- Email: [email protected]
Shape recovery studies for coupled deformations in an epoxy based amorphous shape memory polymers
Polymer Testing 48 (2015) 1e6
Contents lists available at ScienceDirect
Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Material behaviour
Shape recovery studies for coupled deformations in an epoxy based amorphous shape memory polymers R. Sujithra, S.M. Srinivasan, A. Arockiarajan* Department of Applied Mechanics, IIT Madras, Chennai 600036, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 August 2015 Accepted 9 September 2015 Available online 12 September 2015
In this work, the effect of sequence of shape setting on the shape recovery response for an epoxy based amorphous SMP was studied. The shape setting for coupled axial-twist deformations was done at two different temperatures within the glass transition band. A simple set-up with cameras was used to study the shape recovery behavior under free recovery experiments. Results show that the recovery behavior is independent of sequence of shape setting process but a shift in the shape recovery curve is noticed. The shape memory cycle for coupled deformations was also simulated in ABAQUS-VUMAT using the model proposed earlier by the authors based on multiple natural configurations. The simulated results show the capability of the model to analyze the memory effects of an amorphous polymer subjected to coupled deformations. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Shape memory polymer Coupled deformations Shape recovery ABAQUS-VUMAT Modeling memory effects
1. Introduction Shape memory polymers (SMP) are stimuli-responsive polymers which can deform to any temporary shape and revert back to the permanent shape when exposed to a suitable stimulus, for example by heating which is termed thermally induced dual shape memory effect [1]. In amorphous polymers, a change in temperature causes a change in the stiffness (change in entropy) of the material from glassy (Tlow) to rubbery state (Thigh) around the glass transition temperature. This results in the shape memory effect. The key features of the SMP are large recoverable strains by direct or indirect actuation, molded to any complex shape, tailor made properties, low cost, light weight and bio-compatibility. The shape memory effect in polymers is a combination of molecular architecture together with the programming technique, which makes it suitable for many sophisticated applications [2,3]. In this study, epoxy based amorphous shape memory polymer was chosen, as they possess good structural properties, tailor made transition temperature and excellent shape recovery characteristics with no molecular slippage between the chains due to chemical cross-linking [4,5]. The shape recovery properties depend on the curing agent content, type of functional groups [6,7] or the amount
* Corresponding author. E-mail address: [email protected] (A. Arockiarajan). http://dx.doi.org/10.1016/j.polymertesting.2015.09.005 0142-9418/© 2015 Elsevier Ltd. All rights reserved.
of flexibilizer [8]. In most experiments, SMPs are subjected to tension and compression in a small strain region [9], bending [10], twisting [11], large strain tension [12] or cold compression programming [13]. Several thermomechanical experimental studies show that the performance of SMP is also influenced by time and temperature dependent factors, such as rate of deformation, holding time, multiple thermomechanical cycles [14], different deformation levels, heating rate effects [12] and recovery under different thermal conditions [15]. Souri et al. studied the shape recovery behavior of epoxy based SMP by constraint and unconstraint conditions [16]. Yu and Qi showed that the programming temperature and heating rate influences the shape recovery behavior [17]. Sujithra et al. studied the memory characteristics of epoxy based SMP by varying the hardener content, various deformation levels, and loading and unloading at different temperatures [18]. In many applications, the shape setting process is usually done in a single step, or with multiple programming steps for SMPs with several transition temperatures [19]. In sealant application [20], the shape setting process for coupled deformation is done at same temperature, with tension in one direction and compression in the transverse direction to avoid debonding. The shape recovery for this coupled tension-compression occurs simultaneously in both directions. The present work investigates shape recovery behavior of an amorphous polymer based on the effect of sequence of shape setting process at different temperatures within the transition
2
R. Sujithra et al. / Polymer Testing 48 (2015) 1e6
band. A simple experimental set-up was fabricated for shape setting and recovery properties. The shape setting process for coupled deformations was done in two different sequential manners, tension and then twist or in the other way round, twist and then tension, at two different temperatures. The objective of this work is to study the shape recovery characteristics for coupled shape setting processes in free shape recovery conditions. Also, the shape memory cycle for coupled deformations is numerically simulated in ABAQUS-VUMAT using the model based on the theory of multiple natural configurations proposed by the authors [21]. This study also helps to compare the memory effects in modeling. The paper outline is as follows; Section 2 describes the epoxy sample preparation, experimental set-up and procedures for shape fixing and shape recovery measurements. Section 3 presents the experimental results and discusses shape recovery behavior and numerical simulation results for these coupled deformations. Finally, a short summary is in Section 4. 2. Experiments
Fig. 2. Rectangular specimen.
