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Welcome to the IUTAM Symposium on Materials and Interfaces Under High Strain Rate and Large Deformation We are pleased to welcome you at the University of Lorraine in Metz for the IUTAM Symposium on Materials and Interfaces Under High Strain Rate and Large Deformation This symposium is co-organized by the University of Lorraine (LEM3 laboratory) and the Ecole Polytechnique Fédérale de Lausanne (ENAC). Materials and interfaces are subject to extreme conditions in numerous applications such as impacts, explosions, high-speed processes and forming. In many of these problems the mechanical response of the bulk materials is intimately related to the behaviour of material interfaces. Physical mechanisms, which govern the response, span length scales that range from the nano-scale to the level of structures. In this symposium, high strain rate and large deformation response of materials and interfaces will be addressed by different means, with a balance between theoretical developments, experimental work and numerical simulations. We are honoured to welcome such a symposium with such a prestigious attendance, and we are hopeful that this programme will meet all your expectations. Have a fruitful conference in Metz. Enjoy the lectures together with the nearby historical city centre. Yours sincerely,

Sebastien Mercier Jean François Molinari

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IUTAM Symposium Materials and Interfaces under high strain rate and large deformation

Organizing Committee Conference Co-Chairmen

S. Mercier, University of Lorraine, Metz J-F. Molinari, Ecole Polytechnique Fédérale de Lausanne

Local Organizing Committee K. Saidi, University of Lorraine, Metz N. Kasprzak, CNRS, University of Lorraine, Metz A. Blum, University of Lorraine, Metz C. Czarnota, University of Lorraine, Metz G. List, University of Lorraine, Metz M. Martiny, University of Lorraine, Metz A. Salahouelhadj, CNRS, University of Lorraine, Metz G. Sutter, University of Lorraine, Metz

Scientific Committee G. Ravichandran, California Institute of Technology, Pasadena USA M. Ortiz, California Institute of Technology, Pasadena, USA K.T. Ramesh, John Hopkins University, Baltimore, USA G. Kanel, Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia D. Rittel, Technion, Israel Institute of Technology, Haifa, Israel

IUTAM Representatives N.K. Gupta, Indian Institute of Technology, Delhi, New Dehli, India O. Allix, ENS Cachan, Cachan, France

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IUTAM Symposium – General Information

Registration The registration office is open in the Demange amphitheater Sunday, June 16, 5:00 PM - 7:00 PM Monday to Thursday, 8:00 AM – 9:00 AM 10:30 AM – 11:00 AM 3:45 PM – 4:15 PM Friday 8:00 AM – 9:00 AM

Session Information All sessions are held in the Demange Amphitheater. The room is equipped with a projector and a laptop computer. Each session has a chairman. Session chairmen are requested to moderate the discussion and monitor the time for each speaker. Each presentation is allotted 30 minutes. At least 5 minutes should be reserved for discussion at the end of the presentation.

Coffee Breaks Coffee, tea and soft-drinks will be served during each break. The breaks will be at 10:30-11:00 AM and 3:45- 4:15 PM. Participants are requested not to bring any drink in the Amphitheater.

Lunch Breaks Lunch breaks are scheduled for 12:30 to 2:00 PM. Lunch will be served at the Restaurant Universitaire Paul Verlaine.

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Dinner Party A dinner party is organized Tuesday, June 18, at the El Theatris Restaurant, 2 Place de la Comédie, Metz. The restaurant is located nearby the Protestant church. Participants are welcome to attend. Your conference badge will serve as the entry ticket for this event The Reception starts at 7:30 PM. You will enjoy the cold buffet, with a large choice of vegetables, meat, cheese and cakes.

Banquet The banquet is organized at the Magasin aux Vivres Restaurant, 5 Avenue Ney, Metz. The restaurant is located inside the La citadelle Hotel, nearby the concert hall. The banquet will be held on Thursday, June 20 from 8:00 PM to 11:00 PM. We will enjoy a French cuisine menu.

Internet Free wireless internet access is available throughout the University of Lorraine. Please use the login and password provided for that purpose.

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Metz - Maps

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University of Lorraine - Maps

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IUTAM Symposium – Schedule Overview

June 2013 Sunday 16 Monday 17 Tuesday 18 Wednesday 19 Thursday 20 Friday 21

AM

8:00-9:00 Registration

Opening 8h45 Registration Registration Registration Registration

9:00-10:30 Freund

Geubelle Gaitanaros

Ramesh Agnihotri

Bigoni

9:30 Curtin

Ravichandran

Needleman Lebensohn

Jacques

Allix Mohr

Hiermaier

10:30-11:00 Break Break Break Break Break

11:00-12:30 Kanel

Vitelli Corrado

Meyers Mercier Couque

Leblond Cazacu

Hild

JF Molinari van Beeck

Coker

List Chen

Closure

12:30-2:15 Lunch Lunch Lunch Lunch Lunch

PM

2:15-3:45 Inaba

Faciu Leonard

Clifton Deshpande

Ahzi

L 31-33 Rittel Rodriguez-Martinez

Stainier

3:45-4:15 Break Break

Visit

Pompidou Metz

Break

4:15-5:45 Trumel

Rusinek

Triantafyllidis Soldani

Bouchbinder

Pandolfi Marigo Longère

5:00-7:00 Registration

7:30

Get together Dinner Party

El Theatris

Banquet

Le Magasin aux Vivres

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Sunday, June 16 5:00 pm – 7:00pm Registration Demange Amphitheater 7:30 pm – 9:00 pm Get together Welcome Reception

Monday, June 17

8:45 AM-9:00 AM Demange Amphi Opening of the symposium

9:00 AM-10:30 AM Demange Amphi Session Interfaces Session Chair : K. Ravi-Chandar

WHY DO THE SURFACES OF RAPIDLY GROWING CRACKS IN BRITTLE MATERIALS ROUGHEN? L. B. Freund

Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana IL 61801 USA

MOLECULAR TAILORING OF INTERFACES USING SELF-ASSEMBLED MONOLAYERS A. Awasthi, M.E. Grady, N. R. Sottos and P.H. Geubelle University of Illinois at Urbana-Champaign, 306 South Wright Street; Urbana, IL 61801; USA

SHOCK PROPAGATION IN ALUMINUM OPEN-CELL FOAM UNDER IMPACT S. Gaitanaros, A.T. Barnes, S. Kyriakides, K. Ravi-Chandar

Research Center for Mechanics of Solids, Structures & Materials,,The University of Texas at Austin, Austin, TX 78712, USA

10:30 AM-11:00 AM BREAK

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11:00 AM-12:30 PM Demange Amphi Session Waves, Impacts, Shocks Session Chair : M. Meyers

SHOCK RESPONSE OF HOMOGENEOUS SOLIDS: METAL SINGLE CRYSTALS, SAPPHIRE AND SILICATE GLASSES. G.I. Kanel (1), S.V. Razorenov (2), G.V. Garkushin (2), A.S. Savinykh (2)

(1) Joint Institute for High Temperatures of Russian Academy of Sciences, Izhorskaya 13, bld. 2, Moscow, 125412 Russia

(2) Institute of problems of Chemical Physics of Russian Academy of Sciences, Chernogolovka, Moscow region, 142432 Russia

INTERACTION OF STRONGLY NON LINEAR WAVES WITH INTERFACES A. M. Tichler(1), L. Gomez(1), N. Upadhyaya(1), X. Campman(2), V. F. Nesterenko(3), and V. Vitelli(1) (1) Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, 2300 RA Leiden, The Netherlands (2) Shell International E&P B.V., Kessler Park 1, 2288 GS, Rijswijk, The Netherlands (3) Jacobs School of Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California, USA

DYNAMIC BEHAVIOUR OF FINITE THICKNESS COHESIVE INTERFACES M. Corrado and M. Paggi

Politecnico di Torino, Department of Structural, Geotechnical and Building Engineering, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

12:30 PM-14:15 PM LUNCH

14:15 PM- 15:45 PM Demange Amphi Session Waves, Impacts, Shocks Session Chair : G. Kanel

FREQUENCY AND DISPERSION OF FLEXURAL WAVES IN FLUID-FILLED TUBES SUBJECT TO AXIAL IMPACT K. Inaba , K. Takahashi, and K. Kishimoto

Tokyo Institute of Technology, 2-12-1-I6-5 Ookayama, Meguro-ku, Tokyo 152-8550, JAPAN

SHOCK-INDUCED PHASE TRANSITIONS IN THERMOELASTIC BARS: RIEMANN PROBLEMS AND APPLICATIONS C. Făciu ”Simion Stoilow” Institute of Mathematics of the Romanian Academy, Research Unit No. 6, P.O. Box 1-764, RO-014700, Bucharest, Romania

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PULSE SPLITTING, BENDING, AND COMBINING IN 2D AND 3D GRANULAR NETWORKS A. Leonard(1,2), L. Ponson(3), and C. Daraio(1,2) (1) California Institute of Technology, Graduate Aerospace Laboratories (GALCIT), 1200 E California Blvd, Pasadena CA 91125, USA

(2) ETH-Zürich, Department of Mechanical and Process Engineering (D-MAVT),Tannenstrasse 3, 8092 Zürich, Switzerland

(3) Institut Jean le Rond d’Alembert (UMR 7190), CNRS - Université Pierre et Marie Curie, 75005 Paris, France

15:45 PM – 16:15 PM BREAK

16:15 PM – 17:15 Demange Amphi Session Material Response Session Chair : R. Clifton

UNDERSTANDING THE IGNITION OF ENERGETIC MATERIALS UNDER DYNAMIC LOADING: A MULTISCALE THERMOMECHANICAL CHALLENGE M. Biessy(1), J.-L. Brigolle(1), D. Picart(1), H. Trumel(1), J. Vial(1), P. Lambert(2), P. Bortoluzzi(3), A. Fanget(3) (1) CEA, DAM, Le Ripault, F-37260 MONTS, France (2) Sciences et Applications Co., 218 bd Albert 1er, F-33000 BORDEAUX, France (3) CEA, DAM, Gramat, F-46500 GRAMAT, France

DYNAMIC PERFORATION OF THERMOVISCOPLASTIC PLATES BY RIGID PROJECTILES AND SHAPE EFFETCS A. Rusinek(1), M. Kpenyigba(1), T. Jankowiak(2), R. Pesci(3) (1)National Engineering School of Metz, Laboratory of Mechanics, Biomechanics, Polymers and structures, 1 route d'Ars Laquenexy cs65820 57078 Metz cedex 3, France (2)Institute of Structural Engineering, Poznan University of Technology, Piotrowo 5, Poznan, Poland (3)LEM3 UMR CNRS 7239, ENSAM-Arts et Métiers ParisTech CER of Metz, 4 rue Augustin Fresnel 57078 Metz cedex 3, France

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Tuesday, June 18

9:00 AM-10:30 AM Demange Amphi Session Material Response Session Chair :W. Curtin

THE SECRET LIVES OF TWINS K.T. Ramesh, N. Dixit and N. Daphalapurkar Hopkins Extreme Materials Institute, Johns Hopkins University, 3400 North Charles St., Baltimore, MD 21218, USA RATE SENSITIVITY ACCORDING TO DISCRETE DISLOCATION PLASTICITY P.K. Agnihotri and E. Van der Giessen

Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747AG Groningen, the Netherlands

DISLOCATIONS IN PRESTRESSED DUCTILE MATERIALS L. Argani(1), D. Bigoni(1)and G. Mishuris(2)

(1) Department of Civil, Environmental & Mechanical Engineering, University of Trento, via Mesiano 77, Trento, Italy (2) Institute of Mathematical and Physical Sciences, University of Wales, Aberystwyth, UK

10:30 AM-11:00 AM BREAK

11:00 AM-12:30 PM Demange Amphi Session Fracture Session Chair : D. Rittel

DEFORMATION AND FAILURE OF METALS SUBJECTED TO LASER SHOCK LOADING M. A. Meyers1, C. H. Lu1, T. Remington1 , B. Kad1, Y. Tang1, B. A. Remington2, B. R. Maddox2, H. S. Park2, E. M. Bringa3, and C. Ruestes3 1 University of California, San Diego, La Jolla, CA, 92093, USA 2 Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA 3U. Nacional de Cuyo, Mendoza, Argentina CONSTITUTIVE BEHAVIOR OF POROUS DUCTILE MATERIALS ACCOUNTING FOR MICRO-INERTIA AND VOID SHAPE C. Sartori1, S. Mercier1, N. Jacques 2, A. Molinari 1 1 Université de Lorraine, LEM3, UMR CNRS, Ile du Saulcy, 57045 Metz cedex 01, France 2 ENSTA Bretagne, LBMS, 2 rue François Verny, 29806 Brest cedex 9, France

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EVIDENCES OF MATERIAL STRENGHTENING AT VERY HIGH STRAIN RATES – PLASTIC DEFORMATION OF EXPLOSIVELY FORMED PROJECTILES – CHARPY ENERGY AT HIGH IMPACT VELOCITIES H. Couque

Nexter Munitions, 7 route de Guerry,18023 Bourges, France

12:30 PM-14:00 PM LUNCH

14:15 PM- 15:45 PM Demange Amphi Session Material Response Session Chair : J.B. Leblond

HIGH STRAIN RATE RESPONSE OF AN ELASTOMER AT HIGH PRESSURE R. Clifton and T. Jiao School of Engineering, Brown University Providence, RI 02912 USA

THE DYNAMIC PERFORMANCE OF ULTRA HIGH MOLECULAR WEIGHT POLYETHEYLENE FIBRE COMPOSITES J.P. Attwood(1), Karthikeyan K.(1) and V.S. Deshpande(1)

(1) Cambridge University Department of Engineering, Trumpington Street, Cambridge, CB2 1PZ, UK.

DYNAMIC BEHAVIOR OF POLYMERS AND POLYMER NANOCOMPOSITES: MODELING AND SIMULATIONS S. Ahzi ICube Laboratory, University of Strasbourg / CNRS, 2 Rue Boussingault, 67000 Strasbourg, France.

