Measurement of Kirchhoff's stress intensity factors in bending plates

D. Bäcker; M. Kuna; C. Häusler

doi:10.1117/12.2044472

8 March 2014 Measurement of Kirchhoff's stress intensity factors in bending plates

D. Bäcker, M. Kuna, C. Häusler

Proceedings Volume 9061, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2014; 90611Q (2014) https://doi.org/10.1117/12.2044472
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2014, San Diego, California, United States

Abstract

A measurement method of the stress intensity factors defined by KIRCHHOFF’s theory for a crack in a bending plate is shown. For this purpose, a thin piezoelectric polyvinylidene fluoride film (PVDF) is attached to the surface of the cracked plate. The measured electrical voltages are coupled with the load type and the crack tip position relative to the sensor film. Stress intensity factors and the crack tip position can be determined by solving the non-linear inverse problem based on the measured signals. To guarantee solvability of the problem, more measuring electrodes on the film have to be taken in to account. To the developed sensor concept the KIRCHHOFF’s plate theory has been applied. In order to connect the electrical signals and the stress intensity factors the stresses near the crack tip have to be written in eigenfunctions (see WILLIAMS [1]). The presented method was verified by means of the example of a straight crack of the length 2a in an infinite isotropic plate under all- side bending. It was found that the positioning of the electrodes is delimited by two radii. On one hand, the measurement points should not be too close to the crack tip. In this area, the Kirchhoff’s plate theory cannot be used effectively. On the other hand, the measuring electrodes should be placed at a smaller distance to each other and not too far from the crack tip regarding the convergence radius of the WILLIAMS series expansion. Test calculations on a straight crack in an infinite isotropic plate showed the general applicability of the measurement method.

Citation Download Citation

D. Bäcker, M. Kuna, and C. Häusler "Measurement of Kirchhoff's stress intensity factors in bending plates", Proc. SPIE 9061, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2014, 90611Q (8 March 2014); https://doi.org/10.1117/12.2044472

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KEYWORDS

Electrodes

Ferroelectric polymers

Sensors

Inverse problems

Near field

Mechanics

Nonlinear optics

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