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Title:
COMPUTER IMPLEMENTED METHOD TO OBTAIN THE ORIENTATIONS OF FIBRES INSIDE COMPOSITE MATERIALS USING COMPUTED TOMOGRAPHY SCAN
Document Type and Number:
WIPO Patent Application WO/2015/024580
Kind Code:
A1
Abstract:
Computer implemented method to obtain the orientations of fibres inside composite materials using computed tomography scan, comprising: - Obtaining tomography scan images of different cross sections of the composite material; - Converting said images into a set of points, each point representing a pixel of the image with a grey-scale value and 3D coordinates; - Extracting the pixels corresponding to the fibre material by using a threshold gray-scale value; - Clustering the pixels of the fibre material corresponding to the same cross-section in individual fibres according to distance criteria between pixels; - Assembling the individual fibres located in different cross-sections and corresponding to the same single fibre by estimating the position of the centroid of each individual fibre in an immediate cross-section; - Obtaining the interpolation line of each cloud of pixels belonging to a single fibre and, from said interpolation line, obtaining the orientation of each single fibre.

Inventors:
VICENTE CABRERA MIGUEL ANGEL (ES)
GONZALEZ CABRERA DORYS CARMEN (ES)
MINGUEZ ALGARRA JESÚS (ES)
Application Number:
PCT/EP2013/067219
Publication Date:
February 26, 2015
Filing Date:
August 19, 2013
Export Citation:
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Assignee:
UNIV BURGOS (ES)
International Classes:
G01N23/04
Other References:
REQUENA G ET AL: "3D-Quantification of the distribution of continuous fibres in unidirectionally reinforced composites", COMPOSITES PART A: APPLIED SCIENCE AND MANUFACTURING, ELSEVIER SCIENCE PUBLISHERS B.V., AMSTERDAM, NL, vol. 40, no. 2, 1 February 2009 (2009-02-01), pages 152 - 163, XP025772097, ISSN: 1359-835X, [retrieved on 20081108], DOI: 10.1016/J.COMPOSITESA.2008.10.014
GREGORIO M VLEZ-GARCA ET AL: "Unambiguous orientation in short fiber composites over small sampling area in a center-gated disk", COMPOSITES PART A: APPLIED SCIENCE AND MANUFACTURING, ELSEVIER SCIENCE PUBLISHERS B.V., AMSTERDAM, NL, vol. 43, no. 1, 21 September 2011 (2011-09-21), pages 104 - 113, XP028120609, ISSN: 1359-835X, [retrieved on 20110928], DOI: 10.1016/J.COMPOSITESA.2011.09.024
SHEN H ET AL: "Direct observation and measurement of fiber architecture in short fiber-polymer composite foam through micro-CT imaging", COMPOSITES SCIENCE AND TECHNOLOGY, ELSEVIER, UK, vol. 64, no. 13-14, 1 October 2004 (2004-10-01), pages 2113 - 2120, XP027125109, ISSN: 0266-3538, [retrieved on 20040710]
Attorney, Agent or Firm:
CARVAJAL Y URQUIJO, Isabel et al. (MODET & CO.C/Goya no. 11, Madrid, ES)
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Claims:
CLAIMS

1. Computer implemented method to obtain the orientations of fibres inside composite materials using computed tomography scan, characterized in that it comprises:

- obtaining tomography scan images of different cross sections of the composite material;

- converting said images into a set of points, each point representing a pixel of the image with its corresponding grey scale value and three-dimensional coordinates;

- extracting from the set of points the pixels corresponding to the fibre material by using at least one threshold gray scale value;

- clustering the pixels of the fibre material corresponding to the same cross- section in individual fibres according to distance criteria between pixels;

- assembling the individual fibres located in different cross-sections and corresponding to the same single fibre by estimating the position of the centroid of each individual fibre in an immediate cross-section;

- obtaining the interpolation line of each cloud of pixels belonging to a single fibre and, from said interpolation line, obtaining the orientation of each single fibre.

