Automatic Determination of Fiber-Length Distribution in Composite Material Using 3D CT Data
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Determining fiber length distribution in fiber reinforced polymer components is a crucial step in quality assurance, since fiber length has a strong influence on overall strength, stiffness, and stability of the material. The approximate fiber length distribution is usually determined early in the development process, as conventional methods require a destruction of the sample component. In this paper, a novel, automatic, and nondestructive approach for the determination of fiber length distribution in fiber reinforced polymers is presented. For this purpose, high-resolution computed tomography is used as imaging method together with subsequent image analysis for evaluation. The image analysis consists of an iterative process where single fibers are detected automatically in each iteration step after having applied image enhancement algorithms. Subsequently, a model-based approach is used together with a priori information in order to guide a fiber tracing and segmentation process. Thereby, the length of the segmented fibers can be calculated and a length distribution can be deduced. The performance and the robustness of the segmentation method is demonstrated by applying it to artificially generated test data and selected real components.
KeywordsFiber Length Length Distribution Single Fiber Cylindrical Structure Eigenvalue Analysis
Fiber reinforced polymers (FRPs) are used increasingly in the aerospace and automotive industry, since those components facilitate the cost-effective building of lightweight but rigid components. One manufacturing method for the construction of fiber reinforced polymers is the long fiber reinforced thermoplastics (LFRP-D) process, where a matrix material, for example consisting of polypropylene and additives, is heated and mixed with fibers, for example carbon or glass fibers. This process happens directly, that is, without the usage of an intermediate semifinished part. Thereby, components can be manufactured that are capable of acting as supporting elements with respect to rigidity and stability. Due to these properties, many parts made of LFRP are already used in the automotive industry, for example for frontends, underbody casing, supporting elements, or parts of an engine compartment.
The length of the fibers has a strong influence on the strength, stiffness, and impact resistance of the component . From measurements, it is known that 95% of the maximal possible material stiffness is reached at a fiber length of 1 mm. However, the desirable length of fibers within a certain component is strongly dependent on the purpose of the product . Moreover, since fibers can be damaged and divided by the production device during the creation process, there is not only one single fiber length but a distribution of the fiber lengths within a component. Furthermore, the opposite can happen if the cutting of the fibers by the cutting unit does not work well, which results in longer fibers than expected . Because of this uncertainty of the actual fiber length within the component, it is important to determine the distribution of the fibers and their lengths after the production process in order to estimate the quality of the resulting product.
In this paper, a novel method for the determination of the fiber length distribution is proposed using high resolution computed tomography as scanning method. Therefore, the 3D CT image is processed in order to segment the fibers. Subsequently, the length of each segmented fiber can be calculated and their distribution can be quantified. As a consequence, the presented method avoids destruction of the test sample and makes an inspection of in-use products feasible.
The remaining sections of this paper are structured as follows. Section 2 briefly discusses the current methods in fiber length distribution determination. Following in Section 3, our algorithm for automatic fiber segmentation and length calculation on high-resolution CT images of components is explained. The results achieved by applying this method to artificial and real datasets are presented in Section 4. The concluding Section 5 contains a discussion of the presented method and gives an outlook to planned future research topics in this area.
2. Previous Work
The established method for the determination of a fiber length distribution within a component is to pyrolyze its matrix [4, 5]. Therefore, the component is put into an oven which is heated to about Open image in new window . After about 90 minutes, the matrix component is reduced to ashes and the skeleton of the fibers remain. In order to determine their length distribution, several methods are possible and in use. One mechanical process is to sieve the fibers with different sieve sizes. However, this method does not work satisfactory with long fibers that are strongly felted. Another common method is the usage of scanners or high-resolution CCD-cameras and flash devices . For this method, the fibers have to be singularized in order to reduce measurement errors caused by fiber crossings and fiber entanglements. Subsequently, the fibers are segmented with a digital image analysis system and the length of the segmented fibers is determined.
