Abstract

A technique to measure two-dimensional deformation fields of a layer inside materials during dynamic events such as impact experiments is presented. Even optically opaque materials like cement can be evaluated when flash x rays are used. Blocks of polyester and cement were prepared with a layer of x-ray-absorbing lead particles. The specimens were then hit by a 9-mm-diameter steel sphere (ball bearing) fired from a 9-mm-bore gas gun at a velocity of 373.5 ± 3.0 ms-1. A 30-ns-long x-ray pulse exposed one radiograph before impact; another radiograph was exposed a short time after the impact on the specimen. The two-dimensional displacement field was obtained when the x-ray radiographs were digitized by a conventional flatbed scanner, and a digital speckle photography algorithm was used to calculate the displacements. The flash x-ray technique allowed examination of the deformation at the layer inside the material during failure, thus giving interesting data about the material flow field around the impactor.

© 1999 Optical Society of America

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References

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  1. T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “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, W. H. Peters, “Digital image correlation using Newton–Raphson method by partial differential correction,” Exp. Mech. 29, 261–267 (1989).
    [CrossRef]
  3. M. Sjödahl, L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278–2284 (1993).
    [CrossRef] [PubMed]
  4. M. Sjödahl, “Electronic speckle photography: increased accuracy by nonintegral pixel shifting,” Appl. Opt. 33, 6667–6673 (1994).
    [CrossRef] [PubMed]
  5. M. Sjödahl, L. R. Benckert, “Systematic and random errors in electronic speckle photography,” Appl. Opt. 33, 7461–7471 (1994).
    [CrossRef] [PubMed]
  6. S. R. McNeill, W. H. Peters, M. A. Sutton, “Estimation of stress intensity factor by digital image correlation,” Eng. Fracture Mech. 28, 101–112 (1987).
    [CrossRef]
  7. J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
    [CrossRef]
  8. P. Johnson, “Strain field measurements with dual-beam digital speckle photography,” Opt. Lasers Eng. 30, 315–326 (1998).
    [CrossRef]
  9. B. Rose, H. Imam, S. G. Hanson, H. T. Yura, R. S. Hansen, “Laser-speckle angular-displacement sensor: theoretical and experimental study,” Appl. Opt. 37, 2119–2129 (1998).
    [CrossRef]
  10. J. E. Field, “High-speed photography at the Cavendish,” in High-Speed Photography and Photonics, S. F. Ray, ed. (Focal Press, London, 1997), Chap. 21, pp. 301–314.
  11. N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).
  12. S. S. Russell, M. A. Sutton, “Strain-field analysis acquired through correlation of x-ray radiographs of a fiber-reinforced composite laminate,” Exp. Mech. 29, 237–240 (1989).
    [CrossRef]
  13. M. Sjödahl, “Accuracy in electronic speckle photography,” Appl. Opt. 36, 2875–2885 (1997).
    [CrossRef] [PubMed]
  14. R. P. Brent, Algorithms for Minimization without Derivatives (Prentice-Hall, Englewood Cliffs, N.J., 1973).
  15. B. R. Lawn, Fracture of Brittle Solids, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1993).
    [CrossRef]

1998 (2)

1997 (2)

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

M. Sjödahl, “Accuracy in electronic speckle photography,” Appl. Opt. 36, 2875–2885 (1997).
[CrossRef] [PubMed]

1996 (1)

J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
[CrossRef]

1994 (2)

1993 (1)

1989 (2)

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

S. S. Russell, M. A. Sutton, “Strain-field analysis acquired through correlation of x-ray radiographs of a fiber-reinforced composite laminate,” Exp. Mech. 29, 237–240 (1989).
[CrossRef]

1987 (1)

S. R. McNeill, W. H. Peters, M. A. Sutton, “Estimation of stress intensity factor by digital image correlation,” Eng. Fracture Mech. 28, 101–112 (1987).
[CrossRef]

1985 (1)

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital image correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

Benckert, L. R.

Bourne, N. K.

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

Brent, R. P.

R. P. Brent, Algorithms for Minimization without Derivatives (Prentice-Hall, Englewood Cliffs, N.J., 1973).

Bruck, H. A.

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

Chu, T. C.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital image correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

Field, J. E.

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

J. E. Field, “High-speed photography at the Cavendish,” in High-Speed Photography and Photonics, S. F. Ray, ed. (Focal Press, London, 1997), Chap. 21, pp. 301–314.

Forde, L. C.

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

Hansen, R. S.

Hanson, S. G.

Helm, J. D.

J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
[CrossRef]

Imam, H.

Johnson, P.

P. Johnson, “Strain field measurements with dual-beam digital speckle photography,” Opt. Lasers Eng. 30, 315–326 (1998).
[CrossRef]

Lawn, B. R.