2. Method according to claim 1 , wherein the set of points are arranged in a 3D matrix. 3. Method according to any of previous claims, wherein the tomography scan images of the cross sections are taken with a determined pitch distance (Δζ) between images.

4. Method according, to any of previous claims, wherein different threshold gray scale values are set for different zones of the composite material.

5. Method according to any of previous claims, wherein the distance criteria for clustering of pixels in individual fibres comprise checking those pixels in the same cross-section which are within a certain distance threshold. 6. Method according to any of previous claims, wherein the clustering of pixels in individual fibres comprises a filtering process by which the groups of pixels having less size than a threshold size are not considered as individual fibres.

7. Method according to any of previous claims, wherein the individual fibres in immediate cross-sections are considered to belong to the same single fibre if the distance between the real centroid (C2) of the individual fibre of a cross-section and the estimated centroid (C2est) for said cross-section is within a certain threshold (d).

8. Method according to claim 7, wherein the assembling of individual fibres in a single fibre is only considered when there are at least three different individual fibres located in different adjacent cross-sections complying with the threshold (d) requirements.

9. Method according to any of previous claims, wherein if the maximum distance (2a) between the pixels of an individual fibre is bigger than half the length of the fibre, considering this individual fibre as a single fibre.

10. Method according to any of previous claims, further comprising obtaining the density of fibres inside the composite material by calculating the sum of the lengths of the single fibres and their corresponding volumes, and comparing the volume of the fibres with the total volume of the composite material.

Description:
COMPUTER IMPLEMENTED METHOD TO OBTAIN THE ORIENTATIONS OF FIBRES INSIDE COMPOSITE MATERIALS USING COMPUTED TOMOGRAPHY

SCAN Field of the Invention

The invention is comprised in the technical field of composite materials, in which one component is a filamentary or fibrous material. In particular, it refers to a method for obtaining the orientations of fibrous or filamentary components contained inside a composite material, through the post-processing of images scanned by computed tomography scan.

Background of the Invention

The main objective of the incorporation of fibrous and filamentous materials in a matrix is to improve the mechanical characteristics of this composite material. The density and orientation of the fibres or filaments are the main parameters that define the efficiency factor for the improvement of the structural response in a composite material.

Usually the fibrous element assumes the tensile stress capacity while the material that contains this fibrous material assumes the compressive stresses. Therefore the most efficient position of the fibrous material should occupy the composite areas that are subjected to tensile, and also they must be oriented parallel to these tensile stresses.

Knowing the real orientation of the fibers within a composite material can help to optimize the design and manufacturing process. The final result is a more efficient use of the fiber, and therefore an optimal design, from both structural and economical points of views.

There are some indirect methods which allow the evaluation of metallic materials orientations based on the electromagnetic difference in the behaviour between the fibrous material (metal) and the matrix material (non-metallic). These existing methods are inaccurate, i.e. approximate values are obtained with a degree of uncertainty, and its field of application is restricted exclusively to the metallic fibrous materials.

Using computed tomography scan technology there is a semi-direct method to evaluate the orientation of the fibres inside a composite material. It consists on determining the orientation using the apparent length in the three spatial directions. This apparent length is obtained from the projected images of the fibres in each of the three spatial planes. It is based on the hypothesis that orientation is perpendicular to that in which the total length of the fibre apparently shows a minimum value. This semi-direct method is more accurate than the indirect but cannot identify the exact orientation of the fibres.

There is a direct method which consists on obtaining the individually orientation of each fibre by tomography images. Through an image analysis software it is possible to obtain segmentation of each independently fibres, but without providing an automated information of the fibre orientation.

Hence, there is a need to obtain an automatized method for accurately evaluating the density and orientations of fibres inside composite materials.

Description of the Invention

The present invention is a computer implemented method to accurately assess, from the post-processing of images scanned by computed tomography scan (named CT- scan), the orientations of fibrous or filamentary components contained inside a composite material. A composite material contains materials of different densities (fibrous material and matrix), and these have different X-rays absorption capacity, generating different grey levels in scanned images. This allows later identification and separation. The material to be analysed is segmented or separated from the scanned images. Each one of the images pixels which corresponds to the specified component is identified with three-dimensional coordinates. Then the points are clustered in independent fibres using a mathematical algorithm. Next, the interpolation line of each cloud of points belonging to a single fibre is obtained. This line gives the orientation of each of the fibres within the three dimensional space.

