Abstract

Digital image correlation (DIC) is commonly used to measure specimen displacements by correlating an image of a specimen in an undeformed or reference configuration and a second image under load. To establish the correlation between the images, numerical techniques are used to locate an initially square image subset in a reference image. In thisprocess, choosing appropriate coordinates is of fundamental importance to ensure accurate results. Both global and local coordinates can be used in shape functions. However, large rigid body rotations and deformations are accurately obtained by using global rather than local shape functions. In addition, points located after displacement may not be at an integer pixel distance from the original position. Hence subpixel displacement estimation methods such as interpolation or fitting of correlation coefficients are essential. A solution using the least-squares method is employed by choosing proper coordinates, and the feasibility of using local coordinates is demonstrated and validated with a mathematical model. Both simulated and experimental results show that the proper choice of coordinates does ensure the reliability and improve the accuracy of measurements in DIC.

© 2007 Optical Society of America

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References

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  1. T. C. Chu, W. F. Ranson, and M. A. Sutton, "Applications of digital-image-correlation techniques to experimental mechanics," Exp. Mech. 25, 232-244 (1985).
    [CrossRef]
  2. H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, "Digital-image-correlation using Newton-Raphson method for partial differential correction," Exp. Mech. 29, 261-267 (1989).
    [CrossRef]
  3. H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
    [CrossRef]
  4. H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
    [CrossRef]
  5. P. Zhou and K. E. Goodson, "Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC)," Opt. Eng. 40, 1613-1620 (2001).
    [CrossRef]
  6. H. Lu and P. D. Cary, "Deformation measurements by digital image correlation: implementation of a second-order displacement gradient," Exp. Mech. 40, 393-400 (2000).
    [CrossRef]
  7. Y. X. Sun, John H. L. Pang, C. K. Wong, and F. Su, "Finite element formulation for a digital image correlation method," Appl. Opt. 44, 7357-7363 (2005).
    [CrossRef] [PubMed]
  8. R. T. Fenner, Engineering Elasticity: Application of Numerical and Analytical Techniques (Halsted, 1986).
  9. P. Hung and A. S. Voloshin, "In-plane strain measurement by digital image correlation," J. Braz. Soc. Mech. Sci. Eng. 25, 215-221 (2003).
  10. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. (Johns Hopkins U. Press, 1989).

2005 (1)

2003 (1)

P. Hung and A. S. Voloshin, "In-plane strain measurement by digital image correlation," J. Braz. Soc. Mech. Sci. Eng. 25, 215-221 (2003).

2002 (1)

H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
[CrossRef]

2001 (1)

P. Zhou and K. E. Goodson, "Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC)," Opt. Eng. 40, 1613-1620 (2001).
[CrossRef]

2000 (2)

H. Lu and P. D. Cary, "Deformation measurements by digital image correlation: implementation of a second-order displacement gradient," Exp. Mech. 40, 393-400 (2000).
[CrossRef]

H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
[CrossRef]

1989 (1)

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, "Digital-image-correlation using Newton-Raphson method for partial differential correction," Exp. Mech. 29, 261-267 (1989).
[CrossRef]

1985 (1)

T. C. Chu, W. F. Ranson, and M. A. Sutton, "Applications of digital-image-correlation techniques to experimental mechanics," Exp. Mech. 25, 232-244 (1985).
[CrossRef]

Braasch, J. R.

H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
[CrossRef]

Bruck, H. A.

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, "Digital-image-correlation using Newton-Raphson method for partial differential correction," Exp. Mech. 29, 261-267 (1989).
[CrossRef]

Cary, P. D.

H. Lu and P. D. Cary, "Deformation measurements by digital image correlation: implementation of a second-order displacement gradient," Exp. Mech. 40, 393-400 (2000).
[CrossRef]

Chu, T. C.

T. C. Chu, W. F. Ranson, and M. A. Sutton, "Applications of digital-image-correlation techniques to experimental mechanics," Exp. Mech. 25, 232-244 (1985).
[CrossRef]

Fenner, R. T.

R. T. Fenner, Engineering Elasticity: Application of Numerical and Analytical Techniques (Halsted, 1986).

Golub, G. H.

G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. (Johns Hopkins U. Press, 1989).

Goodson, K. E.

P. Zhou and K. E. Goodson, "Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC)," Opt. Eng. 40, 1613-1620 (2001).
[CrossRef]

Hung, P.

P. Hung and A. S. Voloshin, "In-plane strain measurement by digital image correlation," J. Braz. Soc. Mech. Sci. Eng. 25, 215-221 (2003).

Lu, H.

H. Lu and P. D. Cary, "Deformation measurements by digital image correlation: implementation of a second-order displacement gradient," Exp. Mech. 40, 393-400 (2000).
[CrossRef]

McNeill, S. R.

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, "Digital-image-correlation using Newton-Raphson method for partial differential correction," Exp. Mech. 29, 261-267 (1989).
[CrossRef]

Pang, John H. L.

Peters, W. H.

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, "Digital-image-correlation using Newton-Raphson method for partial differential correction," Exp. Mech. 29, 261-267 (1989).
[CrossRef]

Ranson, W. F.

T. C. Chu, W. F. Ranson, and M. A. Sutton, "Applications of digital-image-correlation techniques to experimental mechanics," Exp. Mech. 25, 232-244 (1985).
[CrossRef]

Schreier, H. W.

H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
[CrossRef]

H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
[CrossRef]

Su, F.

Sun, Y. X.

Sutton, M. A.

