by Photographic Method

Transcription

1 Materials Science Forum Vols (27) pp online at (27) Trans Tech Publications, Switzerland Long-term Strain Measuring of Technical Textiles by Photographic Method HEGYI, Dezsı,a, SAJTOS, István,b and SÁNDOR, György 2,c Budapest University of Technology and Economics (BUTE) H- Budapest, Mőegyetem rkp. 3., Hungary 2 H- Budapest, Rokolya utca 7., Hungary a dizso@silver.szt.bme.hu, b sajtos@silver.szt.bme.hu, c epsilon@freestart.hu Keywords: Textile Composites, Creep, Measuring techniques, Shape functions. Abstract. The technical textiles are very sensitive materials. To measure the elongation of such a material needs special care. A photographic procedure has been investigated to measure the plain elongation of textile specimens. It is especially suitable for long-term measuring programs. Some experimental results measured by the described method are published. Introduction The technical textiles are very sensitive. Common measuring processes are usually not proper to measure the long term behavior of PVC coated polyester fibre material. The material is too sensitive to use strain gauge. Mechanical elongation meters have usually too small measuring limit according to the creep elongation. The most common optical instruments cannot be removed during the process and they are too expensive to use them in long term (several months) for several specimens. A photo method was developed for accurate measuring of any plain deformation of a textile []. A calibrated frame for each specimen and a common digital camera is used for the procedure. The concept is the following: the specimens hang with constant load. There are signs drawn with alcoholic pen on the specimens for the measuring procedure (hopefully it has no critical effect on the material). There is a calibrated rectangular frame behind each specimen. Photos are taken of these systems. A computer image processing tool was developed to transform the images to the original size using the dimensions of the calibrated frame. Finally, the real distances can be measured between the drawn signs using the calibrated frame as reference. The relative elongation can be calculated from the distances between the signs on the specimen. The creep curve can be drawn using the time-elongation data. The creep parameters are determined finally with least square method. The main aim of this paper is to show how the image processing works. The image processing Working with pixels. A 3 megapixel digital camera is used to take the pictures. It uses jpg format. On the first step the colour image is turned into binary (black and white pixels). Later it is much simpler to manage black and white pixels than colour or grayscale ones. During the binarization procedure we compare the darkness of the pixels with the average darkness of the pixels around. If the pixel is darker and the difference is bigger than a predefined value, it becomes black, otherwise it becomes white. After this process there are black pixels in a white background (Fig. ). All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, (ID: //6,9:56:33)

2 382 Materials Science, Testing and Informatics III Figure : The original photo and the black and white (binarized) one The lines interesting in the measuring process are close to horizontal or vertical. To search for this kind of lines the so called edge detection is suitable [2]. All the pixels belonging to a line are looked for by this method. The neighboring black pixels that build lines need to be collected together (Fig. 2). Figure 2: The points belong to horizontal and vertical lines

3 Materials Science Forum Vols The intersections of the lines define the coordinates of the signs we search for. The lines can be described mathematically with a function going through the centre of gravity of the thick lines. A polynomial function is fitted to each line built by pixels using least square method. With the usage of functional description of lines the accuracy of the process can be much higher than the resolution of the image. The functions are determined by hundreds of pixels, and they can give back the axis of the lines as the average of the pixel description. Originally the lines are straight. The distortion of the lenses makes them a little bit curved. According to the experiments the second and the third order polynomial functions are the most exact. Higher order functions follow the local distortions better and make the approximation of the straight line worse. Working with lines. If anyone takes a look at an image (Fig. 3), the lines and the points to be used are easy-to-find. Our brain has all the complex information about the images. But a software does not have eyes. Originally the present method was developed for manual treatment, so there are no easy-to-find signs for computers. But the line-work of the images can be well described by ratios and lengths. Finally the lines needed can be found without any manual help. Figure 3 The image and the linen with the intersections On the next step the intersection of the lines needed can be calculated. To describe a horizontal line it is the best to use a y=f(x) function. For a vertical line the x=f(y) type function is suitable. The variant is different. A nonlinear system equation needs to be solved with two unknowns (the polynomial function used to describe the lines is at least second order). The following iteration procedure is used: First step: y = f (x), x =, () x = f( y), y = y. (2)

