Finite deformation thermo-mechanical behavior of thermally induced shape memory polymers

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<ul><li><p>Journal of the Mechanics and Physics of Solids 56 (2008) 17301751</p><p>r 2007 Elsevier Ltd. All rights reserved.</p><p>and morphing structures (Tobushi et al., 1996; Liu et al., 2004; Yakacki et al., 2007).</p><p>ARTICLE IN PRESS</p><p>www.elsevier.com/locate/jmps0022-5096/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.</p><p>doi:10.1016/j.jmps.2007.12.002</p><p>Corresponding author. Tel.: +1 303 492 1270; fax: +1 303 492 3498.E-mail address: qih@colorado.edu (H.J. Qi).Keywords: Shape memory polymers; Constitutive modeling; Finite deformation behavior; Stressstrain behavior; Thermo-mechanical</p><p>behavior</p><p>1. Introduction</p><p>Shape memory polymers (SMPs) have been investigated intensively because of their capability to recover apredetermined shape in response to environmental changes, such as temperatures and light irradiations(Lendlein et al., 2005a, b; Monkman, 2000; Otsuka and Wayman, 1998; Scott et al., 2005). Compared to othershape memory materials, such as NiTi alloy, where the reported maximum deformation due to shape change is8%, SMPs can exhibit large deformations exceeding 400% (Lendlein et al., 2005b). This advantage permitsapplications such as microsystem actuation components, biomedical devices, aerospace deployable structures,Finite deformation thermo-mechanical behavior of thermallyinduced shape memory polymers</p><p>H. Jerry Qia,, Thao D. Nguyenb, Francisco Castroa, Christopher M. Yakackia,Robin Shandasa</p><p>aDepartment of Mechanical Engineering, University of Colorado, 427 UCB, ECME 124, Boulder, CO 80309, USAbDepartment of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA</p><p>Received 12 June 2007; received in revised form 10 December 2007; accepted 13 December 2007</p><p>Abstract</p><p>Shape memory polymers (SMPs) are polymers that can demonstrate programmable shape memory effects. Typically, an</p><p>SMP is pre-deformed from an initial shape to a deformed shape by applying a mechanical load at the temperature TH4Tg.It will maintain this deformed shape after subsequently lowering the temperature to TLoTg and removing the externallymechanical load. The shape memory effect is activated by increasing the temperature to TD4Tg, where the initial shape isrecovered. In this paper, the nite deformation thermo-mechanical behaviors of amorphous SMPs are experimentally</p><p>investigated. Based on the experimental observations and an understanding of the underlying physical mechanism of the</p><p>shape memory behavior, a three-dimensional (3D) constitutive model is developed to describe the nite deformation</p><p>thermo-mechanical response of SMPs. The model in this paper has been implemented into an ABAQUS user material</p><p>subroutine (UMAT) for nite element analysis, and numerical simulations of the thermo-mechanical experiments verify</p><p>the efciency of the model. This model will serve as a modeling tool for the design of more complicated SMP-based</p><p>structures and devices.</p></li><li><p>ARTICLE IN PRESS</p><p>Permanent ShapePredeform (Program)</p><p>H.J. Qi et al. / J. Mech. Phys. Solids 56 (2008) 17301751 1731For a device design using thermally induced SMPs, the SMP will undergo a thermo-mechanical loading-unloading cycle illustrated in Fig. 1. The SMP is isothermally predeformed (or programmed) from an initialshape to a deformed shape by applying a mechanical load at the temperature TH. The material will maintainits deformed shape after subsequently lowering the temperature to TL and removing the external mechanicalload. The unloaded deformed shape at TL is commonly referred to as the temporary or programmed shape.The SMP can largely maintain this shape as long as the temperature does not change. The shape memoryeffect is activated by raising the temperature to TD where the initial shape is recovered. In general, TH and TDare above the glass transition temperature Tg, and TL is below Tg. Recent advances in polymer science hasmade it possible to vary the Tg by controlling the chemistry and/or the structure of SMPs for a variety ofapplications (Yakacki et al., 2007).In principle, most polymers demonstrate a certain degree of shape memory behavior. However, in order to</p><p>achieve a highly recoverable and programmable shape change, crosslinking polymers are typically used.1 Thecrosslinking can be chemical crosslinking, physical crosslinking, or macromolecular chain entanglements.