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echanics model for brittle failure of transversely isotropic solids. Finite...

Kolari

ESPOO 2007ESPOO 2007ESPOO 2007ESPOO 2007ESPOO 2007 VTT PUBLICATIONS 628

Kari Kolari

Damage mechanics model for brittlefailure of transversely isotropic solids

Finite element implementation

A new continuum damage model, the wing crack damage (WCD) model,was developed for the analysis of brittle failure of transversely isotropicsolids. Special attention was paid to the analysis of axial splitting undercompression and tensile cracking under tension. The model wasimplemented in ABAQUS/Standard FE software as a user subroutine.

The proposed method is based on the assumption of pre-existingcracks. The feature can be exploited in studying the effect of orientationand size distribution of pre-existing cracks on the failure of materials. Theunilateral response due to crack closure effect is taken into account.

The validity of the proposed WCD model was verified by numericalsimulation of five specimens in various loading conditions. The specimenswere composed of known transversely isotropic materials like ice andmarble, and concrete that was considered an isotropic material. Themodel was found to be efficient in the analysis of axial splitting andtensile failure modes.

In addition to the WCD model a three-dimensional version of thedamage model proposed by Murakami and Kamiya was enhanced andimplemented in ABAQUS/Standard FE software.

ISBN 978-951-38-6995-3 (soft back ed.) ISBN 978-951-38-6996-0 (URL: http://www.vtt.fi/publications/index.jsp)ISSN 1235-0621 (soft back ed.) ISSN 1455-0849 (URL: http://www.vtt.fi/publications/index.jsp)

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VTT PUBLICATIONS 628

Damage mechanics model for brittle failure of transversely

isotropic solids Finite element implementation

Kari Kolari

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Mechanical Engineering, for public

examination and debate in Auditorium TU1 at Helsinki University of Technology (Espoo, Finland) on the 20th of April, 2007, at 12 noon.

ISBN 978-951-38-6995-3 (soft back ed.) ISSN 1235-0621 (soft back ed.)

ISBN 978-951-38-6996-0 (URL: http://www.inf.vtt.fi/pdf/) ISSN 1455-0849 (URL: http://www.inf.vtt.fi/pdf/)

Copyright VTT 2007

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Kolari, Kari. Damage mechanics model for brittle failure of transversely isotropic solids. Finite element implementation. [Transversaali-isotroopisen materiaalin haurasmurtuman mallintaminen vauriomekaniikan avulla. Implementointi elementtimenetelmn]. Espoo 2007. VTT Publications 628. 195 p. + app. 7 p.

Keywords failure mechanics, brittle failure, anisotropy, continuum mechanics, damagemodels, finite element analysis, solid materials, structural analysis, three-dimensional, transversal isotropy, wing crack

Abstract

A new continuum damage model, the wing crack damage (WCD) model, was developed for the analysis of brittle failure of transversely isotropic solids. Special attention was paid to the analysis of axial splitting under compression and tensile cracking under tension.

In addition to the WCD model a three-dimensional version of the damage model proposed by Murakami and Kamiya was enhanced and implemented in ABAQUS/Standard FE software.

The proposed WCD model is based on the use of the damage vector. The vector represents both the normal direction of the surface of the plane crack and the size of the damaged area. Damaging induces anisotropy in an originally transversely isotropic material. The evolution equations for damage are motivated by the wing crack growth mechanism. The evolution is based on propagation of pre-existing damage.

The proposed model enables modelling of pre-existing cracks. The feature can be exploited in studying the effect of orientation and size distribution of pre-existing cracks on the failure of materials. The model was implemented in ABAQUS/Standard FE software as a user subroutine.

The unsymmetrical behaviour of cracked materials under tension and compression due to the opening and closure of cracks is taken into account in the proposed model. In the work it was shown that the widely used strain-based crack closure criteria cannot be reliably applied in a two- and three-dimensional

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stress state. To attain a deformation localisation zone of finite width, a damage rate-dependent damage surface was introduced.

The validity of the proposed model was verified by testing it against five basic structures composed of known natural materials (ice, marble and concrete). The numerical simulations revealed the capability of the model in modelling brittle failure modes of transversely isotropic materials.

