Buckling-controlled two-way shape memory effect in a ring-shaped bilayer

Hao Li·Xiaoyan Liang·Weibin Song

Abstract Shape memory polymers(SMPs)usually have a one-way shape memory effect.In this paper,an easy-operating method to realize a two-way shape memory effect was demonstrated in a ring-shaped bilayer structure where the two layers are SMPs with different thermal transition temperatures. By designing specific thermomechanical processes, the mismatched deformation between the two layers leads to a morphology change of ring-shaped bilayer structures from a smooth ring to a gear-like buckling shape under cooling and a reversible recovery to the smooth shape under heating. Such a morphology change is ascribed to occurrence and recovery of thermoelastic buckling.This method was validated by finite element simulation.We experimentally investigated the influence of pre-strain on buckling,and it was found that both the buckling occurrence and recovery temperature vary with pre-strain.Furthermore,considering a ring-shaped SMP–SMP bilayer structure,finite element analysis was conducted to study the influence of film thickness and modulus ratio of two layers on buckling behavior.The results showed that the critical buckling wavelength was greatly influenced by film thickness and modulus ratio.We made a theoretical analysis that accorded well with the numerical results.

Keywords Shape memory polymers·Two-way shape memory effect·Buckling·Ring-shaped·Bilayer

1 Introduction

Intelligent materials and structures are getting increasing attention due to enormous application prospects.Shape memory polymers(SMPs)are a new type of intelligent materials that can retain a provisional shape and then return to their initial state under certain exterior stimuli of temperature,light,electricity,and chemical reagents[1–6].Owing to their good deformability, wide shape transition temperature, low cost and easy processing, SMPs have a wide range of applications in aerospace engineering[7–9],biomedical engineering[10–12] and micro-electro-mechanical systems [13]. In the past few decades,a tremendous amount of work has focused on designing advanced SMPs, such as polyurethane-based SMPs [14, 15], epoxy-based SMPs [16–18], cyanate esterbased SMPs [19, 20] and polyamide-based SMPs [21, 22],characterizing the covering performance and fabricating complex structure of SMPs.

Most SMPs exhibit one glass transition temperature for a single material. They can transform from a provisional shape to initial state.Realizing two-way or multistage shape memory effect of SMPs have recently been proposed through composite structures.Among them,more attention has been paid to the film-substrate structures owing to their enormous application prospects in many fields, such as tunable phase optics [23], semiconductor nanoribbons [24] and stretchable electronics [25]. These bilayer structures are usually fabricated by depositing stiff thin films on the pre-drawn conform substrates. The compressive stress at the boundary of bilayer structure leads to the bucking of the film.In their study, Bowden et al. [26] first observed the buckling appearance of bilayer structures,where a gold film was glued to polydimethylsiloxane(PDMS)substrate with a titanium intermediate layer. When the metal film was cooled,the buckling phenomenon happened spontaneously due to mismatched contractions.Later,they fabricated wrinkle patterns with periodic surfaces of various wavelengths, which had been applied in complex three-dimensional (3D) functional architectures.

In order to obtain different buckling phenomenon for bilayer structures, more researchers use SMP as substrate[27,28].Previous investigations of film substrate structures are mainly emphasizing on SMP plates bonded with a thin metal film[29,30].However, the buckling phenomenon of these metal film substrate systems is often irreversible.In this work, we proposed an SMP–SMP bilayer structure, where the two SMP layers have different glass transition temperature,to achieve a two-way shape memory effect(SME).We made a ring-shaped SMP–SMP bilayer structure and demonstrated two-way shape memory effect.The two-way SME is associated with structural transformation from a smooth ring to a gear-like buckling state under cooling and a reversible recovery under heating.

2 Two-way shape memory bilayer ring

A typical shape memory circle is described as follows. An SMP specimen is in perpetual state after fabrication and curing. If the temperature rises above glass transition temperature (Tg), the SMP specimen transforms into a rubber state which can be easily deformed into a provisional shape.A provisional shape will be maintained when keeping the deformed shape in a constrained state and then lowering the temperature below Tg.When reheating the SMP above Tg,it will restore to the initial state.

To achieve two-way SME,in this study,we made a ringshaped film substrate structure. A schematic diagram is presented in Fig. 1. SMPs with different Tgwere used as substrate and film,in which the thermal induction temperature of the substrate(Tg2)is lower than that of the film(Tg1).The complete procedure contains the following steps:

1. The composite ring with a film bonded to the inner substrate is prepared and heated above Tg1.

2. The ring is deformed under uniaxial loading. Keep the deformation and lower the temperature below Tg2,both the SMP substrate and film translate to a glass state.The final shape is fixed after the load is removed.

3. Raise the temperature in-between Tg2and Tg1,the SMP substrate tends to recover the initial state associated with radial shrinkage.The mismatched deformation between film and substrate results in the vertical buckling of the bilayer ring.

4. If the temperature is higher than Tg1, the SMP film shrinks radially.Deformation mismatch decreases gradually and the structure restores to the initial shape.

