Skip to main content
Log in

Extension of the Coherent Gradient Sensor (CGS) to the Combined Measurement of In-Plane and Out-of-Plane Displacement Field Gradients

  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

The Coherent Gradient Sensor (CGS) is extended to the optical differentiation of specular, diffracted wave fronts leading to the combined measurement of in- and out-of-plane displacement field gradients. A derivation of the underlying optical interference principles is presented along with an analysis of the effective instrument sensitivity. In order to demonstrate the capabilities of the technique, experimental measurements of crack-tip deformation fields were conducted under various loading conditions corresponding to mode-I, mode-II, and mixed mode near-tip crack fields. The experimental procedures and results of these tests are presented as validation of the technique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Tippur HV, Krishnaswamy S, Rosakis AJ (1991) A Coherent Gradient Sensor for crack tip deformation measurements—analysis and experimental results. Int J Fract 48(3):193–204.

    Article  Google Scholar 

  2. Tippur HV, Krishnaswamy S, Rosakis AJ (1991) 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(2):91–117.

    Google Scholar 

  3. Tippur HV (1992) Coherent gradient sensing: a Fourier optics analysis and applications to fracture. Appl Opt 31:4428–4439.

    Article  Google Scholar 

  4. Tippur HV, Rosakis AJ (1991) Quasi-static and dynamic crack growth along bimaterial interfaces: A note on crack-tip field measurements using coherent gradient sensing. Journal of Experimental Mechanics 31:243–251.

    Article  Google Scholar 

  5. Bruck HA, Rosakis AJ (1992) On the sensitivity of coherent gradient sensing: Part I—A theoretical investigation of accuracy in fracture mechanics applications. Opt Lasers Eng 17:83–101.

    Article  Google Scholar 

  6. Bruck HA, Rosakis AJ (1993) On the sensitivity of coherent gradient sensing: Part II—An experimental investigation of accuracy in fracture mechanics applications. Opt Lasers Eng 18:25–51.

    Article  Google Scholar 

  7. Rosakis AJ (1993) Two optical techniques sensitive to gradients of optical path difference: The method of caustics and the Coherent Gradient Sensor (CGS). In: Epstein J (ed) Experimental Techniques in Fracture, Chapter 10. Wiley, New Jersey.

    Google Scholar 

  8. Rosakis AJ (1993) Application of Coherent Gradient Sensing (CGS) to the investigation of dynamic fracture problems. Shukla A, Guest (eds) Special Issue of Optics and Lasers in Engineering devoted to Photomechanics Applied to Dynamic Response of Materials, pp 19, 3–41

  9. Lee YJ, Lambros J, Rosakis AJ (1996) Analysis of Coherent Gradient Sensing (CGS) by Fourier optics. Opt Lasers Eng 25:25–53.

    Article  Google Scholar 

  10. Shukla A (2006) Dynamic fracture mechanics, 1st edn. World Scientific, Singapore, p 162.

    MATH  Google Scholar 

  11. Krishnaswamy S, Tippur HV, Rosakis AJ (1992) Measurement of transient crack-tip deformation fields using the method of Coherent Gradient Sensing. J Mech Phys Solids 40:339–372.

    Article  Google Scholar 

  12. Mason JJ, Lambros J, Rosakis AJ (1992) The use of a Coherent Gradient Sensor in dynamic mixed-mode fracture mechanics experiments. J Mech Phys Solids 40:641–661.

    Article  Google Scholar 

  13. Liu C, Lambros J, Rosakis AJ (1993) Highly transient elastodynamic crack growth in a bimaterial interface: higher order asymptotic analysis and optical experiments. J Mech Phys Solids 41:1887–1954.

    Article  MATH  MathSciNet  Google Scholar 

  14. Lambros J, Rosakis AJ (1995) Dynamic decohesion of bimaterials: experimental observations and failure criteria. Int J Solids Struct 32:2677–2702.

    Article  Google Scholar 

  15. Coker D, Rosakis AJ (2001) Experimental observation of intersonic crack growth in asymmetrically loaded unidirectional composites. Philos Mag A 81:571–595.

    Article  Google Scholar 

  16. Rosakis AJ, Singh RP, Tsuji Y, Kolawa E, Moore NR Jr (1998) Full field measurements of curvature using Coherent Gradient Sensing: application to thin film characterization. Thin Solid Films 325:42–54.

