SOME PROBLEMS OF DATA EVALUATION OF PHOTOELASTIC COATING TECHNIQUE IN CASE OF SMALL-SIZE, FIBRE-OPTICS FITTED EQUIPMENT

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1 ICEM1-1th International Conference on Experimental Mechanics 9 August - September, 004 Politecnico di Bari, Italy SOME PROBLEMS OF DATA EVALUATION OF PHOTOELASTIC COATING TECHNIQUE IN CASE OF SMALL-SIZE, FIBRE-OPTICS FITTED EQUIPMENT L. Borbás a a Budapest University of Technology and Economics, Department of Machine Parts and Drives, Budapest, Bertalan L. u.. H-1111, Hungary, borbas@kge.bme.hu ABSTRACT An earlier realised measurement device, the mini-polariscope makes a full range stress analysis possible (definition of fringe order and stress direction that is building in polarisation filters and quarter wave filters, two for each) by developing a remotely controlled, small-scale polarisation filter system. This paper makes the failure analysis of the measurement technique more accurate taking the factors influencing the failure of the measurement technique into account: - by investigating the projection failures of the optical lenses of the mini polariscope, - by analysing the extent of the failure resulting from the convergence of the light ray of the mini polariscope, in the case of specimens with specific geometric parameters, - by comparing the extent of the reinforcing effect caused by the investigating layer with the extent of the momentum/normal force on the investigated cross-section. 1. INTRODUCTION Photostress analysis including photoelastic coating technique is one of the most spectacular experimental methods to make stress and strain visible. A strain, stress measurement of a real machine element queried out by photoelastic coating technique, usually use a traditional polariscope, which has a polarizer filter (and analyser as well) size about mm. The image obtained by the polarizer can be observed directly, or recorded by video recorders or cameras. Traditional polariscopes, due to their sizes, have only limited possibilities to define the investigated stress and strain in several cases (e.g. on almost closed inside surfaces, force inlets, corners, in the vicinity of welding seams and ribs, ). A small reflection polariscope was developed for special purposes mentioned above, proper for a full range of photostress analyses, with a centre distance of the polariser filters mm, (in case of a 10 mm filter diameter) equipped with fibre optic light guide and image transmission bundle. If the observation of the investigated specimen is realised on television screen, the visualized image (on the screen) carries several sources of failure, as follows [1]: - the transformation (projection) failures of the electronic elements - those of the optical units (primarily lenses) transmitting the image - the image carries the failures resulting from the effect of measurement set-up - the mutual effect of the coating and the tested object (reinforcing effect of the coating) 301

2 (Present paper does not involve the failure analyses of the electronic elements of the measurement system, like video recorder (electronic elements of image transfer), or signal transfer elements.). SOME ELEMENTS INFLUENCING THE EVALUATION OF OPTICAL DATA The failure analysis of a photoelastic coating measurement, where the instrument contains optical elements, can be divided into two main parts: - analysis or investigation of the projection failures of the optical lenses built in the measuring device (in this case in the mini polariscope) - interaction of the measuring device and the investigated specimen bounded with photoelastic coating [], [3]:.1. Elements of the projection failure To clarify the distortions of the optical elements of the measuring system, special grids have been generated, like target grid (pattern), on Fig. 1., and chessboard grid, on Fig..: D = 80 mm r = 5 mm Fig.1. target grid (pattern) 80 x 80 mm d x,d y = 100 d sd = mm Fig.. chessboard grid Both patterns were investigated in several positions, in case of two different observing surfaces, namely on plane and curved surfaces, see on Fig. 3. and 4. Fig.3. The theoretical set-up in case of plane observing surface 30

the evaluated target grid distortion can be seen on Fig. 5.

extreme position to the next extreme point on the screen, on Fig. 6. Fig. 5.