The temperature–time and load–time curves of the thermomechanical cycle are schematically shown in Fig.2.

3 Experiments and discussion

Epoxy resin E-51 with different contents of curing agent 4, 4′-methylenedianiline (DDM) was used as the thermoresponsive SMP in this study.The mass ratios of epoxy resin to curing agent in substrate and film were 100:15 and 100:19,respectively.

Temperature has a significant effect on the curing process of epoxy resin-based SMP.Higher temperature leads to faster reaction and shorter curing time while excessive heating may reduce the deformation performance of SMPs.Therefore,it is necessary to design a suitable curing condition. In this study, epoxy resin was stirred for 15 min at 150 rpm after preheating to 110°C.Then,DDM was mixed and stirred for 20 min at 260 rpm.After that,the intermixture was solidified at 80°C for 2.5 h,and then post solidified at 150°C for 2 h.First,the inner substrate was synthesized and processed into a ring.Then,the composite structures of a film with an inner substrate were fabricated.The process of film fabrication was the same as the substrate.

Fig.1 Diagrammatic sketch of the process:(1)axial compressing the SMP ring-shaped structure above T g1;(2)cooling with pre-strain;(3)reheating above T g2 to induce shape recovery of substrate thus causing buckling;(4)reheating above T g1 to induce shape recovery of film

Fig.2 Temperature–time curve and load–time curve of the thermomechanical cycle process of structure

Dynamic mechanical analysis (DMA) was used to measure the mechanical properties of SMP film and substrate.The specimen was balanced at 50 °C and then heated to 180 °C at a rate of 4 °C/min. Figure 3 shows the temperature dependence of storage modulus and shape recovery of SMP film and substrate.In this study,Young’s modulus was replaced by storage modulus.Moreover,Tgof materials was obtained by the peak value of the tangential loss factor in DMA test[31].Tgof film and substrate were 106.2°C and 79.8°C,respectively.

Figure 4 presents the experiment result of bidirectional shape memory process according to the steps in Sect.2.The SMP composite ring with 0.2 mm film thickness, 30 mm inner diameter and 80 mm outer diameter were compressed by 15% axial pre-strain at 130 °C. Then the strain was maintained and the temperature was lowered. After that,the load was removed and the composite ring was fixed to the compression shape.When the structure was reheated to 83 °C, local buckling appeared (Fig. 4b). The buckling phenomenon increased gradually with the increase of temperature(Fig.4c).When the temperature rose to 91°C,the buckling began to decrease and finally disappeared at 115°C(Fig. 4i). The structure was restored to the original smooth shape.

Fig.3 Experimental curves of a storage modulus and b shape recovery rate

Fig.4 Two-way shape memory effect of an SMP ring.Buckling occurred at the temperature higher than T g2 from a to c,and then slowly developed from d to f,finally disappeared at the temperature higher than T g1 from g to i

Two-way SME in the SMP bilayer ring was demonstrated experimentally.Because the physical mechanism was related to the mismatched deformation at the junction of film and substrate,pre-strain may have some effect on the buckling.Here,we designed multiple sets of experiments to investigate the pre-strain effect.The SMP composite ring with 0.2 mm film thickness, 14.5 mm inner diameter and 40 mm outer diameter was compressed by axial pre-strain from 11% to 19% . Figure 5 shows the experimental results of the buckling amplitude of the same structural size with temperature under different pre-strain.The results show that the buckling process consists of three stages. The structure maintained smooth surface at stages I and III with zero amplitude and appeared buckling at stage II with varying amplitudes.Both the buckling occurrence and recovery temperature vary with pre-strain. The buckling occurrence temperature decreased from 89 °C at 11% pre-strain to 81 °C at 19% pre-strain,and the recovery temperature increased from 105°C at 11% pre-strain to 115 °C at 19% pre-strain, as shown in Fig. 6.The larger the pre-strain, the larger the stress at the same temperature,which caused the difference in buckling occurrence and recovery.The pre-strain has an obvious effect on the process of buckling and it can be used to precisely control the buckling point.

4 Finite element simulation

The commercial software ABAQUS was used to analyze the buckling of SMP composite ring.The basic formula for linear isotropic viscoelasticity is

where σ is the instantaneous Cauchy stress,e and φ are the mechanical deviation and volume strain. G and K are bulk relaxation modulus and small-strain shear,τ is the relaxation time.By integral transformation,Eq.(1)can be transformed as

Fig.5 Variation of buckling amplitude with temperature under different pre-strains of 11% ,15% ,19% :no buckling appeared at stages I and III,and buckling occurred at stage II

Fig.6 Buckling occurrence and recovery temperature with different pre-strain

where G0and K0are the instantaneous small strain shear and bulk modulus.For the non-isothermal process,τ denotes the change of time with temperature

where aT(T) is the time–temperature superposition shifting factor,determined by the classic Williams–Landel–Ferry(WLF)equation,

where C1and C2are material constants. Trefis the WLF reference temperature.

