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Research Papers

Modeling the Thermoviscoelastic Properties and Recovery Behavior of Shape Memory Polymer Composites

[+] Author and Article Information
Stephen Alexander

Department of Biomedical Engineering,
Boston University,
Boston, MA 02215
e-mail: stephena@bu.edu

Rui Xiao

e-mail: rxiao4@jhu.edu

Thao D. Nguyen

e-mail: vicky.nguyen@jhu.edu
Department of Mechanical Engineering,
The Johns Hopkins University,
Baltimore, MD 21218

1Corresponding author.

Manuscript received April 24, 2013; final manuscript received July 9, 2013; accepted manuscript posted July 29, 2013; published online September 23, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(4), 041003 (Sep 23, 2013) (11 pages) Paper No: JAM-13-1169; doi: 10.1115/1.4025094 History: Received April 24, 2013; Revised July 09, 2013; Accepted July 29, 2013

This work investigated the effects of stiff inclusions on the thermoviscoelastic properties and recovery behavior of shape memory polymer composites. Recent manufacturing advances have increased the applicability and interest in SMPCs made with carbon and glass inclusions. The resulting biphasic material introduces changes to both the thermal and mechanical responses, which are not fully understood. Previous studies of these effects have been concerned chiefly with experimental characterization and application of these materials. The few existing computational studies have been constrained by the limitations of available constitutive models for the SMP matrix material. The present study applied previously developed finite-deformation, time-dependent thermoviscoelastic models for amorphous SMPs to investigate the properties and shape memory behavior of SMPCs with a hexagonal arrangement of hard inclusions. A finite element model of a repeating unit cell was developed for the periodic microstructure of the SMPC and used to evaluate the temperature-dependent viscoelastic properties, including the storage modulus, tan δ, coefficient of thermal expansion, and Young's modulus, as well as the shape recovery response, characterized by the unconstrained strain recovery response and the constrained recovery stress response. The presence of inclusions in greater volume fractions were shown to lower both the glass transition and recovery temperatures slightly, while substantially increasing the storage and Young's modulus. The inclusions also negligibly affected the unconstrained strain recovery rate, while decreasing the constrained recovery stress response. The results demonstrate the potential of using hard fillers to increase the stiffness and hardness of amorphous networks for structural application without significantly affecting the temperature-dependence and time-dependence of the shape recovery response.

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Figures

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Fig. 1

A schematic of the RUC, where (a) the dashed lines correspond to the equiangular triangles formed by joining the centers of fillers, h and w are the height and width of the RUC, and r is the radius of the fillers; and (b) shows the labels for the boundary surfaces of the RUC

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Fig. 2

Schematic of the external controller of the FEA, which was designed in Matlab to enforce the macrotraction-free periodicity and symmetry requirements. The reaction forces for surfaces S1 and S4 are given by FS1 and FS4. The algorithm shown was used for cases in which both surfaces S1 and S4 were required to be on average traction free.

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Fig. 3

(a) Thermal contraction during cooling, comparing different filler volume fraction and filler Young's modulus, E = 1 GPa (- -) and E = 100 GPa (-). (b) Rubbery and glassy CTE (αr and αg) as a function of filler volume fraction and filler Young's modulus, E = 1 GPa (- -) and E = 100 GPa (-).

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Fig. 4

Effect of volume fraction on storage modulus. The vf0 case and cases with a filler modulus of E = 100 GPa are depicted for the single process model, (a), and multiple process model (b).

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Fig. 5

Effect of filler modulus on the storage modulus for cases using the single process SMP model. Two cases of volume fractions, 10% and 60%, are shown in (a) and (b).

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Fig. 6

Effects of filler modulus and volume fraction on the temperature dependence of the tan δ. Only the vf0, vf60e1, and vf60e100 cases using the single-process model are shown for clarity.

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Fig. 7

The high temperature stress-strain response of the SMPC for the single-process model cases

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Fig. 8

Stress and strain contours at the maximum applied deformation at Thigh = Tg + 45 °C: (a) ɛ22 for the vf10e100 case; (b) ɛ22 for vf30e100; (c) ɛ22 for vf60e100; (d) σ22 for vf10e100; (e) σ22 for vf30e100; (f) σ22 for vf60e100; (g) σ12 for vf10e100; (h) σ12 for vf30e100; and (i) σ12 for vf60e100

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Fig. 9

Simulation results for the rubbery storage modulus (Table 2) and rubbery Young's modulus (Table 3) for different filler volume fraction and Young's modulus. Also plotted for comparison is the Reuss isostress model of the effect of volume fraction and filler modulus on the Young's modulus of the composite.

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Fig. 10

Temperature-dependent unconstrained strain recovery response of the SMPC comparing the effects of (a) filler volume fraction, and (b) filler modulus

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Fig. 11

The volume averaged vertical stress, σ¯22, as a function of temperature during the heating phase of the constrained recovery SMP simulations. All cases used the single process SMP model.

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