2.1. Epoxy sample preparation and characterization Epoxy samples were prepared using commercially available phenolic modified diglycedyl ether of bisphenol-A (EP 286FL) and triethyleneteramine (EH 758) as hardener. The desired stoichiometric quantity of amine for curing was calculated as 9.03 parts of hardener per hundred parts of resin (phr). The monomer and the hardener were mixed for 10 min without air bubbles. Thin rectangular epoxy samples (12 7 0.7 mm3) were molded using Teflon sheet, as shown in Fig. 2. The samples were cured at 60 C for two hours and then post cured at 120 C for 2 h. The DMA test was carried out in a multi-frequency strain mode at 1 Hz with a static force of 0.01 N from 27 C to 140 C with a heating/cooling rate of 2 C/min. The DMA curve for this epoxy sample is shown in Fig. 3. The glass transition temperature Tg was 86 C determined from the tand curve. In the storage modulus curve, a flat region for glassy (Tlow) and rubbery states (Thigh) was observed. The transition between these two states is referred to as the transition band or region.
Storage modulus (MPa)
10000
1,000
Glassy state
Tg
0.6
100
0.4
Rubbery state
10
1 20 Fig. 1. Shape memory cycle for coupled deformation in amorphous polymer.
0.8
0.2
40
60 80 100 Temperature (°C) Fig. 3. DMA curve for epoxy SMP.
120
0
140
tanδ
In the shape recovery experiments, programming was done at different temperatures and the full recovery took place (we will term these as free recovery experiments). These tests were carried out separately for both axial deformation and twist deformation. In addition to the above tests, experiments were conducted to understand the effect of sequence of axial and twist programming temperatures (we will term these as sequence effect experiments). The thermomechanical cycle for the sequence effect experiments is shown in Fig. 1. Two shapes were fixed at different loading temperatures say TLoad1, TLoad2 within the transition band. First, the SMP specimen was subjected to axial deformation (shape 1) at a temperature say TLoad1 (Tg) and, holding this deformation constant, it was then cooled until say TLoad2 (
R. Sujithra et al. / Polymer Testing 48 (2015) 1e6
3
Fig. 6. Permanent and temporary elongated-twisted shape.
2.3. Shape recovery set-up and measurements
Fig. 4. Axial deformation in instron UTM.
2.2. Test setup and conditions for shape fixing An Instron universal testing machine equipped with a thermal chamber was used for axial deformation. The rectangular shape SMP was placed in the UTM, as shown in Fig. 4. The chamber temperature was brought to 86 C (Tg). The initial specimen gage length was marked as 50 mm. As the UTM crosshead moved, the rectangular specimen was elongated to 15% at a rate of 3 mm/min. During cooling, the crosshead displacement was held in this position to store the elongated shape. At room temperature, the temporary elongated specimen was removed from the UTM. The fabricated experimental set-up for twisting is shown in Fig. 5. The elongated rectangular specimen was clamped between the fixed rod at one end and to the rotating clamp at the other end in the thermal chamber. The specimen was twisted by rotating the clamp manually. To measure the twist angle, a circular scale is fixed at the end of the rotating clamp. A screw without head is fixed to the rotating clamp on one end and, on the other end, connected to the fixed frame, as shown in Fig. 5. After twisting, the chamber was allowed to cool naturally. In the free recovery experiments, the same shape setting was done at different temperatures, typically in the Tg band, and the free recovery strains were measured. The shape setting temperatures used were: 95 C (>Tg), 86 C (Tg) and 75 C (
Free shape recovery experiments were conducted on these specimens by increasing the chamber's temperature from 30 to 100 C at a rate of 3 C/min. The chamber temperature was programmed using a PID controller unit and monitored using a thermocouple. The temperature values were recorded using a Data Translation 9837 card. Two cameras were used to measure the coupled deformation. A DIC camera below the thermal chambers slot was used to capture the twist recovery, and a camera featuring 4272 2848 pixels resolution was placed in front of the thermal chamber to capture the axial recovery, as shown in Fig. 7. The captured videos were converted to a sequence of image files in Adobe Photoshop. Two black spots were marked at the crosssectional area, and the gage length was marked on the front surface of the rectangular specimen. DIC images were used to measure twist angle, and camera images to measure axial strain, as shown in Fig. 8. For twist recovery, the line angle was measured by picking two spots and, for axial recovery; the gage length distance was measured using the pixel measurements in Adobe Photoshop. Both images and temperatures were recorded as a function of time. 3. Results and discussion The results obtained from the free recovery tests are discussed based on the programming temperature and the recovery behavior. Here, shape fixity is not measured, instead focussing on the shape recovery behavior. The results from numerical simulations for coupled deformations are also analyzed in this section. 3.1. Free recovery test In free recovery tests, the samples were subjected to tension deformation at different temperatures (Tload ¼ 95 C, 86 C and 75 C), and the free shape recovery for tension is shown in Fig. 9. Similarly, the samples were subjected to twisting at different temperatures (Tload ¼ 86 C, 75 C and 65 C). The free shape recovery for twisting is shown in Fig. 10. The shape recovery for coupled tension (Tload1 ¼ 86 C) - twist (Tload2 ¼ 65 C) and coupled twist (Tload1 ¼ 86 C)-tension (Tload2 ¼ 65 C) deformation is shown in Fig. 11. In all the cases, shift in the shape recovery curve is observed; as the shape setting temperature is above and below Tg. The loading temperature (programming) also influences the shape
Fig. 5. Photograph of thermomechanical setup for twisting.