The main disadvantage of these approaches is that the component has to be destroyed in order to determine fiber lengths. Consequently, these methods can only be applied during the development process for the first article inspection or the evaluation of spot samples. Therefore, it would be strongly desirable to have methods that allow for the non-destructive evaluation of in-use products or parts thereof for quality assessment. However, currently there are only limited non-destructive evaluation technologies available or under active research .
Due to high resolution scanning technology combined with a high image quality, the development of non-destructive evaluation algorithms becomes more and more practical. In the following section, a model-based approach for the automatic detection and segmentation of fibers from such image data is presented.
3. Fiber Segmentation
A model of an ideal fiber is the foundation of the following segmentation approach. It is reasonable to assume that a general fiber is cylindrically shaped. Furthermore, in the high-resolution scans acquired the grey value profile of the fibers exhibited a clear maximum at their centers. Moreover, all fibers of a common class usually have constant and previously known diameters . As a consequence, these characteristic features can be exploited by using a model-based segmentation approach. The segmentation algorithm itself is modeled as a multistep process. Firstly, the whole image is filtered and reduced by a closing operation in order to achieve a good fiber separation in the image data. Then, the image is scanned for fiber-center voxels by the means of a discrimination function based on eigenvalue analysis. The detected center points are then used as starting seeds for the tracing algorithm. Model-based segmentation of a center-axis representation is performed by tracing fiber-center points along the direction determined during eigenvalue analysis.
Using the a-priori known radius of the fibers, a segmentation mask is generated in order to remove the corresponding fiber from the input data. These steps, as explained in detail below, are repeated until the input dataset is fiber-free, that is the algorithm cannot find any remaining cylindrical structures in the image data. Finally, the length of each fiber can be determined and a distribution graph can be created.
3.2. Center Point Determination
For the segmentation of fiber structures from the image, starting seed points have to be determined. Therefore, image voxels have to be checked whether they belong to a fiber or not. Frangi et al.  presented a discrimination function for model-based shape extraction on 3D data, which allows for the association of voxel grey values to estimated shapes.
where Open image in new window is the matrix containing the eigenvectors Open image in new window , Open image in new window and Open image in new window as its columns and Open image in new window are the eigenvalues corresponding to the eigenvectors. For the numerical solution of these equations, the reader is referred to .
The eigenvalues of the Hessian calculated from the image voxel data contain information about the gray value change in the image neighborhood. Since for cylindrical shaped objects a specific change pattern is likely, this analysis allows for the determination of the starting seed points. Moreover, since the eigenvectors belonging to the eigenvalues of the voxel span an orthogonal coordinate frame, the direction and extent of the fiber can be estimated.
In , an overview of different shape interpretations based on the computed eigenvalues is given. For example, finding all eigenvalues to be of high magnitude and positive value indicates a spherical shape. For the purpose of fiber extraction, the most practical combination is the one given for bright tubular structures and is denoted as Open image in new window for the three eigenvalues Open image in new window . Hence, Open image in new window is expected to be of low magnitude, whereas Open image in new window and Open image in new window should expose high magnitude and should be negative.
The parameters Open image in new window , and Open image in new window can be used to tune the sensitivity of the function to deviations. For the ideal fiber, the maximum of Open image in new window is reached at the fiber center, while its value decays smoothly towards the border of a cylindrical structure. Consequently, this discriminator can be used to detect image voxels which exhibit the greatest likelihood of belonging to a fiber center. These points are then used as starting seeds for the model-based fiber tracing.
Since performing eigenvalue analysis and evaluating the discrimination function for each voxel is computationally very expensive, our implementation includes some optimizations. Firstly, only relevant voxels are taken into account when carrying out the calculations, that is voxels whose grey values exceed a predefined threshold Open image in new window . This approach is useful, as every dataset contains many elements which cannot be part of a fiber, for example background voxels and low valued image noise. Furthermore, since the eigenvalue analysis of the image data is an independent process for each individual volume element, this part of the algorithm is ideally suited for a parallel implementation. Consequently, it was implemented running on a high-end consumer graphics card using NVIDIA's CUDA technology .