The method to obtain the orientations of fibres inside composite materials using computed tomography scan comprises the following steps:

- Obtaining tomography scan images of different cross sections of the composite material; - Converting said images into a set of points (preferably arranged in a 3D matrix), each point representing a pixel of the image with its corresponding grey scale value and three-dimensional coordinates;

- Extracting from the set of points the pixels corresponding to the fibre material by using at least one threshold gray scale value;

- Clustering the pixels of the fibre material corresponding to the same cross- section in individual fibres according to distance criteria between pixels;

- Assembling the individual fibres located in different cross-sections and corresponding to the same single fibre by estimating the position of the centroid of each individual fibre in an immediate cross-section;

- Obtaining the interpolation line of each cloud of pixels belonging to a single fibre and, from said interpolation line, obtaining the orientation of each single fibre.

The tomography scan images of the cross sections are preferably taken with a determined pitch distance between images. Different threshold gray scale values may be set for different zones of the composite material.

The distance criteria for clustering of pixels in individual fibres can comprise checking those pixels in the same cross-section which are within a certain distance threshold. The clustering of pixels in individual fibres preferably comprises a filtering process by which the groups of pixels having less size than a threshold size are not considered as individual fibres.

In a preferred embodiment the individual fibres in immediate cross-sections are considered to belong to the same single fibre if the distance between the real centroid of the individual fibre of a cross-section and the estimated centroid for said cross- section is within a certain threshold. The assembling of individual fibres in a single fibre may only be considered when there are at least three different individual fibres located in different adjacent cross-sections complying with the threshold requirements.

If the maximum distance between the pixels of an individual fibre is bigger than half the length of the fibre, this individual fibre is considered as a single fibre.

The method can further comprise obtaining the density of fibres inside the composite material by calculating the sum of the lengths of the single fibres and their corresponding volumes, and comparing the volume of the fibres with the total volume of the composite material.

The present invention provides important advantages over the prior art:

- Automation: Using a single algorithm implemented into a mathematical analysis software (MATLAB, OCTAVE, SCILAB or similar), such that all postprocessing processes of the tomographic scans are automated.

- More accuracy: The segmentation of the fibres is more accurate because this method , uses a predictive detection technique that clusters the spatial points into different fibres to subsequently obtain the fibre orientations. The fact of using a predictive technique, i.e. predict the position of the group of points which are in the same fibre, makes it possible to separate points belonging to different fibres, even there is small distance between them. Clustering the points belonging to a single fibre, the dominant orientation of each of these fibres can be determined automatically using the interpolation line of the points.

- Adjustable, configurable: The entire process is grouped into a single algorithm. Tolerance criteria are introduced as an input value. Therefore, the accuracy of the analysis protocol can be adjusted based on fibre dimensions and computed tomography scan accuracy.

The present invention may be applied to all industries that manufacture or develop any type of composites products in which one material is a fibrous material and also this material has different density from the rest of the materials so it can be segmented in the CT scan.

Brief Description of the Drawings

A series of drawings which aid in better understanding the invention and which are expressly related with an embodiment of said invention, presented as a non-limiting example thereof, are very briefly described below.

Figure 1 shows the centroid prediction of a group of points in a section. Figure 2 shows an explanation of both global and local Cartesian coordinate system. Figure 3 shows correlation between global and local Cartesian coordinate system.

Figure 4 shows a diagram flow of the steps performed by the present invention.

Figure 5 shows figure superposed X-ray section cuts images obtained for an application example.

Figures 6A and 6B show section number 3 before and after the segmentation of the steel fibres, respectively, for the application example.

Figures 7A and 7B show the specimen image before the fibres segmentation and the fibres separated " from the concrete after segmentation, respectively, for the application example.

Figure 8 shows groups of points separated in individual fibres, for the application example.