4
R. Sujithra et al. / Polymer Testing 48 (2015) 1e6
1 T Normalized twist angle recovery
load
= 86 °C
Tload = 75 °C
0.8
Tload = 65 °C
0.6
0.4
0.2
Fig. 7. Photograph of shape recovery set-up.
0 30
40
50
60 70 80 Temperature (°C)
90
100
110
Fig. 10. Twist angle recovery.
3.2. Analysis of shape recovery process by modeling
Fig. 8. Camera images (a) DIC images for twist recovery and (b) camera images for measuring axial recovery.
recovery ratio. In the axial strain recovery, the irrecoverable strain is observed when loaded below Tg. The shape recovery for coupled tension-twist deformations occur simultaneously. with similar shift between the tension and twist recovery curve, as shape setting for tension was done above Tg and twisting below Tg. Similarly, shift is also observed in coupled twist-tension deformation.
Tload = 95°C load
= 86°C 1
Tload = 75°C
0.6
0.4
0.2
0 30
40
50
60 70 80 Temperature (°C)
Fig. 9. Axial strain recovery.
90
100
110
1
Coupled axial−twist Axial (Tload1 = 86°C )
0.8
Twist (T
load2
0.8
= 65°C )
Coupled twist−axial
0.6
0.6
Twist(Tload1 = 86°C ) Axial (T
load2
= 65°C )
0.4
0.4
0.2
0.2
0 30
40
50
60 70 80 Temperature (°C)
90
Fig. 11. Coupled free recovery experiments.
100
0 110
Normalized axial strain recovery
T 0.8
Normalized twist angle recovery
Normalized axial strain recovery
1
In most of the modeling framework, the shape storage process during cooling depends on the deformation history (programming temperature) [22,23]. To analyze the memory characteristics by modeling, the thermomechanical shape memory cycle for the coupled tension-twist deformation was simulated using the small deformation model implemented in ABAQUS-VUMAT proposed by the authors, based on theory of multiple natural configurations [21]. The SMP body will undergo changes in natural configuration during cooling/heating cycles as it passes through the Tg. The shape memory characteristics were modeled by assuming reversible transformation between reference and natural configuration depending on the temperature and the current deformed state. Based on the DMA curve, the natural configuration was tracked using a suitable temperature dependent parameter called the degree of glass transition parameter, which also describes the loading and unloading process from this natural configuration. The
R. Sujithra et al. / Polymer Testing 48 (2015) 1e6
1
0.8
90
Tension T = 86 °C L1
0.6
75 Twist TL2= 65 °C
0.4
0.2
60
45
Temperature Tension Twisting
0 0
30 0.25
0.05 0.1 0.15 0.2 Programming time steps (shape fixing)
Normalized axial strain and twist angle
105
Temperature (°C)
Normalized axial strain and twist angle
1
5
0.8
0.6
0.4
Coupled twist−axial
0.2
Tension (Tload = 65°C)
0 30
Fig. 12. Shape fixity for coupled deformation.
Twist (Tload = 86°C)
40
50
60 70 80 Temperature (°C)
90
100
Fig. 15. Shape storage for coupled twist-axial deformations simulation.
Fig. 13. Finite element model for coupled axial-twist deformations.
transition from one natural configuration to the other takes place on changing this parameter. All material property changes are associated with this parameter that represents the change in natural configuration. The model proposed was based on thermomechanical history of the shape storage process during cooling, and it retraces the path during shape recovery (here storing and releasing are strictly reversible process). The material parameters for this simulation were obtained from characterization results [18]. From the DMA curve, glass transition temperature was found to be 86 C and the temperature range was chosen from 30 C (Tlow) to 97 C (Thigh). Initially, the rectangular
Normalized axial strain and twist angle
0.8
0.6
Coupled tension−twist
0.2
Tension (T = 86°C) load
Twist (Tload = 65°C) 0 30
40
50
4. Summary In amorphous SMPs, the shape recovery behavior under different sequence of shape setting process was investigated in shape memory cycle experiments. The results clearly show that, except for a shift in the shape recovery curve, the shape setting sequence does not affect the recovery process. In other words, the recovery of shape is primarily independent of the sequence of shape setting when the temperature is within the glass transition zone. The sequence of shape storage process was also analyzed using the model based on natural configurations proposed earlier by the authors to show the capability of the model to capture this behavior. The simulation results show that the history of shape storage process predicts the memory characteristics for coupled deformations. This study will help the designer to predict the behavior of SMP elements under various conditions for which the design is to be carried out.
1
0.4
bar was subjected to a pre-defined temperature at 97 C, and then the temperature was reduced to 86 C. Following this, the bar was subjected to 10% of axial strain and cooled to 65 C. Then, the bar was subjected to 45 twisting at 65 C and cooled to 30 C. The shape setting profile is shown in Fig. 12, and a finite element model for the coupled deformations is shown in Fig. 13. In VUMAT, only two-state architecture is stored; the initial values are in old arrays and current values are in new arrays. By using this old stored array at the end of unloading, the new stored strain is released during reheating. Instead of shape recovery, the history of shape storage (stored strain) during cooling for these coupled deformations is shown in Fig. 14 and Fig. 15. Simulation results show that shape storage ratio drops down to 65% when loaded below Tg for both the cases. This loss in shape storage ratio below Tg results in the irrecoverable shape. Due to two-stage storage architecture, the shape recovery profile for this coupled deformation is not captured. This memory characteristic study for coupled deformations helps in modeling and designing smart systems.