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Kolari, Kari. Damage mechanics model for brittle failure of transversely isotropic solids. Finite element implementation. [Transversaali-isotroopisen materiaalin haurasmurtuman mallintaminen vauriomekaniikan avulla. Implementointi elementtimenetelmn]. Espoo 2007. VTT Publications 628. 195 s. + liitt. 7 s.

Avainsanat failure mechanics, brittle failure, anisotropy, continuum mechanics, damagemodels, finite element analysis, solid materials, structural analysis, three-dimensional, transversal isotropy, wing crack

Tiivistelm

Tutkimuksessa on esitetty kaksi vauriomekaniikkaan (Continuum damage mechanics) perustuvaa materiaalimallia: Murakami Kamiyan (MK) malli, sek uusi wing crak damage -malli (WCD). Molemmat mallit on liitetty ABAQUS-elementtimenetelmohjelmistoon UMAT-aliohjelmana.

Esitetty uusi WCD-malli on tarkoitettu transversaali-isotrooppisten materiaalien haurasmurtuman mallintamiseen. Erityist huomiota on kiinnitetty yksiaksiaali-sessa puristuksessa tapahtuvan kuormituksen kanssa yhdensuuntaisen halkea-misen sek yksiaksiaalisessa vedossa tapahtuvan kuormitusta vastaan kohtisuo-rassa olevan srytymisen mallintamiseen.

Esitetty WCD-malli perustuu vauriovektorin kyttn. Vauriovektori edustaa sek tasomaisen srn normaalin suuntaa ett vaurioituneen alueen kokoa. Vau-rioitumisen vuoksi transversaali-isotrooppisesta materiaalista tulee anisotrooppista. Vaurion kasvumekanismi simuloi siipisrn (wing crack) kasvumekanismia.

Uusi WCD-malli mahdollistaa materiaalissa ennen kuormitusta olevien alku-srjen mallintamisen. Piirrett voidaan hydynt tutkittaessa alkusrjen suun-nan ja suuruuden vaikutusta materiaalin vaurioitumiseen.

Halkeilleen materiaalin epsymmetrinen kyttytyminen vedossa ja puristuk-sessa srn avautumisen ja sulkeutumisen vuoksi on otettu huomioon esitetyss mallissa. Tutkimuksessa on osoitettu, ett venymperusteista sulkeutumiskriteeri ei voida luotettavasti soveltaa kaksi- ja kolmiaksiaalisessa jnnitystilassa.

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Esitetyss mallissa vauriopinta on vaurionopeuden funktio. Siksi muodonmuu-tosten paikallistumisvyhykkeen leveys on rellinen.

Esitetyn mallin ptevyys on todennettu testaamalla mallia viidess eri kuormi-tustapauksessa kytten tunnettuja luonnonmateriaaleja (j, betoni ja marmori). Numeeriset testit osoittivat mallin ptevyyden ja tehokkuuden transversaali-isotrooppisten materiaalien haurasmurtuman mallintamisessa.

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Preface

The primary idea for the research reported in this thesis evolved from international and national projects focused on ice loads on offshore structures. The projects were supported by Tekes Finnish Funding Agency for Technology and Innovation [project ARKI, Contract No. 40857/99], the European MAST-III project LOLEIF [Contract No. MAS3-CT-97-0098] and the European FP5 EESD project STRICE [Contract No. EVG1-CT-2000-00024].

I am grateful to my supervisor, Professor Mauri Mttnen, for his positive attitude and for granting me a position at the Helsinki University of Technology (TKK) for two years. Many thanks also to Professor Jukka Tuhkuri for his comments during the final revision of the thesis. I would like to thank the personnel at the Laboratory for Mechanics of Materials at TKK for the encouraging atmosphere.

I am also grateful to my ex-colleague Dr. Tuomo Krn for providing me with the opportunity to carry out research in the field of ice mechanics and dynamics. The idea for this report was hatched as we studied the modelling of brittle failure of natural ice.

I would like to thank my friend Dr. Reijo Kouhia from the Helsinki University of Technology for his advice during countless discussions and for his comments on the manuscripts of this work. I am also grateful to Dr. Kari Santaoja from the Helsinki University of Technology for his help concerning both theoretical and