Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 1 High strain rate photomechanics on composites: use of a ultra high speed camera and the virtual fields method Dr R. Moulart, Prof. F. Pierron Arts et Métiers ParisTech Châlons-en-Champagne, France ACCIS, Aerospace Engineering, University of Bristol, UK Dr S.R. Hallett, Prof. M.R. Wisnom

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 2/19 Perform full-field deformation measurements with a ultra high speed camera  Evaluate performances (quantitative measurements) Process the deformation data to identify stiffnesses  Use of acceleration maps to make up for the lack of force data Objectives

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 3/19 Test set-up

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 4/19 Test set-up Quasi-isotropic lay-up: [-45 2 /90 2 /45 2 /0 2 ] s Input tensile wave y x Thickness: Ø = Cross-line grid: 200  m pitch  Transferred onto specimen  Displacements obtained by spatial phase shifting Test specimen: glass-epoxy composite

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 5/19 Test set-up Ultra high speed camera: Cordin Time resolution: 3.3  s ( fps) – light issues  Maximum frame rate: 4 Mfps! Spatial resolution: 1 Mpixel

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 6/19 Measurements Grey level images

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 7/19 Measurements Problem of bias caused by sensor positions Need for a first set of 62 still images Phase maps obtained sensor by sensor Final resolution: 5  m (2.5% of grid pitch) Ux in  m

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 8/19 Measurements Longitudinal displacement Ux in  m

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 9/19 Measurements Acceleration maps: double temporal differentiation  4 th order polynomial fit over time  Sliding window of 9 images  Resolution: between 1 and m.s -2 m.s -2

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 10/19 Measurements Strain maps: spatial differentiation  Local smoothing (diffuse approximation)  Resolution: 10 -3

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 11/19 Measurements Strain rate maps (s -1 ): temporal differentiation  Calculated through point to point finite difference  Resolution: about 400 s -1

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 12/19 Identification The virtual fields method x y F -F L Integrate over x Plane stress Linear elastic isotropy Homogeneous material

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 13/19 Identification Principle of virtual work No force measurement  In “static”:  Only stiffness ratios ( ) No force measurement  In dynamic  Acceleration forces: distributed volumic load cell! 1 VF: 1 linear equation

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 14/19 Identification Choice of virtual fields: field 1 Spatial differentiation of U x Spatial differentiation of U y Double time differentiation of U y x y L

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 15/19 Identification Choice of virtual fields: field 2 Linear system x y L

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 16/19 Identification Results Young’s modulus (GPa) Time (  s) Reference: 24.5 GPa Mean: 17.2 GPa

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 17/19 Identification Results Poisson’s ratio Time (  s) Reference: 0.35 Mean: 0.28

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 18/19 Measurements  Use of a UHS speed camera  Quantitative data obtained (novel)  Quality can be improved  Increase frame rate (limit: 4 Mfps)  Improve lighting, improve spatial resolution (grid pitch)  Understand origin of bias and noise Identification  Quantitative data obtained  Use of acceleration forces (novel)  Huge future potential: no need for Hopkinson bar setup  Need for better (and cheaper) cameras  Need for new test designs CONCLUSION

Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 19/19 Grant EP/G001715/1 for sabbatical of R. Moulart Access to the Cordin camera through the EPSRC pool of instruments ACKNOWLEDGEMENTS Engineering and Physical Sciences Research Council