60
70
Temperature (°C)
80
90
Fig. 14. Shape storage for coupled axial-twist deformations simulation.
100
References [1] A. Lendlein, S. Kelch, Shape memory polymers, Angew. Chem. Int. Ed. Engl. 41 (2002) 2034e2057.
6
R. Sujithra et al. / Polymer Testing 48 (2015) 1e6
[2] A. Lendlein, M. Behl, Shape memory polymers for biomedical applications, Adv. Sci. Tech. 54 (2008) 96e102. [3] Y. Liu, H. Du, L. Liu, J. Leng, Shape memory polymers composites and their applications in aerospace: a review, Smart Mater. Struct. 23 (2014) 023001. [4] C. Liu, H. Qin, P.T. Mather, Review of progress in shape-memory polymers, J. Mater. Chem. 17 (2007) 1543e1558. [5] A. Rousseau, Challenges of shape memory polymers: a review of the progress toward overcoming SMP's Limitations, Polym. Eng. Sci. (2008) 2075e2089. [6] A. Rousseau, T. Xie, Shape memory epoxy: composition, structure, properties and shape memory performances, J. Mater. Chem. 20 (2010) 3431e3441. [7] T. Xie, I.A. Rousseau, Facile tailoring of thermal transition temperatures of epoxy shape memory polymers, Polymer 50 (2009) 1852e1856. [8] B. Zhou, X. Wu, Y. Liu, J. Leng, Study on shape recovery behaviors of epoxybased shape memory polymer, Adv. Mat. Res. 179e180 (2011) 325e328. [9] Y. Liu, K. Gall, M.L. Dunn, A.R. Greenberg, J. Diani, Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modelling, Int. J. Plast. 22 (2006) 279e313. [10] Y. Liu, K. Gall, M.L. Dunn, P. McCluskey, Thermomechanical recovery couplings of shape memory polymers in flexure, Smart Mater. Struct. 12 (2003) 947e954. [11] J. Diani, C. Fredy, P. Gilormini, Y. Merckel, G. Regnier, I. Rousseau, A torsion test for the study of the large deformation recovery of shape memory polymers, Polym. Test. 30 (2011) 335e341. [12] B.L. Volk, D.C. Lagoudas, Y.C. Chen, K.S. Whitley, Analysis of the finite deformation response of shape memory polymers: I. Thermomechanical characterization, Smart Mater. Struct. 19 (2010) 075005. [13] G. Li, W. Xu, Thermomechanical behavior of thermoset shape memory polymer programmed by cold-compression: testing and constitutive modeling, J. Mech. Phys. Solids 59 (2011) 1231e1250.
[14] J.W. McClung, G.P. Tandon, J.W. Baur, Deformation rate, hold time, and cycledependent shape-memory performance of Veriflex-E resin, Mech. Time Depend. Mater. 17 (2013) 39e52. [15] F. Castro, K.K. Westbrook, J. Hermiller, D.U. Ahn, Y. Ding, H.J. Qi, Time and temperature dependent recovery of epoxy based shape memory polymers, J. Eng. Mater. T. ASME 133 (2011) 021025. [16] M. Souri, Y.C. Lu, A. Erol, S.S. Pulla, H.E. Karaca, Characterization of unconstraint and constraint shape recoveries of an epoxy based shape memory polymer, Polym. Test. 41 (2015) 231e238. [17] K. Yu, H.J. Qi, Temperature memory effect in amorphous shape memory polymers, Soft Matter 10 (2014) 9423e9432. [18] R. Sujithra, S.M. Srinivasan, A. Arockiarajan, Memory characteristics studies for large deflections in amorphous polymers: experiments and numerical simulation, J. Intel. Mater. Syst. Struct. (2015), http://dx.doi.org/10.1177/ 1045389X15586587. [19] H. Meng, H. Mohamadian, M. Stubblefield, D. Jerro1, S. Ibekwe1, S. Pang, G. Li, Various shape memory effects of stimuli-responsive shape memory polymers, Smart Mater. Struct. 22 (2013) 093001. [20] G. Li, M. ASCE, T. Xu, Thermomechanical characterization of shape memory polymerebased self-healing syntactic foam sealant for expansion joints, J. Transp. Eng. 137 (2011) 805e814. [21] R. Sujithra, S.M. Srinivasan, A. Arockiarajan, Modelling memory effects in amorphous polymer, Int. J. Eng. Sci. 84 (2014) 95e112. [22] Y.C. Chen, D.C. Lagoudas, A constitutive theory for shape memory polymers. Part I: Large deformations, J. Mech. Phys. Solids 56 (2008) 1752e1765. [23] G. Barot, I.J. Rao, K.R. Rajagopal, A thermodynamic framework for the modeling of crystallisable shape memory polymers, Int. J. Eng. Sci. 46 (2008) 325e351.