15:45 PM – 16:15 PM BREAK

16:15 PM – 17:15 Demange Amphi Material Instabilities, Strain Localization Session Chair : KT Ramesh

DYNAMIC STABILITY OF TRANSIENT STATES IN STRUCTURES SUBJECTED TO HIGH STRAIN RATE T. Putelat (1), K. Ravi-Chandar (1), (2) and N. Triantafyllidis (1), (3), (4), (5)

(1)Laboratoire de Mecanique des Solides, C.N.R.S. UMR7649, Ecole Polytechnique, Palaiseau 91128, FRANCE (2)Aerospace Engineering & Engineering Mechanics Department, The University of Texas, Austin, TX 78712-0235 USA (3)Departement de Mecanique, Ecole Polytechnique, Palaiseau 91128, FRANCE (4)Aerospace Engineering Department & Mechanical Engineering Department (emeritus), The University of Michigan, Ann Arbor, MI 48109-2140 USA

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ANALYSIS OF ADIABATIC SHEAR BANDING IN MACHINING X. Soldani(1), A. Molinari(2), J. Díaz(1), H. Miguélez(1)

(1) Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avda. Universidad 30, 28911, Leganés, Madrid (2) Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux, LEM3, Labex Damas Université de Lorraine, Ile du Saulcy, 57045, Metz cedex, France INSTABILITIES IN DYNAMIC FRACTURE E. Bouchbinder

Weizmann Institute of Science, Rehovot 76100, Israel

Wednesday, June 19

9:30 AM-10:30 AM Demange Amphi Session Material Response Session Chair : D. Bigoni

ATOMISTIC MECHANISMS OF DYNAMIC STRAIN AGING AND THEIR IMPACT ON DUCTILITY IN AL-MG W. A. Curtin

Ecole Polytechnique Federale de Lausanne, EPFL-STI-IGM-LAMMM, Station 9, 1015 Lausanne, Switzerland

HIGH-PRESSURE HUGONIOT MEASUREMENTS USING MACH REFLECTIONS J.L. Brown and G. Ravichandran

California Institute of Technology,, Pasadena, CA 91125, USA

10:30 AM-11:00 AM BREAK

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11:00 AM-12:30 PM Demange Amphi Session Fracture Session Chair : A. Needleman

NUMERICAL IMPLEMENTATION AND APPLICATION OF A MODEL FOR PLASTIC POROUS MATERIALS INCORPORATING VOID SHAPE EFFECTS J.B. Leblond and L. Morin

UPMC Univ Paris 6 and CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France NEW ANALYTIC CRITERION DESCRIBING THE COMBINED EFFECT OF PRESSURE AND THIRD INVARIANT ON YIELDING OF POROUS AGGREGATES O. Cazacu Department of Mechanical and Aerospace Engineering, University of Florida, REEF, 1350 N. Poquito Rd, Shalimar, FL 32579, USA. ON CHARACTERISTIC PARAMETERS INVOLVED IN DYNAMIC FRAGMENTATION PROCESSES F. Hild

LMT-Cachan, ENS Cachan / CNRS / UPMC / PRES UniverSud Paris, 61 avenue du Président Wilson, F-94235 Cachan Cedex, France

12:30 PM-14:00 PM LUNCH

15:45 PM Visit of Pompidou Museum

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Thursday, June 20

9:00 AM-10:30 AM Demange Amphi Session Fracture Session Chair B. Freund

EFFECT OF RATE ON THE STATISTICS OF DUCTILE FRACTURE SURFACE ROUGHNESS A. Needleman

Department of Materials Science and Engineering,University of North Texas, Denton, TX USA

MICROSTRUCTURAL EFFECTS ON DUCTILE DAMAGE OF POLYCRYSTALLINE MATERIALS R.A. Lebensohn

Materials Science and Technology Division, Los Alamos National Laboratory, MS G755, Los Alamos, NM, USA. SOME ASPECTS OF INERTIA IN POROUS DUCTILE SOLIDS SUBJECTED TO DYNAMIC LOADING N. Jacques 1, S. Mercier 2, A. Molinari 2 1 ENSTA Bretagne, LBMS, 2 rue François Verny, 29806 Brest cedex 9, France 2 Université de Lorraine, LEM3, UMR CNRS, Ile du Saulcy, 57045 Metz cedex 01, France

10:30 AM-11:00 AM BREAK

11:00 AM-12:30 PM Demange Amphi Session Interfaces Session Chair : P.H. Geubelle

SLIP PRECURSORS AT FRICTIONAL INTERFACES D.S. Kammer, M. Radiguet and J.F. Molinari Computational Solid Mechanics Laboratory (lsms.epfl.ch), School of Architecture, Civil and Environmental Engineering (ENAC), School of Engineering (STI) , Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

EFFECT OF DEFORMATION OF DEFORMATION-INDUCED SURFACE ROUGHENING ON METAL-POLYMER INTERFACE INTEGRITY J. van Beeck(1,2), P.J.G. Schreurs(1) and M.G.D. Geers(1)

(1) Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands (2) Materials Innovation Institute (M2i), PO Box 5008, 2600 GA Delft, The Netherlands

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DYNAMIC CRACK GROWTH ALONG CURVED INTERFACES IN COMPOSITE AND BONDED POLYMER MATERIALS D. Coker(1,2), D. Yavas(1,2) and B. Gozluklu(1,3)

(1) Department of Aerospace Engineering, Middle East Technical University, Ankara, Turkey (2) METU Center for Wind Energy, Middle East Technical University, Ankara, Turkey (3) Turkish Aerospace Industries (TAI), 06980, Ankara, Turkey

12:30 PM-14:00 PM LUNCH

14:15 PM- 15:45 PM Demange Amphi Material Instabilities, Strain Localization Session Chair : F. Hild

ON THE ONSET OF ADIABATIC SHEAR FAILURE D. Rittel(1), S. Osovski(1), A. Venkert(2) and P. Landau(2)

(1) Faculty of Mechanical Engineering, Technion, 32000 Haifa, Israel

(2) Department of Physics, NRCN, 84190 Beer-Sheva, Israel

ON THE COMPLETE EXTINCTION OF SELECTED IMPERFECTION WAVELENGTHS IN DYNAMICALLY EXPANDED DUCTILE RINGS J. A. Rodríguez-Martínez, G. Vadillo, R. Zaera, J. Fernández-Sáez Department of Continuum Mechanics and Structural Analysis. University Carlos III of Madrid. Avda. de la Universidad, 30. 28911 Leganés, Madrid, Spain ENERGY-BASED VARIATIONAL MODELLING FOR ADIABATIC SHEAR BAND STRUCTURE S. Su and L. Stainier

Research Institute in Civil and Mechanical Engineering - GeM (UMR 6183 CNRS), École Centrale Nantes, 1 rue de la Noë, BP 92101, F-44321 Nantes, France

15:45 PM – 16:15 PM BREAK

16:15 PM – 17:45 Demange Amphi Session Fracture Session Chair : S. Hiermaier

DYNAMIC FRAGMENTATION IN DUCTILE MATERIALS VIA OPTIMAL TRANSPORTATION MESHFREE METHOD A. Pandolfi(1), B. Li(2), M. Ortiz(2)

(1) Politecnico di Milano, Dipartimento di Ingegneria Civile and Ambientale, Piazza Leonardo da Vinci 32, 20133 Milano (Italy)

(2) Engineering & Applied Science Division, California Institute of Technology, 1200 East California Blvd, Pasadena CA, 91125 (USA)

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GRADIENT DAMAGE MODELS COUPLED WITH PLASTICITY R. Alessi(1,2) and J.J. Marigo(1) and S. Vidoli(2)

(1) Laboratoire de Mécanique des Solides, Ecole Polytechnique, 91128 Palaiseau Cedex, France

(2) Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, Via Eudossiana 18,00184 Roma, Italy DYNAMIC VS QUASI-STATIC SHEAR FAILURE OF HIGH STRENGTH METALLIC ALLOYS: EXPERIMENT AND MODELLING P. Longère(1) and A. Dragon(2)

(1) Université de Toulouse, ISAE- ICA (EA 814), 10 avenue Edouard Belin, BP 54032, 31055 Toulouse cedex 4, France

(2) Institut Pprime, DPMM (UPR CNRS 3346) / ENSMA, 1 avenue Clément Ader, BP 40109, 86961 Futuroscope - Chasseneuil du Poitou, France

Friday, June 21

9:00 AM-10:30 AM Demange Amphi Session Fracture Session Chair : G. Ravichandran

ON BOUNDED RATE CONSTITUTIVE MODEL : APPLICATION TO OBJECTIVE FAILURE PREDICTION O. Allix LMT-Cachan, ENS Cachan/CNRS/PRES UniverSud Paris, 61, avenue du président Wilson, F-94230 Cachan, France

EFFECT OF STRAIN RATE, STRESS TRIAXIALITY AND LODE PARAMETER ON DUCTILE FRACTURE M. Dunand(1,2) and D. Mohr (1,2)

(1) Solid Mechanics Laboratory (CNRS-UMR 7649), Department of Mechanics, École Polytechnique, Palaiseau, France (2) Impact and Crashworthiness Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge MA, USA

COHESIVE ZONE MODELLING OF DYNAMIC FAILURE IN BRITTLE MATERIALS S. Hiermaier(1), M. Büttner(1), P. Seiterich(1) and M. Sauer(1)

(1) Fraunhofer Institute for High-Speed-Dynamics, Ernst-Mach-Institute (EMI)

Eckerstr. 4, 79104 Freiburg, Germany

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10:30 AM-11:00 AM BREAK

11:00 AM-12:00 PM Demange Amphi Session Interfaces Session Chair : O. Allix

STUDY OF FRICTION AND WEAR MECHANISMS AT HIGH SLIDING SPEED.G. List, G. Sutter, JJ. Arnoux, A. Molinari

University of Lorraine, LEM3, Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (UMR n° 7239), Ile du Saulcy, F-57045 Metz - cedex 01,

CRACK PROPAGATION THROUGH GLASS-ADHESIVE INTERFACE DRIVEN BY DYNAMIC LOADING H. Park(1), N. D. Parab(1) and W. Chen(1)

(1) Schools of Aeronautics/Astronautics and Materials Engineering, Purdue University, 710 West Stadium Avenue, West Lafayette, Indiana, USA-47906

12:30 PM-14:00 PM LUNCH

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WHY DO THE SURFACES OF RAPIDLY GROWING CRACKS IN BRITTLE MATERIALS ROUGHEN?

L. B. Freund

Department of Materials Science and Engineering University of Illinois at Urbana-Champaign, Urbana IL 61801 USA

The theory of dynamic fracture mechanics has been reasonably successful as a framework for characterization and quantitative analysis of rapid crack growth phenomena in both relatively brittle engineering materials and geological materials. The focus of the theory is on the phenomenon of growth of a single dominant crack through a nominally elastic material undergoing relatively small amplitude deformation. Nonetheless, the literature is replete with reports that the theory ``fails’’ for growth conditions involving very fast crack growth and/or extreme loading conditions. In fact, the reported deviations from the theory are most commonly the result of the system exhibiting behavior that departs from the range of behaviors over which that theory can be expected to be valid. Perhaps the most common examples of such behavior are multiple crack formation, non-planar growth, and large deformation. Over the years since dynamic elastic fracture mechanics has come together in the form summarized in [1], little progress has been made toward a mechanistic understanding of the reasons underlying these departures from the prevailing theory. Here, we seek a possible explanation for one of these deviations, namely, the transition from fracture advance as a dominant crack with a flat crack surface to growth with roughened, nonplanar crack surfaces on a small size scale. This is pursued on the basis of recent advances in understanding the influence of loading rate on the resistance of molecular/atomic bonds to forced separation [2,3,4]. Examination of the statistics of the behaviour of many bonds being forcibly separated simultaneously leads to a constitutive description of forced separation of surfaces which may provide clues to the reasons underlying the onset of crack surface roughening during dynamic crack growth in a brittle material. References [1] Freund, L. B., Dynamic Fracture Mechanics, Cambridge University Press, 1990.

[2] Evans, E. and Ritchie, K., Dynamic strength of molecular adhesion bonds, Biophysical Journal, 72, 1997, 1541-1555.

[3] Freund, L. B., Characterizing the resistance generated by a molecular bond as it is forcibly separated, Proceedings of the National Academy of Sciences (USA), 106, 2009, 8818-8823

[4] Christian, J. W., Transformations in Metals and Alloys, 2nd edition, 1975, Pergamon Press.

_____ Corresponding Author :L. B. Freund lbf@illinois.edu

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MOLECULAR TAILORING OF INTERFACES USING SELF-ASSEMBLED MONOLAYERS

A. Awasthi, M.E. Grady, N. R. Sottos and P.H. Geubelle

University of Illinois at Urbana-Champaign

306 South Wright Street; Urbana, IL 61801; USA

Due to the flexibility they offer in the selection of the end groups attached to the substrate and film materials, self-assembled monolayers (SAMs) composed of very short (nanometer-long) aligned polymer chains have been proposed as a unique way to tailor the electrical, thermal and mechanical properties of interfaces. This combined experimental and computational study aims at shedding some light on the impact of the SAMs on the failure properties of a silicon/gold interface. In this study, we investigate SAMs with methyl (-CH3), mercapto (-SH), amino (-NH3) and bromo (-Br) terminated functional groups (Fig. 1). In the initial phase of the experimental component of the project, we adopt a non-contact laser-based spallation technique to measure the failure strength of a fused silica/SAM/gold system. This method, which has been used in the testing of a wide variety of metallic films and polymeric coatings, consists in converting the thermal energy imparted by a very short (ten nanoseconds-long) Yag laser pulse to an absorbing layer placed on the back side of the substrate into a compressive acoustic pressure pulse that propagates through the substrate toward the interface of interest. Upon reflection from the free surface of the film, the pulse loads the film/substrate in tension, leading to its spallation failure. Preliminary results show a strong dependence of the failure strength of the interface on the choice of SAM. Detailed AFM and XPS analyses performed on the post-spallation surfaces provide information on the roughness profile and chemical composition of the failure surface. To support these experiments, MD simulations of the spallation event are performed using LAMMPS with CVFF and ReaxFF force field models. Loading rates similar to those used in the experiments are applied to the MD model. Emphasis is placed on predicting the impact of the functional end-group on the evolution and location of the failure event, and on extracting cohesive failure relations to be used in continuum descriptions of the film/substrate failure event. _______ Corresponding Author : Philippe H. Geubelle e-mail: geubelle@illinois.edu.

Fig. 1. Schematic of a self-assembled monolayer functionalized interface between a substrate and a thin film.

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SHOCK PROPAGATION IN ALUMINUM OPEN-CELL FOAM UNDER IMPACT

S. Gaitanaros, A.T. Barnes, S. Kyriakides, K. Ravi-Chandar

Research Center for Mechanics of Solids, Structures & Materials

The University of Texas at Austin Austin, TX 78712, USA

Lightweight cellular materials such as foams exhibit excellent energy absorption characteristics and are widely used for impact mitigation in a variety of applications. We will present results from combined experimental and analytical efforts that investigate the behavior of an Al-alloy open-cell foam under impact. The experiments involve direct and stationary impact tests on cylindrical foam specimens at impacts speeds in the range of 20-160 m/s using a gas gun. The stress at the distal end is recorded using a pressure bar while the deformation of the entire foam specimen is monitored with high-speed photography. Specimens impacted at velocities of 60 m/s and above developed nearly planar shocks that propagated at well-defined velocities crushing the specimen. The shock-impact speed ( &s−Vb ) as well as the densification strain-impact speed (εD −Vb) Hugoniots were both

extracted directly from the sequence of high-speed images recorded. The &s−Vb Hugoniot follows a

linear relationship and the εD −Vb Hugoniot asymptotically approaches a strain of approximately 90% at higher velocities. The compaction energy dissipation across the shock is shown to be significantly greater than the corresponding quasi-static one. At impact speeds of 40 m/s and lower the stress remains nearly constant throughout the specimen, crushing initiates at the weakest site in the specimen and spreads in the same manner as in quasi-static crushing. Micromechanically accurate models of random foams are used to simulate the impact experiments. They are shown to faithfully reproduce the formation and evolution of shocks including the force acting at the two ends, the shock front velocity, and the energy absorbed. Numerical models are subsequently used to expand and elucidate the experimental results and observations, and examine the transition to non-shock behavior at lower speeds.

_______ Corresponding Author : Stelios Kyriakides, e-mail: skk@mail.utexas.edu

26

SHOCK RESPONSE OF HOMOGENEOUS SOLIDS: METAL SINGLE CRYSTALS, SAPPHIRE AND SILICATE GLASSES.

G.I. Kanel (1), S.V. Razorenov (2), G.V. Garkushin (2), A.S. Savinykh (2)

(1) Joint Institute for High Temperatures of Russian Academy of Sciences

Izhorskaya 13, bld. 2, Moscow, 125412 Russia (2) Institute of problems of Chemical Physics of Russian Academy of Sciences

Chernogolovka, Moscow region, 142432 Russia

Shock-wave studies of dynamic yielding and fracture in single crystals and glasses open the way to get information about elementary mechanisms and kinetics of these processes. In the presentation, we summarize new and the earlier obtained results of investigations of behavior of metal single crystals (Al, Cu, Zn, Mg, and Cu+Si solid solution), sapphire and silicate glasses under shock wave loading. In the experiments with single crystals, we varied the load direction and the wave propagation distance. In the experiments with metals, we also varied the test temperature. The response of single crystals and glasses is compared with behavior of pure and commercial polycrystalline metals and ceramics.