B. R. Lawn, Fracture of Brittle Solids, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1993).
[CrossRef]

McNeill, S. R.

J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
[CrossRef]

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

S. R. McNeill, W. H. Peters, M. A. Sutton, “Estimation of stress intensity factor by digital image correlation,” Eng. Fracture Mech. 28, 101–112 (1987).
[CrossRef]

Millett, J. C. F.

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

Peters, W. H.

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

S. R. McNeill, W. H. Peters, M. A. Sutton, “Estimation of stress intensity factor by digital image correlation,” Eng. Fracture Mech. 28, 101–112 (1987).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital image correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

Ranson, W. F.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital image correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

Rose, B.

Russell, S. S.

S. S. Russell, M. A. Sutton, “Strain-field analysis acquired through correlation of x-ray radiographs of a fiber-reinforced composite laminate,” Exp. Mech. 29, 237–240 (1989).
[CrossRef]

Sjödahl, M.

Sutton, M. A.

J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
[CrossRef]

S. S. Russell, M. A. Sutton, “Strain-field analysis acquired through correlation of x-ray radiographs of a fiber-reinforced composite laminate,” Exp. Mech. 29, 237–240 (1989).
[CrossRef]

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

S. R. McNeill, W. H. Peters, M. A. Sutton, “Estimation of stress intensity factor by digital image correlation,” Eng. Fracture Mech. 28, 101–112 (1987).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital image correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

Yura, H. T.

Appl. Opt. (5)

Eng. Fracture Mech. (1)

S. R. McNeill, W. H. Peters, M. A. Sutton, “Estimation of stress intensity factor by digital image correlation,” Eng. Fracture Mech. 28, 101–112 (1987).
[CrossRef]

Exp. Mech. (3)

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “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, W. H. Peters, “Digital image correlation using Newton–Raphson method by partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

S. S. Russell, M. A. Sutton, “Strain-field analysis acquired through correlation of x-ray radiographs of a fiber-reinforced composite laminate,” Exp. Mech. 29, 237–240 (1989).
[CrossRef]

J. Phys. IV France Colloq. C3 (1)

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

Opt. Eng. (1)

J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
[CrossRef]

Opt. Lasers Eng. (1)

P. Johnson, “Strain field measurements with dual-beam digital speckle photography,” Opt. Lasers Eng. 30, 315–326 (1998).
[CrossRef]

Other (3)

J. E. Field, “High-speed photography at the Cavendish,” in High-Speed Photography and Photonics, S. F. Ray, ed. (Focal Press, London, 1997), Chap. 21, pp. 301–314.

R. P. Brent, Algorithms for Minimization without Derivatives (Prentice-Hall, Englewood Cliffs, N.J., 1973).

B. R. Lawn, Fracture of Brittle Solids, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1993).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of the setup.

Fig. 2
Fig. 2

(a) Image of a polyester sample (the lead layer is 10 mm from the top surface), (b) the random intensity pattern of the lead absorbers seen from above.

Fig. 3
Fig. 3

Radiograph shows a polyester sample 41 µs after impact. The specimen, the holder, and the fiducial markers are marked in the figure, and the area of interest is defined. Note the light spots; they are the x-ray shadows of the lead grains.

Fig. 4
Fig. 4

Measured deformation of the polyester samples after (a) 20 µs, (b) 30 µs, (c) 41 µs, (d) 53 µs.

Fig. 5
Fig. 5

High-speed camera sequence taken with an Imacon shows the impact of a 9-mm ball bearing on one of the polyester specimens. The camera is looking on the specimen from the same position as the x-ray setup; the dark spots in the image are the lead grains. The interframe time is 5 µs; the first image is taken 15 µs after impact. The four images in the second column are taken at roughly the same time after impact as the four x-ray radiographs.

Fig. 6
Fig. 6

Formation of a cone crack. The material under the impactor suffers compression; the material to the side of the impactor is pushed laterally and put into tension. This opens up a cone crack, which moves along a shear line (marked in the figure).

Fig. 7
Fig. 7

Result of the cement experiment. On the right-hand side the upper graph shows the lateral deformation (in the x direction) and the lower graph shows the deformation in the direction of the impact. It can be noted that the compression of the cement block is higher than that of the polyester samples. The reason is that the cement is a porous granular material, which polyester is not, and thus allows a higher degree of fragmentation and compression in the region of impact. 2-D, two dimensions.

Tables (1)

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Table 1 Expected and Calculated Random Errorsa

Equations (3)

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cp, q=-1HS1*HS2,
e=k σ2B1-γγ,
e=0.030σ1.671-γγ.

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