Contents lists available at ScienceDirect
Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Material behaviour
Shape recovery studies for coupled deformations in an epoxy based amorphous shape memory polymers R. Sujithra, S.M. Srinivasan, A. Arockiarajan* Department of Applied Mechanics, IIT Madras, Chennai 600036, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 August 2015 Accepted 9 September 2015 Available online 12 September 2015
In this work, the effect of sequence of shape setting on the shape recovery response for an epoxy based amorphous SMP was studied. The shape setting for coupled axial-twist deformations was done at two different temperatures within the glass transition band. A simple set-up with cameras was used to study the shape recovery behavior under free recovery experiments. Results show that the recovery behavior is independent of sequence of shape setting process but a shift in the shape recovery curve is noticed. The shape memory cycle for coupled deformations was also simulated in ABAQUS-VUMAT using the model proposed earlier by the authors based on multiple natural configurations. The simulated results show the capability of the model to analyze the memory effects of an amorphous polymer subjected to coupled deformations. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Shape memory polymer Coupled deformations Shape recovery ABAQUS-VUMAT Modeling memory effects
1. Introduction Shape memory polymers (SMP) are stimuli-responsive polymers which can deform to any temporary shape and revert back to the permanent shape when exposed to a suitable stimulus, for example by heating which is termed thermally induced dual shape memory effect [1]. In amorphous polymers, a change in temperature causes a change in the stiffness (change in entropy) of the material from glassy (Tlow) to rubbery state (Thigh) around the glass transition temperature. This results in the shape memory effect. The key features of the SMP are large recoverable strains by direct or indirect actuation, molded to any complex shape, tailor made properties, low cost, light weight and bio-compatibility. The shape memory effect in polymers is a combination of molecular architecture together with the programming technique, which makes it suitable for many sophisticated applications [2,3]. In this study, epoxy based amorphous shape memory polymer was chosen, as they possess good structural properties, tailor made transition temperature and excellent shape recovery characteristics with no molecular slippage between the chains due to chemical cross-linking [4,5]. The shape recovery properties depend on the curing agent content, type of functional groups [6,7] or the amount
* Corresponding author. E-mail address: [email protected] (A. Arockiarajan). http://dx.doi.org/10.1016/j.polymertesting.2015.09.005 0142-9418/© 2015 Elsevier Ltd. All rights reserved.
of flexibilizer [8]. In most experiments, SMPs are subjected to tension and compression in a small strain region [9], bending [10], twisting [11], large strain tension [12] or cold compression programming [13]. Several thermomechanical experimental studies show that the performance of SMP is also influenced by time and temperature dependent factors, such as rate of deformation, holding time, multiple thermomechanical cycles [14], different deformation levels, heating rate effects [12] and recovery under different thermal conditions [15]. Souri et al. studied the shape recovery behavior of epoxy based SMP by constraint and unconstraint conditions [16]. Yu and Qi showed that the programming temperature and heating rate influences the shape recovery behavior [17]. Sujithra et al. studied the memory characteristics of epoxy based SMP by varying the hardener content, various deformation levels, and loading and unloading at different temperatures [18]. In many applications, the shape setting process is usually done in a single step, or with multiple programming steps for SMPs with several transition temperatures [19]. In sealant application [20], the shape setting process for coupled deformation is done at same temperature, with tension in one direction and compression in the transverse direction to avoid debonding. The shape recovery for this coupled tension-compression occurs simultaneously in both directions. The present work investigates shape recovery behavior of an amorphous polymer based on the effect of sequence of shape setting process at different temperatures within the transition
2
R. Sujithra et al. / Polymer Testing 48 (2015) 1e6
band. A simple experimental set-up was fabricated for shape setting and recovery properties. The shape setting process for coupled deformations was done in two different sequential manners, tension and then twist or in the other way round, twist and then tension, at two different temperatures. The objective of this work is to study the shape recovery characteristics for coupled shape setting processes in free shape recovery conditions. Also, the shape memory cycle for coupled deformations is numerically simulated in ABAQUS-VUMAT using the model based on the theory of multiple natural configurations proposed by the authors [21]. This study also helps to compare the memory effects in modeling. The paper outline is as follows; Section 2 describes the epoxy sample preparation, experimental set-up and procedures for shape fixing and shape recovery measurements. Section 3 presents the experimental results and discusses shape recovery behavior and numerical simulation results for these coupled deformations. Finally, a short summary is in Section 4. 2. Experiments
Fig. 2. Rectangular specimen.
2.1. Epoxy sample preparation and characterization Epoxy samples were prepared using commercially available phenolic modified diglycedyl ether of bisphenol-A (EP 286FL) and triethyleneteramine (EH 758) as hardener. The desired stoichiometric quantity of amine for curing was calculated as 9.03 parts of hardener per hundred parts of resin (phr). The monomer and the hardener were mixed for 10 min without air bubbles. Thin rectangular epoxy samples (12 7 0.7 mm3) were molded using Teflon sheet, as shown in Fig. 2. The samples were cured at 60 C for two hours and then post cured at 120 C for 2 h. The DMA test was carried out in a multi-frequency strain mode at 1 Hz with a static force of 0.01 N from 27 C to 140 C with a heating/cooling rate of 2 C/min. The DMA curve for this epoxy sample is shown in Fig. 3. The glass transition temperature Tg was 86 C determined from the tand curve. In the storage modulus curve, a flat region for glassy (Tlow) and rubbery states (Thigh) was observed. The transition between these two states is referred to as the transition band or region.