</p><p>TL &lt; Tg</p><p>TL &lt; Tg</p><p>Temporary Shape</p><p>Deploy (Recover)</p><p>TD &gt;Tg</p><p>TH &gt;Tg TH &gt;Tg</p><p>Fig. 1. A typical thermo-mechanical loading/unloading cycle in a SMP application.Lendlein et al. (2005b) and Liu et al. (2006) gave in-depth discussions of the underlying physical mechanism ofthermally induced shape memory effects. The shape memory effect is caused by the transition of a crosslinkingpolymer from a state dominated by entropic energy (rubbery state) to a state dominated by internal energy(glassy state) as the temperature decreases. At temperatures above the glassy transition temperature Tg,individual macromolecular chains undergo large random conformational changes, which are constrained bythe crosslinking sites formed during material processing. Deforming the material reduces the possibleconguration and hence the congurational entropy of the macromolecular chains, leading to the well-knownentropic behavior of elastomers. After the removal of the external load at a temperature above Tg, thetendency of the material to increase its entropy will recover the undeformed (processed) shape dened bythe spatial arrangement of crosslinking sites. However, this shape recovery can be interrupted by lowering thetemperature below Tg. There, the mobility of macromolecular chains is signicantly reduced by the reductionin free volume, and the conformational change of individual macromolecules becomes increasingly difcult.Instead, cooperative conformational change of neighboring chains becomes dominant, and deformation thusrequires much higher energy. Therefore, the removal of the mechanical load at temperatures below Tg only</p><p>1There are some other polymers that can be termed as thermally induced shape memory polymers but not necessarily be cross-linking</p><p>polymers. For example, the shape change of some liquid crystal elastomers can be activated by temperatures. However, the shape memory</p><p>effects in liquid crystal elastomers are due to a molecular transition between trans to cis state under proper temperature conditions. The</p><p>mechanism of shape memory effects is therefore distinct from SMPs studied in this paper. Signicant research efforts have been carried on</p><p>liquid crystal elastomers, including constitutive modeling and computational implementation. The readers are referred to Wanner and</p><p>Terentjev (2003) for liquid crystal elastomers.</p></li><li><p>ARTICLE IN PRESSH.J. Qi et al. / J. Mech. Phys. Solids 56 (2008) 173017511732induces a small amount of shape recovery and most of the deformation incurred at the temperature above Tgis retained (stored, or frozen). The shape memory effect is invoked as the temperature increases above Tg,where the individual macromolecular chains become active again and the shape recovery mechanism describedabove is permitted. In this sense, shape memory effect is simply a temperature-delayed recovery.In the applications of SMPs, because of large and complicated deformation involved, it is highly desirable</p><p>that the deformation history of SMPs can be predicted and the recovery properties can be optimized. Thisrequires a nite deformation constitutive model that is based on the fundamental understanding ofstructurefunction relationships and can capture the thermo-mechanical response of SMPs. Most of theexisting constitutive models of SMPs have been limited to one-dimensional (1D) small deformations (Tobushiet al., 1996; Liu et al., 2006). For example, considering the SMP as a mixture of two phases (active phase andfrozen phase), Liu et al. (2006) developed a 1D small deformation model. There, a stored strain was used tomemorize the predeformation. Note that the intensive research on shape memory alloys (SMAs) in the pasthas resulted in the developments of sophisticated constitutive models for SMAs (such as Thamburaja andAnand, 2002; Lagoudas et al., 2006, etc.). However, these models cannot be applied to SMPs because of thefundamental differences in the underlying mechanism for shape memory effects. In this paper, thermo-mechanical experiments were conducted to identify key features of nite deformation behaviors of SMPs.Based on the experimental observations and the concept of phase transitions, a three-dimensional (3D) nitedeformation constitutive model that describes the thermo-mechanical response of SMPs is developed. Thismodel is implemented into a user material subroutine (UMAT) in the nite element software packageABAQUS. The paper was arranged as the following. Section 2 presents nite deformation thermo-mechanicalexperiments performed to explore the properties and shape memory behavior of SMPs. Based on observationsfrom these experiments, a 3D nite deformation constitutive model is proposed in Section 3. Comparisonsbetween model prediction and experimental results are presented in Section 4, and future work is discussed inthe concluding section.</p><p>2. Thermo-mechanical behavior of SMPs</p><p>2.1. Material and sample preparations</p><p>Sheets of SMPs were synthesized following the procedure in Yakacki et al. (2007). Briey, tert-butyl acrylate(tBA) monomer and crosslinker poly(ethylene glycol) dimethacrylate (PEGDMA) in liquid forms, and photopolymerization initiator (2, 2-dimethoxy-2-phenylacetophenone) in powder form were mixed in a beakeraccording to a pre-calculated ratio. The beaker was shaken for about 10 s to ensure a good mixture. Thesolution was injected onto the surface of a specially designed glass slide or a glass tube, which then was placedunder the UV lamp for polymerization. After 10min, the SMP material was removed from the glass slide ortube and was put into an oven for 1 h at 80 1C. The SMP materials were machined into the proper shapes fordifferent experiments. In order to eliminate variations in the material properties caused by processing, thesamples from the same prepared batch were used for a series of thermo-mechanical experiments, includingdynamic mechanical analysis (DMA), isothermal uniaxial compression, and cooling/heating experiments.Each experiment is described below, together with the corresponding result. For each type of experiment, atleast three tests were conducted to conrm the repeatability, but only result from one test was shown for thesake of clarity.</p><p>2.2. DMA tests</p><p>DMA tests were conducted using a Perkin-Elmer DMA Tester (Model 7 Series) with Perkin-ElmerIntracooler 2 cooling system to determine the glass transition temperature Tg of the SMP specimens. The testprocedure follows the one applied in Liu et al. (2006). A rectangular bar with dimensions of 10 2 1mm3was placed into a DMA three point bending device. A small dynamic load at 1Hz was applied to the platenand the temperature was lowered at a rate of 1 1C/min. Fig. 2 shows the storage modulus and tan d vstemperature curves from one DMA test. It was determined that the glass transition temperature Tg of the SMP</p><p>samples was 49 1C.