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Arthur Coré
Dynamic fracture of composite hollow spheres Experimental and numerical approach
May 10, 2016 5th International Carbon Composites Conference Arcachon A. C ORÉ, J.B. KOPP, P. V IOT, F. DAU, J.L. C HARLES Arts et Métiers ParisTech, I2M-DUMAS, UMR 5295 CNRS, 33400 Talence, France
Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Objective Industrial context
Objective Introduction Compression tests
SAMBA project : Shock Absorber Material for Birdshield Application Technological solution Hollow spheres Aim : To study the energy dissipation mechanisms (fracture, friction...) under dynamic solicitations.
Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Outline 1
Introduction
2
Compression tests
3
Numerical modelling
4
Multi-impacts
5
Conclusions and perspectives
Objective Introduction Compression tests Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Outline 1
Introduction
2
Compression tests
3
Numerical modelling
4
Multi-impacts
5
Conclusions and perspectives
Objective Introduction Compression tests Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Introduction : structural characteristics
Objective Introduction
Hollow spheres made by ATECA (french PME, Montauban) Geometry 1 to 30 mm in diameter Constitutive material epoxy resin with aggregates Mechanical behaviour elastic-brittle, subjected to dynamic crack propagation
Compression tests Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Introduction : structural characteristics
Objective Introduction Compression tests Numerical modelling Multi-impacts
Hollow spheres made by ATECA (french PME, Montauban) Geometry 1 to 30 mm in diameter Constitutive material epoxy resin with aggregates Mechanical behaviour elastic-brittle, subjected to dynamic crack propagation
Methodology Characterization of a hollow sphere in quasi-static and dynamic compression Numerical model of one hollow sphere Towards a macroscopic model : multi impacts modelling and experiments
Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Outline 1
Introduction
2
Compression tests
Objective
Quasi-static Dynamic
Introduction Compression tests
3
Numerical modelling
4
Multi-impacts
5
Conclusions and perspectives
Quasi-static Dynamic
Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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05/10/2016 IC3 2016 Arcachon
Dynamic fracture of composite hollow spheres
Compression tests : Quasi-static Experimental procedure
Objective Introduction
Uni-axial compressive tests conducted on one classical compression machine at room temperature Geometry Hollow sphere of 30 mm in diameter and 1.2 mm thick Compressive velocity 5 mm/min
Compression tests Quasi-static Dynamic
Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Compression tests : Quasi-static Observations
Objective Introduction
Elastic-brittle behaviour Elastic phase with failure→ dynamic fracture Significant dispersion → geometrical defaults of hollow spheres induced by the manufacturing process
Compression tests Quasi-static Dynamic
Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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05/10/2016 IC3 2016 Arcachon
Dynamic fracture of composite hollow spheres
Compression tests : Dynamic Experimental procedure
Objective Introduction
Uni-axial compressive tests conducted on a fly wheel machine at room temperature Geometry Hollow sphere of 30 mm in diameter and 1.2 mm thick Compressive velocity 2 m/s
Compression tests Quasi-static Dynamic
Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Compression tests : Dynamic Observations
Objective Introduction
Elastic-brittle behaviour but with : Increase of rigidity and force at failure Fmax + 50% Greater dispersion → dynamic effects
Compression tests Quasi-static Dynamic
Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Outline 1
Introduction
2
Compression tests
3
Numerical modelling
Objective Introduction Compression tests
Discrete Element Method Cohesive beams Elastic calibration Failure criterion Results
Numerical modelling Discrete Element Method Cohesive beams
4
Multi-impacts
5
Conclusions and perspectives
Elastic calibration Failure criterion Results
Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Discrete Element Method Avantages
Objective
Adapted to dynamic simulations (explicit scheme) Natural dynamic fracture
Introduction
Open source
Compression tests Numerical modelling Discrete Element Method
Principles
Cohesive beams Elastic calibration
undeformable elements interacting
Failure criterion Results
Multi-impacts
Interactions : contacts, springs, potential forces, beams
Conclusions and perspectives
A. C ORÉ
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05/10/2016 IC3 2016 Arcachon
Dynamic fracture of composite hollow spheres
Cohesive beams Discrete element method to simulate continuous material
Objective Introduction Compression tests
linear elastic macroscopic mechanical behaviour Calibration procedure : microscopic Young Modulus and radius ratio (RRµ = beams
Rbeam RDE
) of
Failure criterion based on the virial stress tensor
Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Failure criterion Results
Multi-impacts Conclusions and perspectives
A. C ORÉ
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05/10/2016 IC3 2016 Arcachon
Dynamic fracture of composite hollow spheres
Elastic calibration
Objective Introduction Compression tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Failure criterion Results
Multi-impacts Conclusions and perspectives
We find RRµ = 0.3 and Eµ = 356 GPa
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Failure criterion Characterization
Objective Introduction Compression tests Numerical modelling
Compression tests of composite cylinders (ASTM D695)