The h.c.p. zinc and magnesium crystals demonstrate large anisotropy of the yield stress. Shock compression along the c-axis causes inelastic deformation by means of pyramidal slip and twinning and is associated with the largest value of the Hugoniot elastic limit (HEL). As a result of anomalously large compressibility of zinc in this direction, its plastic deformation is found to begin at a shock compression pressure above 15 GPa and is not accompanied by splitting of the shock wave into an elastic precursor and a plastic compression wave. The easiest basal slip was activated by shock loading along the inclined, off-axis direction and is associated with the smallest HEL value. The resolved shear stresses in basal slip planes at the HEL increase with the temperature. Deformation of h.c.p. crystals in pyramidal and prismatic slip systems, as well as the shock-wave deformation of f.c.c. crystals at high temperatures are associated with accelerating relaxation of stress which is an evidence of intense multiplication of dislocations. This phenomenon is also observed in pure polycrystalline f.c.c. metals at elevated temperatures but not in alloys or metals of commercial purity. The h.c.p. crystals demonstrate the largest spall strength at shock loading along the a-axis and the smallest one at shock loading in off-axis direction.

The measured HEL values of sapphire depend on peak shock stress and the direction of shock compression. The highest HEL values reaching 24 GPa have been recorded at the shock loading along c-axis and perpendicularly to it (c- and m-directions) whereas the shock compression along the s-direction is accompanied with the smallest heterogeneity of the deformation and the smallest rise time in plastic shock wave. The HEL of dense alumina ceramics is practically equal to the smallest HEL value of sapphire. Sapphire exhibits the highest spall strength at shock loading below the HEL but its resistance to spall fracture drops to zero when the plastic deformation begins. Unlike to hard brittle crystals, the spall strength of glasses is high after the shock compression both below and above the HEL. _______ Corresponding Author: Gennady I. Kanel, e-mail: kanel@ficp.ac.ru

27

INTERACTION OF STRONGLY NONLINEAR WAVES WITH INTERFACES

A. M. Tichler(1), L. Gomez(1), N. Upadhyaya(1), X. Campman(2),

V. F. Nesterenko(3), and V. Vitelli(1)

(1) Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, 2300 RA Leiden, The Netherlands

(2) Shell International E&P B.V., Kessler Park 1, 2288 GS, Rijswijk, The Netherlands

(3) Jacobs School of Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California, USA

The interaction of a solitary wave front with an interface formed by two strongly-nonlinear non-cohesive granular lattices (sonic vacuum) displays rich behavior, characterized by the breakdown of continuum equations of motion in the vicinity of the interface [1]. By treating the solitary wave as a quasiparticle with an effective mass, we construct an intuitive (energy and linear momentum conserving) discrete model to predict the train of solitary waves generated when an incident solitary wave front, parallel to the interface, moves from a denser to a lighter granular hexagonal lattice. Our findings are corroborated with numerical simulations. This model was extended to oblique interfaces, where the angle of refraction and refection of a solitary wave follows, below a critical value, an analogue of Snell's law, while a novel phenomenon of delayed refection is observed for post critical angle of incidence. In this granular analog of Snell's law, the solitary wave speed replaces the speed of sound, which is absent in the sonic vacuum. References [1] Vitali F. Nesterenko, Dynamics of Heterogeneous Materials, Springer-Verlag, 2001, New York, Chapter 1. _______ Corresponding Author: V. Vitelli e-mail: vitelli@lorentz.leidenuniv.nl

28

DYNAMIC BEHAVIOUR OF FINITE THICKNESS COHESIVE INTERFACES

M. Corrado(1) and M. Paggi

Politecnico di Torino, Department of Structural, Geotechnical and Building Engineering

Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Finite thickness interfaces are observed in material microstructures and in composites. In the former case, an example is the segregation of a distinct phase along the grain boundary of polycrystalline materials; in the latter, the finite thickness is associated to the presence of an adhesive layer bonding two different components. From the computational point of view, often these finite thickness regions are simply neglected. However, since their properties are responsible for material failure, suitable constitutive models should be defined, accounting for the finite thickness properties. In this communication, the features of the cohesive zone model (CZM) for finite thickness interfaces recently proposed in [1,2] are briefly reviewed. It is shown that the introduction of a damage variable dependent on the relative displacements evaluated at the boundary of the finite thickness region can effectively describe the nonlinear phenomena occurring inside the interfacial zone. Using this approach, a generalization of the bounds to the elastic properties of composite materials with imperfect (not perfectly bonded) interfaces has been proposed in [3].

As a development with respect to this research direction, the dynamic response of these heterogeneous systems under moderate or high strain rates is herein analysed and discussed in details. It is shown that the mass of finite thickness interfaces, a property not easy to define within an approach based on classical zero-thickness CZMs, can be properly evaluated in the framework of the present interface constitutive model. The role of the interface stiffness and mass on the dynamic response of the mechanical system is numerically investigated by performing ad hoc numerical tests, both on standard scheme, such as the double cantilever beam, and on more complex polycrystalline structures. As regards the solution strategy, comparisons between the classical explicit approach used in the case of high strain rates [4] and an implicit solution scheme (Newmark constant-average-acceleration method) are provided. Finally, the effects of a rate-dependent CZM on the dynamic response are also investigated [4]. References [1] Paggi M. and Wriggers P., A nonlocal cohesive zone model for finite thickness interfaces – Part I: mathematical formulation and validation with molecular dynamics, Computational Materials Science, 50, 1625-1633, 2011. [2] Paggi M. and Wriggers P., A nonlocal cohesive zone model for finite thickness interfaces – Part II: FE implementation and application to polycrystalline materials, Computational Materials Science, 50, 1634-1643, 2011. [3] Paggi M. and Wriggers P., Stiffness and strength of hierarchical polycrystalline materials with imperfect interfaces, Journal of the Mechanics and Physics of Solids, 60, 557-571, 2012. [4] Zhou F., Molinari J.F. and Shioya T., A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials, Engineering Fracture Mechanics, 72, 1383-1410, 2005. _______ Corresponding Author : Mauro Corrado e-mail: mauro.corrado@polito.it

29

FREQUENCY AND DISPERSION OF FLEXURAL WAVES IN FLUID-FILLED TUBES SUBJECT TO AXIAL IMPACT

K. Inaba(1) , K. Takahashi, and K. Kishimoto

(1) Tokyo Institute of Technology

2-12-1-I6-5 Ookayama, Meguro-ku, Tokyo 152-8550, JAPAN

The present study experimentally investigates flexural waves propagating through polycarbonate (PC) and steel tubes coupling with pressure waves in water. The flexural waves were initiated by the impact between the free-falling piston and the water filled in the vertical mounting tube. We measured hoop strain histories of flexural waves at several locations by strain gages (as shown in Fig. 1) and analyzed histories using the wavelet transform method. The wavelet power spectrum near the flexural wave fronts revealed that high frequency components around 4-6 kHz propagate at lower speed than the main disturbances. By tracing the dispersion curve from the time-frequency signal, it is revealed that the water hammer front have a dispersion tendency. Moreover, the measured frequencies with the PC tube indicated a reasonable agreement with the Skalak's theory [1, 2] in Fig. 2 while the steel tube showed lower frequencies than those in the theory.

Fig. 1 Hoop strain histories with PC tube. Fig. 2 Wave front frequencies with PC tube. (m strain = 0.1% strain) References [1] Skalak, R., An extension to the theory of water hammer, Transactions of the ASME, 78, 105–116, 1956. [2] Tijsseling, A. S., Lambert, M. F., Simpson, A. R., Stephens, M. L., Vitkowsky, J. P., and Bergant, A., Skalak’s extended theory of water hammer, Journal of Sound and Vibration, 310, 718–728, _______ Corresponding Author : Kazuaki Inaba e-mail: inaba@mech.titech.ac.jp

30

SHOCK-INDUCED PHASE TRANSITIONS IN THERMOELASTIC BARS: RIEMANN PROBLEMS AND APPLICATIONS

Cristian Făciu

”Simion Stoilow” Institute of Mathematics of the Romanian Academy, Research Unit No. 6, P.O. Box 1-764, RO-014700, Bucharest, Romania

The longitudinal impact of two shape memory alloy (SMA) bars has been proposed in [1] as an effective mean for investigating the propagation of phase transformation fronts. A traditional elastic approach based on an explicit three-wells Helmholtz free-energy potential, or equivalently, a non-monotone stress-strain relation, that describes a material capable of existing in three solid phases, the austenite phase (A) and two variants of martensite (M), has been used. In order to incorporate the important thermal effects due to the large amount of latent heat released or absorbed during a phase transformation we have considered in [2] a thermoelastic model for a SMA bar. This adiabatic thermodynamic framework, which permits the temperature to jump, leads to non-unique discontinuous solutions, even when the entropy inequality is satisfied. For such materials various admissibility criteria has been derived by introducing additional physical mechanisms. In [2], one has considered an augmented theory, which includes strain-rate and stress-rate effects, called Maxwellian rate-type effects, as dissipative mechanisms. We have established that the admissibility condition induced by the Maxwellian rate-type approach, coupled or not with Fourier heat conduction law is the chord criterion with respect to the Hugoniot locus in the strain-stress plane. In this paper, by using a piecewise linear thermoelastic model for a three phase SMA bar and the chord criterion one determines unique solutions to the complete set of Riemann step-data problems. These consist of shock waves, wave fans and phase boundaries. Next, one uses systematically our Riemann solvers to construct solutions for the longitudinal impact of two SMA bars for a variety of impact conditions. One explores the interaction between thermoelastic shock waves and phase boundaries. We found critical values of the impact velocity such that an impact-induced phase boundary continues to move forward after its interaction with an unloading elastic wave, or come to rest, or starts to move down the bar. We focus on the effect of these interactions on the variation of the particle velocity at the free-end of the target and on the temperature variation in the bar. References [1] Făciu, C., Molinari, A., On the longitudinal impact of two phase transforming bars. Elastic versus a rate-type approach. Part I: The elastic case. Part II: The rate-type case. Int. J. Solids Structures 43, 497–522 and 523–550, 2006. [2] Făciu, C., Molinari, A., The structure of shock and interphase layers for a heat conducting Maxwellian rate-type approach to solid-solid phase transitions. Part I: Thermodynamics and admissibility. Part II: Numerical study for a SMA model. Acta Mechanica, doi:10.1007/s00707-013-0847-9; doi: 10.1007/s00707-013-0846-x. ______ Corresponding Author : Cristian Făciu e-mail: Cristian.Faciu@imar.ro

31

PULSE SPLITTING, BENDING, AND COMBINING IN 2D AND 3D GRANULAR NETWORKS

A. Leonard(1,2), L. Ponson(3), and C. Daraio(1,2)

(1) California Institute of Technology, Graduate Aerospace Laboratories (GALCIT)

1200 E California Blvd, Pasadena CA 91125, USA (2) ETH-Zürich, Department of Mechanical and Process Engineering (D-MAVT)

Tannenstrasse 3, 8092 Zürich, Switzerland (3) Institut Jean le Rond d’Alembert (UMR 7190), CNRS - Université Pierre et Marie Curie, 75005

Paris, France

We study the dynamic force transmission through ordered networks of interconnected chains of particles. Figure 1 shows an experimental setup for both a 2D and 3D network. This work builds on the well-studied phenomenon of solitary wave propagation in 1D granular chains of particles1. The unique behaviour of the compact pulses, or solitary waves, traveling through the networks allows us to derive theoretical expression for the pulse splitting, bending, and combining, by modelling traveling pulses with effective particles

possessing identical momentum and kinetic energy1,2. Additionally, we use a discrete particle model to numerically simulate the nonlinear dynamic behaviour of each system for comparison with experiments and theoretical predictions. In the present study, a single branching angle was chosen for each system, 2D and 3D, to maximize the force transmission, while maintaining experimental feasibility. The experimental results are in good agreement with both numerical simulations and theoretical predictions based on the quasi-particle model. We observe an exponential decay in the leading pulse amplitudes, both with distance from the impact (with respect to branching level, N) and in the distribution of leading pulses perpendicular to the line of impact (at a given branching level, N). The rapid amplitude decay exhibited by these granular networks makes

them highly attractive for impact mitigation applications. Additionally, the observed exponential decay can be related to the dynamic load transfer along force chains in disordered granular media described in recent studies3. This work provides both insight into the behaviour of natural granular pilings and demonstrates the potential for controlling wave propagation pathways through material design.

References [1] Nesterenko, V. F., Dynamics of Heterogeneous Materials, Springer, USA (2001). [2] Job, S., Melo, F., Sokolow, A., Sen, S., Granular Matter 10, 13–20 (2007). [3] Owens, E. T., Daniels, K. E., Eur. Phys. Lett. 94, 54005 (2011). _______ Corresponding Author : Chiara Daraio e-mail: daraio@ethz.ch

Figure 1. Picture of 2D (Left) and 3D (Right) experimental setups for branching level N=2.

32

UNDERSTANDING THE IGNITION OF ENERGETIC MATERIALS UNDER DYNAMIC LOADING

A MULTISCALE THERMOMECHANICAL CHALLENGE

M. Biessy(1), J.-L. Brigolle(1), D. Picart(1), H. Trumel(1), J. Vial(1), P. Lambert(2), P. Bortoluzzi(3), A. Fanget(3) (1) CEA, DAM, Le Ripault, F-37260 MONTS, France

(2) Sciences et Applications Co., 218 bd Albert 1er, F-33000 BORDEAUX, France (3) CEA, DAM, Gramat, F-46500 GRAMAT, France

Energetic materials, i.e. explosives and solid propellants, have been used for ages. Yet, they remain poorly known in many respects. One of the most fascinating issues is the question of ignition, i.e. the production of a macroscopic flame, under dynamic, macroscopically adiabatic, loading. Chemical reaction in energetic materials is known to be a thermally activated process, such that ignition cannot be triggered but by some temperature increase. It is well known that the conditions for ignition correspond only to slight increases of macroscopic temperature. In other words, chemical processes are triggered by sub-macroscopic dissipative processes, usually called “hot-spots”. Although this concept was brought about more than half a century ago, the physical nature of hot spots remains unravelled. The present talk describes the effort undertaken by our team to contribute to a better understanding of the problem, restricted to elastomers filled with a (very) high amount of energetic crystals, and to mild dynamic loading (confining pressures up to a few hundred MPa, strain rates up to a few 104 s-1, and strains up to 1). Dynamic deformation occurs prior to ignition, associated dissipative heating acting as a trigger for chemical reaction. The materials at stake behave somewhat similarly to concrete-like materials, displaying especially a strong sensitivity to the state of stress, together with marked viscoelastic response. Depending upon the level of confining pressure, the material responds in a viscoelastic-damage and/or a (visco)-elasto-plastic like fashion. At present, it is felt that confining pressure is the paramount loading parameter. Therefore, specific developments were undertaken to characterize the behaviour under relatively high confining pressures, up to ~ 1 GPa, this including large strain (quasi-static) triaxial and confined Hopkinson bar (dynamic) experiments. Since ignition takes place at the sub-macroscopic level, we have endeavoured to determine the micro-mechanisms of deformation under a wide range of loading parameters. This has primarily been done through optical microscopy on post-mortem samples. The initial microstructure appears as a distribution of large crystals in a composite matrix made of small crystals and the rubbery binder. The analysis of post-mortem microstructures draws a rather complex picture, involving matrix irreversible deformation, grain-matrix de-bonding, and large crystals micro-cracking, plasticity and rotation. The relative importance of those elementary phenomena is triggered mainly by confining pressure and to a lesser extent by strain rate. The detailed effect of strain has not yet been examined closely. Besides, a limited set of quantitative analyses were performed. In the case of dynamic uniaxial straining, in particular, large crystals were found to have rotated without measurable plastic straining, indicating strong local irreversible motions of the matrix, probably involving small crystal friction. As said earlier, ignition is triggered at hottest locations. The latter should be randomly distributed in the case of quasi-homogeneous deformation, i.e. for stable behaviour. However, it is also likely to occur during unstable phases, i.e. when strain localization takes place. It is thus crucial to study the conditions _______ Corresponding Author: Hervé Trumel e-mail: herve.trumel @cea.fr

33

for strain localization. Some clues of both ignition processes were found. In homogeneously strained samples, including quasi-statically strained ones, indications of melting and/or of material outgassing could be observed. The same was found, together with recrystallization-like patterns, along localization (shear) bands, either due to local plastic strain gradients or to frictional slip of closed macro-crack lips. An effort was recently undertaken towards real-time spatially resolved optical observations coupled with mesoscopic finite element calculations. Despite numerous experimental difficulties, mostly due to confinement, it could be demonstrated that, for the range of loads investigated, the largest crystals undergo limited plastic strain but quite significant crystal rotations, together with strong matrix irreversible motions. This confirms previous findings on post-mortem samples and suggests ignition by small crystals friction in the matrix. The effort is being pushed towards larger confining pressures, strains rates and strains and towards the real-time study of the mechanisms of strain localization. Besides, post-mortem studies are going on, and will now focus on the study of samples recovered after interrupted experiments, in order to get detailed insights into the sequence of events taking place during deformation and/or ignition. _______ Corresponding Author: Hervé Trumel e-mail: herve.trumel @cea.fr

34

DYNAMIC PERFORATION OF THERMOVISCOPLASTIC PLATES BY RIGID PROJECTILES AND SHAPE EFFECTS

A. Rusinek1, M. Kpenyigba1, T. Jankowiak2, R. Pesci3

1National Engineering School of Metz, Laboratory of Mechanics, Biomechanics, Polymers and structures, 1 route d'Ars Laquenexy cs65820 57078 Metz cedex 3, France 2Institute of Structural Engineering, Poznan University of Technology, Piotrowo 5, Poznan, Poland 3LEM3 UMR CNRS 7239, ENSAM-Arts et Métiers ParisTech CER of Metz, 4 rue Augustin Fresnel 57078 Metz cedex 3, France

Keywords: Experiments, Perforation, Ballistic, Numerical models, Dynamic failure.