Storage modulus (MPa)
10000
1,000
Glassy state
Tg
0.6
100
0.4
Rubbery state
10
1 20 Fig. 1. Shape memory cycle for coupled deformation in amorphous polymer.
0.8
0.2
40
60 80 100 Temperature (°C) Fig. 3. DMA curve for epoxy SMP.
120
0
140
tanδ
In the shape recovery experiments, programming was done at different temperatures and the full recovery took place (we will term these as free recovery experiments). These tests were carried out separately for both axial deformation and twist deformation. In addition to the above tests, experiments were conducted to understand the effect of sequence of axial and twist programming temperatures (we will term these as sequence effect experiments). The thermomechanical cycle for the sequence effect experiments is shown in Fig. 1. Two shapes were fixed at different loading temperatures say TLoad1, TLoad2 within the transition band. First, the SMP specimen was subjected to axial deformation (shape 1) at a temperature say TLoad1 (Tg) and, holding this deformation constant, it was then cooled until say TLoad2 (
R. Sujithra et al. / Polymer Testing 48 (2015) 1e6
3
Fig. 6. Permanent and temporary elongated-twisted shape.
2.3. Shape recovery set-up and measurements
Fig. 4. Axial deformation in instron UTM.
2.2. Test setup and conditions for shape fixing An Instron universal testing machine equipped with a thermal chamber was used for axial deformation. The rectangular shape SMP was placed in the UTM, as shown in Fig. 4. The chamber temperature was brought to 86 C (Tg). The initial specimen gage length was marked as 50 mm. As the UTM crosshead moved, the rectangular specimen was elongated to 15% at a rate of 3 mm/min. During cooling, the crosshead displacement was held in this position to store the elongated shape. At room temperature, the temporary elongated specimen was removed from the UTM. The fabricated experimental set-up for twisting is shown in Fig. 5. The elongated rectangular specimen was clamped between the fixed rod at one end and to the rotating clamp at the other end in the thermal chamber. The specimen was twisted by rotating the clamp manually. To measure the twist angle, a circular scale is fixed at the end of the rotating clamp. A screw without head is fixed to the rotating clamp on one end and, on the other end, connected to the fixed frame, as shown in Fig. 5. After twisting, the chamber was allowed to cool naturally. In the free recovery experiments, the same shape setting was done at different temperatures, typically in the Tg band, and the free recovery strains were measured. The shape setting temperatures used were: 95 C (>Tg), 86 C (Tg) and 75 C (
Free shape recovery experiments were conducted on these specimens by increasing the chamber's temperature from 30 to 100 C at a rate of 3 C/min. The chamber temperature was programmed using a PID controller unit and monitored using a thermocouple. The temperature values were recorded using a Data Translation 9837 card. Two cameras were used to measure the coupled deformation. A DIC camera below the thermal chambers slot was used to capture the twist recovery, and a camera featuring 4272 2848 pixels resolution was placed in front of the thermal chamber to capture the axial recovery, as shown in Fig. 7. The captured videos were converted to a sequence of image files in Adobe Photoshop. Two black spots were marked at the crosssectional area, and the gage length was marked on the front surface of the rectangular specimen. DIC images were used to measure twist angle, and camera images to measure axial strain, as shown in Fig. 8. For twist recovery, the line angle was measured by picking two spots and, for axial recovery; the gage length distance was measured using the pixel measurements in Adobe Photoshop. Both images and temperatures were recorded as a function of time. 3. Results and discussion The results obtained from the free recovery tests are discussed based on the programming temperature and the recovery behavior. Here, shape fixity is not measured, instead focussing on the shape recovery behavior. The results from numerical simulations for coupled deformations are also analyzed in this section. 3.1. Free recovery test In free recovery tests, the samples were subjected to tension deformation at different temperatures (Tload ¼ 95 C, 86 C and 75 C), and the free shape recovery for tension is shown in Fig. 9. Similarly, the samples were subjected to twisting at different temperatures (Tload ¼ 86 C, 75 C and 65 C). The free shape recovery for twisting is shown in Fig. 10. The shape recovery for coupled tension (Tload1 ¼ 86 C) - twist (Tload2 ¼ 65 C) and coupled twist (Tload1 ¼ 86 C)-tension (Tload2 ¼ 65 C) deformation is shown in Fig. 11. In all the cases, shift in the shape recovery curve is observed; as the shape setting temperature is above and below Tg. The loading temperature (programming) also influences the shape
Fig. 5. Photograph of thermomechanical setup for twisting.
