Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 30 Aug 2022

Numerical Modeling and Experimental Investigation of Thermal Shrinkage in Polymeric Cords. II: Numerical Implementation

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Page Range: 63 – 80
DOI: 10.2346/tire.22.22001b
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ABSTRACT

In this Part II of a two-part paper, a way of modeling axisymmetric rebars to represent the thermal shrinkage of polymeric cords within a thermo-mechanically coupled algorithm is presented without the assumption of a smeared layer. The mechanical characteristics of the proposed approach are compared to the classical approach using only one four-node axisymmetric element with unit dimensions. In addition, the shrinkage behavior of a simplified model made only of plies is discussed. The deformation behavior of polymeric cords during the tire manufacturing process, from the in-molding where a tire is formed by a mold under high pressure and temperature to curing and cooling, is addressed. Finally, the predicted profiles with and without post-cure inflation are compared to the test results.

Keywords: tire; polymeric cords; rebar; thermo-mechanical properties; shrinkage behavior
FIG. 1
FIG. 1

Two-node rebar description.

FIG. 2
FIG. 2

Deformed shape (green, commercial; orange, proposed) with respect to the angle of the rebar.

FIG. 3
FIG. 3

Comparison of displacement in (a) radial and (b) lateral direction with respect to the angle of the rebar between the commercial (green) and proposed elements (orange).

FIG. 4
FIG. 4

Deformation behavior and temperature change of the simplified ply model with respect to time.

FIG. 5
FIG. 5

Description of the model for curing and cooling simulation.

FIG. 6
FIG. 6

Simulation results from in-molding, curing, post-curing process.

FIG. 7
FIG. 7

Comparison of deformed shape between the model with (orange) and without (green) shrinkage properties.

FIG. 8
FIG. 8

Stretch with respect to time at four different points of model (a) without shrinkage properties, (b) with shrinkage properties.

FIG. 9
FIG. 9

Shrinkage stretch with respect to time at four different points of the model with shrinkage properties.

FIG. 10
FIG. 10

Shrinkage with respect to time at air-cooling condition from 170 °C to 50 °C and 10 g after the shrinkage test at 170 °C and 1000 g for 5 minutes.

FIG. 11
FIG. 11

Temperature distribution of the tire cross-section (a) with and (b) without PCI during the cooling process.

FIG. 12
FIG. 12

Profile comparison between the predicted (blue) and measured (black) results with (solid) and without PCI (dotted) under 0.25 bar inflation pressure.

Contributor Notes

1 Institute for Structural Analysis (ISD), Technische Universität Dresden, Georg-Schumann-Straße 7, Dresden, 01062, Germany. Email: sanghyeub.kim@tu-dresden.de
2 Institute for Structural Analysis (ISD), Technische Universität Dresden, Georg-Schumann-Straße 7, Dresden, 01062, Germany. Email: thomas.berger@tu-dresden.de
3 Virtual Technology Team, Hankook Tire & Technology Co., Ltd., Yuseong-daero 935, Daejeon, South Korea. Email: mj.piao@hankookn.com
4 Institute for Structural Analysis (ISD), Technische Universität Dresden, Georg-Schumann-Straße 7, Dresden, 01062, Germany. Email: imadeddin.zreid@tu-dresden.de
5 Corresponding author. Institute for Structural Analysis (ISD), Technische Universität Dresden, Georg-Schumann-Straße 7, Dresden, 01062, Germany. Email: michael.kaliske@tu-dresden.de
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