A hyper-elastic thermal aging constitutive model for rubber-like materials

Abstract

Different phenomenological, empirical, and micromechanical constitutive models have been proposed to describe the behavior of incompressible isotropic hyper-elastic materials. Among these models, very few have accounted for the thermal aging effect on the model constants and parameters. This article introduces a new empirical constitutive hyper-elastic model for thermally aged hyper-elastic materials. The model named “the weight function based (WFB) model” considers the effect of aging temperature and time on its parameters. The WFB model formulation can facilitate fatigue analysis and lifetime prediction of rubber-like materials under aging conditions. The WFB model in this article defines all rubber-like material properties, such as fracture stretch, strength, and stiffness, by predicting the full stress–strain curve at any aging time and temperature. The WFB model was tested on natural rubber for uniaxial and biaxial loading conditions. More than 100 specimens were aged and tested uniaxially under various temperatures and aging times to extract the stress–strain behavior. The temperatures used in the test ranged from 76.7°C to 115.5°C, and the aging time ranged from 0 to 600 hours (hrs). A classical bulge test experiment was generated to extract the biaxial natural rubber material behavior. An ABAQUS finite element analysis model was created to simulate and verify the generated biaxial stress–strain curve. The proposed model represents the aging effect on the tested natural rubber under uniaxial and biaxial loading conditions with an acceptable error margin of less than 10% compared to experimental data.

Keywords

Hyper-elasticity thermal aging rubber-like weight function based uniaxial biaxial bulge

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References

Ogden

. Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubberlike solids. Proceed Royal Soc A, Mathemat, Phys Eng Sci 1972; 326: 565–584.

Yeoh

. Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber Chem Technol 1990; 63: 792–805.

Yeoh

. Some forms of the strain energy function for rubber. Rubber Chem Technol 1993; 66: 754–771.

Korba

Barkey

. New model for hyper-elastic materials behavior with an application on natural rubber. In: Proceedings of the ASME 2017 12th International Manufacturing Science and Engineering Conference Los Angeles, CA, USA, 4–8 June 2017, vol. 2, pp. 1–10.

Paul

Mokarram

Gunnar

. Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data. Arch Appl Mech 2012; 82: 1183–1217.

Mooney

. A theory of large elastic deformation. J Appl Phys 1940; 11: 582–596.

Swanson

. A constitutive model for high elongation elastic materials. J Eng Mater Technol 1985; 107: 110–115.

Swanson

Christensen

Ensign

. Large deformation finite element calculations for slightly compressible hyperelastic materials. Comput Struct 1985; 21: 81–82.

Isihara

Hashitsume

Tatibana

. Statistical theory of rubber-like elasticity. IV. (Two-Dimensional Stretching). J Chem Phys 1951; 19: 1508–1512.

10.

Gent

Thomas

. Forms for the stored (strain) energy function for vulcanized rubber. J Polym Sci 1958; 28: 625–628.

11.

Arruda

Boyce

. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J Mech Phys Solids 1993; 41: 389–412.

12.

Bystritskaya

Pomerantsev

Rodionova

. Prediction of the aging of polymer materials. Chemometric Intel Lab Syst 1999; 47: 175–178.

13.

Rodionova

Pomerantsev

. Prediction of rubber stability by accelerated aging test modeling. J Appl Polym Sci 2004; 95: 1275–1284.

14.

Sasso

Palmieri

Chiappini

, et al. Characterization of hyperelastic rubber-like materials by biaxial and uniaxial stretching tests based on optical methods. Polym Test 2008; 27: 995–1004.

15.

Sasso

Papalini

Chiappini

, et al. Characterization of time-dependent materials by biaxial stretching tests. In: Proceedings of SEM Annual Conference, Springfield, MA, USA, 3–6 June 2007.

16.

Korba

Abhishek

Barkey

. A model for hyper-elastic material behavior under thermal aging with an application to natural rubber. In: Proceedings of the ASME 2018 13th International Manufacturing Science and Engineering Conference, College Station, Texas, USA, 18–22 June 2018, vol. 2, pp. 1–10.

17.

Korba

Kumar

Sun

, et al. A Model for calculating hyperelastic material properties under thermal aging. J Eng Mater Technol 2018; 140: 1–9.