The paper studies the influence of projectile nose shape on the perforation of thin steel sheets. Experimental, analytical and numerical investigations have been carried out to analyze in details the perforation process. The projectiles have conical, blunt and hemispherical tipped noses; additional test results are also reported for six different angles to analyze their effect on the process of perforation. All the projectiles are 13mm in diameter and the plates are 1 mm thick. Moreover, the mass ratio (projectile mass/steel sheet mass) is assumed constant and equal to 0.38. A wide range of impact velocities from 35 to 180 m/s has been covered during the tests. The deformation, failure mode and the ballistic curve of all projectile nose shapes were obtained through experiments and reproduced through simulation using Abaqus/Explicit finite element code. Different failure modes have been observed, including petaling, plug ejection and circumference necking. The complete energy balance is also reported and the absorbed energy by the steel sheets has been obtained by measuring initial and residual projectile velocities. A more detailed study on the effect of the vertex angle of conical shape projectile on the process of perforation has been made. A decrease of the number of petals with the nose angle is observed. An analytical model for the number of petals prediction proposed by Atkins et al. [1] has been used.

References [1] Atkins A. G., Afzal Khan M., M. Liu J. H, Necking and radial cracking around perforations in thin sheets at normal incidence, International Journal of Impact Engineering, 1998, 21(7), 521-539. _______ Corresponding Author : A. Rusinek e-mail: rusinek@enim.fr

35

THE SECRET LIVES OF TWINS

K.T. Ramesh, N. Dixit and N. Daphalapurkar

Hopkins Extreme Materials Institute Johns Hopkins University

3400 North Charles St. Baltimore, MD 21218, USA

We examine the dynamics of twin boundaries in metallic materials using a combination of fundamental experiments, theoretical modeling and focused molecular dynamics and crystal plasticity simulations. Three basic crystal structures are considered: face-centered-cubic (aluminum, copper and nickel), body-centered-cubic (tantalum) and hexagonal-close-packed (magnesium). The experimental methods used include high-strain-rate and wave propagation experiments in Kolsky bars and plate impact, coupled with microscale characterization of recovered samples using EBSD and TEM. These methods are used to obtain estimates of twin boundary velocities and twin growth rates as a function of the applied stress under multiaxial stress states. Computational estimates of twin boundary kinetics are then derived from molecular dynamics simulations, and these estimates are compared to the experimental measures and to theoretical limits based on assumed twin growth mechanisms. Finally, the implications of the measured boundary velocities are considered for some extreme dynamic loading conditions. _______ Corresponding Author : K.T. Ramesh e-mail: ramesh@jhu.edu

36

RATE SENSITIVITY ACCORDING TO DISCRETE DISLOCATION PLASTICITY

P.K. Agnihotri and E. Van der Giessen (1)

(1) Zernike Institute for Advanced Materials, University of Groningen

Nijenborgh 4, 9747AG Groningen, the Netherlands

Discrete dislocation plasticity (DDP) has evolved into a mature paradigm in the multiscale modeling of plasticity. As it naturally addresses phenomena occuring at length scales in between atomistics and continuum plasticity, it has proved capable of resolving a number of issues that are outside the range of applicability of these two traditional methods. As time and length scales are typically coupled, DDP operates in an intermediate regime of strain rates. But, does it capture the correct kinetics of plasticity? In this paper, we address this question by performing two-dimensional DDP simulations based on the usual simple constitutive rules for glide and dislocation nucleation [1, 2]. These rules endow the model with only two time scales, yet we will demonstrate that quite realistic values of the strain rate sensitivity parameter emerge as the consequence of the collective dynamics of dislocations. The origin of minor discrepancies will be discussed as well as the effect of obstacles that obstruct the motion of dislocations. References [1] Van der Giessen, E. and Needleman, A., Discrete Dislocation Plasticity: A Simple Planar Model, Mod. Simul. Mat. Sci. Engrg. 3 (1995) 689-735. [2] Shishvan, S.S. and Van der Giessen, E., Distribution of dislocation source length and the size dependent yield strength in freestanding thin films, J. Mech. Phys. Solids. 58 (2010) 678-695. _______ Corresponding Author : Prabhat Agnihotri e-mail: P.K.Agnihotri@rug.nl

37

DISLOCATIONS IN PRESTRESSED DUCTILE MATERIALS

L. Argani(1), D. Bigoni(1)and G. Mishuris(2)

(1) Department of Civil, Environmental & Mechanical Engineering, University of Trento, via Mesiano 77, Trento, Italy

(2) Institute of Mathematical and Physical Sciences, University of Wales, Aberystwyth, UK

The effect of prestress on dislocation (and inclusion) fields in nonlinear elastic solids is analysed by extending previous solutions by Eshelby and Willis [1-4], via a methodology based on results obtained by Bigoni and Capuani [5-7]. Employing a plane strain constitutive model (for incompressible incremental nonlinear elasticity) to describe the behaviour of ductile metals (the J2–deformation theory of plasticity [8]), we show that when the level of prestress is high enough that shear band formation is approached, strongly localized strain patterns emerge, when a dislocation dipole is emitted by a source. These may explain cascade activation of dislocation clustering along slip band directions. References [1] Eshelby, J. D. (1956) The Continuum Theory of Lattice Defects, Solid State Phys. 3, 79-144. [2] Eshelby, J. D. (1957) The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems, Proc. R. Soc. London, Ser. A, Mathematical and Physical Sciences, 241, 376-396. [3] Eshelby, J. D. (1966) A simple derivation of the elastic field of an edge dislocation, British Journal of Applied Physics (B.J.A.P.), 17, 1131-1135. [4] Willis, J. R. (1965) Dislocations and inclusions, Pergamon Press Ltd., J. Mech. Phys. Solids, 13, 377-395. [5] Bigoni, D., Capuani, D. (2002) Green’s function for incremental nonlinear elasticity: shear bands and boundary integral formulation, J. Mech. Phys. Solids, 50, 471-500. [6] Bigoni, D., Capuani, D., Bonetti, P., Colli, S. (2007) A novel boundary element approach to time-harmonic dynamics of incremental non-linear elasticity: the role of pre-stress on structural vibrations and dynamic shear banding. Comp. Meth. Appl. Mech. Eng. 196, 4222-4249. [7] Bigoni, D., Dal Corso, F. (2008) The unrestrainable growth of a shear band in a prestressed material, Proc. Royal Soc. A, 464, 2365-2390. [8] Hutchinson, J, W., Neale, K. W. (1979) Finite strain J2-deformation theory. In: Carlson, D. E., Shield, R.T.(eds), Proc. IUTAM Symp. on Finite Elasticity, Martinus Nijhoff, The Hague-Boston-London, 237-247. _______ (2) Corresponding Author : Davide Bigoni e-mail: bigoni@ing.unitn.it

38

DEFORMATION AND FAILURE OF METALS SUBJECTED TO LASER SHOCK LOADING

M. A. Meyers1, C. H. Lu1, T. Remington1 , B. Kad1, Y. Tang1, B. A. Remington2, B. R. Maddox2, H. S. Park2, E. M. Bringa3, and C. Ruestes3

1 University of California, San Diego, La Jolla, CA, 92093, USA 2 Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA

3U. Nacional de Cuyo, Mendoza, Argentina The principal results of a fifteen-year program on the effects of high amplitude ( up to 150 GPa) short duration (1-10 ns) pulsed lasers are reviewed with emphasis on the fundamental deformation and failure mechanisms. Two principal lasers were used: The Laboratory for Laser Energetics at the U. of Rochester (Omega facility) and the Jupiter Laser Facility (Janus) at LLNL [1]. These laser pulses were applied to the FCC metals copper, Cu-Al, and nickel [2] and to BCC tantalum [3, 4]. Monocrystalline, polycrystalline, and nanocrystalline specimens were compressed and remarkable differences in the defect structure were found under different conditions. The incidence of dislocations, stacking faults, twins, and phase transformations is documented and shown to be determined by material and shock wave parameters. For copper and nickel, both experiments and molecular dynamics simulations show the formation of partial dislocations with stacking faults at lower pressures, transitioning to cells and then to mechanical twins. The predictions of a homogeneous dislocation generation model match the MD simulations in the loaded state very well. The density of dislocations predicted by molecular dynamics decreases abruptly upon unloading and reaches levels close to those experimentally observed by transmission electron microscopy. For tantalum (model BCC), the observed dislocation density is much lower and MD simulations do not match results successfully. A threshold pressure for the onset of twinning is measured experimentally and calculated for both FCC and BCC metals and is strongly dependent on grain size increasing with decreasing grain size. For Cu-Al, it also shows a significant stacking-fault energy dependency. The failure of these metals by spalling was also investigated experimentally [5], analytically [6], and computationally [7]. The spall stress in laser pulse loading was found to be much higher than in gas-gun loading because of the much lower duration of the pulse, void/crack nucleation and growth being time dependent phenomena. The strong effect of grain boundaries on the spall failure was confirmed in the nanosecond regime: in polycrystalline V and Ta the grain boundaries play an important role by being nucleation sites for voids. Acknowledgement : Research funded by LLNL, UC Labs, and DOE/NSAA. References [1] Meyers MA, Jarmakani H, Remington BR, Bringa EM, Dislocations in Shock Compression and Release, in "Dislocations in Solids," ed. J.P. Hirth, Elsevier, Vol. 15, pp. 95-196, Chapter 89, 2009. _______ Corresponding Author : Marc Meyers e-mail: mameyers@ucsd.edu

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[2]Jarmakani HN, Bringa EM, Erhart P, Remington BA, Wang YM, Vo NQ, Meyers MA. Acta Mater 2008; 56:5584. [3]Lu CH, Remington BA, Maddox BR, Kad B, Park HS, Prisbrey ST, and Meyers MA. Acta Mater 2012; 60:6601. [4]Lu CH, Remington BA, Maddox BR, Kad B, Park HS, Kawasaki M, Langdon TG, Meyers MA, Acta Mater submitted, 2013. [5]Jamakani H, Maddox BR, Wei CT, Kalantar D, Koniges A, Eder D, and Meyers MA. Acta Mater 2010; 58:4604. [6]Tang Y, Bringa EM, Meyers MA, Acta Mater 2012; 60: 4856-4865. [7]Tang Y, Bringa EM, Remington BA, Meyers MA, Acta Mater 2011; 59:1354. _______ Corresponding Author : Marc Meyers e-mail: mameyers@ucsd.edu

40

CONSTITUTIVE BEHAVIOR OF POROUS DUCTILE MATERIALS ACCOUNTING FOR MICRO-INERTIA AND VOID SHAPE

C. Sartori1, S. Mercier1, N. Jacques 2, A. Molinari 1

1 Université de Lorraine, LEM3, UMR CNRS, Ile du Saulcy, 57045 Metz cedex 01, France 2 ENSTA Bretagne, LBMS, 2 rue François Verny, 29806 Brest cedex 9, France

From various works of the literature, it is clear that the fracture of ductile materials may involve inertial effects when dynamic loading is considered. In addition, fracture may occur under loading with different stress triaxiality. As a consequence, it is worth a constitutive behaviour which integrates both effects of local inertia and void shape, which is the goal of the present work.

We develop a multi-scale model for the behaviour of porous ductile materials. Based on the work of Molinari and Mercier [1], the macroscopic stress is decomposed as the sum of quasistatic and dynamic parts. The quasistatic component can be derived from usual homogenization approaches neglecting the role of inertia at the microscale. In [1], the dynamic part has been evaluated and a closed form expression was obtained for spherical voids.

In the present work, the results obtained in [1] are extended by integrating the void shape effect. A Representative Volume Element (RVE) containing a prolate void is considered. The RVE is subject to homogeneous velocity applied at the remote boundary. Axisymetric loading is investigated and the orientation of the void is assumed to be aligned with principal axes of the loading. Based on the velocity field proposed by Gologanu et al [2] for prolate voids, an analytical expression for the dynamic part of the macroscopic stress is found. This micro-inertia term is related to the macroscopic strain rate and its time derivative and to the void shape.

To validate the modelling, finite element calculations have been performed. A unit cell containing a prolate void is defined. It is found that the shape of the dynamic yield surface is correctly predicted by the averaging model. Microscale inertia enhances the size of the yield surface, especially for high triaxiality. The yield surface appears as the results of the combination of microscale inertia effects with void shape effects, the latter being also of primary importance at large triaxiality.

References [1] Molinari A., Mercier S., Micromechanical modelling of porous materials under dynamic loading, Journal of the Mechanics and Physics of Solids 49, 1497-1516, 2001 [2] Gologanu M., Leblond J., Devaux J., Approximate models for ductile metals containing non-spherical voids - Case of axisymmetric prolate ellipsoidal cavities, Journal of the Mechanics and Physics of Solids 41, 1723-1754, 1993, _______ Corresponding Author : Sebastien Mercier e-mail: sebastien.mercier@univ-lorraine.fr

41

EVIDENCES OF MATERIAL STRENGHTENING AT VERY HIGH STRAIN RATES – PLASTIC DEFORMATION OF EXPLOSIVLY FORMED PROJECTILES – CHARPY ENERGY

AT HIGH IMPACT VELOCITIES

H. Couque

Nexter Munitions, 7 route de Guerry,18023 Bourges, France

The analysis of the plastic deformation and failures occurring at significant impact velocities (0,01 to 100 m/s) is discussed based on the stress strain rate dependences encountered with strain rates varying from 100-100000 s-1. When dealing with low impact velocities (0,01 to 10 m/s), the thermally activity dependence of the motion of the dislocations implies a linear dependence between the yield strength and the logarithm of the strain rate. When the overall strain rate is less than about 1000 s-1, like in crashworthiness studies, it is sufficient to take in account this thermally activated dependence. For higher impact velocities (10-150 m/s), it is key to take in account the viscous drag behaviour of the dislocations occurring at strain rates greater than 1000 s-1 resulting in a drastic increase of the material yield strength, described with an exponential dependence of the yield strength with the strain rate. Such requirement is based on a study of the author dealing with the numerical simulation of explosively formed projectiles (EFP) [1]. When this strengthening is not taken in account, the plastic deformation of the associated liner is not stabilized, resulting in stretch projectile in length several times the real length. In this study, Steinberg’s argument which stipulates that at a given strain rate all effect of strain rate have saturated and the material strength becomes independent of strain rates, identified at a threshold yield strength, has been considered. In fact, numerical simulations taking in account the exponential dependence of the yield strength with the strain rate without a threshold yield strength provide stiff liners. The use of a threshold yield strength favours the plastic deformation when the given strain rate is reached, resulting in a projectile shape close to the reality. Another experience of the author is with the unusual result of a tungsten alloy kinetic projectile which has impacted the ground at 1000 m/s resulting in an unbroken projectile with a S shape. How come such an alloy recognized to have a low notch Charpy energy did not fail under such severe loading conditions? An investigation was undertaken, looking into the flexural strength as a function of the impact velocity for a selection of metals including a series of tungsten alloys and a stainless steel [2]. High Charpy energies of unnotched and notched specimens were recorded up 1000 Joule/cm2 using a technique involving a striker launched at velocities ranging from 10 to 150 m/s against a Charpy like specimen placed against two Hopkinson pressure bars. Numerical simulations reveal that the loading conditions are in the regime where the viscous drag behaviour of the dislocations prevailed. The associated strengthening along with the analysis of fractographs of the failed Charpy specimens provides an interpretation of the increase of the Charpy energy with the increase of the impact velocity.