Temperature : −40◦ C to +80◦ C Compression velocity : 5 mm/min to 500 mm/min (Hopkinson bars tests planned) Identification of Ree-Eyring law constants
Qβ −1 Qα σmax = Aα (log (2Cα ) ˙ + ) + Aβ sinh (Cβ ˙ exp ( )) T RT RT
(1)
Discrete Element Method Cohesive beams Elastic calibration Failure criterion Results
Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Failure criterion Brittle calibration
Objective Introduction
Choice of the failure criterion : principal stress, hydrostatic stress Consideration of the strain rate dependency Validation
Compression tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Failure criterion Results
Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Results Numerical model of a hollow sphere
Objective
Random packing creation of hollow spheres made of thousands of elements (10 000 to 100 000 elements)
Dynamic compression tests at 2 m/s Introduction
Quasi-static compression tests at low velocity
Compression tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Failure criterion Results
Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Objective
Results
Micro cracking micro cracks prior the main failure are taken into account
Introduction Compression tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Failure criterion Results
Multi-impacts Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Results High velocity impact
Objective
Experimental procedure : gas gun, force sensor, high speed camera (150k fps) Velocity range : 50 to 150 m/s (maximum of 60 bars)
Introduction
Good qualitative results for high velocity impact
Compression tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Failure criterion Results
Multi-impacts Conclusions and perspectives
F IGURE – From left to right : experimental, strain-rate dependent model and strain rate independent model
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Outline 1
Introduction
2
Compression tests
3
Numerical modelling
4
Multi-impacts
5
Conclusions and perspectives
Objective Introduction Compression tests Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
18 / 24
Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Why multi-impacts tests ? Establishment of a brittle hollow sphere constitutive law dependent on :
Number and force of contacts Objective Introduction
Compression velocity Geometry of the hollow sphere
Compression tests Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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05/10/2016
Dynamic fracture of composite hollow spheres
IC3 2016 Arcachon
Validation on simple multi-impacts test Objective Introduction
Two points contact (column) Six points contact (pyramid) Quasi-static and dynamic compression tests
Compression tests Numerical modelling Multi-impacts Conclusions and perspectives
A. C ORÉ
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05/10/2016
Dynamic fracture of composite hollow spheres
IC3 2016 Arcachon
Validation on simple multi-impacts test Objective
Two points contact (column) Six points contact (pyramid)
Introduction
Quasi-static and dynamic compression tests
Compression tests Numerical modelling Multi-impacts Conclusions and perspectives
F IGURE – Dynamic tests (2 m/s)
A. C ORÉ
20 / 24
Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Outline 1
Introduction
2
Compression tests
3
Numerical modelling
4
Multi-impacts
5
Conclusions and perspectives
Objective Introduction Compression tests Numerical modelling Multi-impacts
Conclusions Perspectives
Conclusions and perspectives Conclusions Perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Conclusions Experimental
Objective
Sensitivity to strain rate → increase of the force at failure Energy dissipated mainly by dynamic fracture
Introduction Compression tests Numerical modelling
Numerical Fracture taken into account by the Discrete Element Method
Good qualitative results Strain rate sensitivity Ability to conduct multi-impact tests
Multi-impacts Conclusions and perspectives Conclusions Perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Perspectives Macroscopic model
Objective Introduction Compression tests
One sphere becomes one element in the DEM model Contact law between spheres / elements given by a parametric analysis conducted on the multi impact model Contact forces, impact velocity between spheres, geometry of the spheres (thickness, diameter), temperature... → variables of the contact law Modelling of a soft impact on an assembly of hollow spheres
Numerical modelling Multi-impacts Conclusions and perspectives Conclusions Perspectives
F IGURE – Impact of Gelatin (v= 50 m/s), numerical and experimental results (in progress)
A. C ORÉ
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Thanks for your attention Any questions ? Arthur C ORÉ
PhD candidate
Arts & Métiers ParisTech - Centre de Bordeaux - Talence, I2M Dynamic department Esplanade des Arts et Métiers, 33400 Talence
[email protected]
Dynamic fracture of composite hollow spheres
05/10/2016 IC3 2016 Arcachon
Détermination du facteur de correction dynamique sur sphères creuses 1. Validation sur plaque Appendix
Mise sous tension d’une plaque (déplacement imposé) Rupture manuelle des poutres à vitesse imposée (0.01 Cr à 1 Cr ) Bilan d’énergie, J-Integral, CTOD Comparaison et validation avec le résultat analytique de Broberg sur plaque semi-infinie 2. Application sur sphères creuses par la même méthodologie
Crack propagation on a discrete element plate (from right to left)
A. C ORÉ
Appendix
05/10/2016
Dynamic fracture of composite hollow spheres
IC3 2016 Arcachon
Modèle macroscopique d’un assemblage de sphères creuses 1. Mise en place d’essais numériques et expérimentaux de multi-contacts Appendix
2. Analyse paramétrique numérique dépendant de la géométrie des sphères et de leurs chargements 3. Modélisation macroscopique : une sphère devient un élément 4. Essais de choc mou sur une éprouvette de type bouclier
A. C ORÉ
Appendix
