Dynamic fracture of composite hollow spheres Experimental and numerical approach
August 23, 2016 24th International Congress of Theoretical and Applied Mechanics Montréal 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
08/23/2016 ICTAM 2016 Montréal
Industrial context Objective Introduction Experimental 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 Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Outline 1
Introduction
2
Experimental tests
3
Numerical modelling
4
Application on hollow spheres
5
Conclusions and perspectives
Objective Introduction Experimental tests Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Outline 1
Introduction
2
Experimental tests
3
Numerical modelling
4
Application on hollow spheres
5
Conclusions and perspectives
Objective Introduction Experimental tests Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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08/23/2016
Dynamic fracture of composite hollow spheres
ICTAM 2016 Montréal
structural characteristics Hollow spheres made by ATECA (french PME, Montauban)
Objective
Geometry 1 to 30 mm in diameter Constitutive material epoxy resin with aggregates Mechanical behaviour elastic-brittle, subjected to dynamic crack propagation
Introduction Experimental tests Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
structural characteristics Hollow spheres made by ATECA (french PME, Montauban)
Objective
Geometry 1 to 30 mm in diameter Constitutive material epoxy resin with aggregates Mechanical behaviour elastic-brittle, subjected to dynamic crack propagation
Introduction Experimental tests Numerical modelling
Methodology Characterization of a hollow sphere in quasi-static and dynamic compression Numerical model of the dynamic fracture Estimation of the critical dynamic energy release rate
Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Outline 1
Introduction
2
Experimental tests
Objective
Compression tests in quasi-static Compression tests in dynamic Crack tip velocity Rayleigh wave speed Conclusions
Introduction Experimental tests Compression tests in quasi-static Compression tests in dynamic
3
Numerical modelling
4
Application on hollow spheres
5
Conclusions and perspectives
Crack tip velocity Rayleigh wave speed Conclusions
Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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08/23/2016
Dynamic fracture of composite hollow spheres
ICTAM 2016 Montréal
Experimental procedure Uni-axial compressive tests conducted on one classical compression machine at room temperature
Objective
Geometry Hollow sphere of 30 mm in diameter and 1.2 mm thick Compressive velocity 5 mm/min
Introduction Experimental tests Compression tests in quasi-static Compression tests in dynamic Crack tip velocity Rayleigh wave speed Conclusions
Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Observations Elastic-brittle behaviour
Objective
Elastic phase with failure→ dynamic fracture Significant dispersion → geometrical defaults of hollow spheres induced by the manufacturing process
Introduction Experimental tests Compression tests in quasi-static Compression tests in dynamic Crack tip velocity Rayleigh wave speed Conclusions
Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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08/23/2016
Dynamic fracture of composite hollow spheres
ICTAM 2016 Montréal
Experimental procedure Uni-axial compressive tests conducted on a fly wheel machine at room temperature
Objective
Geometry Hollow sphere of 30 mm in diameter and 1.2 mm thick Compressive velocity 2 m/s
Introduction Experimental tests Compression tests in quasi-static Compression tests in dynamic Crack tip velocity Rayleigh wave speed Conclusions
Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Observations Elastic-brittle behaviour but with :
Objective
Increase of rigidity and force at failure Fmax + 50% Greater dispersion → dynamic effects
Introduction Experimental tests Compression tests in quasi-static Compression tests in dynamic Crack tip velocity Rayleigh wave speed Conclusions
Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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08/23/2016 ICTAM 2016 Montréal
Dynamic fracture of composite hollow spheres
Crack tip velocity calculation High speed cinematography with Photron SA-5 : 75 000 fps, resolution of 320x264 pixels
Crack tip position measurement Objective
Spherical coordinates → taking into account out of plane displacement Linear least square to calculate the crack tip average velocity
Introduction Experimental tests Compression tests in quasi-static Compression tests in dynamic Crack tip velocity Rayleigh wave speed Conclusions
Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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08/23/2016
Dynamic fracture of composite hollow spheres
ICTAM 2016 Montréal
Rayleigh wave speed calculation Wave speed measurement on a cylindrical specimen (24 mm in diameter and 10 mm in length)
Objective Introduction Experimental tests
Longitudinal wave speed cl = 3250 ± 50 m.s−1 Shear wave speed ct = 1760 ± 50 m.s−1 Rayleigh wave speed cr = 1632 ± 50 m.s−1 cr ≈
0.87 + 1.12ν 1+ν
(1)
ct
Compression tests in quasi-static Compression tests in dynamic Crack tip velocity Rayleigh wave speed Conclusions
Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Critical energy release rate Objective Introduction
Elastic energy stored before failure → energy dissipated through the creation of new surfaces
GIc =
δW b∆a
∆l ∆t
(m/s) 0.08 2
Welas (J) 0.60±0.08 0.81±0.10
GIc (kJ/m2 ) 4.2±0.6 3.4±0.6
Experimental tests Compression tests in quasi-static Compression tests in dynamic Crack tip velocity Rayleigh wave speed Conclusions
Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Critical energy release rate Objective Introduction Experimental tests Compression tests in quasi-static
Elastic energy stored before failure → energy dissipated through the creation of new surfaces
GIc =
Welas (J) 0.60±0.08 0.81±0.10
GIc (kJ/m2 ) 4.2±0.6 3.4±0.6
Dynamic correction factor f (a) ˙ to take into account inertial effects : (2)
GIdc = f (a)G ˙ Ic First approximation (*) for a crack (mode I) in semi-infinite plate :
Rayleigh wave speed
f (a) ˙ =1−
Conclusions
Numerical modelling
(m/s) 0.08 2