In constitutive Eq.(2),the bulk modulus can be regarded as a constant and the shear modulus G(t)can be indicated by Prony series

where G∞is the shear modulus at time t=∞,τ i and Giare series of relaxation times and relaxation modulus, respectively.The viscoelastic theory above can be implemented in ABAQUS and all parameters can be calculated and obtained from the stress relaxation test[32].

The finite element model (FEM) and the thermomechanical process are shown in Sect. 3. Figure 7 shows the deformation and stress diagram of the structure at different temperatures.The results show the evolution of buckling with increasing temperature.At 80°C,there was no buckling,and the stress between film and substrate gradually increased.When the stress reached critical value,the buckling appeared,and it increased with the increase of temperature.When the temperature was raised to Tgof the SMP film,buckling began to recover and the structure eventually became smooth.The whole buckling process was basically consistent with the experimental results in Fig.4.

According to previous studies,the buckling geometry of thin film on the flexible substrate may also be effected by film thickness and modulus ratio of film and substrate.Here we studied the influence of modulus ratio on critical buckling wavelength.The thickness of film was taken as 0.2 mm,the inner and outer diameters were 14.5 mm and 40 mm,respectively. The modulus ratio ranged from 150 to 510. It was assumed that Poisson’s ratio of the film and substrate was the same, i.e. νs= νf= 0.45. In order to save computation time, 1/4 models were built. Simulation results were shown in Fig. 8. The results showed that the critical buckling wavelengths vary significantly in the range of modulus ratios considered.With the increased of modulus ratio from 150 to 510 with 60 intervals, the wavelengths increased as well,from 4.7 to 7.1 mm.The modulus ratio was positively correlated with the critical buckling wavelength.

Then the finite element calculation results were compared with the theoretically predicted buckling wavelengths.Epoxy-based SMP material can achieve 100% elastic strain under rubber state.According to linear elastic buckling theory,the critical buckling wavelength λcrwas given by[13]

Fig.7 I Deformation and II stress of the film substrate composite ring at different temperatures

Fig.8 Critical buckling shape of the structure with various modulus ratio of film and substrate from 150 to 510

Fig.9 Influence of modulus ratio on critical buckling wavelength with different R/t

where R is outer diameter of ring-shaped substrate;t is the thickness of film;and Esare Young’s modulus of the film and substrate; ν f and νsare Poisson’s ratio of the film and substrate,respectively.Based on the theoretical model, we can determine the relationship between critical buckling wavelength and modulus ratio in different structural sizes. Figure 9 shows that the larger the outer diameter, the greater the wavelength. In addition, for each line with a certain outer diameter, the wavelength increase with the increase of the modulus ratio,which has the same trend as the simulation results.

Fig.10 Comparison between the theoretical model and FEM results on critical buckling wavelength as modulus ratios are varied

Figure 10 shows the comparison of finite element results with theoretical results within a certain modulus ratio. The relationship between the critical buckling wavelength and film thickness of finite element simulation agrees well with the theoretical curve.This also proves that simulation has a good prediction effect on critical buckling wavelength.The second group of simulations was carried out by different thicknesses of film. The modulus ratio of film and substrate was taken as 150, the film thickness ranged from 0.2 to 0.55 mm.The other parameters were the same as the former model.Simulation results are shown in Fig.11.The results show that with the increase of film thickness from 0.2 to 0.55 mm with 0.05 mm interval,the critical buckling wavelengths increase from 4.2 to 9.7 mm as well.The wavelengths vary greatly as the thickness of the film changes.

Fig.11 Critical buckling shape of the structure with various film thickness from 0.2 to 0.55 mm

Fig.12 Theoretical model and simulation results on critical buckling wavelength with different film thickness

Because of the property of viscoelastic materials, the modulus ratio changes greatly with temperature during the experiment. It is, therefore, difficult to analyze the critical buckling wavelength under certain modulus ratio through the experiment.Figure 12 shows the finite element results compared with the theoretical results for the varying thickness case. The curves were basically matched. Thus, the critical buckling wavelength can be predicted quantitatively by finite element simulation.

5 Conclusions

An effective and simple method to realize two-way shape memory effect was proposed and demonstrated. A ring shaped structure consisting of an SMP film with higher thermal transition temperature Tgbonded to SMP substrate with lower Tgwas fabricated.By pre-programming the SMP ring-shaped structure,an axial compressive stress field was created in the film as the composite structure was heated and shape recovery was initiated. The mismatched deformation between the two layers due to the difference in Tgled to the morphology change of ring-shaped bilayer structure from a smooth ring to a gear-like buckling shape under cooling and a reversible recovery to the smooth shape under heating.Such a morphology change was ascribed to occurrence and recovery of thermal-elastic buckling.The influence of pre-strain on buckling occurrence and recovery temperature were investigated, which can be used to precisely control the buckling point. Finite element analysis was carried out to study the influence of film thickness and modulus ratio of film substrate on critical buckling wavelength. The results were in good agreement with the theoretical prediction.

AcknowledgementsThis work was supported by the National Natural Science Foundations of China(Grant 11272044)and the Fundamental Research Funds for the Central Universities(Grant 2018JBM305).