</p></li><li><p>ARTICLE IN PRESSH.J. Qi et al. / J. Mech. Phys. Solids 56 (2008) 17301751 1733Sto</p><p>rag</p><p>e M</p><p>od</p><p>ulu</p><p>s (</p><p>MP</p><p>a)</p><p>103</p><p>102</p><p>101</p><p>tan</p><p>0.4</p><p>0.8</p><p>1.2</p><p>1.6</p><p>2</p><p>tan Storage Modulus2.3. CTE measurement</p><p>The coefcients of thermal expansion (CTE) were measured using the Perkin-Elmer DMA Tester.Cylindrical samples of 10mm in diameter and 10mm in height were cut from the synthesized SMPs. Thesample was placed between two plates inside the DMA tester. A small compressive force of 1mN was appliedand maintained to ensure the contact between the sample and the plates during the CTE measurement. As thetemperature was varied, the height of the sample changed due to thermal expansion. The displacement of thetop plate was recorded by the DMA tester. To measure the CTE, a sample was rst heated from roomtemperature (25 1C) to 70 1C at 5 1C/min and allowed to equilibrate at 70 1C for 20min. The sample then wascooled from 70 to 0 1C at 1 1C/min. The sample was kept at 0 1C for 10min. It was then reheated to 70 1C at1 1C/min. The height change of the sample during cooling and reheating was recorded.Fig. 3 shows the measurement of CTEs during the cooling from 70 to 0 1C. The curve for heating from 0 to</p><p>70 1C shows similar result and is not presented here for the sake of clarity. In Fig. 3, the thermal expansionstrain (L/L01) is plotted versus the temperature. The reference height (L0) is the sample height at 70 1C.</p><p>0</p><p>40 60 80 100100</p><p>20</p><p>Temperature (C)</p><p>Fig. 2. DMA test of the SMP dynamic mechanical properties.</p><p>0</p><p>1.48104</p><p>1</p><p>2.53104</p><p>(L/L</p><p>0-1)</p><p> (%</p><p>)</p><p>0.2</p><p>0</p><p>-0.2</p><p>-0.4</p><p>-0.6</p><p>-0.8</p><p>-1</p><p>-1.2</p><p>-1.4</p><p>Temperature (C)</p><p>10 20 30 40 50 60 70</p><p>1</p><p>Fig. 3. CTE measurement of the SMP during cooling.</p></li><li><p>The portions below and above Tg are used to obtain the slopes, which are the CTEs. In this paper, we usedlinear regressions of the curve between 10 and 20 1C to obtain the CTE below Tg, and the curve between 50and 60 1C to obtain the CTE above Tg. From Fig. 3, the CTEs were measured as a1 2:53 104 fortemperatures above Tg and a2 1:48 104 for temperatures below Tg.</p><p>2.4. Isothermal uniaxial compression tests</p><p>In order to investigate the large deformation behavior of SMPs under different temperature conditions,isothermal uniaxial compression tests were conducted by using a universal materials testing machine (InstronModel 5565 with load capacity of 5 kN). The machine is equipped with a temperature-controlled chamber(Instron Model 3119-405-21 with a Euro 2408 controller). A thermocouple was placed close to the sample</p><p>ARTICLE IN PRESS</p><p>0 10</p><p>10</p><p>20</p><p>30</p><p>40</p><p>50</p><p>60</p><p>70</p><p>50</p><p>60</p><p>70</p><p>-Tru</p><p>e S</p><p>tress (</p><p>MP</p><p>a)</p><p>-True Strain</p><p>0.750.50.25</p><p> (M</p><p>Pa)</p><p>T = 60C</p><p>rate = 0.1s-1rate = 0.01s-1</p><p>T = 0C</p><p>T = 10C</p><p>T = 20C</p><p>T = 30C</p><p>T = 60C</p><p>H.J. Qi et al. / J. Mech. Phys. Solids 56 (2008) 17301751173400</p><p>-True Strain</p><p>0.25 0.5 0.75 1</p><p>Fig. 4. (A) Stressstrain behaviors of the SMP from isothermal uniaxial compression experiments at different temperatures. The strain10</p><p>20</p><p>30</p><p>40</p><p>-Tru</p><p>e S</p><p>tress</p><p>T = 20C</p><p>T = 0Crate is 0.01/s. (B) Stressstrain behaviors of the SMP at different strain rates and at different temperatures.</p></li><li><p>surface to maintain the chamber temperature. Cylindrical samples of the same dimensions as those in the CTEmeasurements were used. Previous studies showed that the effects of barreling and buckling could be reducedas long as the ratio of sample height and diameter was within the range of 0.52.0 (Qi and Boyce, 2005;Bergstrom and Boyce, 1998). In order to further reduce the effects of friction, Teon sheets were placedbetween the sample and the platens. In an isothermal test, the sample was rst placed on the bottom platen;the chamber temperature then was changed to the desired temperature; nally, the sample was given 20minto reach a thermal equilibrium before the uniaxial compression started. Uniaxial compression experimentswere conducted at two different strain rates of 0.01 and 0.1/s. Whilst most of the samples were tested to break,a few samples...</p></li></ul>