Figure 9 shows centroid and direction vector in the XY plane of a set of points, for the application example.

Figure 10 shows an image of the fibres segmented within the complete specimen.

Figure 1 1 represents the interpolation line of a fibre.

Figure 12A, 12B and 12C shows the angles histograms obtained from each of the fibers with the X, Y and Z axes, respectively.

Figures 13A, 13B and 13C shows angles histograms obtained from each of the fibres with the radial, circumferential and radial axes.

Description of a Preferred Embodiment of the Invention

The present invention refers to an automatized method to accurately assess the orientations of fibrous or filamentary components contained inside a composite material, by post-processing computed tomography scanned images. The method is divided into different processes:

1. Tomography scans of the composite material to be analysed.

2. Image identification.

3. Image segmentation.

4. Clustering the points.

5. Assembling the groups of points in different cross sections on a same fibre.

6. Obtaining orientations. > , Firstly, tomography scans of the composite material are obtained. This scan consists in obtaining the cross sections images of the part or component to be analysed with X-ray emission. Separation between each section will depend on the level of detail required. The obtained images have a grayscale format. The materials with higher densities have increased absorption of the emitted radiation and the grayscale values are closer to white, while less dense materials have darker values in the grey scale.

From this point all procedures are accomplished by implementing mathematical algorithms in mathematical analysis software (MATLAB, OCTAVE, SCILAB or similar). An algorithm is generated to rename the image files with a consecutive number to automate the images processing.

Secondly, an image identification step is performed. The images obtained during the scanning process are converted into a numerical matrix where each element of the array represents a pixel of the image with a grey scale value. Using an algorithm all the points are identified, using four parameters: X-coordinate, Y-coordinate, Z-coordinate and the grey colour value. The Z coordinate is defined as the result of multiplying the number of the cut (n) by the pitch distance between cuts (Δζ).

Z = Az - n

The coordinate X and Y are calculated by multiplying the pixel position within the matrix by the image pixel size.

Thirdly, an image segmentation step is carried out. Segmentation consists in separating the different materials with different densities, i.e. extract from the matrix the fibre material. The threshold value of the grey scale must be set in the algorithm. This value marks the boundary between one material and the other.

Using this threshold value, the image points that correspond exclusively to the fibrous material are separated from the composite. The final result of this process is a group of sections which contains the fibrous material points.

Depending on the materials densities and the size of the piece to be analysed, the greyscale of the scanned image may be variable for the same material located in different zones. There will be differences between the shallow and deep areas due to the X-ray absorption inside the material. In this case for a better segmentation two or more threshold grayscale values should be set for each different zone.

In a fourth step, the points are clustered. In each cross-section of the part to be analysed each fibre is separated independently. The implemented algorithm takes an arbitrary point of the point cloud and seeks out those points of the total points that are closer to this, with a tolerance limit. The point within this limit is clustered with the starting point. The search algorithm starts again searching a new point comparing the distances with each point of the cluster generated.

Then, clustered points are removed from the search engine. The process is repeated until there are no points within tolerance. Those points which are in the separation limit correspond to points of the same fibre. Once the fibre points are grouped, another new point is taken and the process is repeated so a new set of points representing a new fibre is obtained. If any of the groups have less size than the expected size then they are eliminated from the process, because they correspond to pixels to be ignored in the process. In a fifth step, the groups of .points in different cross sections corresponding to the same fibre are assembled: An algorithm seeks out those groups of fibre points using a predictive technique which predicts the position of the centroid of a group of points on a fibre in a section immediately above from the initial one. If cylindrical fibres are analysed the cross-sectional image of this fibres produce more or less slanting cuts on the fibres depending on the degree of orientation with the horizontal plane.

Therefore, the centroid of the upper level will not be in the same X and Y coordinates but rather these will be displaced a different value depending on the degree of inclination of the cut fibre. Therefore, from the centroid of a group of points corresponding to a fibre, and the dimensions of the ellipse generated in the oblique cutting of the fibre, it is possible to estimate the coordinates of the centroid of the group of points of a fibre at the next level, as shown in Figure 1.