References [1] Couque H. and Boulanger R., “EFP Simulations with Johnson-Cook Models", 23rd International Symposium on Ballistic, Edited by F. Gálvez F. & Sánchez-Gálvez V., 255, 2007. [2] Couque H., “The influence of the dynamic loading rate on tensile failure properties of metallic materials”, Conf. DYMAT 2012, The European Physic Journal - Web of Conf., Editions de Physique, 02012-1,2012 _______ Corresponding Author : Hervé Couque h.couque@nexter-group.fr .

42

HIGH STRAIN RATE RESPONSE OF AN ELASTOMER AT HIGH PRESSURE

R. Clifton(1) and T. Jiao

School of Engineering, Brown University Providence, RI 02912 USA

Pressure-shear plate impact (PSPI) experiments have been conducted to study the mechanical response of an elastomer (polyurea – a block co-polymer) at high pressures (up to 9GPa) and high strain rates:

5 6 110 10 s−− . Samples with thicknesses in the range 100 μm - 400 μm are sandwiched between two tungsten carbide (WC) plates. Compressive and shear deformations up to 30% are obtained. The previously determined isentrope has been extended to 9 GPa. At pressures of 9 GPa, the high-strain-rate shearing resistance of polyurea is approximately 500 MPa ― comparable to, or greater than, that of high strength steels. Consequently, its strength-to-weight ratio at high pressures and high strain rates is exceptionally favorable. It was also found that, after dynamic loading to high pressures, polyurea exhibits surprising extension before the longitudinal compressive stress is reduced to zero. Various explanations are being considered and will be discussed – including the possibility that the large deformations induced in these experiments cause the microstructure of the elastomer to become quite inhomogeneous. A new symmetric pressure-shear plate impact (SPSPI) configuration has been developed in order to enable the direct measurement of the thickness-averaged nominal strain rates of the sample ― as well as the tractions on both of its interfaces with the bounding linear elastic plates. This enhancement of the information obtainable from SPSPI experiments is made possible by using a symmetric configuration for which the velocity of the mid-plane of the sample is known from symmetry to be one-half of the impact velocity. Thin (e.g. 70μm thick) layers of polyurea are cast onto the impact faces of both a WC flyer plate and a WC anvil plate. A diffraction grating is copied onto the rear surface of the anvil plate to enable the interferometric measurement of both normal and transverse components of the rear-surface velocity. One-dimensional elastic wave theory is used to obtain tractions and particle velocities at the sample/anvil interface from the measured rear-surface velocities. From symmetry, the tractions and particle velocities at the flyer/sample interface are obtained as well. In this way, nominal strain-rate histories are obtained for both longitudinal and shear strains. Integration of these strain rates, and use of the measured traction histories, provides dynamic stress-strain curves that provide insight for developing constitutive models for elastomers at the high strain rates and pressures of these experiments. Acknowledgement This research was supported by the US Office of Naval Research. _______ Corresponding Author : Rodney Clifton e-mail: Rodney_Clifton@brown.edu

43

THE DYNAMIC PERFORMANCE OF ULTRA HIGH MOLECULAR WEIGHT POLYETHEYLENE FIBRE COMPOSITES

J.P. Attwood(1), Karthikeyan K.(1) and V.S. Deshpande(1)

(1) Cambridge University Department of Engineering, Trumpington Street, Cambridge, CB2 1PZ, UK.

Fibre composites comprising Ultra High Molecular Weight Polyethylene (UHMWPE) fibres in a polyurethane or polyethylene matrix are now extensively used for ballistic protection applications. This interest arises from a recognition that the ballistic limit of fibre composites scales linearly with the so-

called Cunniff [1] velocity c* given by c* =σ f ε f

2ρ f

Ef

ρ f

⎛

⎝⎜⎜

⎞

⎠⎟⎟

1/3

where σ f and ε f are tensile failure

strength and strain of the fibres, respectively while Ef is the tensile modulus of the fibres and ρ f is the

density of the fibres. Based on this parameter the UHMWPE fibres outperform most known materials. Typically the Cunniff parameter is rationalized using the Phoenix and Porwal [2] membrane stretching model. A detailed experimental investigation to understand the failure and penetration mechanisms the UHMWPE composites reveals some gaps in our understanding, viz: (i) the ballistic performance of fibre based composites and strongly dependent on the shear strength of matrix and (ii) penetration of low shear strength composites like the UHMWPE composites does not occur in a membrane mode but rather in progressive manner, such that the number of failed plies increases with increasing impact velocity. Penetration experiments reveal that progressive failure under the projectile occurs by an indirect tension mechanism due to the extreme anisotropy and the strongly pressure dependent shear strength of the UHMWPE composites. We present a ply-by-ply based model for this indirect tension mechanism and demonstrate its validity by comparing predictions and measurements of the static compressive and indentation response of UHMWPE composites. Intriguingly, these static measurements are shown to predict the dynamic penetration responses to a high level of accuracy as the failure mechanisms under static and dynamic loading conditions are identical. We conclude by discussing the challenges in developing predictive homogenised models for such composites wherein each ply is not discretely modelled. References [1] Cunniff PM. Dimensionless parameters for optimization of textile-based body armor systems, In: Reinecke WG, editor. Proceedings of the 18th International Symposium on Ballistics, San Antonio, TX. Lancaster: Technomic,1999 p.1303-1310. [2] Phoenix SL, Porwal PK. A new membrane model for the ballistic impact response and V50 performance of multi-ply fibrous systems. Int J Solids Struct 2003;40:6723-65. _______ Corresponding Author : Vikram Deshpande e-mail: vsd@eng.cam.ac.uk

44

DYNAMIC BEHAVIOR OF POLYMERS AND POLYMER NANOCOMPOSITES: MODELING AND SIMULATIONS

Saïd Ahzi

ICube Laboratory, University of Strasbourg / CNRS, 2 Rue Boussingault, 67000 Strasbourg, France In this presentation, we will address some of the new developments in the micromechanical modeling and simulation of the thermomechanical behavior of polymers and polymer nanocomposites. For this, different polymer matrices unfilled or filled with different nanofillers such as clay nanoparticles are considered. We will particularly address the effect of temperature and strain rate on the elastic and yield behavior. For this, quasi-static and dynamic loadings are considered along with test temperatures ranging from well below to above the glass transition. For the semi-crystalline matrices and for the nanocomposites, we will address different homogenization techniques used to compute the effective elastic properties and yield behavior under a wide range of temperatures and strain rates. While our focus will be on the dynamic behavior, our developed models are valid under a wide range of temperatures and strain rates. The obtained results will be discussed as function of the microstructure such as the crystallinity of the matrix, the distribution of the nanofillers in the polymer matrix and the shape effects of these fillers. We will also confront the predicted results to our experimentally measured ones. References J. Richeton, S. Ahzi, L. Daridon and Y. Rémond, “A Formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperature”, Polymer, Vol. 46 (16), pp. 6035-6043, 2005. J. Richeton, G. Schlatter, K. Vecchio, Y. Remond and S. Ahzi, “A unified model for stiffness modulus of amorphous polymers across transition temperatures and strain rates”, Polymer, Vol. 46, pp. 8194-8201, 2005. J. Richeton, S. Ahzi, K. S. Vecchio, F. Jiang and R. R. Adharapurapu, “Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: characterization and modeling of the compressive yield stress”, International Journal of Solids and Structures, Vol. 43, Issue 7-8, pp. 2318-2335, 2006. J. Richeton S. Ahzi and K.S. Vecchio, F.C. Jiang and A. Makradi, “Modeling and Validation of the Large Deformation Inelastic Response of Amorphous Polymers over a Wide range of Temperature and Strain Rates”. International Journal of Solids and Structure, Vol. 44, N. 24, pp. 7938-7954, 2007 J. Richeton, S. Ahzi and L. Daridon, “Thermodynamic investigation of yield stress models for amorphous polymers”, Philosophical Magazine, Vol. 87, No. 24, pp. 3629-3643, 2007. R. Matadi Boumbimba, K. Wang, N. Bahlouli, S. Ahzi, Y. Rémond, F. Addiego, “Experimental investigation and Micromechanical Modelling of high strain rate compressive yield stress of a melt mixing polypropylene/organoclay nanocomposite”; Mechanics of Materials, Vol. 52, pp. 58-68, 2012. K. Wang, Ahzi, R. Matadi Boumbimba, N. Bahlouli, F. Addiego, Y. Rémond; “Micromechanical modeling of elastic behavior of a polypropylene based organoclay nanocomposites under a wide range of temperatures and strain rates/frequencies”; Mechanics of Materials, in press 201. _______ Corresponding Author : Said Ahzi ahzi@unistra.fr

45

DYNAMIC STABILITY OF TRANSIENT STATES IN STRUCTURES SUBJECTED TO HIGH STRAIN RATE

T. Putelat (1), K. Ravi-Chandar (1), (2) and N. Triantafyllidis (1), (3), (4)

(1)Laboratoire de Mecanique des Solides, C.N.R.S. UMR7649, Ecole Polytechnique, Palaiseau 91128, FRANCE

(2)Aerospace Engineering & Engineering Mechanics Department, The University of Texas, Austin, TX 78712 0235 USA

(3)Departement de Mecanique, Ecole Polytechnique, Palaiseau 91128, FRANCE (4)Aerospace Engineering Department & Mechanical Engineering Department (emeritus)

The University of Michigan, Ann Arbor, MI 48109-2140 USA

Of interest here is the influence of loading rate on the stability of structures where inertia is taken into account. This is an important research area that has attracted considerable attention for the last few decades. The approach that is currently used in the literature to analyze these stability problems, is the method of modal analysis that determines the structure’s fastest growing wavelength, which is meaningful only for cases where the velocity of the perfect structure is significantly lower than the associated characteristic wave propagation speeds. The novel idea here is to analyze the time-dependent response to initial imperfections or to perturbations of the transient (high strain rates) states of these structures, in order to understand the initiation of the corresponding failure mechanisms. We are particularly motivated by recent experimental studies [1], [2] on the high strain rate extension and compression of thin rings that show no evidence of a dominant wavelength in their failure mode and no influence of strain-rate sensitivity on the failure strains. In the interest of analytical tractability, for the case of tension we study the high strain extension of an incompressible nonlinearly elastic bar and for the case of compression we study an elastic ring subjected to external hydrostatic pressure, which is applied at different rates ε. The stability of these structures is studied by following the evolution of localized small perturbations introduced at different times t0. It is shown that for large values of the applied loading rate these structures fail by a localized mode of deformation and that the failure pattern is dictated by the distribution of defects and has no dominant wavelength mode, exactly as observed experimentally. References [1] Zhang, H. and Ravi-Chandar, K. (2006). On the dynamics of necking and fragmentation – I. real-time and post-mortem observations in al 6061-O. International Journal of Fracture, 142:183–217. [2] Mainy, A. (2012). Dynamic buckling of thin metallic rings under external pressure. Master’s thesis, University of Texas. _______ Corresponding Author : Nicolas Triantafyllidis e-mail: nick@lms.polytechnique.fr

46

ANALYSIS OF ADIABATIC SHEAR BANDING IN MACHINING

X. Soldani(1), A. Molinari(2), J. Díaz(1), H. Miguélez(1)

(1) Department of Mechanical Engineering, Universidad Carlos III de Madrid Avda. Universidad 30, 28911, Leganés, Madrid

(2) Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux, LEM3, Labex Damas Université de Lorraine

Ile du Saulcy, 57045, Metz cedex, France

This work is focused on the analysis of adiabatic shear banding in orthogonal cutting of Ti6Al4V alloy. Segmented chip results from adiabatic shear banding, depending on the competition of thermal softening and strain and strain rate hardening. The role of cutting conditions on adiabatic shear banding and chip serration is investigated by combining finite element calculations (fig. 1) and analytical modelling. Also the role of friction at the interface chip-tool and the effect of rheological parameters of the constitutive equation are analyzed. Experimental tests from the literature are used as a reference to validate the models [1,2]. The mechanism of plastic flow localization is analyzed in terms of shear band spacing, shear band width, frequency of segmentation and cutting forces. This leads to the characterization and classification of different regimes of shear banding and the determination of scaling laws which involve dimensionless parameters representative of thermal and inertia effects. The analysis gives new insights into the physical aspects of plastic flow instability in chip formation.

Figure 1: Evolution of chip morphology of Ti alloy with the cutting speed V, equivalent plastic strain level

contours are shown.

References [1] Molinari, A., Musquar, C., Sutter, G., 2002. Adiabatic shear banding in high speed machining of Ti–6Al–4V experiments and Modeling, Int. J. Plast. 18, 443–459 [2] Cotterell, M., Byrne, G., 2008b. Characterization of chip formation during orthogonal cutting of titanium alloy Ti–6Al–4V, CIRP Ann-Manuf. Technol. 81–85 _______ Corresponding Author : Xavier Soldani xsoldani@ing.uc3m.es

47

INSTABILITIES IN DYNAMIC FRACTURE

E. Bouchbinder(1)

(1) Weizmann Institute of Science, Rehovot 76100, Israel

Rapidly propagating cracks are known to undergo a variety of dynamic instabilities. While some of these bear similarities to other rather well-understood instabilities is condensed matter physics, e.g. side-branching in dendritic crystal growth,  as of yet we have no comparable understanding of dynamic fracture instabilities. In this talk I will briefly review the experimental observation of various crack instabilities and explain the origin of the difficulties involved. I will then discuss recent progress in understanding some of these instabilities: the “Weakly nonlinear theory of dynamic fracture” and its relation to the oscillatory crack instability in 2D and crack front corrugation instability in 3D. Open challenges will be briefly discussed.

