# Measurement of Sub-micron Deformations and Stresses at Microsecond Intervals in Laterally Impacted Composite Plates Using Digital Gradient Sensing

## Abstract

Visualization and quantification of surface topography and stresses from measured slope data is of considerable importance to study many engineering problems including response of structural plates to stress wave loading. In this work, a full-field optical technique called Digital Gradient Sensing (DGS) is implemented in the reflection-mode to quantify time-resolved surface slopes in composite plates at microsecond intervals as they are impact loaded. The method being capable of determining two orthogonal surface slopes by measuring angular deflections of light rays, as small as a few micro-radians, surface topography can be quantified using a Higher-order Finite-difference-based Least-squares Integration (HFLI). Numerical differentiation of surface slopes, on the other hand, provides all three curvatures enabling estimation of stresses. Carbon fiber reinforced composite plates of different layups are subjected to dynamic impact loading using a Hopkinson pressure bar. Ultrahigh-speed digital photography is used to record deformations using DGS. The out-of-plane deformations are obtained by post-processing data from DGS at each time instant using HFLI whereas stresses are estimated by evaluating instantaneous curvatures obtained by differentiating measured slopes.

## Keywords

Composite plates Impact loading Vision-based measurements Surface slopes Deflections and stresses Ultrahigh-speed photography## Notes

### Acknowledgements

Authors thank the financial and equipment support from Grants (U.S. Army) W31P4Q-14-C-0049, ARMY-W911NF-16-1-0093 and W911NF-15-1-0357 (DURIP). The assistance of Dr. Dongyeon Lee, Toray Composite Materials America, Inc. for supplying CFRP sheets studied in this work is gratefully acknowledged.

## Supplementary material

Supplementary material 1 (MP4 407 KB)

Supplementary material 2 (MP4 724 KB)

Supplementary material 3 (MP4 686 KB)

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