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Modeling of fracture and damage in rubber under dynamic and quasi-static conditions
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
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.
Series
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 0581
National Category
Applied Mechanics
Research subject
Solid Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-178048ISBN: 978-91-7595-749-4 (print)OAI: oai:DiVA.org:kth-178048DiVA: diva2:876354
Public defence
2015-12-18, sal B2, Brinellvägen 23 (02 tr), KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20150203

Available from: 2015-12-03 Created: 2015-12-03 Last updated: 2015-12-31Bibliographically approved
List of papers
1. Numerical analysis of dynamic crack propagation in rubber
Open this publication in new window or tab >>Numerical analysis of dynamic crack propagation in rubber
2012 (English)In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 177, no 2, 163-178 p.Article in journal (Refereed) Published
Abstract [en]

In the present paper, dynamic crack propagation in rubber is analyzed numerically using the finite element method. The problem of a suddenly initiated crack at the center of stretched sheet is studied under plane stress conditions. A nonlinear finite element analysis using implicit time integration scheme is used. The bulk material behavior is described by finite-viscoelasticity theory and the fracture separation process is characterized using a cohesive zone model with a bilinear traction-separation law. Hence, the numerical model is able to model and predict the different contributions to the fracture toughness, i.e. the surface energy, viscoelastic dissipation, and inertia effects. The separation work per unit area and the strength of the cohesive zone have been parameterized, and their influence on the separation process has been investigated. A steadily propagating crack is obtained and the corresponding crack tip position and velocity history as well as the steady crack propagation velocity are evaluated and compared with experimental data. A minimum threshold stretch of 3.0 is required for crack propagation. The numerical model is able to predict the dynamic crack growth. It appears that the strength and the surface energy vary with the crack speed. Finally, the maximum principal stretch and stress distribution around steadily propagation crack tip suggest that crystallization and cavity formation may take place.

Keyword
Rubber, Crack, Viscoelasticity, Cohesive zone, Dynamic fracture
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-104370 (URN)10.1007/s10704-012-9761-8 (DOI)000309353200005 ()2-s2.0-84867248444 (Scopus ID)
Note

QC 20121109

Available from: 2012-11-09 Created: 2012-11-01 Last updated: 2017-12-07Bibliographically approved
2. Numerical analysis of dynamic crack propagation in biaxially strained rubber sheets
Open this publication in new window or tab >>Numerical analysis of dynamic crack propagation in biaxially strained rubber sheets
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.

Keyword
Rubber, Crack, Viscoelasticity, Rate-dependent, Cohesive zone, Kelvin-Voigt element, Dynamic fracture
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-148616 (URN)10.1016/j.engfracmech.2014.04.025 (DOI)000338816700001 ()2-s2.0-84901989849 (Scopus ID)
Note

QC 20140811

Available from: 2014-08-11 Created: 2014-08-11 Last updated: 2017-12-05Bibliographically approved
3. A multiscale continuum modeling of strain-induced cavitation damageand crystallization in rubber-like materials
Open this publication in new window or tab >>A multiscale continuum modeling of strain-induced cavitation damageand crystallization in rubber-like materials
2015 (English)Report (Other academic)
Abstract [en]

A multiscale continuum model for strain-induced cavitation damage and crystallization for rubber-like materials is proposed. The constitutive behavior is determined by homogenization over different length scales, namely, the nano-scale, micro-scale and macro-scale. The microstructure of a filled rubber-like material is seen as interaction between clusters of the filler particles and long-chain molecules that form two networks, between cross-links and between the filler aggregates. The network between cross-links in the nano-scale is modeled using the full network approach of semi-crystalline chains. A phenomenological law is proposed to describe the crystallite nucleation law. The network between the filler particles is described by statistical mechanics in the nano- and/or micro-scale where the polymer chains sliding on and/or debonding from filler aggregate surface is incorporated. The debonding process is regarded as the main mechanism of the nucleation of nano-cavities which introduces non-affine deformation to the network between cross-links. Hence, The nanoscopic initially non-cavitated network between cross-links is homogenized over the micro-scale assuming a spherical representative volume element using the kinematics proposed by Hang-Sheng and Abeyaratne (Hang-Sheng and Abeyaratne in Journal of the Mechanics and Physics of Solids 40 (3), 571592,1992). The constitutive model is presented in form of an averaged strain energy function. The predictive capabilities of the model are then tested via comparisons with experimental data from literature.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2015
Series
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 579
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-178049 (URN)
Note

QC 20151203

Available from: 2015-12-03 Created: 2015-12-03 Last updated: 2016-03-01Bibliographically approved
4. An experimental method for estimating the tearing energy inrubber-like materials using the true stored energy
Open this publication in new window or tab >>An experimental method for estimating the tearing energy inrubber-like materials using the true stored energy
2015 (English)Report (Other academic)
Abstract [en]

A method for determining the critical tearing energy in rubber-like materials is proposed. In this method, the energy required for crack propagation in a rubber-like material is determined by the change of the recovered elastic energy. Hence, the dissipated energy due to different inelastic processes is deducted from the total strain energy applied to a system. Therefore, the classical method proposed by Rivlin and Thomas (Rivlin and Thomas in Journal of Polymer Science 10(3):291-318,1953) using the pure shear tear test is modified using the actual stored elastic energy. The elastically stored energy in a pure shear is determined experimentally using cyclic loading. The experimental results show that the classical method overestimates the critical tearing energy by approximately $15\%$. Moreover, the effect of the unloading rate on the determination of the elastically stored energy is investigated and found to be minimal suggesting that the crack propagation velocity has a minor effect in the change of the elastically stored energy.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2015
Series
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 580
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-178050 (URN)
Note

QC 20151203

Available from: 2015-12-03 Created: 2015-12-03 Last updated: 2016-03-01Bibliographically approved
5. Experimental investigations of crack propagation in rubber under dif-ferent loading rates, temperatures and fracture modes
Open this publication in new window or tab >>Experimental investigations of crack propagation in rubber under dif-ferent loading rates, temperatures and fracture modes
2015 (English)Report (Other academic)
Abstract [en]

In the present paper, the fracture behavior of carbon-black natural rubber material is experimentally studied. The cracked pure shear and the single edge notch specimens were used for investigating both pure mode I and mixed mode I and II fracture behavior, respectively. Further, different testing conditions were employed in the case of the cracked pure shear specimens. The specimens were subjected to three different loading rates and they were tested in two different temperatures. For studying the crack growth, a high speed camera at up to 7000 frames/s was used to follow the progress of the crack and later a post-processor was used to obtain the crack trajectory and velocity at different stages. The method introduced previously by the present author (Elmukashfi in report 580, Department of Solid Mechanics, Royal Institute of Technology (KTH), 2015) was used to obtain the critical tearing energy using the cracked pure shear specimens. Hence, the uncracked pure shear specimens were subjected to cyclic loading history in order to obtain the true elastic energy in pure shear. The single edge notch specimens were tested in room temperature under quasi-static loading. The pure mode I results suggest that the critical tearing depends strongly on the loading rate as well as the temperature. The tearing behavior shows stick-slip pattern at low tearing rates and smooth propagation at high velocities. The size of the stick-slip region is reduced significantly by increasing the loading rate as well as the temperature. In the mixed mode I and II, the transition from the stick-slip to smooth propagation and the transition from mixed mode I and II take place approximately simultaneously.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2015
Series
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 580
National Category
Applied Mechanics
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:kth:diva-178051 (URN)
Note

QC 20151203

Available from: 2015-12-03 Created: 2015-12-03 Last updated: 2015-12-10Bibliographically approved

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