3.3. Fiber Tracing
Having detected possible fiber center point candidates, the algorithm starts the tracing process in order to extract a centerline from the fibers. Since the fiber shape is known a-priori, a model-based cylinder approximation scheme is used. For this purpose, one candidate is selected as a starting point and the fiber is traced along the minimum eigenvector Open image in new window in both, positive and negative, directions. As known from previous analysis, this vector is directed along the central axis of the cylindrical structure (Figure 4).
Since the radius of the fibers is material dependent and known beforehand, this segmentation approach is very robust to the presence of image noise on the fiber borders. Once a fiber is fully segmented, it is used as a mask on the original data in order to remove it from the image entirely. The process is repeated until no more fibers can be found in the image. However, due to the nature of the data, there are a few special cases that have to be dealt with, namely crossing fibers and partial fiber segmentation.
3.3.1. Crossing Fibers
Furthermore, if a voxel is encountered that allows more than one propagation direction, it is again added to the seed point list. Thereby, the voxel is not marked as already segmented and can be reused while tracing the crossing fiber. If no adequate continuation direction is found, the tracing process stops. This can lead to partial fiber segmentation, another possible problem.
3.3.2. Partial Fiber Segmentation
For the evaluation of the presented method, two types of data were used. First of all, artificial test datasets were created. They contained varying types of fibers with different densities and lengths. The major advantage of this data type was that the length of each individual fiber was known beforehand and thus allowed an exact evaluation of the produced results.
Moreover, the algorithm was also evaluated on CT scans of real plastic components. Two of them will be presented in this paper. The first component was built of straight and long cylindrical fibers, approximating the ideal fiber very closely. The second dataset, however, was more difficult to deal with. It contained mostly short, curved, and heavily overlapping fibers. Nevertheless, good segmentation results were achieved in all cases.
4.1. Artificial Test Data
Correlation between the real length of the artificial fibers and the automatic detection results.
Correlation in %
4.2. Real Test Data
The dimensions of dataset two were Open image in new window with an isotropic voxel size of Open image in new window . The fibers in this component are less tightly packed, shorter in size with respect to the dataset size and they exhibit a curved structure which indicates a more problematic segmentation task for the presented algorithm.
In this paper, a novel, model-based approach for the automatic detection, segmentation, and length distribution calculation of fibers in CT data of fiber reinforced polymers was presented. Since fiber length distribution within the material is essential for the stability of an assembly, having a non-destructive evaluation method is highly desirable.
The presented approach uses a segmentation scheme which was shown to be robust even in the presence of curved fibers and image noise. The algorithm is also able to handle tightly packed and crossing fibers, though the accuracy suffers in these cases, as not all fibers may be detected fully or gaps may occur within single fibers. In order to estimate a systematic error in this situations, more datasets have to be investigated and the automatic results have to be compared to the outcome of a pyrolysis analysis. Moreover, current Open image in new window scanning devices are still restricted to scanning small sample sizes only, which currently limits the practical applicability of this method.
However, the results show that the presented algorithm can achieve a reasonably good segmentation and thus can act as a basis for further research on this topic. Further research will include the acquisition of reference data by pyrolizing the investigated sample components. Moreover, distribution statistics and error measurements of real samples have to be included in the evaluation of our material testing approach in order to devise a systematic error measurement. These steps are important for an intense evaluation and will be carried out in the near future.
With the current advent of high-resolution Open image in new window scanning devices that are capable of taking images of bigger structures, the presented method could become a valuable tool for broad inspection of varying material. This could be especially useful in industries where material function is vital and undetected wearout could have severe impacts.
The authors are thankful to T. Potyra and M. Reif (Fraunhofer ICT) for providing the samples used for evaluation. This paper was cofinanced by the European Union and the Free State of Bavaria, Germany.
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