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Measurement of Orthogonal Stress Gradients Due to Impact Load on a Transparent Sheet using Digital Gradient Sensing Method

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Abstract

A full-field optical method called Digital Gradient Sensing (DGS) for measuring stress gradients due to an impact load on a planar transparent sheet is presented. The technique is based on the elasto-optic effect exhibited by transparent solids due to an imposed stress field causing angular deflections of light rays quantified using 2D digital image correlation method. The measured angular deflections are proportional to the in-plane gradients of stresses under plane stress conditions. The method is relatively simple to implement and is capable of measuring stress gradients in two orthogonal directions simultaneously. The feasibility of this method to study material failure/damage is demonstrated on transparent planar sheets of PMMA subjected to both quasi-static and dynamic line load acting on an edge. In the latter case, ultra high-speed digital photography is used to perform time-resolved measurements. The quasi-static measurements are successfully compared with those based on the Flamant solution for a line-load acting on a half-space in regions where plane stress conditions prevail. The dynamic measurements, prior to material failure, are also successfully compared with finite element computations. The measured stress gradients near the impact point after damage initiation are also presented and failure behavior is discussed.

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Notes

  1. For simplicity, this approach was used instead of the solution to the Lamb problem [40]. Lamb solutions are available for a line pulse or a suddenly imposed constant line load on an elastic half-space; for large values of time, the latter case reduces to the elastostatic solution. The applied load history in this case being approximately a ramp transitioning to a constant value, elastostatic behavior is to be expected behind the shear wave front.

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Acknowledgments

Partial support for this research through grants W911NF-12-1-0317 from the U.S. Army Research Office and NSF-CMMI-1232821 from the National Science Foundation is gratefully acknowledged.

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  1. Department of Mechanical Engineering, Auburn University, Auburn, AL, 36849, USA

    C. Periasamy & H. V. Tippur

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  1. C. Periasamy
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  2. H. V. Tippur
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Correspondence to H. V. Tippur.

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Periasamy, C., Tippur, H.V. Measurement of Orthogonal Stress Gradients Due to Impact Load on a Transparent Sheet using Digital Gradient Sensing Method. Exp Mech 53, 97–111 (2013). https://doi.org/10.1007/s11340-012-9653-x

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