Using an algorithm the centroid Ci of initial group of points is obtained. The "a" value is obtained by calculating the maximum distance among all points and the centroid (hence, "a" would be the semi-major axis of the ellipse). The angle "a" is obtained:

diameter / 2

Q! = arcsin

a wherein "diameter/2" is the radius of the cylindrical fibre. "L" is defined as the projection of the fibre generatrix G on the XY plane. Its value is given by the following expression:

tan(a) where Δζ is the value of the distance between the scan cuts (i.e between cross-

- sections). Δχ and Ay values are obtained with interpolation line v of the points cloud belonging to said cross-section that gives the vector which defines the value of the angle β with respect to the axis X and Y. β = arccos

Δ = cos( ?) · L

Ax = sen( ) L There are two possible estimated centroid solutions, since the orientation of the oblique cut may be to one side or to the other. Therefore an algorithm is generated to check which of the two solutions is correct. A tolerance level is established to compare the distance "d" between the real centroid C 2 of the groups of points in the next cross- section and the estimated centroid C 2es t-

In order to validate the group of points is necessary that at the next level there is a set of points whose centroid is within tolerance. Once verified that three groups of points in different sections are in the centroids tolerance limit they will be grouped into a single fibre.

For those fibres with an orientation parallel to the XY plane and its cross section generates only a single group of points, and therefore the above process may not be valid a new criterion must be established. If the distance 2 - a (maximum distance between the points of the group) is bigger than half the length of the fibre (the length of the fibre is previously known) this group is isolated as a single fibre and its orientation is defined by the angles a and β.

When the algorithm does not find groups of points that are within the tolerance the process will conclude and the fibre will be completely determined. The process ends when there are no points to cluster.

Finally, the orientations are obtained. Once the point clouds are clustered into a fibre, an adjust straight js obtained using an algorithm. This line defines the vector of the fibre orientation in the three coordinate axes.

The a

2. Center of gravity: °

With this information, we can obtain the orientation of the fibre. It can be shown in two different coordinate systems: global Cartesian coordinate system and local Cartesian coordinate system (see Figure 2). Next, both of these Cartesian coordinate systems are explained: a. Global Cartesian Coordinate System

The orientation of the fibre is obtained, according to the Global Cartesian axes X, Y and Z:

1. X-axis orientation a% : corresponding to the angle between fibre and X axis.

2. Y-axis orientation >' : corresponding to the angle between fibre and Y axis.

3. Z-axis orientation a - " : corresponding to the angle between fibre and Z axis.

The orientation of this fibre is obtained as following:

Repeating this process to all the fibres, the orientation of all of them is obtained. In order to evaluate the dominant orientation of the fibres, a histogram for each of the three directions is drawn. In the abscissa the angle is collected, and on the ordinate, the frequency of occurrence.

The dominant direction of the fibres corresponds to the angles that show highest frequency of occurrence.

Also the efficiency of the fibres in each of the three directions is defined:

1. X-axis efficiency e% : according to X axis.

2. Y-axis efficiency y : according to Y axis.

3. Z-axis efficiency e - ~ : according to Z axis.

These values are obtained according to following equations: ∑(2-f x (a x l ) cos (a X ))

e. ∑(2-/ ; (a )cos(«,, )) where:

' " " ·' ' : frequency of each bar of the histogram corresponding to Z-axis orientation.

The efficiency value can vary between 0 and 2. A value of 2 indicates that the fibres are completely aligned to the corresponding axis. A value of 1 indicates that the fibres are not orientated in this axis at all. And a value of 0 indicates that the fibres are orientated in a perpendicular direction to the corresponding axis. b. Local Cartesian Coordinate System

In some applications it may be interesting to know the dominant direction of the fibre in a local Cartesian coordinate system, were X'-axis corresponds to radial direction, Y'- axis corresponds to circumferential direction and Z'-axis corresponds to vertical direction. This occurs, for example, in specimens having outer and/or inner circular contour. In this case, fibre should be oriented in radial and circumferential directions. Using this local Cartesian coordinate system this orientation can be observed, but this phenomenon cannot be observed using a global Cartesian coordinate system.

