Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 01 Sept 2009

Test Methods for Hyperelastic Characterization of Rubber4

,
, and
Page Range: 165 – 186
DOI: 10.2346/1.3138763
Save
Download PDF

Abstract

Optical methods using digital image correlation (DIC) are utilized in developing rubber constitutive tests. Two and three dimensional DIC systems are employed to measure strains on rubber specimens subjected to uniaxial, planar, and biaxial stress states. A special membrane inflation test was developed and is described for providing the biaxial constitutive data. Deformation-induced material property changes for the three modes of testing are quantified using a concept based on energy dissipation. The constitutive test strain ranges for each of the three modes are separately selected to equalize the material states. The methodology is applied to filled rubber compounds in order to characterize them in terms of hyperelastic behavior. Evaluation and comparison of several common hyperelastic models are given, and application to finite element modeling of a structural rubber specimen is described.

Keywords: hyperelastic; biaxial stress; digital image correlation; material characterization; rubber; membrane inflation; stress softening; tire modeling
Copyright: The Tire Society
FIG. 1.
FIG. 1.

Examples of the application of hyperelastic modeling in tires.

FIG. 2.
FIG. 2.

Second degree polynomial hyperelastic model derived from (a) uniaxial stress data alone and (b) three modes of test data.

FIG. 3.
FIG. 3.

Membrane inflation device.

FIG. 4.
FIG. 4.

Dual camera setup for membrane inflation testing and DIC analysis.

FIG. 5.
FIG. 5.

Normal displacement field of inflation loaded membrane.

FIG. 6.
FIG. 6.

A typical biaxial stress-strain load-unload data cycle from membrane testing.

FIG. 7.
FIG. 7.

Uniaxial and planar test specimens.

FIG. 8.
FIG. 8.

Speckled surface of a planar test specimen.

FIG. 9.
FIG. 9.

Planar specimen stress reduction at edges.

FIG. 10.
FIG. 10.

Examples of material stiffness change (softening) with cyclic strain amplitude.

FIG. 11.
FIG. 11.

Multimode testing at common maximum strain levels can induce inconsistent changes in the constitutive state.

FIG. 12.
FIG. 12.

Energy dissipation as a method of quantifying material change or “damage.”

FIG. 13.
FIG. 13.

The concept of equalizing damage energy for different modes of material testing as a means of achieving consistent constitutive data.

FIG. 14.
FIG. 14.

Damage energy measurements from testing a carbon black filled rubber in three modes of stress.

FIG. 15.
FIG. 15.

Typical hyperelastic models supported in commercial finite element codes.

FIG. 16.
FIG. 16.

Sample multimode data fits of two hyperelastic models.

FIG. 17.
FIG. 17.

RMS errors in fitting eight hyperelastic models to common multimode data sets.

FIG. 18.
FIG. 18.

Sample multimode data fits of two hyperelastic models at lower strain ranges (ε<20%).

FIG. 19.
FIG. 19.

Uniaxially extended rubber sheet with central hole.

FIG. 20.
FIG. 20.

Full field displacement comparisons between experiment and measurement.

FIG. 21.
FIG. 21.

Full field strain comparisons between experiment and measurement.

FIG. 22.
FIG. 22.

Comparison of measured and predicted principal strains along the horizontal axis of the hole.

FIG. 23.
FIG. 23.

The effect of hyperelastic model choice on strain predictions in high gradient regions

  • Download PDF