Editorial Type:
Article Category: Research Article
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Online Publication Date: 01 Oct 2015

A Cohesive Zone Model to Predict Dynamic Tearing of Rubber

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Page Range: 297 – 324
DOI: 10.2346/tire.15.430403
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ABSTRACT

Tire failures, such as tread separation and sidewall zipper fracture, occur when internal flaws (cracks) nucleate and grow to a critical size as result of fatigue or cyclic loading. Sudden and catastrophic rupture takes place at this critical crack size because the strain energy release rate exceeds the tear energy of the rubber in the tire. The above-mentioned tire failures can lead to loss of vehicle stability and control, and it is important to develop predictive models and computational tools that address this problem. The objective of this article was to develop a cohesive zone model for rubber to numerically predict crack growth in a rubber component under dynamic tearing. The cohesive zone model for rubber was embedded into the material constitutive equation via a user-defined material subroutine (VUMAT) of ABAQUS. It consisted of three parts: (1) hyperviscoelastic behavior before damage, (2) damage initiation based on the critical strain energy density, and (3) hyperviscoelastic behavior after damage initiation. Crack growth in the tensile strip and pure shear specimens was simulated in ABAQUS Explicit, and good agreement was reported between finite element analysis predictions and test results.

Keywords: cohesive zone model; rubber; hyperviscoelastic; finite element analysis
FIG. 1
FIG. 1

Traction-separation law of a cohesive zone model.

FIG. 2
FIG. 2

Uniaxial tension test results.

FIG. 3
FIG. 3

Tensile strip specimen.

FIG. 4
FIG. 4

Tensile strip test deformation and corresponding force-displacement curve at 76.2-cm drop height.

FIG. 5
FIG. 5

Pure shear specimen.

FIG. 6
FIG. 6

Pure shear test deformation and corresponding force-displacement curve at 76.2-cm drop height.

FIG. 7
FIG. 7

Growth of a crack in rubber: (a) cohesive zone and (b) equivalent traction-separation law.

FIG. 8
FIG. 8

Loading-unloading behaviors in (a) undamaged state and (b) damaged state.

FIG. 9
FIG. 9

Rheological model for a hyperviscoelastic material.

FIG. 10
FIG. 10

Viscosity distributions at different strain rate in NR25.

FIG. 11
FIG. 11

Rate-dependent material response: (a) simulations and (b) tests.

FIG. 12
FIG. 12

Damage initiation function based on Ucrit.

FIG. 13
FIG. 13

Uniaxial tension in a single finite element (a) FEA model and (b) Cauchy stress versus extension ratio with various m.

FIG. 14
FIG. 14

FEA model of tensile strip specimen: (a) full specimen and (b) quarter model.

FIG. 15
FIG. 15

Side-by-side comparison of tensile strip tearing in FEA and test for 76.2-cm drop height.

FIG. 16
FIG. 16

Close-up view of crack tip of tensile strip specimen during test at 76.2-cm drop height.

FIG. 17
FIG. 17

Comparisons of force history and crack growth positions in test and FEA for tensile strip experiments at drop heights (a–b) 76.2 cm, (c–d) 50.8 cm, and (e–f) 101.6 cm.

FIG. 18
FIG. 18

FEA model of pure shear specimen: (a) full specimen and (b) quarter model.

FIG. 19
FIG. 19

Side-by-side comparison of pure shear tearing in FEA and test for 76.2-cm drop height.

FIG. 20
FIG. 20

Close-up view of crack tip in pure shear specimen during test at 76.2-cm drop height.

FIG. 21
FIG. 21

Comparisons of force history and crack growth positions in test and FEA for pure shear experiments at drop heights of (a–b) 76.2 cm, (b–d) 50.8 cm, and (e–f) 101.6 cm.

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