First of all, it is necessary to define the local Cartesian coordinate system. Figure 3 shows correlation between global and local Cartesian coordinate system.

V ' = j V , V , V , I

Next, it is necessary to redefine the orientation vector ' y ' : ' , according to this coordinate system: The orientation of the fiber is obtained, according to the local Cartesian axes X', Y' and Z':

1. X'-axis orientation a * ' : corresponding to angle between line and X' axis.

OL

2. Y'-axis orientation v' : corresponding to angle between line and Y' axis.

3. Z'-axil orientation corresponding to angle between line and Z' axis.

The orientation of this fibre is obtained as following

■v..

, = r-^

' V Repeating this process to all the fibres, the orientation of all of them is obtained. Also the efficiency of the fibres in each of the three directions is defined:

1. X'-axis efficiency e . : according to X' axis.

2. Y'-axis efficiency ' : according to Y' axis. 3. Z'-axis efficiency β;' : according to Z' axis.

These values are obtained according to following equations:

e- =∑(2-/ I . (a.. ,/ ) cos(a.., )) where

N,

: number of bars of the histogram

: frequency of each bar of the histogram corresponding to X-axis orientation. : frequency of each bar of the histogram corresponding to Y-axis orientation. ; . frequency of each bar of the histogram corresponding to Z-axis orientation.

The efficiency value can vary between 0 and 2. A value of 2 indicates that the fibres are completely aligned to the corresponding axis. A value of 1 indicates that the fibres are not orientated in this axis at all. And a value of 0 indicates that the fibres are orientated in a perpendicular direction to the corresponding axis.

Figure 4 schematically shows the different steps of the present method.

All the process is entirely automated, so the determination of the dominant orientations in a specimen can be done in very short time and with a high reliability (without human uncertainties). Moreover, the volume of fibres is obtained by multiplying the measured length of the fibres by its diameter and by the number of fibres obtained. Fibre density is the ratio of fibre volume and the total volume of the specimen. . , .

A practical application of the process was developed on a 100x200 mm. cylindrical specimen. The material used to make the specimen is concrete reinforced with steel fibres. The fibres are DRAMIX 45/50 with a diameter of 1.05 mm. and the fibre content is 1 % of the concrete volume.

First, the specimen is scanned using computerized tomography in an X-ray equipment (Y.CT Compact YXLON equipment). A section cut of the specimen is made horizontally with a range of 1 mm gap. As the specimen is 200 mm. high, the scan provides 200 cross-sectional images. The images obtained are 8-bit with a resolution of 1024x1024 pixels. Figure 5 shows the superposed X-ray section cuts images obtained.

Secondly, the cloud points from each of the images of the cross sections are obtained. In this case, pixel size of 0.12445 mm.; Z coordinate of each image between 1 and 200 mm.

Thirdly, fibres segmentation from the concrete is performed, using 90 as a grey threshold value within a range between 0 and 255 in the grey scale. Figures 6A and 6B show section number 3 before and after the segmentation of the steel fibres, respectively. Figures 7A and 7B show the specimen image before the fibres segmentation and the fibres separated from the concrete after segmentation, respectively.

Fourthly, segmentation of the groups of points in individual fibres is carried out, setting a maximum distance between points of 0.40 mm. Figure 8 shows groups of points separated in individual fibres.

Next, fibres are clustered using the prediction algorithm of the points groups centre-ids. Figure 9 shows centroid and direction vector in the XY plane of a set of points. Figure 10 shows an image of the fibres segmented within the complete specimen. In a subsequent step, the interpolation line of each fibre is obtained, as shown in Figure 11.

Next, the orientation histograms according to the coordinate axes are obtained. Figures 12A, 12B and 12C shows the angles histograms obtained from each of the fibers with the X, Y and Z axes.

With the obtained results we can have the local Cartesian coordinate system directions from the central axis of the specimen, as shown in Figures 13A, 13B and 13C (angles histograms obtained from each of the fibres with the radial, circumferential and radial axes, respectively).