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The moiré method for measuring large-plane nonhomogeneous deformations

The techniques and equations for measuring and calculating deformation and strain-tensor components for large-plane nonhomogeneous deformations are presented

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Abstract

Moiré-fringe equations have been developed for directly determining the components of Green's and Cauchy's deformation tensors from measurements of fringe pitch and angle. The equations, which were previously verified for large-plane homogeneous deformations, are used to determine the deformation-tensor components for nonhomogeneous strain fields. The results are compared to theoretical values. Specifically, the deformations investigated are pure bending of a rectangular block, and extension of a tapered plane specimen.

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Abbreviations

C JK :

Green's deformation tensor

c jk :

Cauchy's deformation tensor

D :

constant related to magnitude of bending of a block

E JK :

Lagrangian strain tensor

e jk :

Eulerian strain tensor

F,f :

initial, final fringe pitch

g JK :

metric tensor of undeformed coordinates

g jk :

metric tensor of deformed coordinates

H,h :

initial, final fringe pitch

L :

constant related to magnitude of bending of a block

M,m :

initial, final master-grating pitch

N,n :

initial, final master-grating pitch

r i :

radii of deformed beam

S,s :

initial, final specimen-grid pitch

T,t :

initial, final specimen-grid pitch

X K :

general underformed coordinates

x k :

general deformed coordinates

α:

angle of bending of a block

Γ,γ:

inital, final specimen-grid angle

Θθ:

initial, final master-grid angle

ϒ,ν:

initial, final master-grid angle

Φ,ϕ:

initial, final moiré-fringe angle

Ψ,Ψ:

initial, final moiré-fringe angle

Ω,ω:

initial, final specimen-grid angle

References

  1. Martin, L. P. andJu, F. D., “The Moiré Method for Measuring Large-plane Deformations,”ASME Paper No. 69-APMW-21, Trans. ASME, Jnl Appl. Mech.,36 (3),385–391 (Sept. 1969).

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  2. Theocaris, P. S., Moiré Fringes in Strain Analysis Pergamon Press, Oxford (1969).

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  3. Sciammarella, C. A. andDurelli, A. J., “Moiré Fringes as a Means of Analyzing Strains,”Trans., Am. Soc. Civ. Eng.,127,Part 1, 582–608 (1962).Pages 582–603.

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  4. Truesdell, C. andToupin, R., “The Classical Field Theories,”Handbuch der Physik, Vol. III, Springer-Verlag, Berlin, 241–309 (1960).

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  5. Eringen, A. C., Nonlinear Theory of Continuous Media, McGraw-Hill, New York, (1962).

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  6. Martin, L. P., “Measurement of Deformations in a Large Displacement Gradient Field,” dissertation, Univ. N. M. (June 1968).

  7. Morse, S., Durelli, A. J. andSciammarella, C. A., “Geometry of Moiré Fringes in Strain Analysis,”Proc. Am. Soc. Civ. Eng., LXXXVI (EM4),105–126 (August 1960).

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Authors and Affiliations

  1. Mechanical Engineering, University of New Mexico, Albuquerque, N.M.

    L. P. Martin (Assistant Professor) & F. D. Ju (Professor)

Authors
  1. L. P. Martin
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  2. F. D. Ju
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Martin, L.P., Ju, F.D. The moiré method for measuring large-plane nonhomogeneous deformations. Experimental Mechanics 10, 521–528 (1970). https://doi.org/10.1007/BF02320615

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  • DOI: https://doi.org/10.1007/BF02320615

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