Abstract

A method of constructing digital shear-strain moiré patterns with pure shear-strain fringes is proposed here with the help of digital image processing techniques and moiré carrier patterns of rotation. This method is developed from a digital pure secondary moiré pattern method. The pure shear-strain moiré patterns do not require a high fringe density of primary moiré patterns. It can give the shear-strain values at every point over the whole field and give the visible distribution of the shear-strain field.

© 1992 Optical Society of America

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References

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  1. A. J. Durelli, V. J. Parks, Moire Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970).
  2. E. M. Weissman, D. Post, “Full-field displacement and strain rosettes by moire interferometry,” Exp. Mech. 22, 324–328 (1982).
    [CrossRef]
  3. K. Patorski, “Shearing interferometry and the moire method for shear strain determination,” Appl. Opt. 27, 3567–3572 (1988).
    [CrossRef] [PubMed]
  4. D. Post, R. Czarnek, D. Joh, “Shear-strain contours from moire interferometry,” Exp. Mech. 25, 282–287 (1985).
    [CrossRef]
  5. Q. F. Yu, “Constructing pure digital secondary moire patterns,” Exp. Mech. 30, 247–252 (1990).
    [CrossRef]
  6. A. S. Voloshin, C. P. Burger, R. E. Rowlands, T. G. Richard, “Fractional moire strain analysis using digital image techniques,” Exp. Mech. 26, 254–258 (1986).
    [CrossRef]
  7. Q. F. Yu, “Spin filtering processes and automatic extraction of fringe centerlines in digital interferometric patterns,” Appl. Opt. 27, 3782–3784 (1988).
    [CrossRef] [PubMed]
  8. Q. F. Yu, “Fringe multiplication methods for digital interferometric fringes,” Appl. Opt. 28, 4323–4327 (1989).
    [CrossRef] [PubMed]

1990 (1)

Q. F. Yu, “Constructing pure digital secondary moire patterns,” Exp. Mech. 30, 247–252 (1990).
[CrossRef]

1989 (1)

1988 (2)

1986 (1)

A. S. Voloshin, C. P. Burger, R. E. Rowlands, T. G. Richard, “Fractional moire strain analysis using digital image techniques,” Exp. Mech. 26, 254–258 (1986).
[CrossRef]

1985 (1)

D. Post, R. Czarnek, D. Joh, “Shear-strain contours from moire interferometry,” Exp. Mech. 25, 282–287 (1985).
[CrossRef]

1982 (1)

E. M. Weissman, D. Post, “Full-field displacement and strain rosettes by moire interferometry,” Exp. Mech. 22, 324–328 (1982).
[CrossRef]

Burger, C. P.

A. S. Voloshin, C. P. Burger, R. E. Rowlands, T. G. Richard, “Fractional moire strain analysis using digital image techniques,” Exp. Mech. 26, 254–258 (1986).
[CrossRef]

Czarnek, R.

D. Post, R. Czarnek, D. Joh, “Shear-strain contours from moire interferometry,” Exp. Mech. 25, 282–287 (1985).
[CrossRef]

Durelli, A. J.

A. J. Durelli, V. J. Parks, Moire Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970).

Joh, D.

D. Post, R. Czarnek, D. Joh, “Shear-strain contours from moire interferometry,” Exp. Mech. 25, 282–287 (1985).
[CrossRef]

Parks, V. J.

A. J. Durelli, V. J. Parks, Moire Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970).

Patorski, K.

Post, D.

D. Post, R. Czarnek, D. Joh, “Shear-strain contours from moire interferometry,” Exp. Mech. 25, 282–287 (1985).
[CrossRef]

E. M. Weissman, D. Post, “Full-field displacement and strain rosettes by moire interferometry,” Exp. Mech. 22, 324–328 (1982).
[CrossRef]

Richard, T. G.

A. S. Voloshin, C. P. Burger, R. E. Rowlands, T. G. Richard, “Fractional moire strain analysis using digital image techniques,” Exp. Mech. 26, 254–258 (1986).
[CrossRef]

Rowlands, R. E.