_______ Corresponding Author : Eran Bouchbinder e-mail: eran.bouchbinder@weizmann.ac.il

48

ATOMISTIC MECHANISMS OF DYNAMIC STRAIN AGING AND THEIR IMPACT ON DUCTILITY IN AL-MG

W. A. Curtin

Ecole Polytechnique Federale de Lausanne

EPFL-STI-IGM-LAMMM, Station 9, 1015 Lausanne, Switzerland Low ductility in Al alloys is a major barrier to their replacement of steels in automotive and other applications where failure by localization limits component design. Low ductility in Al-Mg alloys has long been associated with Dynamic Strain Aging (DSA) – the material is stronger at lower strain rates, which encourages localization and instabilities. Phenomenological models qualitatively predict Portevin-LeChatelier bands and other DSA effects but quantitative predictions with mechanistic constitutive models have remained elusive. Here, we present a model that uses a hierarchical multiscale approach to relate atoms to ductility. The four components of the model are:

(1) discovery of a new atomic-scale mechanism of cross-core diffusion, in which only solutes on the atomic plane on one side of the dislocation core migrate to the atomic plane on the other side of the core [1];

(2) recognition that the cross-core diffusion mechanism operates on forest dislocations, leading to strengthening of forest dislocation junctions at the mesoscale [2];

(3) development of a full thermokinetic model for the evolution of the plastic strain versus stress and time, leading the time/rate/temperature-dependent flow behavior of the material [e];

(4) reformulation of the thermokinetic model into a macroscopic constitutive model which can be implemented in standard explicit finite-element codes. The model quantitatively explains the entire scope of steady-state flow behavior as a function of strain-rate, plastic strain, temperature, and alloy composition, in Al-Mg alloys, with only one parameter for the evolution of forest hardening [2]. The continuum model predicts that the ductility of Al-Mg alloys is reduced in an intermediate range of temperature and/or strain rate, in very good agreement with experimental studies [4]. The ductility reduction is thus tied directly to atomistic features of the material behavior, with essentially no adjustable parameters. Together with a new first-principles model for the strain-rate and temperature-dependent solute strengthening [5], we are now designing new formable Al alloys to solve the low-ductility problem and enable the use of Al alloys in a broader suite of automotive and other applications. References [1]. W.A. Curtin, D.J. Olmsted, and L.G. Hector Jr., Nature Matls 5, 875-880 (2006) [2]. M. Soare and W.A. Curtin, 2008. Acta Materialia 56, 4046-4061 (2008)

[3]. F. Zhang, A. Bower, and W.A. Curtin, Int. J. Num. Methods Eng. (2010) [4]. S. S. Chakravarthy, A. Bower, W.A. Curtin, S. Keralavarma, unpublished. [5]. G. Leyson, W. A. Curtin, L.G. Hector, C. Woodward, Nature Matls 9, 750-755 (2010) _______ Corresponding Author : William Curtin e-mail: william.curtin@epfl.ch

49

HIGH-PRESSURE HUGONIOT MEASUREMENTS USING MACH REFLECTIONS

J.L. Brown and G. Ravichandran

California Institute of Technology

Pasadena, CA 91125, USA

It has long been recognized that high pressure equation of state (Hugoniot) measurements in solids can be determined by subjecting the material to a one dimensional plane shock wave. Shock waves of this type are usually generated by the planar impact of two flat plates and, as a result, the shock amplitude is inherently limited by the velocity of the impacting plate. In an effort to dramatically increase the range of pressures which can be studied with available impact velocities, a new experimental technique has been developed [1]. A target consisting of two concentric cylinders aligned with the axial direction parallel to the loading is subjected to planar impact. The target is designed such that upon initial impact, the outer cylinder will have a higher shock velocity than the inner material of interest. Conically converging shocks are generated at the interface between the two materials due to the impedance mismatch. Upon convergence, an irregular reflection occurs and the conical analog of a Mach reflection develops and grows until it reaches a steady state. The resulting high pressure Hugoniot state behind the Mach stem is measured using velocity interferometry (VISAR). The new technique is demonstrated using planar mechanical impact generated by a powder gun to study the shock response of copper. Two systems are examined which utilize either a low impedance (6061-T6 aluminum) or a high impedance (molybdenum) outer cylinder. The results from the experiments are presented and compared to both numerical simulations and a hydrodynamic model based on shock polars which is used in solving gas dynamics problems. The feasibility of measuring an entire Hugoniot curve in a single experiment using full field velocity interferometry (ORVIS) is discussed, and initial experimental results are presented. References [1] Brown, J. L., Ravichandran, G., Reinhart, W. D., Trott, W. M., High pressure Hugoniot measurements

using converging shocks, Journal of Applied Physics, 109, DOI: 10.1063/1.3590140, 2011. _______ Corresponding Author : Guruswami Ravichandran e-mail: ravi@caltech.edu

50

NUMERICAL IMPLEMENTATION AND APPLICATION OF A MODEL FOR PLASTIC

POROUS MATERIALS INCORPORATING VOID SHAPE EFFECTS

J.B. Leblond and L. Morin

UPMC Univ Paris 6 and CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France

Madou and Leblond [1,2] recently proposed a model for porous ductile solids containing arbitrary ellipsoidal voids. This model stands as an extension of the so-called GLD model [3] for spheroidal voids, which itself extended Gurson’s classical model [4] for spherical ones. This work describes the numerical implementation of Madou and Leblond’s model into some finite element code and some preliminary applications. The major feature of the numerical implementation is an algorithm for the “projection” of the elastic predictor (elastically computed stress tensor) onto the yield locus. The algorithm is based on an implicit (backward) Euler scheme ensuring existence and uniqueness of the solution. The problem is reduced to solving a system of only two nonlinear equations on two unknowns. The first applications envisaged pertain to the behaviour of a single homogeneous element subjected to various loading conditions. Special attention is paid to situations involving an initially ellipsoidal but non-spheroidal void and/or an overall stress state not diagonal in the principal axes of this void. The numerical results suggest a simple enhancement of the model incorporating the possible contact of the void’s boundary with the enclosed inclusion, or the closure of the void in a certain direction. Such effects are bound to be important under conditions of low triaxiality, for instance in pure shear. References [1] Madou K., Leblond J.B. A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids - I: Limit-analysis of some representative cell; II: Determination of yield criterion parameters. J. Mech. Phys. Solids, 60, 1020-1036 and 1037-1058, 2012. [2] Madou K., Leblond J.B. Numerical studies of porous ductile materials containing arbitrary ellipsoidal voids - I: Yield surfaces of representative cells; II: Evolution of the magnitude and orientation of the void axes. Submitted to Eur. J. Mech. A/Solids, 2013. [3] Gologanu M., Leblond J.B., Perrin G., Devaux J. Recent extensions of Gurson's model for porous ductile metals. In: Continuum Micromechanics, P. Suquet, ed., Springer-Verlag, New-York, pp. 61-130, 1997. [4] Gurson A.L. (1977). Continuum theory of ductile rupture by void nucleation and growth: Part I - Yield criteria and flow rules for porous ductile media. ASME J. Engng. Materials Technol., 99, 2-15, 1977. _______ Corresponding Author : Jean.Baptiste Leblond e-mail: jbl@lmm.jussieu.fr

51

NEW ANALYTIC CRITERION DESCRIBING THE COMBINED EFFECT OF PRESSURE

AND THIRD INVARIANT ON YIELDING OF POROUS AGGREGATES

Oana Cazacu

Department of Mechanical and Aerospace Engineering, University of Florida, REEF, 1350 N.

Poquito Rd, Shalimar, FL 32579, USA.

A new plastic potential for porous solids with von Mises perfectly-plastic matrix containing spherical cavities is derived using a rigorous limit analysis approach. For stress-triaxialities different from 0 and ±∞, the dilatational response depends on the signs of the mean stress and the third invariant of the stress deviator. The classic Gurson potential is an upper-bound of the new criterion. A full-field dilatational viscoplastic Fast Fourier Transform (FFT)-based approach is also used to generate numerical gauge surfaces for the porous material. The numerical calculations confirm the new features of the dilatational response, namely: a very specific dependence with the signs of the mean stress and the third invariant that results in a lack of symmetry of the yield surface with both the deviatoric and hydrostatic axes _______ Corresponding Author : Oana Cazacu e-mail: cazacu@reef.ufl.edu

52

ON CHARACTERISTIC PARAMETERS INVOLVED IN DYNAMIC FRAGMENTATION PROCESSES

F. Hild(1)

(1) LMT-Cachan, ENS Cachan / CNRS / UPMC / PRES UniverSud Paris

61 avenue du Président Wilson, F-94235 Cachan Cedex, France

Dynamic loadings produce high stress waves leading to the fragmentation of brittle materials such as ceramics, concrete, glass, and rocks, or ductile materials such as steels and alloys. The main mechanism used to explain the change of the number of fragments with strain and stress rates is an obscuration (or shielding) phenomenon associated with cracking or cavitation. A probabilistic framework, which is based upon a Poisson point process, is introduced and scalings are proposed. They lead to the introduction of nonlocal damage models that account for multiple crack initiations or void nucleations, and subsequent growth. This approach allows characteristic parameters involved in the fragmentation processes (e.g., size, stress, and time) to be introduced. Examples are discussed to illustrate the use of these characteristic parameters in the analysis of dynamic fragmentation of ceramics [1], concrete [2, 3] and spalling of tantalum [4]. It is worth noting that this type of scaling also applies to quasi-static loading conditions when studying the gradual degradation of composite materials [5, 6], or thermal striping in stainless steels [7]. References [1] F. Hild, X. Brajer, C. Denoual, P. Forquin, On the Probabilistic-Deterministic Transition Involved in a Fragmentation Process of Brittle Materials, Comput. Struct., 81 (2003) 1241-1253. [2] P. Forquin, B. Erzar, Dynamic fragmentation process in concrete under impact and spalling tests, International Journal of Fracture, 163 (2010) 193-215. [3] P. Forquin, F. Hild, A probabilistic damage model of the dynamic fragmentation process in brittle materials, Adv. Appl. Mech., 44 (2010) 1-72. [4] H. Trumel, F. Hild, G. Roy, Y.-P. Pellegrini, C. Denoual, On Probabilistic Aspects in the Dynamic Degradation of Ductile Materials, J. Mech. Phys. Solids, 57 (2009) 1980-1998. [5] S.L. Phoenix, R. Raj, Scalings in Fracture Probabilities for a Brittle Matrix Fiber Composite, Acta Metall. Mater., 40 (1992) 2812-2828. [6] W.A. Curtin, Exact Theory of Fiber Fragmentation in Single-Filament Composite, J. Mater. Sci., 26 (1991) 5239-5253. [7] N. Malésys, M. Seyedi, L. Vincent, F. Hild, On the formation of crack networks in high cycle fatigue, C. R. Mécanique, 334 (2006) 419-424. _______ Corresponding Author: François Hild e-mail: hild@lmt.ens-cachan.fr

53

EFFECT OF RATE ON THE STATISTICS OF DUCTILE FRACTURE SURFACE ROUGHNESS

A. Needleman(1)

(1) Department of Materials Science and Engineering, University of North Texas, Denton, TX USA

Experimental observations have shown that the roughness of fracture surfaces exhibits certain characteristic scaling properties. In particular, the self-affine nature of the roughness of fracture surfaces has been observed in a wide variety of materials and under a wide variety of loading conditions. Here, finite element, finite deformation analyses of ductile crack growth are described that permit modeling of a three dimensional material microstructure and the statistics of the resulting fracture surface roughness. An elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid is used to model the material. Two populations of void nucleating second phase particles are represented, large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. The larger inclusions are represented discretely with their size and spacing introducing a microstructurally based characteristic length into the formulation. Calculations are carried out for various imposed loading rates and results are presented for the fracture toughness and for the statistics of the fracture surface The extent, if any, to which the statistics of the fracture surface roughness depend on the imposed rate and the connection, if any, between the statistics of the fracture surface roughness and the resistance to crack growth will be discussed.

This is joint work with V. Tvergaard of the Technical University of Denmark, E. Bouchaud of ESPCI Paris Tech, Y. Cao and L. Ponson of Université Pierre et Marie Curie, and A. Srivastava and S. Osovski of the University of North Texas.

_______ Corresponding Author : Alan Needleman e-mail: needle@unt.edu

54

MICROSTRUCTURAL EFFECTS ON DUCTILE DAMAGE OF POLYCRYSTALLINE

MATERIALS

R.A. Lebensohn(1)

(1) Materials Science and Technology Division, Los Alamos National Laboratory, MS G755, Los Alamos, NM, USA.

In an effort to understand the mechanical behavior of engineering materials at high strain rate and large deformation, we present numerical simulations for polycrystals with intergranular voids, in which the dilatational effects associated with the presence of cavities must be accounted for, and standard models for incompressible polycrystal plasticity or dilatational plasticity with isotropic matrix are not appropriate. We first make use of a full-field approach based on Fast Fourier transforms [1,2], adapted to dilatational plasticity of polycrystals [3], and extended to account for growth of individual pores [4]. The model predicts that the plastic anisotropy of single crystals linking interacting voids is critical to determine the strength of this interaction and eventually the localization of deformation leading to void coalescence and ductile fracture. These predictions are validated by comparison with EBSD images of spall Cu samples [5], and also compared with results of non-linear homogenization [3,6] and limit-analysis theories adapted to the case of porous polycrystals [7,8]. References [1] H. Moulinec and P. Suquet, Comput. Methods Appl. Mech. Eng. 157, 69 (1998). [2] R.A. Lebensohn, Acta Mater. 49, 2723 (2001). [3] R.A. Lebensohn, M.I. Idiart, P. Ponte Castañeda and P.G. Vincent, Phil. Mag. 91, 3038 (2011). [4] R.A. Lebensohn et al. in preparation. [5] J.P. Escobedo, E.K. Cerreta, D. Dennis-Koller, B.M. Patterson, C. Bronkhorst, B. Hansen, D. Tonks and R.A. Lebensohn, J. Appl. Phys. 110, 033513 (2011). [6] P. Ponte Castañeda, J. Mech. Phys. Solids 50, 737 (2002). [7] J.B. Stewart and O. Cazacu, Int. J. Solids. Struct. 48, 357 (2011). [8] R.A. Lebensohn and O. Cazacu, Int. J. Solids. Struct 49, 3838 (2012). _______ Corresponding Author : R.A. Lebensohn e-mail: lebenso@lanl.gov

55

SOME ASPECTS OF INERTIA IN POROUS DUCTILE SOLIDS

SUBJECTED TO DYNAMIC LOADING

N. Jacques 1, S. Mercier 2, A. Molinari 2

1 ENSTA Bretagne, LBMS, 2 rue François Verny, 29806 Brest cedex 9, France 2 Université de Lorraine, LEM3, UMR CNRS, Ile du Saulcy, 57045 Metz cedex 01, France

The fracture of ductile materials is often the result of the nucleation, growth and coalescence of microscopic voids. Under dynamic loading conditions, these mechanisms take place over a short period time (of the order of a few microseconds) and may induce inertial effects at the scale of the microstructure of the material. The aim of the presentation is to discuss the influence of micro-scale inertia in dynamic fracture.

The role of inertia in void coalescence is first considered. The most common void-coalescence

mechanism is necking of the inter-void ligaments. We carried dynamic finite element simulations of a unit-cell of a voided solid. It was observed that the development of ligament necking may be significantly delayed due to inertia. Besides, for sufficiently high loading rates, coalescence is found to occur by direct impingement instead of by ligament necking, in agreement with experimental observations (Jacques et al., Int. J. Fract 173:203-213, 2012).

