کنترل کیفیت از CFRP با استفاده از پردازش تصویر دیجیتال و تجزیه و تحلیل الگوی نقطه نظر آماری

Although fiber-reinforced composite materials have often been considered as periodic materials in theoretical models, the distribution of fibers is random in real materials. This random distribution of fibers is closely related to their transverse failure behavior. This paper proposes the use of statistical functions which describe random point patterns as a quantification of the dispersion of the transverse failure properties of several carbon fibre reinforced polymers (CFRP). It is shown that the analysis of the K function is the most meaningful for this purpose.

At the microscopical level, the main morphological characteristics of long fibre reinforced polymers are heterogeneity and anisotropy. In spite of this, composite materials have classically been modeled by means of periodical unit cells, that is, without taking into account neither the heterogeneity nor the geometrical disorder of fibers. The periodicity hypothesis leads to simplifications which make possible the application of homogenization methods [1], [2] and [3], it provides good estimations for the elastic properties [4], and it can also be employed with good results in non-linear two-scale methods [5], [6], [7], [8] and [9]. Also, in computational mechanics, the periodicity assumption leads to lower computational costs whereas other approaches may be computationally unaffordable. However, a simple optical microscope observation reveals that long fiber reinforced composites (i.e. carbon or glass fiber-reinforced thermoset matrices) are far from being ordered materials since the fiber is randomly distributed through the matrix, sometimes showing areas with fiber clusters and resin pockets. These heterogeneities lead to local stress values in the matrix which are higher than those obtained assuming a periodical distribution and, consequently, they are more likely to produce damage, matrix cracking, or to cause degradation phenomena [10]. For this reason, the local damage in a transverse section of the composite (that is, matrix cracking and matrix-fiber debonding) is expected to depend strongly on the random distribution of the reinforcement. On the other hand, because of the growing importance of composite materials in mechanical and structural engineering together with the lack of knowledge about many issues related to their failure, damage and fatigue behavior, there is a demand from the industry for quality control methods. This quality control methods should provide information on the defects within the material produced during manufacturing, the tolerance to these kind of defects, the relation between the material properties and its micro-scale structure. Traditionally, volume fraction is used as a measure of the quality of a laminate and ultrasound devices are normally used to complement this information by detecting voids and bubbles within the matrix. Some researchers have proposed sophisticated and highly technological procedures such as thermal imaging techniques [11] and [12], optical coherence tomography [13], near-infrared spectroscopy [14] and [15] or X-ray tomography [16] for the inspection of fiber-reinforced composites. Although these techniques are extremely precise, they usually require high technology machinery, sophisticated interpretation techniques and highly specified and qualified personnel. This makes them unusable for most industries. The widespread use of computers in industry prompted some pioneering work, like that by Berryman [17], in data acquisition using digital image processing for heterogeneous materials. The quantitative techniques for digital image processing of composites are widely employed in metal matrix composites (MMCs) [18] and [19] and some research has applied Fourier transformation to detect the orientation of reinforcement in reinforced concrete [20]. In fiber-reinforced polymers, much of the work devoted to the geometrical characterization of materials via digital image processing has been focused on braided composites [21]. Summerscales and co-workers computed total perimeter and total area of inter-tow pore spaces in woven laminates produced by RTM [22] and [23] and applied Voronoi tessellation and fractal dimensions to quantify the microstructure of woven composites [24]. The full characterization of glass and carbon fiber reinforced composites has also been addressed by means of optical microscopy [25] and digital image processing of micrographies has been employed by Joffe and Mattsson [26]. This work is part of a line of research which tries to bridge stress and strain fields at the macroscale with damage initiation and other microstructural phenomena by considering the random distribution of the fibers within the composite. This approach provides probability distribution functions for the stress and strain components, and is therefore useful for structural reliability purposes. The methodology presented here starts from micrographies and, using image processing techniques together with spatial statistics tools, measures the homogeneity of the distribution of the fiber within the composite. Although the distribution of the fiber within the material is random, it is homogeneous – as will be shown in the next section the statistical homogeneity can be mathematically defined – if the fiber is correctly spread through out the material and, in this way, regions containing matrix pockets are avoided. This homogeneity can be seen as a measure of the quality of the fiber distribution since, as this paper will show, homogeneity in the material leads to lower mechanical property dispersion.

The statistical point patterns of fiber positions have been analyzed for three different carbon fiber-reinforced polymers. Data for the statistical analysis has been obtained through digital image processing: (i) filtering and radiometric correction, and (ii) fiber segmentation and localization. In this way, 40 digital images for three different CFRPs have been analyzed. The volume fraction and the position of the fiber centers has been obtained for each digital image. Together with a statistical analysis of the volume fraction, the functions K(r) and g(r) which describe the random distribution of fibers within the material have been computed and compared with the respective functions for a Complete Spatial Random (CSR) pattern. The results of this analysis reveal that the materials showing a distribution of fibers which is more different from a CSR pattern have a larger dispersion in their failure behavior,and the analysis of the K function is the most meaningful. The tools presented could be easily employed in an industrial environment as quality control measurements, since the small dispersion in failure behavior is a desired property in mechanic engineering materials.