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Research Papers

Constitutive Relations and Parameter Estimation for Finite Deformations of Viscoelastic Adhesives

[+] Author and Article Information
G. O. Antoine

Department of Biomedical Engineering and
Mechanics (M/C 0219),
Virginia Polytechnic Institute and State University,
Blacksburg, VA 24061
e-mail: antoineg@vt.edu

R. C. Batra

Fellow ASME
Department of Biomedical Engineering and
Mechanics (M/C 0219),
Virginia Polytechnic Institute and State University,
Blacksburg, VA 24061
e-mail: rbatra@vt.edu

1Corresponding author.

Manuscript received July 17, 2014; final manuscript received November 9, 2014; accepted manuscript posted November 13, 2014; published online December 11, 2014. Assoc. Editor: Weinong Chen.

J. Appl. Mech 82(2), 021001 (Feb 01, 2015) (21 pages) Paper No: JAM-14-1316; doi: 10.1115/1.4029057 History: Received July 17, 2014; Revised November 09, 2014; Accepted November 13, 2014; Online December 11, 2014

We propose a constitutive relation for finite deformations of nearly incompressible isotropic viscoelastic rubbery adhesives assuming that the Cauchy stress tensor can be written as the sum of elastic and viscoelastic parts. The former is derived from a stored energy function and the latter from a hereditary type integral. Using Ogden’s expression for the strain energy density and the Prony series for the viscoelastic shear modulus, values of material parameters are estimated by using experimental data for uniaxial tensile and compressive cyclic deformations at different constant engineering axial strain rates. It is found that values of material parameters using the loading part of the first cycle, the complete first cycle, and the complete two loading cycles are quite different. Furthermore, the constitutive relation with values of material parameters determined from the monotonic loading during the first cycle of deformations cannot well predict even deformations during the unloading portion of the first cycle. The developed constitutive relation is used to study low-velocity impact of polymethylmethacrylate (PMMA)/adhesive/polycarbonate (PC) laminate. The three sets of values of material parameters for the adhesive seem to have a negligible effect on the overall deformations of the laminate. It is attributed to the fact that peak strain rates in the severely deforming regions are large, and the corresponding stresses are essentially unaffected by the long time response of the adhesive.

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References

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Figures

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Fig. 1

One-dimensional rheological analog interpretation of the material model

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Fig. 3

Contributions to the small-strain instantaneous Young’s modulus from the elastic and the viscoelastic parts of the constitutive relation

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Fig. 5

Predicted tangent modulus as a function of the axial stretch for the IM800A material

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Fig. 7

Experimental and predicted true axial stress as a function of the axial stretch for cyclic tensile deformations of DFA4700 at 0.01/s

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Fig. 8

Experimental and predicted true axial stress as a function of the axial stretch for cyclic tensile deformations of IM800A at 0.1/s

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Fig. 2

One-dimensional Maxwell model

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Fig. 4

Predicted tangent modulus as a function of the axial stretch for the DFA4700 material

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Fig. 6

Predicted tangent modulus at 10% engineering strain (λ = 1.1) as a function of the engineering strain rate ɛ·Eng=λ·

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Fig. 9

Storage modulus, loss modulus, and tangent delta as a function of the frequency f = ω/(2π) for uniaxial deformations. Note that the frequency is plotted by using the logarithmic scale.

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Fig. 10

Predicted tangent shear modulus for simple shear deformations of the DFA4700 material

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Fig. 11

Predicted tangent shear modulus for simple shear deformations of the IM800A material

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Fig. 12

One-dimensional rheological analog interpretation of the constitutive relation for an incompressible material

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Fig. 13

Schematic sketch of the impact problem studied

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Fig. 20

For values of material parameters corresponding to cases 1, 2, and 3, the normalized total energy E˜vise,ve due to viscous deformations as function of time for the impact of PMMA/adhesive/PC plates with either DFA4700 or IM800A as adhesive

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Fig. 14

Time histories of the experimental [23] and the computed contact force for the impact of the (a) PMMA/DFA4700/PC and (b) PMMA/IM800A/PC plates

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Fig. 15

(a) Experimental (from Ref. [23]) and simulated ((b)–(d)) postimpact crack patterns in the PMMA layer of the PMMA/DFA4700/PC assembly impacted at 22 m/s. The three sets of material parameters for the DFA4700 interlayer are used in the simulations.

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Fig. 16

(a) Experimental (from Ref. [23]) and simulated ((b)–(d)) postimpact crack patterns in the PMMA layer of the PMMA/IM800A/PC assembly impacted at 22 m/s. The three sets of material parameters for the IM800A interlayer are used in the simulations.

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Fig. 17

Time histories of the in-plane extension of cracks formed in the PMMA layer for the normal impact of the (a) PMMA/DFA4700/PC and (b) PMMA/IM800A/PC plates

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Fig. 18

Fringe plots of the effective plastic strain near the center of the back surface of the PC layer of the PMMA/DFA4700/PC laminate

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Fig. 19

Fringe plots of the effective plastic strain near the center of the back surface of the PC layer of the PMMA/IM800A/PC laminate

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