H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
[CrossRef]

H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, "Digital-image-correlation using Newton-Raphson method for partial differential correction," Exp. Mech. 29, 261-267 (1989).
[CrossRef]

T. C. Chu, W. F. Ranson, and M. A. Sutton, "Applications of digital-image-correlation techniques to experimental mechanics," Exp. Mech. 25, 232-244 (1985).
[CrossRef]

Van Loan, C. F.

G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. (Johns Hopkins U. Press, 1989).

Voloshin, A. S.

P. Hung and A. S. Voloshin, "In-plane strain measurement by digital image correlation," J. Braz. Soc. Mech. Sci. Eng. 25, 215-221 (2003).

Wong, C. K.

Zhou, P.

P. Zhou and K. E. Goodson, "Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC)," Opt. Eng. 40, 1613-1620 (2001).
[CrossRef]

Appl. Opt. (1)

Exp. Mech. (4)

T. C. Chu, W. F. Ranson, and M. A. Sutton, "Applications of digital-image-correlation techniques to experimental mechanics," Exp. Mech. 25, 232-244 (1985).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, "Digital-image-correlation using Newton-Raphson method for partial differential correction," Exp. Mech. 29, 261-267 (1989).
[CrossRef]

H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
[CrossRef]

H. Lu and P. D. Cary, "Deformation measurements by digital image correlation: implementation of a second-order displacement gradient," Exp. Mech. 40, 393-400 (2000).
[CrossRef]

J. Braz. Soc. Mech. Sci. Eng. (1)

P. Hung and A. S. Voloshin, "In-plane strain measurement by digital image correlation," J. Braz. Soc. Mech. Sci. Eng. 25, 215-221 (2003).

Opt. Eng. (2)

P. Zhou and K. E. Goodson, "Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC)," Opt. Eng. 40, 1613-1620 (2001).
[CrossRef]

H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
[CrossRef]

Other (2)

G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. (Johns Hopkins U. Press, 1989).

R. T. Fenner, Engineering Elasticity: Application of Numerical and Analytical Techniques (Halsted, 1986).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the deformationprocess for a planar object (a) before deformation and (b) after deformation.

Fig. 2
Fig. 2

Rotation case (a) reference image, (b) rotated image, (c) calculated results.

Fig. 3
Fig. 3

Uniaxial tensile case (a) reference image, (b) calculated results using Eq. (8), (c) calculated results using Eq. (5).

Fig. 4
Fig. 4

Experimental setup using DIC.

Fig. 5
Fig. 5

Results of rotation case (a) image of specimen (small rotation), (b) results for small angles, (c) errors in small angles, (d) results for large angles, (e) errors in large angles.

Fig. 6
Fig. 6

Results for pure bending: (a) setup for pure bending test, (b) calculated slope values ( u / y ) , (c) calculated strains values ( ε x ) .

Fig. 7
Fig. 7

Calculated displacements using surface fitting (a) global coordinates, (b) local coordinates.

Equations (11)

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C = { i = 1 m j = 1 n [ f ( x i , y j ) f ¯ ] [ g ( x i * , y j * ) g ¯ ] } 2 i = 1 m j = 1 n [ f ( x i , y j ) f ¯ ] 2 i = 1 m j = 1 n [ g ( x i * , y j * ) g ¯ ] 2 ,
x * = a 1 + a 2 x + a 3 y , y * = a 4 + a 5 x + a 6 y ,
ξ = x * x = a 1 + ( a 2 1 ) x + a 3 y
η = y * y = a 4 + a 5 x + ( a 6 1 ) y .
ξ = a 1 + ( a 2 1 ) ( x 0 + Δ x ) + a 3 ( y 0 + Δ y ) = ξ 0 + ( a 2 1 ) Δ x + a 3 Δ y ,
η = a 4 + a 5 ( x 0 + Δ x ) + ( a 6 1 ) ( y 0 + Δ y ) = η 0 + a 5 Δ x + ( a 6 1 ) Δ y .
ξ = u + u x Δ x + u y Δ y , η = v + v x Δ x + v y Δ y .
e = [ f ( x ) y ] 2 .
C ( x i , y j ) = a 0 + a 1 x i + a 2 y j + a 3 x i 2 + a 4 x i y j + a 5 y j 2 ,
C = B a ,
C = [ i = 1 9 C i i = 1 9 C i x i i = 1 9 C i y i i = 1 9 C i x i 2 i = 1 9 C i x i y i i = 1 9 C i y i 2 ] , B = [ i = 1 9 1 i = 1 9 x i i = 1 9 y i i = 1 9 x i 2 i = 1 9 x i y i i = 1 9 y i 2 i = 1 9 x i i = 1 9 x i 2 i = 1 9 x i y i i = 1 9 x i 3 i = 1 9 x i 2 y i i = 1 9 x i y i 2 i = 1 9 y i i = 1 9 x i y i i = 1 9 y i 2 i = 1 9 x i 2 y i i = 1 9 x i y i 2 i = 1 9 y i 3 i = 1 9 x i 2 i = 1 9 x i 3 i = 1 9 x i 2 y i i = 1 9 x i 4 i = 1 9 x i 3 y i i = 1 9 x i 2 y i 2 i = 1 9 x i y i i = 1 9 x i 2 y i i = 1 9 x i y i 2 i = 1 9 x i 3 y i i = 1 9 x i 2 y i 2 i = 1 9 x i y i 3 i = 1 9 y i 2 i = 1 9 x i y i 2 i = 1 9 y i 3 i = 1 9 x i 2 y i 2 i = 1 9 x i y i 3 i = 1 9 y i 4 ] , a = [ a 0 a 1 a 2 a 3 a 4 a 5 ] .

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