A. S. Voloshin, C. P. Burger, R. E. Rowlands, T. G. Richard, “Fractional moire strain analysis using digital image techniques,” Exp. Mech. 26, 254–258 (1986).
[CrossRef]

Voloshin, A. S.

A. S. Voloshin, C. P. Burger, R. E. Rowlands, T. G. Richard, “Fractional moire strain analysis using digital image techniques,” Exp. Mech. 26, 254–258 (1986).
[CrossRef]

Weissman, E. M.

E. M. Weissman, D. Post, “Full-field displacement and strain rosettes by moire interferometry,” Exp. Mech. 22, 324–328 (1982).
[CrossRef]

Yu, Q. F.

Appl. Opt. (3)

Exp. Mech. (4)

E. M. Weissman, D. Post, “Full-field displacement and strain rosettes by moire interferometry,” Exp. Mech. 22, 324–328 (1982).
[CrossRef]

D. Post, R. Czarnek, D. Joh, “Shear-strain contours from moire interferometry,” Exp. Mech. 25, 282–287 (1985).
[CrossRef]

Q. F. Yu, “Constructing pure digital secondary moire patterns,” Exp. Mech. 30, 247–252 (1990).
[CrossRef]

A. S. Voloshin, C. P. Burger, R. E. Rowlands, T. G. Richard, “Fractional moire strain analysis using digital image techniques,” Exp. Mech. 26, 254–258 (1986).
[CrossRef]

Other (1)

A. J. Durelli, V. J. Parks, Moire Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970).

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Figures (10)

Fig. 1
Fig. 1

Rotating angles of moiré carrier patterns of rotation.

Fig. 2
Fig. 2

Shape and dimensions of a three-point bending specimen.

Fig. 3
Fig. 3

Carrier moiré pattern of a U field with a positive carrier angle in the right half of the specimen.

Fig. 4
Fig. 4

Carrier moiré pattern of a U field with a negative carrier angle in the right half of the specimen.

Fig. 5
Fig. 5

Carrier moiré pattern of a V field with a positive carrier angle in the right half of the specimen.

Fig. 6
Fig. 6

Carrier moiré pattern of a V field with a negative carrier angle in the right half of the specimen.

Fig. 7
Fig. 7

Pure secondary moiré pattern of ΔUy of Fig. 3

Fig. 8
Fig. 8

Pure secondary moiré pattern of ΔVx of Fig. 5.

Fig. 9
Fig. 9

Digital pure shear-strain moiré pattern from Figs. 7 and 8.

Fig. 10
Fig. 10

Wrong resultant pattern that uses Eq. (18) for the patterns of Figs. 4 and 5.

Equations (24)

