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Numerical analysis of dynamic crack propagation in biaxially strained rubber sheets
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
2014 (English)In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 124, 1-17 p.Article in journal (Refereed) Published
Abstract [en]

This paper proposes a computational framework for dynamic crack propagation in rubber in which a nonlinear finite element analysis using cohesive zone modeling approach is used. A suddenly initiated crack at the center of biaxially stretched sheet problem is studied under plane stress conditions. A transient dynamic analysis using implicit time integration scheme is performed. In the constitutive modeling, the continuum is characterized by finite-viscoelasticity theory and coupled with the fracture processes using a cohesive zone model. This computational framework was introduced previously by the present authors (Elmukashfi and Kroon, 2012). In the current work, the use of a rate-dependent cohesive model is examined in addition to investigation of generalized biaxial loading cases. A Kelvin-Voigt element is used to describe the rate-dependent cohesive model wherein the spring is described by a bilinear law and dashpot with a constant viscosity is adopted. An explicit integration is used to incorporate the rate-dependent cohesive model in the finite element environment. A parametric study over the cohesive viscosity is performed and the steady crack propagation velocity is evaluated and compared with experimental data. It appears that the viscosity varies with the crack speed. Further, the total work of fracture is estimated using rate-independent cohesive law such that the strength of the cohesive zone is assumed to be constant and the separation work per unit area is determined form the experimental data. The results show that fracture-related processes, i.e. creation of new surfaces, cavitation and crystallization; contribute to the total work of fracture in a contradictory manner.

Place, publisher, year, edition, pages
2014. Vol. 124, 1-17 p.
Keyword [en]
Rubber, Crack, Viscoelasticity, Rate-dependent, Cohesive zone, Kelvin-Voigt element, Dynamic fracture
National Category
Materials Engineering
URN: urn:nbn:se:kth:diva-148616DOI: 10.1016/j.engfracmech.2014.04.025ISI: 000338816700001ScopusID: 2-s2.0-84901989849OAI: diva2:737000

QC 20140811

Available from: 2014-08-11 Created: 2014-08-11 Last updated: 2015-12-03Bibliographically approved
In thesis
1. Modeling of fracture and damage in rubber under dynamic and quasi-static conditions
Open this publication in new window or tab >>Modeling of fracture and damage in rubber under dynamic and quasi-static conditions
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Elastomers are important engineering materials that have contributed to the different technical developments and applications since the 19th century. The study of crack growth mechanics for elastomers is of great importance to produce reliable products and therefore costly failures can be prevented. On the other hand, it is fundamental in some applications such as adhesion technology, elastomers wear, etc. In this thesis work, crack propagation in rubber under quasi-static and dynamic conditions is investigated.

In Paper A, theoretical and computational frameworks for dynamic crack propagation in rubber have been developed. The fracture separation process is presumed to be described by a cohesive zone model and the bulk behavior is assumed to be determined by viscoelasticity theory. The numerical model is able to predict the dynamic crack growth. Further, the viscous dissipation in the continuum is found to be negligible and the strength and the surface energy vary with the crack speed. Hence, the viscous contribution in the innermost of the crack tip has been investigated in Paper B. This contribution is incorporated using a rate-dependent cohesive model. The results suggest that the viscosity varies with the crack speed. Moreover, the estimation of the total work of fracture shows that the fracture-related processes contribute to the total work of fracture in a contradictory manner.

A multiscale continuum model of strain-induced cavitation damage and crystallization in rubber-like materials is proposed in Paper C. The model adopts the network decomposition concept and assumes the interaction between the filler particles and long-chain molecules results in two networks between cross-links and between the filler aggregates. The network between the crosslinks is assumed to be semi-crystalline, and the network between the filler aggregates is assumed to be amorphous with the possibility of debonding. Moreover, the material is assumed to be initially non-cavitated and the cavitation may take place as a result from the debonding process. The cavities are assumed to exhibit growth phase that may lead to complete damage. The comparison with the experimental data from the literature shows that the model is capable to predict accurately the experimental data.

Papers D and E are dedicated to experimental studies of the crack propagation in rubber. A new method for determining the critical tearing energy in rubber-like materials is proposed in Paper D. The method attempts to provide an accurate prediction of the tearing energy by accounting for the dissipated energy due to different inelastic processes. The experimental results show that classical method overestimates the critical tearing energy by approximately 15%. In Paper E, the fracture behavior of carbon-black natural rubber material is experimentally studied over a range of loading rates varying from quasi-static to dynamic, different temperatures, and fracture modes. The tearing behavior shows a stick-slip pattern in low velocities with a size dependent on the loading rate, temperature and the fracture mode. Smooth propagation results at high velocities. The critical tearing depends strongly on the loading rate as well as the temperature.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. xv, 37 p.
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 0581
National Category
Applied Mechanics
Research subject
Solid Mechanics
urn:nbn:se:kth:diva-178048 (URN)978-91-7595-749-4 (ISBN)
Public defence
2015-12-18, sal B2, Brinellvägen 23 (02 tr), KTH, Stockholm, 10:00 (English)

QC 20150203

Available from: 2015-12-03 Created: 2015-12-03 Last updated: 2015-12-31Bibliographically approved

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