4
R. Sujithra et al. / Polymer Testing 48 (2015) 1e6
1 T Normalized twist angle recovery
load
= 86 °C
Tload = 75 °C
0.8
Tload = 65 °C
0.6
0.4
0.2
Fig. 7. Photograph of shape recovery set-up.
0 30
40
50
60 70 80 Temperature (°C)
90
100
110
Fig. 10. Twist angle recovery.
3.2. Analysis of shape recovery process by modeling
Fig. 8. Camera images (a) DIC images for twist recovery and (b) camera images for measuring axial recovery.
recovery ratio. In the axial strain recovery, the irrecoverable strain is observed when loaded below Tg. The shape recovery for coupled tension-twist deformations occur simultaneously. with similar shift between the tension and twist recovery curve, as shape setting for tension was done above Tg and twisting below Tg. Similarly, shift is also observed in coupled twist-tension deformation.
Tload = 95°C load
= 86°C 1
Tload = 75°C
0.6
0.4
0.2
0 30
40
50
60 70 80 Temperature (°C)
Fig. 9. Axial strain recovery.
90
100
110
1
Coupled axial−twist Axial (Tload1 = 86°C )
0.8
Twist (T
load2
0.8
= 65°C )
Coupled twist−axial
0.6
0.6
Twist(Tload1 = 86°C ) Axial (T
load2
= 65°C )
0.4
0.4
0.2
0.2
0 30
40
50
60 70 80 Temperature (°C)
90
Fig. 11. Coupled free recovery experiments.
100
0 110
Normalized axial strain recovery
T 0.8
Normalized twist angle recovery
Normalized axial strain recovery
1
In most of the modeling framework, the shape storage process during cooling depends on the deformation history (programming temperature) [22,23]. To analyze the memory characteristics by modeling, the thermomechanical shape memory cycle for the coupled tension-twist deformation was simulated using the small deformation model implemented in ABAQUS-VUMAT proposed by the authors, based on theory of multiple natural configurations [21]. The SMP body will undergo changes in natural configuration during cooling/heating cycles as it passes through the Tg. The shape memory characteristics were modeled by assuming reversible transformation between reference and natural configuration depending on the temperature and the current deformed state. Based on the DMA curve, the natural configuration was tracked using a suitable temperature dependent parameter called the degree of glass transition parameter, which also describes the loading and unloading process from this natural configuration. The
R. Sujithra et al. / Polymer Testing 48 (2015) 1e6
1
0.8
90
Tension T = 86 °C L1
0.6
75 Twist TL2= 65 °C
0.4
0.2
60
45
Temperature Tension Twisting
0 0
30 0.25
0.05 0.1 0.15 0.2 Programming time steps (shape fixing)
Normalized axial strain and twist angle
105
Temperature (°C)
Normalized axial strain and twist angle
1
5
0.8
0.6
0.4
Coupled twist−axial
0.2
Tension (Tload = 65°C)
0 30
Fig. 12. Shape fixity for coupled deformation.
Twist (Tload = 86°C)
40
50
60 70 80 Temperature (°C)
90
100
Fig. 15. Shape storage for coupled twist-axial deformations simulation.
Fig. 13. Finite element model for coupled axial-twist deformations.
transition from one natural configuration to the other takes place on changing this parameter. All material property changes are associated with this parameter that represents the change in natural configuration. The model proposed was based on thermomechanical history of the shape storage process during cooling, and it retraces the path during shape recovery (here storing and releasing are strictly reversible process). The material parameters for this simulation were obtained from characterization results [18]. From the DMA curve, glass transition temperature was found to be 86 C and the temperature range was chosen from 30 C (Tlow) to 97 C (Thigh). Initially, the rectangular
Normalized axial strain and twist angle
0.8
0.6
Coupled tension−twist
0.2
Tension (T = 86°C) load
Twist (Tload = 65°C) 0 30
40
50
4. Summary In amorphous SMPs, the shape recovery behavior under different sequence of shape setting process was investigated in shape memory cycle experiments. The results clearly show that, except for a shift in the shape recovery curve, the shape setting sequence does not affect the recovery process. In other words, the recovery of shape is primarily independent of the sequence of shape setting when the temperature is within the glass transition zone. The sequence of shape storage process was also analyzed using the model based on natural configurations proposed earlier by the authors to show the capability of the model to capture this behavior. The simulation results show that the history of shape storage process predicts the memory characteristics for coupled deformations. This study will help the designer to predict the behavior of SMP elements under various conditions for which the design is to be carried out.
1
0.4
bar was subjected to a pre-defined temperature at 97 C, and then the temperature was reduced to 86 C. Following this, the bar was subjected to 10% of axial strain and cooled to 65 C. Then, the bar was subjected to 45 twisting at 65 C and cooled to 30 C. The shape setting profile is shown in Fig. 12, and a finite element model for the coupled deformations is shown in Fig. 13. In VUMAT, only two-state architecture is stored; the initial values are in old arrays and current values are in new arrays. By using this old stored array at the end of unloading, the new stored strain is released during reheating. Instead of shape recovery, the history of shape storage (stored strain) during cooling for these coupled deformations is shown in Fig. 14 and Fig. 15. Simulation results show that shape storage ratio drops down to 65% when loaded below Tg for both the cases. This loss in shape storage ratio below Tg results in the irrecoverable shape. Due to two-stage storage architecture, the shape recovery profile for this coupled deformation is not captured. This memory characteristic study for coupled deformations helps in modeling and designing smart systems.