In the second part of the talk, we introduce a micromechanical model of dynamic damage by micro-

voiding. An original feature of the modelling is to take into account inertial effects due to void growth. The proposed constitutive framework has been applied to the study of the dynamic fracture of several specimens. In all cases, it was observed that micro-inertia has a strong influence on the crack growth behaviour. Because micro-inertia prevents damage to develop too rapidly, a regularizing effect is observed which reduces the mesh sensitivity of the simulations. Micro-inertia was also found to lead to lower crack speed and higher fracture toughness (Jacques et al., J. Mech. Phys. Solids 60:665-690, 2012). _______ Corresponding Author : Nicolas Jacques e-mail: Nicolas.jacques@ensta-bretagne.fr

56

SLIP PRECURSORS AT FRICTIONAL INTERFACES

D.S. Kammer, M. Radiguet and J.F. Molinari(1)

(1) Computational Solid Mechanics Laboratory (lsms.epfl.ch) School of Architecture, Civil and Environmental Engineering (ENAC), School of Engineering (STI)

Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland Local slip instabilities, which involve rupture initiation and propagation along interfaces, are of fundamental importance to engineering and geosciences. The mechanics behind these local slip events is however highly complex and not well understood. Recent experimental observations [1] reveal that the propagation speed of the slip front varies along its path and is coupled to the static local shear to normal stress ratio. In order to reproduce these laboratory-earthquakes experiments, we simulate with the finite-element method the propagation of slip fronts at frictional interfaces between viscoelastic solids. The adopted friction law is based on the experimental Prakash-Clifton law [2] to smoothen the variation of the interface shear strength due to an instantaneous variation in the normal stress, and to avoid the ill-posedness of the Coulomb friction law [3]. We show that the slip front speed varies with a changing static stress state along the interface, which is coherent with experimental observation [1]. However, the simulations reveal that a static stress criterion is not sufficient to describe the propagation speed of the interface rupture. Instead, we bring evidence that a dynamic energetic criterion, which relates the slip front speed with the relative rise of the energy density at the slip tip, is more appropriate [4]. We also discuss the transition from sticking to sliding at the frictional interface, which is marked by the occurrence of local slip events, called slip precursors, which initiate at shear levels much below the global static friction coefficient threshold. These precursors stop before propagating over the entire interface, and their length increases with increasing shear force. Our results show that these events can in some cases occur at very slow rupture velocities (i.e. slow rupture fronts), or propagate at sub-Rayleigh rupture velocities. We also show that the propagation of a given slip event is significantly influenced by the slip history on the interface. Interestingly, the heterogeneous state of stress at the interface created by each precursor event cumulate, leading to highly non-uniform interface stresses by the time the rupture propagates through the complete interface (macroscopic sliding). References : [1] O. Ben-David, G. Cohen, and J. Fineberg, “The dynamics of the onset of frictional slip”, Science, 330(6001):211, 2010. [2] V. Prakash and R.J. Clifton, “Time resolved dynamic friction measurements in pressure-shear”, ASME, Experimental Techniques in the Dynamics of Deformable Solids, 165, 33-48, 1993. [3] A. Cochard and J.R. Rice, “Fault rupture between dissimilar materials: Ill-posedness, regularization, and slip-pulse response”, J. Geophys. Res., 105(B11):25891, 2000. [4] D.S. Kammer, V.A. Yastrebov, P.Spijker, and J.F. Molinari, “On the propagation of slip fronts at frictional interfaces”, Tribol. Lett., 48(1), 27-32, 2012. ______ Corresponding Author : Jean-François Molinari e-mail: jean-francois.molinari@epfl.ch

57

EFFECT OF DEFORMATION OF DEFORMATION-INDUCED SURFACE ROUGHENING ON METAL-POLYMER INTERFACE INTEGRITY

J. van Beeck(1,2), P.J.G. Schreurs(1) and M.G.D. Geers(1)

(1) Department of Mechanical Engineering, Eindhoven University of Technology PO Box 513, 5600 MB Eindhoven, The Netherlands

(2) Materials Innovation Institute (M2i) PO Box 5008, 2600 GA Delft, The Netherlands

Metal-polymer laminates are increasingly used in food and beverage packaging. Pre-coating packaging steels leads to a significant reduction of energy consumption and CO2 emission, and a reduction of process water consumption as well as of solid wastes to practically zero. During production, the material is subjected to large deformations at increased temperatures and high strain rates. Throughout this process, the metal-polymer interface roughens, due to the deformation-induced roughening of the steel surface. After production, the material may not exhibit any interface damage, even after a relatively long shelf-life period, as this damage triggers corrosion and compromises the quality of the content [1]. In this contribution, the effect of roughening on the interface integrity is studied. A new methodology to experimentally determine the three-dimensional surface deformation field has been developed. Global Digital Image Correlation is applied to extract the surface deformation from evolving surface height profiles. The displacement fields, extracted from a tensile experiment on packaging steel, reveal the full-field kinematics accompanying the roughening mechanism. Local deviations from the (average) global displacements are the result of the formation, growth, and stretching of hills and valleys on the surface. As such, the proposed method provides new quantitative information for various surface deformation phenomena, and hence out-performs conventional methods using average height values. The extracted surface displacements are next applied in a two-dimensional numerical model consisting of a polymer layer with cohesive zone elements describing the polymer-steel interface. The simulations reveal the initiation and propagation of the interface delamination as a result of the interface roughening. The amount and size of the damage can be related to the reduction in interface strength. Furthermore, the effects of polymer ageing are studied. With the predictions, specific properties of the steel and the polymer can be tailored to reduce or even prevent damage and therefore improve the long-term reliability of products manufactured out of these materials. References [1] van den Bosch, M.J., Schreurs, P.J.G., Geers, M.G.D., van Maris, M.P.F.H.L., Interfacial characterization of pre-strained polymer coated steel by a numerical-experimental approach., Mech Mater, 40, 302-317, 2009. _______ Corresponding Author : J. van Beeck, e-mail: J.v.Beeck@tue.nl

58

DYNAMIC CRACK GROWTH ALONG CURVED INTERFACES IN COMPOSITE AND BONDED POLYMER MATERIALS

D. Coker(1,2), D. Yavas(1,2) and B. Gozluklu(1,3)

(1) Department of Aerospace Engineering, Middle East Technical University, Ankara, Turkey (2) METU Center for Wind Energy, Middle East Technical University, Ankara, Turkey

(3) Turkish Aerospace Industries (TAI), 06980, Ankara, Turkey Failure of curved weak interfaces is important in bonded joints, curved composite laminates and earthquake faults. Crack growth in curved weak interfaces may occur dynamically as a result of curvature and loading even under quasi-static loading conditions. In this paper, dynamic crack growth along curved interfaces under quasistatic loading is investigated experimentally and computationally in unidirectional graphite-epoxy laminates and in bonded L-shaped PMMA plates. The effect of initial crack length on the stability of the crack growth is examined. In the experimental study, a unique testing fixture with a sliding platform is designed to create a displacement loading perpendicular to one of the arms in a curved beam (Figure 1a). The full-field optical techniques of digital image correlation and photoelasticity are used in conjunction with a high speed camera in order to visualize stress and strain fields around the interface crack. In the computational study, debonding at the interface of the curved interface is modeled using dynamic (explicit) finite element analysis in conjunction with Xu-Needleman cohesive zone model with a pure vertical displacement loading to reflect the same loading condition as the experiment. Experimental and finite element analysis results are found to be in agreement in terms of load-displacement behavior, stress distribution, and crack tip speeds. Stable and unstable crack growth regimes, depending on the pre-crack length, are identified in agreement with energy release rate calculations. In the unstable crack growth regime, crack tip velocities at the material wave speeds are observed (Figure 1b). _______ Corresponding Author : Demirkan Coker e-mail: coker@metu.edu.tr

Figure 1 (a) Loading Fixture for perpendicular displacement loading of the arm, (b) A sequence of high speed camera photos showing delamination initiation and propagation in [0/90]s composite L-beam laminate (Interframe time-1/300,000 s).

l59

ON THE ONSET OF ADIABATIC SHEAR FAILURE

D. Rittel(1), S. Osovski(1), A. Venkert(2) and P. Landau(2)

(1) Faculty of Mechanical Engineering

Technion, 32000 Haifa, Israel (2) Department of Physics,

NRCN, 84190 Beer-Sheva, Israel

Adiabatic shear failure is a dynamic failure mechanism that has been extensively investigated since the early 1940’s. The prevailing assumption is that thermal softening plays a dominant role as a destabilizing factor leading to the formation of localized shear surfaces, referred to as adiabatic shear bands (ASB). Considered as an instability, the phenomenon has been quite successfully modeled using perturbation analysis which leads to the prediction of a critical failure strain. In the recent years, we have re-examined the prevailing assumption of a dominant thermal softening from an experimental point of view, showing that for a sufficiently large number of materials studied, thermal excursions are of a quite limited extent for several alloys that indeed fail by ASB, but at relatively small strains, such as Ti6Al4Vand maraging steel among others. This observation has led to the identification of a critical value of the strain energy (density), with emphasis on its athermal component, the so-called stored energy of cold work (SECW). This parameter is particularly attractive as it ties smoothly the mechanics of ASB formation and its physics through microstructural evolutions. In this presentation, we will review some of the more important results in this subject, related to the measurement and rate-dependence of this critical value of the SECW. Emphasis will be put on the identification and the interplay between the 2 main deformation mechanisms, namely dislocations slip and twinning. A fully coupled numerical model, in which the microstructural evolutions are included, will be described. This model can be used to differentiate microstructural from thermal softening, and the contribution of each mechanism. The main outcome of this work is that, whereas perturbation analyses are quite adequate to represent ASB formation, we suggest that the perturbation should not solely concentrate on thermal fields and associated softening effects, but also consider softening microstructural evolutions to provide a more complete picture. _______ Corresponding Author : Daniel Rittel e-mail: merittel@technion.ac.i

60

ON THE COMPLETE EXTINCTION OF SELECTED IMPERFECTION WAVELENGTHS IN DYNAMICALLY EXPANDED DUCTILE RINGS

J. A. Rodríguez-Martínez(1), G. Vadillo, R. Zaera, J. Fernández-Sáez

Department of Continuum Mechanics and Structural Analysis. University Carlos III of Madrid. Avda. de la Universidad, 30. 28911 Leganés, Madrid, Spain

In this work the inception and development of multiple necks in dynamically expanded ductile rings with ab initio geometric imperfections has been addressed. Finite element simulations and linear perturbation analysis have been applied for that task. In the numerical calculations a selected wavelength is included into the model defining along the circumference of the ring an array of periodic geometric imperfections of predefined amplitude. In the stability analysis a perturbation of a given mode is added to the background solution and the growth rate of the perturbation is evaluated. The attention has been focused on the extinction of both long and short wavelength imperfections and the appearance of a dominant necking pattern which emerges when the geometric imperfections are vanished. The role played by the loading rate on the extinction of imperfections is also addressed. Moreover, the necking strain is found to be dependent on the imperfection pattern and the loading rate. Its maximum value is registered for the loading cases in which the initial imperfections distribution is completely extinguished. _______ Corresponding Author : J. A. Rodríguez-Martínez e-mail: jarmarti@ing.uc3m.es

61

ENERGY-BASED VARIATIONAL MODELLING FOR ADIABATIC SHEAR BAND STRUCTURE

S. Su and L. Stainier(1)

Research Institute in Civil and Mechanical Engineering - GeM (UMR 6183 CNRS)

École Centrale Nantes, 1 rue de la Noë, BP 92101, F-44321 Nantes, France

An Adiabatic Shear Band (ASB) is a relatively narrow band presenting large deformation and high temperature, occurring in various ductile materials. It is well established that ASBs can be difficult to represent accurately because of mesh dependence problems in numerical simulations of this localization phenomenon. In this respect, several discontinuous models have been proposed and widely applied for overcoming this difficulty. Yet some crucial conditions are substantially required to build and improve these models, such as an accurate description of strain and temperature profiles, additional constitutive relations in multi-physical approaches and the prediction of bandwidth evolution. We thus propose a new energy-based variational approach to model adiabatic shear banding structure, including elasticity, work hardening and heat conduction, yet avoiding the use of a mesh. Conservation laws are formulated as a mathematical optimization problem with respect to a limited set of scalars. Consequently by means of canonical expressions [1] of displacement and temperature, the bandwidth and the central temperature can be accurately computed as internal variables, both in steady and transient state. Based on this thermo-mechanical coupled variational framework, we can verify the generality of the proposed analytical approach with respect to constitutive models, as illustrated through various thermal softening laws such as power laws or the popular Johnson-Cook model. In addition, accounting for work hardening and elasticity, we propose an effective (or macroscopic) thermo-elasto-viscoplastic model of the shear localization zone. A new loading/unloading condition, stemming as a Kuhn-Tucker relation, is introduced for this variational model. The stress evolution and the capacity of the approach to handle cyclic loading are analysed, presenting a very good correspondence with ASB simulations by finite element method. Finally, it will be shown how this approach can be used to derive a traction-separation law, combined to a heat production law, in the context of a thermo-mechanical two-scale localized shear band model. References [1] Leroy Y. M. and Molinari A., Stability of steady states in shear zones, J. Mech. Phys. Solids, 40, 181-212, 1992. _______ Corresponding Author : Laurent Stainier, e-mail: Laurent.Stainier@ec-nantes.fr

62

DYNAMIC FRAGMENTATION IN DUCTILE MATERIALS VIA OPTIMAL TRANSPORTATION MESHFREE METHOD

A. Pandolfi(1), B. Li(2), M. Ortiz(2)

(1) Politecnico di Milano, Dipartimento di Ingegneria Civile and Ambientale

Piazza Leonardo da Vinci 32, 20133 Milano (Italy) (2) Engineering & Applied Science Division, California Institute of Technology

1200 East California Blvd, Pasadena CA, 91125 (USA)

Meshfree methods are numerical algorithms that do not rely on the definition of a grid, but use directly the geometry of the system. Meshfree methods facilitate the simulation of difficult problems, including nonlinear behaviors, complex geometry, singularities, and others. A static version of a Meshfree method, recently proposed for the analysis of the dynamics of solids and fluids [1], has been developed in view of the simulation of explicit crack propagation in brittle and ductile materials. The method discretizes the system into a finite number of particles, representative of the surrounding material. In the spirit of element erosion procedures [2], the propagation of cracks is modeled by removing material particles upon the attainment of an energy-based fracture criterion. The failure criterion relies on the epsilon-neighborhood construction [3] to capture the local degeneration of the material at the crack tip. In the present study, we evaluate the performance of the approach in predicting dynamic fragmentation in ductile materials. We consider an application involving high rate deformations and strain localization. The evaluation takes the form of a conventional validation analysis, supported by the experimental results on spherical shell caps undergoing explosive loading, as documented in [4]. The simulations have been conducted in concurrent computing setting. The complex outcomes of the experimental tests are captured by the numerical simulations, in terms of extension of the fully damaged area, crack pattern, velocity of flying cap, fragment size distribution. References [1] B. Li, F. Habbal, and M. Ortiz. Optimal transportation meshfree approximations schemes for uid and plastic ows. International Journal for Numerical Methods in Engineering, 83:1541-1579, 2010. [2] M. Ortiz and A. E. Giannakopoulos. Crack propagation in monolithic ceramics under mixed mode loading. International Journal of Fracture, 44:233-258, 1990. [3] B. Schmidt, F. Fraternali, and M. Ortiz. Eigenfracture: an eigendeformation approach to variational fracture. SIAM Journal on Multiscale Modeling and Simulation, 7:1237-1266, 2009. [4] G. H. Campbell, G. C. Archbold, O. A. Hurricane, and P. L. Miller. Fragmentation in biaxial tension. Journal of Applied Physics, 101:033540, 2007. _______ Corresponding Author : Anna Pandolfi e-mail: anna.pandolfi@polimi.it

63

GRADIENT DAMAGE MODELS COUPLED WITH PLASTICITY R. Alessi(1,2) and J.J. Marigo(2) and S. Vidoli(1)

(1) Laboratoire de Mécanique des Solides, Ecole Polytechnique, 91128 Palaiseau Cedex, France

(2) Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, Via Eudossiana 18,00184 Roma, Italy

It is now well established that gradient damage models are very e_cient to account for the behavior of brittle and quasi-brittle materials. Their basic ingredients are: (i) a decreasing dependency of the stiffness E(α) on the damage variable α; (ii) no more rigidity at the ultimate damage state (say E(1) = 0); (iii) a critical stress σc; (iv) a softening behavior with a decrease of the stress from σc to 0 when the damage goes to 1; (v) a gradient damage term in the energy which necessarily contains an internal length l and which limits the damage localization. Accordingly, the process of crack nucleation is as follows [3]: (i) a first damage occurs when the stress field reaches the critical stress somewhere in the body; (ii) then, because of the softening character of the material behavior, damage localizes inside a strip the width of which is controlled by the internal length l ; (iii) the damage grows inside this strip, but not uniformly in space (the damage is maximal at the center of the strip and is continuously decreasing to 0 so that to match with the undamaged part of the body at the boundary of the strip); (iv) a crack appears at the center of the strip when the damage reaches there its ultimate value (say α = 1). During this crack nucleation process, some energy is dissipated inside the damage strip and this dissipated energy involves a quantity Gc which can be considered as the effective surface energy of Griffith's theory. Therefore, Gc becomes a byproduct of the gradient damage model which can be expressed in terms of the parameters of the model (specifically, Gc is proportional to )0(/2 Elcσ ).