4 384 Materials Science, Testing and Informatics III The next steps: i y = f( x), i x = f( y), x = x i (3) i y= y. (4) If x x ε i i 6 =, the iteration is finished. The stability of the recursion is not worked out theoretically. But all the functions calculated have only one intersection on the specimen (it comes from the geometry). It means that there is only one fixed point. Up to the present the iteration gave result rapidly in every situation. After this step the coordinates of the signs are ready in the coordinate system of the image. Transformation to the real size. The calibrated rectangular frame is used to store the real dimensions in the images. With the help of this frame the coordinates in the image can be transformed back to the real size. Two transformations are used: (i) the so called shape functions are used in a parametric coordinate system and then (ii) a simple scaling. i: In the first step the image is transformed to a parametric coordinate system. This method is used frequently in the finite-element-method. An eight-node system (element) is applied. There are four corner nodes and four nodes on the sides. The four corner nodes are the corners of the rectangular frame. The side nodes are signed points on the sides of the rectangle (Fig. 4). With this eight-node system a second order approximation can be used. It helps to eliminate the spherical distortion of the lens of the camera. Figure 4 The coordinate system of the picture and the parametric system In the original frames the side nodes were not in the middle of the sides of the rectangular frames, so the ordinary shape functions were not suitable. An improved transformation is applied here [3]. With this method the transformation can be linear between the two systems with any position of the middle point. The images have been taken close to perpendicular to the surface of the specimens but a small perspective distortion cannot be avoided. At this point we neglect this problem. The transformation using the shape functions is very comfortable if we look for a coordinate in the global (image) system for a point known in the parametric system. In this situation the known coordinates are in the global (image) system (x, y) and the parametric coordinates are searched (ξ,η). 8 x N ξη x =, (5) ( ) i i

5 Materials Science Forum Vols y N ξη y =. (6) ( ) i i (x and y are the coordinates in the image, ξ and η are the coordinates in the parametric system. x i and y i (i=-8) are the coordinates of the corner and side nodes of the parametric system in the global system, N (ξ,η)i are the second order shape functions) From the general formula (Eq. 5, 6) it can be seen that it is a non-linear system equation with two unknowns (the shape functions are second order). A specialized Newton-Raphson-method is used to solve this equation. The x axis of the image is close to parallel to the ξ axis of the parametric system and the y axis is close to parallel to the η. The iteration can be very fast, if we search for the ξ coordinates from the first equation (using the ξ derivative of (5)) and we use the second equation for the η. In the first equation η is used as a known parameter from previous iteration step (η nξ =η n-, η ξ =). The same technique is used for ξ in the second equation (ξ nη = ξ n-, ξ η = ). Usually less then steps are enough to reach an acceptable accurate result. The coordinates of the parametric system are ready than. As in the previous iteration the stability of the recursion is not worked out theoretically. But there is one-to-one onto function between the parametric and global system. It means there can only be one fixed point. In every situation the iteration gave the result rapidly. ii: Both the parametric and the frame coordinate systems (the real frame) are perpendicular and they have parallel axes. Simple scaling can transform the coordinates between the two systems (Fig. 5). Figure 5 The parametric system and the frame system The elongation. Elongation is the relative displacement between two points of the specimen. The distances between the points can be calculated from the real coordinates of the frame system. There are three pairs of points for the measuring of the elongation and three pairs of points for the perpendicular elongation. The average of these is taken into account. Conclusion A measuring process was developed to get knowledge about the long-term behavior of the PVC coated polyester fibre membrane materials. With the computer measuring tool the elongation can be calculated. The described method is suitable for measuring any plain deformations of any kind of material. The investigated photo method can be used to measure up to,% elongation. The accuracy is

6 386 Materials Science, Testing and Informatics III higher than the resolution of the digital image. It comes from the mathematical description of the line-work of the images. The accuracy can be improved by using grayscale image processing and by taking the small perspective distortion into consideration. A set of creep parameter can be found in the Appendix. It was worked out from measured data got by the measuring method described above. Appendix One set of measuring was done on PVC coated polyester fibre material. Two different fibre directions and two load levels were used in unidirectional measuring. A two-direction measurement was also done. To describe the long term elongation the -creep-model combined with was used (Fig. 6, Burgers-creep-modell) (7). The parameters of the models were developed from the experimental data by the least square method. Figure 6 The Burgers-creep-model ε ( t) σ σ σ = + t+ e E µ E2 E 2 µ 2 t, (7) where ε (t) is the relative elongation, σ is the stress level (constant during the process, if the stress changes, we need to integrate according to the stress as well), t is the time, µ, E, µ 2 and E 2 are the material parameters (Fig. 6). The next parameters are found for a 7 g/m 2 ordinary PVC coated polyester fibre material. The load level was between 3 and 6 N/5cm. The duration of the loading was 3 days. parameters warp direction 6 N with weft direction 3 N with weft direction 6 N with two direction 45 N warp with weft with E [kn/cm] µ [kn*day/cm] E 2 [kn/cm] µ 2 [kn*day/cm] ν (Poisson-number) Table The experimental material parameters

7 Materials Science Forum Vols REFERENCES [] D. Hegyi: Mőszaki textília alakváltozásainak mérése fotó eljárással, Anyagvizsgálók lapja, Vol. 5/, 5-7 (25), in Hungarian, (Strain measuring of technical textile by a photographic method). [2] R. C. Gonzalez and R. E. Woods: Digital Image Processing, Prentice-Hall (22) [3] M. A. Celia and W. G. Gray: An improved isoparametric transformation for finite element analysis, Int. J. Numer. Meth. Engng, Vol. 2, (987) [4] D. Hegyi, K. Hincz: Long-term analysis of prestressed membrane structures, Journal of Computational and Applied Mechanics, Vol. 6/2, (25)