilled water. The saturated salt solutions (MgCl2, NaNO2 and KCl) enable different relative humidities to be maintained in a local environment and were used to generate relative humidities of 33%, 65% and 85%, respectively, [29]. Fig. 11 shows the maximum wt% moisture content that the composite samples achieved in each of the environments over a period of 20 days. All samples had reached equilibrium within the 20 day time frame, determined by no further measurable gain in mass. Comparing Fig. 11 with Eq. (8), it can be seen that the coefficients are a = 0.0286 and b = 0.8532 for this composite material (AS4/8552). This relationship allows the prediction of the maxi-

mum moisture content for a composite laminate of this type, which can be subsequently utilised in the prediction of the residual curvature for a bistable composite laminate. 6. Relationship between load and radius of curvature A further development of the analysis considered the relationship between snap-through load and the radius of curvature of the plate. Assuming the plate acts as a one-dimensional beam then:

EI R PL EI ¼ ; 4 R

M¼

gives PR ¼

ð9Þ

4EI L

Maximum mositure content (wt%)

1.8 1.6 1.4 1.2 1 0.8 0.6 0.8532

y = 0.0286 x 2 R = 0.9674

0.4 0.2 0 30

40

50

60

70

80

Relative humdity (%) Fig. 11. Results from moisture absorption testing.

90

100

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Table 1 Experimental PR ratios. Samples

Radius (mm)

Load (N)

PR (N m)

Day Day Day Day Day Day

58.0 89.1 104.1 111.1 114.9 144.2

3.2 1.84 1.52 1.38 1.32 1.08

0.186 0.164 0.158 0.153 0.152 0.156

0 1 2 3 4 7

where M is bending moment, P is applied load, L is length, E is Elastic modulus, R is radius of curvature and I is second moment of area. By using the appropriate reduced stiffness for E [30], to reflect the unsymmetric nature of the plates

E¼

t3  12d11

References

ð10Þ

with 

½d 1 ¼ ½D  ¼ ½D  ½B½A1 ½B

ð11Þ

gives the following constant relationship:

PR ¼ 0:1568 Nm

This work has shown that through the use of a first-order strain energy model the geometrical changes due to moisture absorption can be predicted. If this model is used in conjunction with an understanding of the relationship between relative humidity of the environment and the resulting moisture content for a CFRP laminate, a prediction of the residual component geometry in any given environment will be possible. The next stage of this work will be to examine the effect of moisture on the multistability of these unsymmetric laminates as the temperature varies. The influence of thermal and hygrothermal strains will compete as the temperature is altered leading to variations in the geometric and mechanical response of these composite laminates.

ð12Þ

From the data obtained during the investigation of moisture effects on the snap-though loading of the bistable plate, the experimental values of PR can be calculated as shown in Table 1. When these values are compared with the theoretical value of 0.1568 it can be seen that there is good correlation with the majority of the data, less than 5% difference. It is believed that the main reason that the result from Day 0 exhibits a large discrepancy, 18%, compared to the theoretical prediction is the significant local deformation that this sample showed during loading, as previously described in Section 3.2. Considering the simplistic nature of the model presented through Eqs. (10–12) the correlation with experimental results is excellent. The model assumes one dimensional response such that anticlastic behaviour due to Poisson’s ratios effects is ignored. Indeed, such an assumption is viable for the lay-ups considered herein where the effective Poisson’s ratios for cross-ply plates are of the order of 0.05, which is a small value. Note, for other lay-ups, a twodimensional model would need to be developed. Furthermore, the snap-through load is captured by P, which assumes that snapthrough occurs when the plate has reduced its curvature by an amount R, i.e. the plate is flat at snap-through. Whilst we know the plate to have significantly reduced curvature, the actual situation is complicated by a non-uniform curvature across the plate at snap-through. Previously [6], it has been observed that snapthrough is characterised by a two-part mechanism whereby half the plate bifurcates to a metastable state followed by the remaining part of the plate to the new stable shape. So, despite the fact that the simple model does not capture snap-through geometry in any detail, it does show good correlation with experimental results. 7. Conclusions This experimental study has demonstrated that substantial changes occur in the characteristics of bistable CFRP laminates when exposed to moisture. Substantial changes in the curvature of the laminates are observed and, while the samples retained their bistable behaviour, the load required to cause transformation between stable states is dramatically reduced. This response to moisture uptake has a direct bearing on how and where multistable morphing structures are deployed. The presence of moisture in the surrounding environment will have to be fully considered for any morphing system which uses thermally induced stresses to provide multistability.

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