The wandering the points of chess-board, from one ultimate position to the

. The effect of oblique incidence and the reinforcing of the coating The

3 Fig.4. The theoretical set-up in case of curved observing surface One example for the evaluated target grid distortion can be seen on Fig. 5., and for the wandering of one pattern (chess-board distortion) from one extreme position to the next extreme point on the screen, on Fig. 6. Fig. 5. The target-grid distorsion Fig. 6. The wandering the points of chess-board, from one ultimate position to the next one.. The effect of oblique incidence and the reinforcing of the coating The target of the investigation was a curved shaped reinforced plastic material, the shape and loading conditions are on the next figure (Fig. 7.) The geometric data can be seen on Fig 8. Fig. 7. The investigated specimen Fig. 8. The geometric data of the investigated specimen 303

4 a/f [mm -3 ] y 0 [mm] The failure analysis as a result of the reinforcing effect of the coating, and in case of oblique incidence can be discussed only in the full knowledge of the following things [1]: - external loading conditions (type, arrangement), - geometric data of the instrument (polariscope), the data of the observation, - geometric and material properties of the investigated element, - geometric and material properties of the photoelastic coating. The mechanical model of the evaluated area of the specimen loaded by a moment, and a normal force (see Fig. 8.) is the following (Fig. 9.): Fig. 9. The mechanical model of the evaluated area The introduced stress state of the measured points was evaluated without and with photoelastic coating. The movement of the neutral fiber can be connected with the reinforcing effect of the photoelastic coating, as can be seen on Fig y 0 a * /F a/f x [mm] Fig.10. The connection of the movement of the neutral fibre with the reinforcing effect of the coating, in case of a moment and normal force loaded cross-section 304

coating is realized using the same material which is investigated. The investigations were carried out both at points which are in plane stress and in plane strain state, see in Fig. 11.

5 The most important conclusions of Fig.10. are, that the evaluation error originating from the reinforcing effect can be decreased in the case, when the external moment dominates the normal force, and when the calibration of the photoelastic coating is realized using the same material which is investigated. The investigations were carried out both at points which are in plane stress and in plane strain state, see in Fig. 11. Fig. 11. The cases of the plane-stress states, and the plan-strain states, in case of photoelastic coating investigation The specific error originating from the reinforcing effect of the coating, at the given conditions (geometric and material properties), can be calculated by the following equation (Eq.1): C P 1 E E xc C xp P 1 E 1 P bfa 1 E afa h t C y0 3 h Where parameters subscript C for the coating, subscript P for the investigated plate, and the specific values (a*/f) without coating, (a/f) with coating are respecting. This equation shows the ratio of the strains measured in the coating related to the calculated ones. The results of the failure calculations summarized in the Table I. Table I. The failure results, concerning the investigated points introduced on Fig

geometric parameters of measurement set-up are well known. 3.

3. The specific error originating from the reinforcing effect of the coating, at the given conditions (geometric and material properties of the investigated reinforced plastic material), in extreme

6 3. CONCLUSION 3.1. The correct failure analysis of a photoelastic coating measurement can be realized, if the external loading conditions, the geometric and material properties of the specimen and coating, and the geometric parameters of measurement set-up are well known. 3.. The projection failure of the mini-polariscope - in case of the investigated conditions - even in extreme distortion of the investigated pattern is smaller than 8 percent The specific error originating from the reinforcing effect of the coating, at the given conditions (geometric and material properties of the investigated reinforced plastic material), in extreme case reaches 40 percent. This error can be decreased when the calibration of the photoelastic coating is realized using the same material which is investigated The failure of oblique incidence during the checked conditions remained under 10 percent. A second generation of the measurement set-up of the instrumentation, and the measurement head of the mini-polariscope can be seen on Fig. 1. and Fig 13. Fig. 1 A second generation measurement set-up of the mini polariscope, fitted to fibre optics Fig 13. The measurement head of the mini-polariser in dismounted, and in mounted state 306

7 REFERENCES [1] Lajos Borbás: Development of the photoelastic coating technique using fibre optics. Ph.D. Dissertation at Budapest University of Technology and Economics, 001. No.: 1078/Ph.D./001. [] Thamm, F., Borbás, L.: Anwendungsgebiete und Genauigkeitsprobleme des Oberflächenschichtverfahrens der Spannungsoptik. 6. Schule. Experimentelle Methoden der Festkörpermechanik. Akademie der Wissenschaften der DDR, Institut für Mechanik. Proceedings pp.: Karl-Marx-Stadt. DDR, [3] Borbás, L.: Accuracy analysis of a fibre optic connected reflection polariscope. 19 th Danubia-Adria-Symposium, Polanica Zdroj, Poland, September , 00. p.:

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