 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
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| In English (Mech. Solids): | | 4810 |
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| R. V. Goldstein, V. M. Kozintsev, A. V. Podlesnykh, A. L. Popov, and D. A. Chelyubeev, "A method of electronic speckle pattern interferometry for solving some inverse problems of mechanics of elastic bodies," Mech. Solids. 41 (2), 1-9 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
2 |
Pages |
1-9 |
| Title |
A method of electronic speckle pattern interferometry for solving some inverse problems of mechanics of elastic bodies |
| Author(s) |
R. V. Goldstein (Moscow)
V. M. Kozintsev (Moscow)
A. V. Podlesnykh (Moscow)
A. L. Popov (Moscow)
D. A. Chelyubeev (Moscow) |
| Abstract |
Theoretical and experimental techniques are presented for solving some inverse
problems of mechanics of elastic bodies associated with the diagnostics of the
delamination of thin coatings applied to the substrate body, the identification
of mechanical characteristics of the coating material and shrinkage stresses in
the coatings, and the determination of the magnitude and the place of
application of the local load acting on the substrate. These characteristics
are determined on the basis of small displacements of the surface of the object
observed by means of an electronic speckle interferometer as a system of
interference bands.
Theoretical solutions of inverse problems of elasticity in which, for example,
the applied loads are to be restored for a given displacement field are based
on the displacement functions defined in elastic bodies. A specific feature of
the inverse problems of elasticity is that various loads of the body can lead
to the same stress-strain state. Such problems are ill-posed. In problems of
this type, important are the accuracy of measurement of the displacement field
to be detected and additional information that sheds light on the nature of the
applied loads. The experimental component, laser-computer interferometry,
involved in the technique for solving inverse problems enables small elastic
displacements of the body to be measured with high degree of accuracy.
In the present study, such an approach is utilized for solving a series of
inverse problems related to the diagnostics of the delamination of thin
coatings. This study continues the investigation of the delamination of thin
coatings that has been started in [1] and extend them to the case of
multi-layered coatings and 2D plate-like model of the substrate. To identify
the delamination, we utilize the difference in the deformation of delaminated
and non-delaminated segments that manifests itself when bending the substrate.
A mathematical model of such differences is constructed for bending of a
multi-layered coating on a round plate-like substrate. The delamination of the
coating is modeled by a hemisphere of small radius and the bending load by a
normal point force applied eccentrically. In parallel, the residual shrinkage
stresses appearing during the application of the coating on the substrate and
the mechanical characteristics of the substrate material were determined. When
doing so, we partly utilized the concepts that have been laid in the classical
study by Stoney [2] and then developed in [3].
At the experimental stage, the electronic speckle pattern interferometry
technique was utilized to measure small displacements of the substrate and
coating. When matching the speckle images of the initial and bent coated
plates, the difference in the displacements in the non-delaminated and
delaminated portions of the coating manifests itself by local
irregularities of the system of bands of the resulting interferogram. These
bands correspond to the lines of equal deflections of the substrate plate.
The ability of the inverse problem for the plate bending, i.e., that of
determining the magnitude and the point of application of the force acting
on the plate proceeding from the number and configuration of the
interference bands, to be solved theoretically and experimentally was
investigated. In this case, the plate subject to loading can serve as a
sensing element. This, in addition, enables one to define the possibilities
for this approach to be utilized as a method for contactless determination
of forces and pressures in various devices and structures. By adjusting the
geometrical parameters (diameter and thickness) of the plate one can
provide the desired sensitivity with respect to the quantities to be
measured. |
| References |
| 1. | R. V. Goldstein, V. M. Kozintsev, A. L. Popov, and
G. N. Chernyshev, "An experimental-theoretical method for the detection of
detachments of thin coatings," PMM [Applied Mathematics and Mechanics],
Vol. 64, No. 2, pp. 332-336, 2000. |
| 2. | G. G. Stoney, "The tension of metallic films deposited by
electrolysis," Proc. Roy. Soc. London. Ser. A, Vol. 82, No. 553, pp. 172-175,
1909. |
| 3. | V. G. Fokin, "Residual stresses and hogging due to the coating
shrinkage," Vestnik SamGTU. Ser. Tekn. Nauki, No. 10, pp. 40-45, 2000. |
| 4. | I. A. Birger and Ya. G. Panovko (Editors), Strength. Stability.
Vibrations. A Handbook. Volume 1 [in Russian], Mashinostroenie, Moscow,
1968. |
| 5. | R. V. Goldstein, V. M. Kozintsev, A. V. Podlesnykh, et al.,
Multilayered Thin Coatings and Their Diagnostics by Means of Laser-computer
Interferometry. Preprint No. 741 [in Russian], In-t Problem Mekhaniki RAN,
Moscow, 2003. |
| 6. | S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and
Shells, McGraw-Hill, New York, 1959. |
| 7. | B. S. Kasatkin, A. B. Kudrin, L. M. Lobanov, et al., Experimental
Methods for Studying Strains and Stresses: A Handbook [in Russian], Naukova
Dumka, Kiev, 1981. |
|
| Received |
07 October 2005 |
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