Critical dynamic energy release rate
Compression tests in dynamic Crack tip velocity
∆l ∆t
δW b∆a
∆l ∆t
(mm/s) 0.08 2000
a/c ˙ r 0.12 ±0.02 0.14 ±0.02
a ˙
(3)
cr 2 G∗ Idc (kJ/m ) 3.7±0.6 2.9 ±0.6
Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Outline 1
Introduction
2
Experimental tests
3
Numerical modelling
Objective Introduction Experimental tests
Discrete Element Method Cohesive beams Elastic calibration Node release technique
Numerical modelling Discrete Element Method
4
Application on hollow spheres
5
Conclusions and perspectives
Cohesive beams Elastic calibration Node release technique
Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Avantages Adapted to dynamic simulations (explicit scheme) Objective
Natural dynamic fracture Open source
Introduction Experimental tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Node release technique
Principles undeformable elements interacting Interactions : contacts, springs, potential forces, beams
Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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08/23/2016
Dynamic fracture of composite hollow spheres
ICTAM 2016 Montréal
Discrete element method to simulate continuous material linear elastic macroscopic mechanical behaviour Objective Introduction
Calibration procedure : microscopic Young Modulus and radius ratio (RRµ = beams
Rbeam RDE
) of
Failure criterion based on the virial stress tensor and fracture energys Experimental tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Node release technique
Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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08/23/2016
Dynamic fracture of composite hollow spheres
ICTAM 2016 Montréal
Objective Introduction Experimental tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Node release technique
Application on hollow spheres
We find RRµ = 0.3 and Eµ = 356 GPa
Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Node release technique Crack history (position, time) → Critical dynamic energy release rate
Objective
Plate size : L = 20 mm, H = 40 mm and B = 2 mm 20 000 elements
Introduction Experimental tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Node release technique
Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Fracture process zone Parameters of the fracture process zone :
Length of the damaged zone → set to 1 radius Objective
Relaxation scheme → set to a linear scheme
Introduction Experimental tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Node release technique
Application on hollow spheres Conclusions and perspectives F IGURE – Comparison of different lengths of the FPZ
F IGURE – Comparison of different relaxation schemes
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Results Good agreement with analytical and finite element results
Objective
The DEM model allows to create complex crack paths
Introduction Experimental tests Numerical modelling Discrete Element Method Cohesive beams Elastic calibration Node release technique
Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Outline 1
Introduction
2
Experimental tests
3
Numerical modelling
4
Application on hollow spheres
5
Conclusions and perspectives
Objective Introduction Experimental tests Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
19 / 26
08/23/2016
Dynamic fracture of composite hollow spheres
ICTAM 2016 Montréal
Objective Introduction Experimental tests Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
20 / 26
08/23/2016
Dynamic fracture of composite hollow spheres
ICTAM 2016 Montréal
Objective Introduction Experimental tests Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
20 / 26
Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Results in mode I for hollow spheres High inertial effects Decrease of the dynamic correction factor with the thickness of the hollow sphere
Objective Introduction Experimental tests Numerical modelling Application on hollow spheres Conclusions and perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Results in mode I for hollow spheres High inertial effects Decrease of the dynamic correction factor with the thickness of the hollow sphere
Objective Introduction Experimental tests Numerical modelling Application on hollow spheres Conclusions and perspectives
Application : new calculation of the critical dynamic energy release rate ∆l ∆t
(mm/s) 0.08 2000
a/c ˙ r 0.12 ±0.02 0.14 ±0.02
2 G∗ Idc (kJ/m ) 3.7±0.6 2.9 ±0.6
GIdc (kJ/m2 ) 0.84 ±0.5 0.4 ±0.3
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Outline 1
Introduction
2
Experimental tests
3
Numerical modelling
4
Application on hollow spheres
5
Conclusions and perspectives
Objective Introduction Experimental tests Numerical modelling Application on hollow spheres
Conclusions Perspectives
Conclusions and perspectives Conclusions Perspectives
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Conclusions Experimental
Objective Introduction
Compression tests on composite hollow spheres
Increase of the force at failure with the compressive velocity Increase of the crack tip velocity with the compressive velocity
Experimental tests Numerical modelling Application on hollow spheres Conclusions and perspectives
Energy dissipated mainly by dynamic fracture
Numerical Critical dynamic energy release rate estimated with the Discrete Element Method
Relaxation scheme parameters identified Close to analytical and finite element results for crack propagation on a semi-infinite plate Dynamic correction factor estimated for crack propagation on hollow spheres
Conclusions Perspectives
F IGURE – Example of a sinusoidal crack path on a plate with the DEM
A. C ORÉ
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Dynamic fracture of composite hollow spheres
08/23/2016 ICTAM 2016 Montréal
Perspectives Experimental
Objective
Strip Band Specimen (SBS) tests for more accurate measurements Evaluate the critical dynamic energy release rate for different crack tip velocity
Introduction Experimental tests Numerical modelling
Numerical Stress - energy failure criterion with the DEM Multi-spheres model Macroscopic model
Application on hollow spheres Conclusions and perspectives Conclusions Perspectives
F IGURE – Multi-Spheres test
F IGURE – Multi-sphere DEM model
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, France
[email protected]