However, this type of “quasi-brittle" models are not able to account for residual strains and consequently cannot be used in ductile fracture. Moreover there is no discontinuity of the displacement in the damage strip before the loss of rigidity at its center, i.e. before the nucleation of a crack. In other words such a model cannot account for the nucleation of cohesive cracks, i.e. the existence of surface of discontinuity of the displacement with a non vanishing stress. The natural way to include such effects is to introduce plastic strains into the model and to couple their evolution with damage evolution. Of course, this idea is not new and a great number of damage models coupled with plasticity have been developed from the eighties in the spirit of [2]. But our purpose is to construct such models in a softening framework with gradient of damage terms and to see how these models can account for the nucleation of cracks in presence of plasticity. In our knowledge, the previous works are not able to go so far. Here we will adopt a variational approach in the spirit of our previous works [1]. The main ingredients are the following ones: (i) one defines the total energy of the body in terms of the state fields which include the displacement field and the internal variable fields, namely the damage, the plastic strain and the cumulated plastic strain fields; (ii) one postulates that the evolution of the internal variables is governed by the three principles of irreversibility, stability and energy balance. In particular, the stability condition is essential as well for constructing the model in a rational and systematic way as for obtaining and proving general properties. Besides, we have the chance that the variational approach works and has been already developed both in plasticity and in damage mechanics, even though only separately up to now. So, it “suffices” to introduce the coupling by choosing the form of the total energy to obtain, by virtue of our plug and play device, a model of gradient damage coupled with plasticity. A part of our paper will be devoted to this task. Specifically, our model, presented here in a three-dimensional setting, contains three _______ Corresponding Author : J.J. Marigo email : marigo@lms.polytechnique.fr

64

state functions, namely E(α), d(α) and )(ασ p which give the dependence of the stiffness, the local damage dissipated energy and the plastic yield stress on the damage variable. So, our choice of coupling is minimalist in the sense that it simply consists in introducing this dependence of the yield plastic stress

)(ασ p on the damage variable (with the natural assumption that )(ασ p goes to 0 when the damages

goes to 1). In turn, by virtue of the variational character of the model, the product pp )(' ασ of the

derivative of the state function )(ασ p by the cumulated plastic strain p enters in the damage criterion

and this coupling plays a fundamental role in the nucleation of a cohesive crack.

Figure 1. Localization damage process with nucleation of a cohesive crack

at the center of the damage zone References [1] B. Bourdin, G. A. Francfort, and J.-J. Marigo. The variational approach to fracture. Journal of Elasticity, 91(1-3):5-148, 2008. [2] J. Lemaitre and J. Chaboche. Mécanique des matériaux solides. Bordas, 1985. [3] K. Pham, H. Amor, J.-J. Marigo, and C. Maurini. Gradient damage models and their use to approximate brittle fracture. International Journal of Damage Mechanics, 20(4):618-652, 2011.

_______ Corresponding Author : J.J. Marigo email : marigo@lms.polytechnique.fr

65

DYNAMIC VS. QUASI-STATIC SHEAR FAILURE OF HIGH STRENGTH METALLIC ALLOYS: EXPERIMENT AND MODELLING

P. Longère(1) and A. Dragon(2)

(1) Université de Toulouse, ISAE- ICA (EA 814)

10 avenue Edouard Belin, BP 54032, 31055 Toulouse cedex 4, France (2) Institut Pprime, DPMM (UPR CNRS 3346) / ENSMA

1 avenue Clément Ader, BP 40109, 86961 Futuroscope - Chasseneuil du Poitou, France

In many industrial processes, such as e.g. cutting and punching, or accidental events, such as e.g. crash or impact, cracks may initiate and propagate under low stress triaxiality. Dealing with ductile fracture at low stress triaxiality is consequently of major interest, while being not trivial and still remaining a challenge in terms of experimental investigation, constitutive modelling and numerical simulation. Starting from experimental observations, the present work aims at reproducing via a unified model the consequences of two deterioration mechanisms occurring under low and high strain rate shear loadings, respectively, namely void growth induced damage and adiabatic shear banding. The material considered is a high strength Ti6Al4V titanium alloy. In order to study the underlying mechanisms at the origin of shear failure in the material at stake, we have carried out experiments involving shear-pressure combined loading at low and high strain rates. To observe the current and ultimate deterioration states, some tests were interrupted before fracture and other ones were conducted until ultimate failure. At low strain rate, involving quasi isothermal conditions, the material failure has been seen to result from void growth and further dimple formation, in spite of the pressure applied. At high strain rate, involving quasi adiabatic conditions, the material failure has been found to result from the adiabatic shear banding (ASB) localisation mechanism, as expected for this class of alloys. On the modeling side, the back mean stress concept, see [1], and the embedded band based approach, see [2], have been incorporated in a unified constitutive framework in order to describe the behaviour and shear failure of high strength Ti6Al4V titanium alloys. The former concept is linked to void growth induced damage, when strain rate is low, the latter approach to adiabatic shear banding induced deterioration, when strain rate is high enough. The performance of numerical simulations using the model is evaluated in view of the experimental results mentioned. References [1] LONGÈRE P., DRAGON A., 2013, Description of shear failure in ductile metals via back stress concept linked to damage-microporosity softening, Eng. Fract. Mech., 98, pp.92-108 [2] LONGÈRE P., DRAGON A., DEPRINCE X., 2009, Numerical study of impact penetration shearing employing finite strain viscoplasticity model incorporating adiabatic shear banding, J. Eng. Mat. Tech., ASME, 131, pp.011105.1-14 _______ Corresponding Author : Patrice Longère e-mail: patrice.longere@isae.fr

66

ON BOUNDED RATE CONSTITUTIVE MODEL : APPLICATION TO OBJECTIVE FAILURE PREDICTION

O. Allix (1)

(1) LMT-Cachan, ENS Cachan/CNRS/PRES UniverSud Paris

61, avenue du président Wilson, F-94230 Cachan, France

The more widespread approach to overcome the lack of consistency of material model with respect to failure is the one of non-local approach. A huge literature has been devoted to non-local model with variants from non-local integral approaches to explicit and implicit gradient approaches or Cosserat models [1]. Despite of all this studies the development of these approaches in an industrial context is still seldom. The main reason is probably the fact that non-locality implies many and non-obvious code developments, identification practices are also an issue. That is why we have sought for another, even if maybe less general, possibility, to overcome the difficulty, the use of rate dependent models. Needleman was possibly the first to discuss how, in statics, the use of viscosity can help to conserve the elliptic property of the incremental equilibrium equations and, thus, eliminate pathological mesh-sensitivity [2]. For example a rate-dependent model of the Johnson-Cook type has been carefully studied in [3] and it is conclude that spurious localization is not circumvent. That is why we have proposed in [4] the concept of bounded damage rate model, which has been extended latter for other type of phenomenon such as ductile failure [5]. After a short analysis of the problem several examples will serve to illustrate the main property of bounded rate dependent model and their identification: (i) ductile failure of metallic material, (ii) dynamic delamination [6], failure and erosion of laminates submitted to high velocity impact. References [1] Peerlings,R.H.J., Geers, M.G.D., De Borst, R., Brekelmans, W.A.M., 2001. A critical comparison of non local, gradient enhanced softening continua. In: International Journal of Solids and Structures, 38, 7723-7746. [2] Needleman, A., 1988. Material rate dependence, mesh sensitivity in localization problems. In: Computer Methods in Applied Mechanics and Engineering, 63, 69-85. [3] Flatten, A.,Klingbeil, D., Svendsen, B., 2007 Non-local modelling of thermomechanical localization in metals. Proc. of CFRAC 2007 - 1st International Conference on Computational Fracture and Failure of Materials and Structures. [4] Allix, O., Feissel, P., Thevenet, P., 2003. A delay damage mesomodel of laminates under dynamic loading: basic aspects, identification issues. In: Computers and Structures, 81, 1177-1191. [5] Allix, O.,. The bounded rate concept: a framework to deal with objective failure predictions in dynamic within a local constitutive model. To appear in Int Jal of Damage Mechanics. [6] Guimard, J.M., Allix, O., Pechnick, N., Thevenet, P. Characterization and modeling of rate effects in the dynamic propagation of Mode-II delamination in composite laminates. Int Jal of Fracture. Vol 160. Num 1. Pages 55-71. 2009 _______ Corresponding Author : Olivier Allix e-mail: allix@lmt.ens-cachan.fr

67

EFFECT OF STRAIN RATE, STRESS TRIAXIALITY AND LODE PARAMETER ON DUCTILE FRACTURE

M. Dunand(1,2) and D. Mohr (1,2)

(1) Solid Mechanics Laboratory (CNRS-UMR 7649), Department of Mechanics,

École Polytechnique, Palaiseau, France

(2) Impact and Crashworthiness Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge MA, USA

Motivated by the assumption that ductile fracture is imminent after the localization of plastic flow within a narrow band at the microscale, a three-dimensional unit cell model is built to predict the effect of stress state and strain rate on the onset of plastic localization. The unit cell model is built such that the stress state remains constant throughout loading. Furthermore, the direction of the macroscopic principal stresses is constantly updated to account for the effect of material rotation (co-rotational loading). The results are presented for a Levy-von Mises material (TRIP780 steel) with an initially spherical defect within a cuboidal unit cell. The results confirm the well-known effect of the stress triaxiality on the macroscopic equivalent plastic strain at the onset of localization. At the same time, it is found that the localization strain is a non-symmetric convex function of the Lode angle parameter. The results also show that the localization strain decreases as a function of the strain rate for adiabatic conditions. _______ Corresponding Author : Dirk Mohr, e-mail: mohr@lms.polytechnique.fr

68

COHESIVE ZONE MODELLING OF DYNAMIC FAILURE IN BRITTLE MATERIALS

S. Hiermaier(1), M. Büttner(1), P. Seiterich(1) and M. Sauer(1)

(1) Fraunhofer Institute for High-Speed-Dynamics, Ernst-Mach-Institute (EMI)

Eckerstr. 4, 79104 Freiburg, Germany

Failure mechanisms in dynamically loaded brittle materials lead to the propagation of cracks and the formation of internal free surfaces. The inherent wave propagation effects result in multiaxial transient loading situations. As a consequence, complex and possibly history dependent material behaviour is observed and needs to be modelled by adequate numerical methodologies. Therefore, predictive material models for dynamic processes require complex formulations in the deviatoric and, if shock waves are involved, in the volumetric regime. Aside from the constitutive model, discretization is an additional challenge. The formation of new free surfaces and the quantity of released energy as well as the development of new contact surfaces are extremely demanding components of a numerical methodology suited for modelling of failure in brittle materials. In this paper, an implementation of cohesive zone element (CZE) formulations into the EMI code MESOFEM, developed by Knell [1], is presented. Specific advantages of the code are the availability of adaptively inserted CZE along with a non-locking formulation for linear tetrahedral elements, and an efficient implementation making it suitable for 3D applications with multiple cracking and fragmentation. Recently, a robust contact algorithm has been added. The contribution will present application to spall failure in concrete under tensile Hopkinson loading conditions (Knell et al. [2]) and to failure propagation in ceramic specimens loaded in the Edge-on-Impact test (EoI) (experiments of Straßburger [3]) in comparison to experimental results. Finally, impact tests designed by Zinszner et al. [4] are modelled and the results are compared to the literature data to further assess the potential of the method. References [1] Knell S., A numerical modeling approach for the transient response of solids at the mesoscale, PhD thesis, Fraunhofer Institute for High-Speed Dynamics, Freiburg, 2011. [2] Knell S., Sauer M., Million O. and Riedel W., Mesoscale simulation of concrete spall failure, EPJ-ST, 206, 139-148 (2012). [3] Straßburger E., Senf H., ARL report ARL-CR-214, 1995. [4] Zinszner J.-L., Forquin P. and Rossiquet G., Design of an experimental configuration for studying the dynamic fragmentation of ceramics under impact, EPJ-ST, 206, 107-115 (2012). _______ Corresponding Author: Stefan Hiermaier e-mail: hiermaier@emi.fhg.de

69

STUDY OF FRICTION AND WEAR MECHANISMS AT HIGH SLIDING SPEED.

G. List(1), G. Sutter(1), JJ. Arnoux(1), A. Molinari(1)

(1) University of Lorraine, LEM3, Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux

(UMR n° 7239), Ile du Saulcy, F-57045 Metz - cedex 01,

The aim of this work is to propose an analysis of mechanisms inducing surface damage by friction and thus wear during high speed interaction. A specific ballistic device [1] was used in a first step to reproduce extreme sliding conditions combining high speed and high pressure. Two pairs of materials are chosen for this study, a mild steel C22/C22 and a couple titanium alloy/tantalum to differentiate the deposits. The tangential force measurement will be used to follow the evolution of the friction coefficient at a macroscopic scale, depending on the speed and the pressure. A detailed analysis of the recorded signal during the test will permit to separate the contribution of the load sensor in the measurement and to obtain only the contribution linked to friction effects. In a second step, numerical modelling of contact [2] at the asperities scale (on a microscopic scale), will be presented to illustrate the scenarios involved during the sliding. Several types of interaction [3] will be considered depending on the contact pressure and thus the depth of interaction. Following the roughness, different behaviours must be taken into account in order to investigate the global forces generated by the contact. Each asperity of the surface should be classified according to its action or not during friction [4]. A parameter αactif is proposed to characterize the activity of asperities during sliding. The evolution of the sliding surface was analysed by Scanning Electron Microscopy and confocal 3D microscope to evaluate this parameter. Measurements and numerical results will be used to validate the proposed approach. Particular attention is paid to the behaviour of Ti / Ta which under certain conditions can cause micro junctions [5]. An evaluation of the temperature will be proposed and confirmed experimentally [1]. References [1] G. Sutter, N. Ranc, Flash temperature measurement during dry friction process at high sliding speed,

Wear. 268 (2010) 1237–1242. [2] R. Vijaywargiya, I. Green, A finite element study of the deformations, forces, stress formations, and

energy losses in sliding cylindrical contacts, International Journal of Non-Linear Mechanics. 42 (2007) 914–927.

[3] Bowden F.P., Tabor D., The area of contact between stationary and between moving surfaces, in: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences,: pp. 391–413. 1939.

[4] A. Molinari, Y. Estrin, S. Mercier, Dependence of the coefficient of friction on the sliding conditions in the high velocity range, ASME, Journal of Tribology 121 (1999) 35-41.

[5] S. Pineau, M. Veyrac, M. Hourcade, B. Hocheid, Étude et réalisation de jonctions titane-tantale soudées par diffusion à haute température (855-920° C): Influence des paramètres température, temps, pression et rugosité sur les propriétés mécaniques et optimisation des conditions de soudage, Journal of the Less Common Metals. 109 (1985) 169–196. _______ Corresponding Author: Gautier List e-mail: gautier.list@univ-lorraine.fr

70

CRACK PROPAGATION THROUGH GLASS-ADHESIVE INTERFACE DRIVEN BY

DYNAMIC LOADING

H. Park(1), N. D. Parab(1) and W. Chen(1)

(1) Schools of Aeronautics/Astronautics and Materials Engineering

Purdue University 710 West Stadium Avenue, West Lafayette, Indiana, USA-47906

We study the dynamic crack propagation at the interface of glass and adhesive to understand the failure mechanisms and crack propagation properties in glass and at the glass-adhesive interface. The glass specimens were notched and then joined edgewise using different adhesive thicknesses. Glass plates with different surface finishes on the joined edges were used to study the effects of surface finish. Notched glass specimens were impacted with high velocity, plastic projectiles using a light gas gun. Notching of the glass ensured that only single crack propagated through the first plate. The crack propagation behaviour was recorded using a high speed camera. The crack propagation behavior was observed to be dependent on the thickness of the adhesive layer between two glass plates. The crack stopped at the interface, propagated as a single crack or branched into multiple cracks as the thickness of the adhesive layer was increased as seen in Figure 1.

Figure 2: Effect of adhesive thickness on crack propagation: (a) Adhesive thickness = 0.1mm (b) Adhesive thickness = 1.3mm (c) Adhesive thickness = 2.5mm Surface finish also affected the crack propagation behavior. The mirror like smooth finish was observed to provide more resistance to crack initiation as compared to rough finishes. Etching of the glass surface with hydrofluoric acid was observed to further increase the crack initiation resistance. _______ Corresponding Author: W. Chen, e-mail: wchen@purdue.edu