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I ¯ ( x , y ) = I 0 ( x , y ) + I 1 ( x , y ) cos [ 2 π U ( x , y ) / P ] + I n ( x , y ) ,
I ¯ u ( x , y ) = I 0 ( x , y ) + I 1 ( x , y ) cos { 2 π [ U ( x , y ) - θ u y ] / P } + I n ( x , y ) ,
I u ( x , y ) = I 0 + I 1 cos { 2 π [ U ( x , y ) - θ u y ] / P } ,
γ x y = U / y + V / x ,
I v ( x , y ) = I 0 + I 1 cos { 2 π [ V ( x , y ) + θ v x ] / P } ,
J u ( x , y ) = I 0 + I 1 sin { 2 π [ U ( x , y ) - θ u y ] / P } ,
J v ( x , y ) = I 0 + I 1 sin { 2 π [ V ( x , y ) - θ v x ] / P } .
I u ( x , y + Δ y ) = I 0 + I 1 cos { 2 π [ U ( x , y ) + Δ U - θ u ( y + Δ y ) ] / P } ,
J u ( x , y + Δ y ) = I 0 + I 1 sin { 2 π [ U ( x , y ) + Δ U - θ u ( y + Δ y ) ] / P } .
M 1 = [ I u ( x , y ) - I 0 ] [ I u ( x , y + Δ y ) - I 0 ] = I 1 2 ( cos [ 2 π ( Δ U - θ u Δ y ) / P ] + cos { 2 π [ 2 U ( x , y ) + Δ U - 2 θ u y - θ u Δ y ] / P } ) / 2 ,
M 2 = [ J u ( x , y ) - I 0 ] [ J u ( x , y + Δ y ) - I 0 ] = I 1 2 ( cos [ 2 π ( Δ U - θ u Δ y ) / P ] - cos { 2 π [ 2 U ( x , y ) + Δ U - 2 θ u y - θ u Δ y ] / P } ) / 2.
M u = [ M 1 ( x , y ) + M 2 ( x , y ) ] / I 0 + I 0 = I 0 + I 1 cos [ 2 π ( Δ U - θ u Δ y ) / P ] = I 0 + I 1 cos [ 2 π ( Δ U / Δ y - θ u ) / γ 0 ] ,
M u = I 0 + I 1 sin [ 2 π ( Δ U / Δ y - θ u ) / γ 0 ] .
M v = I 0 + I 1 cos [ 2 π ( Δ V / Δ x + θ v ) / γ 0 ] ,
M v = I 0 + I 1 sin [ 2 π ( Δ V / Δ x - θ v ) / γ 0 ] .
Δ U / Δ y - θ u = 0             or             = 0 ,
Δ V / Δ x + θ v = 0             or             = 0 ,
M ( x , y ) = { [ M u ( x , y ) - I 0 ] [ M v ( x , y ) - I 0 ] - [ M u ( x , y ) - I 0 ] × [ M v ( x , y ) - I 0 ] } / I 0 + I 0 = I 1 { cos [ 2 π ( Δ U / Δ y - θ u ) / γ 0 ] cos [ 2 π ( Δ V / Δ x + θ v ) / γ 0 ] - sin [ 2 π ( Δ U / Δ y - θ u ) / γ 0 ] sin [ 2 π ( Δ V / Δ x + θ v ) / γ 0 ] } + I 0 = I 0 + I 1 cos { 2 π [ Δ U ( x , y ) / Δ y + Δ V ( x , y ) / Δ x - θ u + θ v ] / γ 0 } .
M ( x , y ) = I 0 + I 1 cos { 2 π [ γ x y ( x , y ) + γ c ] / γ 0 } ,
M ( x , y ) = { [ M u ( x , y ) - I 0 ] [ M v ( x , y ) - I 0 ] + [ M u ( x , y ) - I 0 ] × [ M v ( x , y ) - I 0 ] } / I 0 + I 0 = I 1 { cos [ 2 π ( Δ U / Δ y - θ u ) / γ 0 ] cos [ 2 π ( Δ V / Δ x + θ v ) / γ 0 ] + sin [ 2 π ( Δ U / Δ y - θ u ) / γ 0 ] sin [ 2 π ( Δ V / Δ x + θ v ) / γ 0 ] } + I 0 = I 0 + I 1 cos { 2 π [ Δ U ( x , y ) / Δ y - θ u - Δ V ( x , y ) / Δ x + θ v ] / γ 0 } = I 0 + I 1 cos { 2 π [ Δ U ( x , y ) / Δ y + Δ V ( x , y ) / Δ x - θ u + θ v ] / γ 0 } = I 0 + I 1 cos { 2 π [ γ x y ( x , y ) + γ c ] / γ 0 } .
γ x y = γ 0 2 π arccos { [ M ( x , y ) - I 0 ] / I 1 } - γ c .
2 π ( γ x y + γ c ) / γ 0 = 2 k π ,             k = ± 0 , 1 , 2 , ,
γ x y = k γ 0 - γ c ,             k = ± 0 , 1 , 2 , .
γ x y = ( k + 1 / 2 ) γ 0 - γ c ,             k = 0 , 1 , 2 , .

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