60
70
Temperature (°C)
80
90
Fig. 14. Shape storage for coupled axial-twist deformations simulation.
100
References [1] A. Lendlein, S. Kelch, Shape memory polymers, Angew. Chem. Int. Ed. Engl. 41 (2002) 2034e2057.
6
R. Sujithra et al. / Polymer Testing 48 (2015) 1e6
[2] A. Lendlein, M. Behl, Shape memory polymers for biomedical applications, Adv. Sci. Tech. 54 (2008) 96e102. [3] Y. Liu, H. Du, L. Liu, J. Leng, Shape memory polymers composites and their applications in aerospace: a review, Smart Mater. Struct. 23 (2014) 023001. [4] C. Liu, H. Qin, P.T. Mather, Review of progress in shape-memory polymers, J. Mater. Chem. 17 (2007) 1543e1558. [5] A. Rousseau, Challenges of shape memory polymers: a review of the progress toward overcoming SMP's Limitations, Polym. Eng. Sci. (2008) 2075e2089. [6] A. Rousseau, T. Xie, Shape memory epoxy: composition, structure, properties and shape memory performances, J. Mater. Chem. 20 (2010) 3431e3441. [7] T. Xie, I.A. Rousseau, Facile tailoring of thermal transition temperatures of epoxy shape memory polymers, Polymer 50 (2009) 1852e1856. [8] B. Zhou, X. Wu, Y. Liu, J. Leng, Study on shape recovery behaviors of epoxybased shape memory polymer, Adv. Mat. Res. 179e180 (2011) 325e328. [9] Y. Liu, K. Gall, M.L. Dunn, A.R. Greenberg, J. Diani, Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modelling, Int. J. Plast. 22 (2006) 279e313. [10] Y. Liu, K. Gall, M.L. Dunn, P. McCluskey, Thermomechanical recovery couplings of shape memory polymers in flexure, Smart Mater. Struct. 12 (2003) 947e954. [11] J. Diani, C. Fredy, P. Gilormini, Y. Merckel, G. Regnier, I. Rousseau, A torsion test for the study of the large deformation recovery of shape memory polymers, Polym. Test. 30 (2011) 335e341. [12] B.L. Volk, D.C. Lagoudas, Y.C. Chen, K.S. Whitley, Analysis of the finite deformation response of shape memory polymers: I. Thermomechanical characterization, Smart Mater. Struct. 19 (2010) 075005. [13] G. Li, W. Xu, Thermomechanical behavior of thermoset shape memory polymer programmed by cold-compression: testing and constitutive modeling, J. Mech. Phys. Solids 59 (2011) 1231e1250.
[14] J.W. McClung, G.P. Tandon, J.W. Baur, Deformation rate, hold time, and cycledependent shape-memory performance of Veriflex-E resin, Mech. Time Depend. Mater. 17 (2013) 39e52. [15] F. Castro, K.K. Westbrook, J. Hermiller, D.U. Ahn, Y. Ding, H.J. Qi, Time and temperature dependent recovery of epoxy based shape memory polymers, J. Eng. Mater. T. ASME 133 (2011) 021025. [16] M. Souri, Y.C. Lu, A. Erol, S.S. Pulla, H.E. Karaca, Characterization of unconstraint and constraint shape recoveries of an epoxy based shape memory polymer, Polym. Test. 41 (2015) 231e238. [17] K. Yu, H.J. Qi, Temperature memory effect in amorphous shape memory polymers, Soft Matter 10 (2014) 9423e9432. [18] R. Sujithra, S.M. Srinivasan, A. Arockiarajan, Memory characteristics studies for large deflections in amorphous polymers: experiments and numerical simulation, J. Intel. Mater. Syst. Struct. (2015), http://dx.doi.org/10.1177/ 1045389X15586587. [19] H. Meng, H. Mohamadian, M. Stubblefield, D. Jerro1, S. Ibekwe1, S. Pang, G. Li, Various shape memory effects of stimuli-responsive shape memory polymers, Smart Mater. Struct. 22 (2013) 093001. [20] G. Li, M. ASCE, T. Xu, Thermomechanical characterization of shape memory polymerebased self-healing syntactic foam sealant for expansion joints, J. Transp. Eng. 137 (2011) 805e814. [21] R. Sujithra, S.M. Srinivasan, A. Arockiarajan, Modelling memory effects in amorphous polymer, Int. J. Eng. Sci. 84 (2014) 95e112. [22] Y.C. Chen, D.C. Lagoudas, A constitutive theory for shape memory polymers. Part I: Large deformations, J. Mech. Phys. Solids 56 (2008) 1752e1765. [23] G. Barot, I.J. Rao, K.R. Rajagopal, A thermodynamic framework for the modeling of crystallisable shape memory polymers, Int. J. Eng. Sci. 46 (2008) 325e351.