Two Modified Digital Gradient Sensing with Higher Measurement Sensitivity for Evaluating Stress Gradients in Transparent Solids

  • Chengyun Miao
  • Hareesh V. TippurEmail author
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Two modified full-field Digital Gradient Sensing (DGS) methods with higher measurement sensitivity are presented for quantifying small angular deflections of light rays caused by a non-uniform state-of-stress in a transparent solid. These methods are devised by combining or altering previously proposed methods, reflection-mode DGS (r-DGS) (Periasamy and Tippur, Meas Sci Technol 24:025202, 2013) and transmission-mode DGS (t-DGS) (Periasamy and Tippur, Appl Opt 51:2088–2097, 2012). In this presentation, the working principles of r-DGS and t-DGS are introduced first. Then, the so-called t2-DGS method is proposed with the aid of a separate reflective planar surface located behind the transparent solid. The sensitivity of t2-DGS is shown to be twice that of t-DGS. Next, an even higher sensitivity method called the transmission-reflection DGS or simply tr-DGS is developed by making the back surface of a transparent planar solid specularly reflective. The governing equations of tr-DGS are proposed followed by a comparative demonstration of t2-DGS and tr-DGS methods by measuring stress gradients in the crack tip region during a dynamic fracture experiment. The tr-DGS is ∼1.5 times more sensitive than t2-DGS, and at least three times more sensitive than t-DGS approach.


Digital gradient sensing Quantitative visualization Angular deflections Full-field measurements Photomechanics 



Support for this research through Army Research Office grants W911NF-16-1-0093 and W911NF-15-1-0357 (DURIP) are gratefully acknowledged.


  1. 1.
    Periasamy, C., Tippur, H.V.: A full-field reflection-mode digital gradient sensing method for measuring orthogonal slopes and curvatures of thin structures. Meas. Sci. Technol. 24, 025202 (2013)CrossRefGoogle Scholar
  2. 2.
    Periasamy, C., Tippur, H.V.: Full-field digital gradient sensing method for evaluating stress gradients in transparent solids. Appl. Opt. 51(12), 2088–2097 (2012)CrossRefGoogle Scholar
  3. 3.
    Sutton, M.A., Orteu, J.J.: Image Correlation for Shape, Motion and Deformation Measurements. Springer, New York (2009)Google Scholar
  4. 4.
    Pankow, M., Justusson, B., Waas, A.M.: Three-dimensional digital image correlation technique using single high-speed camera for measuring large out-of-plane displacements at high framing rates. Appl. Opt. 49, 3418–3427 (2010)CrossRefGoogle Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Miao, C., Sundaram, B.M., Huang, L., Tippur, H.V.: Surface profile and stress field evaluation using digital gradient sensing method. Meas. Sci. Technol. 27, 095203 (2016)CrossRefGoogle Scholar
  7. 7.
    Miao, C., Tippur, H.V.: Measurement of orthogonal surface gradients and reconstruction of surface topography from digital gradient sensing method. In: Advancement of Optical Methods in Experimental Mechanics, pp. 203–206. Springer, Cham (2017)CrossRefGoogle Scholar
  8. 8.
    Miao, C., Tippur, H.V.: Measurement of Sub-micron Deformations and Stresses at Microsecond Intervals in Laterally Impacted Composite Plates Using Digital Gradient Sensing. J. Dynamic Behav. Mat. 1–23 (2018). CrossRefGoogle Scholar
  9. 9.
    Sundaram, B.M., Tippur, H.V.: Dynamic crack growth normal to an interface in Bi-Layered materials: an experimental study using digital gradient sensing technique. Exp. Mech. 56, 37–57 (2015)CrossRefGoogle Scholar
  10. 10.
    Sundaram, B.M., Tippur, H.V.: Dynamics of crack penetration vs. branching at a weak interface: an experimental study. J. Mech. Phy. Solids. 96, 312–332 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Sundaram, B.M., Tippur, H.V.: Dynamic mixed-mode fracture behaviors of PMMA and polycarbonate. Eng. Fract. Mech. 176, 186–212 (2017)CrossRefGoogle Scholar
  12. 12.
    Sundaram, B.M., Tippur, H.V.: Dynamic fracture of soda-lime glass: a full-field optical investigation of crack initiation, propagation and branching. J, Mech. Phy Solids. (2018). CrossRefGoogle Scholar
  13. 13.
    Sundaram, B.M., Tippur, H.V.: Full-field measurement of contact-point and crack-tip deformations in soda-lime glass. Part-I: Quasi-static Loading. Int. J. Appl. Glas. Sci. 9, 114–122 (2018)CrossRefGoogle Scholar
  14. 14.
    Sundaram, B.M., Tippur, H.V.: Full-field measurement of contact-point and crack-tip deformations in soda-lime glass. Part-II: Stress wave loading. Int. J. Appl. Glas. Sci. 9, 123–136 (2018)CrossRefGoogle Scholar
  15. 15.
    Miao, C., Tippur, H.V.: Higher sensitivity DigitalGradient Sensing configurations for quantitative visualization of stress gradients in transparent solids. Opt. Lasers Eng. 108, 54–67 (2018)CrossRefGoogle Scholar
  16. 16.
    Tippur, H.V., Krishnaswamy, S., Rosakis, A.J.: Optical mapping of crack tip deformations using the methods of transmission and reflection coherent gradient sensing: a study of crack tip K-dominance. Int. J. Fract. 52, 91–117 (1991)Google Scholar
  17. 17.
    Xu, L., Tippur, H., Rousseau, C.-E.: Measurement of contact stresses using real-time shearing interferometry. Opt. Eng. 38, 1932–1937 (1999)CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringAuburn UniversityAuburnUSA

Personalised recommendations