    Article  Google Scholar 

  17. Singh RP, Rosakis AJ (2001) Determination of the yield properties of thin films using enhanced Coherent Gradient Sensing. Journal of Experimental Mechanics 41(4):403–411.

    Article  Google Scholar 

  18. Lee H, Rosakis AJ, Freund LB (2001) Full field optical measurement of curvatures in ultra-thin-film-substrate systems in the range of geometrically nonlinear deformations. J Appl Phys 89:6116–6129.

    Article  Google Scholar 

  19. Park T-S, Suresh S, Rosakis AJ, Ryu J (2003) Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry. J Mech Phy Solids 51(11–12):2191–2211.

    Article  Google Scholar 

  20. Brown MA, Park T-S, Rosakis A, Ustundag E, Huang Y, Tamura N, Valek B (2006) A comparison of X-ray micro diffraction and Coherent Gradient Sensing in measuring discontinuous curvatures in thin film—substrate systems. Journal of Applied Mechanics—Transactions of the ASME 73(5):723–729.

    MATH  Google Scholar 

  21. Rosakis AJ, Xia K, Lykotrafitis G, Kanamori H (2007) Dynamic shear rupture in frictional interfaces; speeds, directionality, and modes. In: Schubert G (ed) Treatise on Geophysics, volume 4, pp 153–192.

  22. Hung YY, Rowlands RE, Daniel IM (1975) Speckle-shearing interferometric technique—full-field strain gauge. Appl Opt 14(3):618–622.

    Article  Google Scholar 

  23. Weissman EM, Post D, Asundi A (1984) Whole-field strain determination by Moiré shearing interferometry. J Strain Anal Eng Des 19(2):77–80.

    Article  Google Scholar 

  24. Patorski K, Post D, Czarnek R, Guo Y (1987) Real-time optical differentiation for moiré interferometry. Appl Opt 26(10):1977–1982.

    Article  Google Scholar 

  25. Creath K (1985) Phase-shifting speckle interferometry. Appl Opt 24(18):3053–3058.

    Article  Google Scholar 

  26. Cloud GL (1995) Optical methods of engineering analysis. Cambridge University Press, New York.

    Google Scholar 

  27. Malacara D (1992) Optical shop testing. Wiley, New York.

    Google Scholar 

  28. Patorski K, Olszak A (1997) Digital in-plane electronic speckle pattern shearing interferometry. Opt Eng 367:2010–2015.

    Article  Google Scholar 

  29. Nakadate S, Saito H (1985) Fringe scanning speckle-pattern interferometry. Appl Opt 24(14):2172–2180.

    Article  Google Scholar 

  30. Rastogi PK (1996) Measurement of in-plane strains using electronic speckle and electronic speckle-shearing pattern interferometry. J Mod Opt 43(8):1577–1581.

    Google Scholar 

  31. Post D, Han B, Ifju P (1994) High sensitivity Moiré: experimental analysis for mechanics and materials. Springer, New York.

    Google Scholar 

  32. Kim KS, Clifton RJ, Kumar P (1977) A combined normal and transverse displacement interferometer with an application to impact of Y-cut quartz. J Appl Phys, 48(10):4132–4139.

    Article  Google Scholar 

  33. Espinosa HD, Mello M, Xu Y (1997) A variable sensitivity displacement interferometer with application to wave propagation experiments. Journal of Applied Mechanics—Transactions of the ASME 64:123–131.

    Google Scholar 

  34. Tada H, Paris PC, Irwin GR (1973) The stress analysis of cracks handbook. Del Research Corp., Hellertown, PA.

    Google Scholar 

  35. He MY, Hutchinson JW (2000) Asymmetric four-point crack specimen. Journal of Applied Mechanics—Transactions of the ASME 67(1):207–209.

    MATH  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support of the US Department of Energy (Grant DE-FG52-06NA 26209, ASC grant B523297 (LLNL), and the Office of Naval Research through a Caltech MURI grant, N0014-06-1-0730—Dr. Y.D.S Rajapakse, Program Manager.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Mello.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mello, M., Hong, S. & Rosakis, A.J. Extension of the Coherent Gradient Sensor (CGS) to the Combined Measurement of In-Plane and Out-of-Plane Displacement Field Gradients. Exp Mech 49, 277–289 (2009). https://doi.org/10.1007/s11340-008-9147-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-008-9147-z

Keywords

Navigation