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Dieser Artikel untersucht den Einsatz digitaler Bildkorrelation (DIC) zur Beurteilung der mechanischen Eigenschaften von Naturfaserverbundwerkstoffen aus Kiefer in der additiven Fertigung. Die Studie konzentriert sich auf die Variabilität dieser Eigenschaften und die Bedeutung statistischer Analysen für eine genaue Charakterisierung. Wichtige Themen sind das experimentelle Verfahren zur Herstellung und Prüfung von Proben, die Anwendung von 2D-DIC zur Messung von Dehnungen und Verschiebungen sowie die statistische Analyse mechanischer Variablen. Die Ergebnisse unterstreichen die intrinsische Variabilität von Naturfaserverbundstoffen und die Notwendigkeit robuster Techniken, um diese Effekte abzumildern. Die Schlussfolgerung betont das Potenzial, DIC mit stochastischen Finite-Elemente-Methoden zu kombinieren, um die Zuverlässigkeit von Bio-Verbundwerkstoffen in der additiven Fertigung zu verbessern.
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Abstract
This research presents a protocol based on Digital Image Correlation (DIC) to evaluate the mechanical behavior of Additively Manufactured (AM) composites derived from Natural Fiber Composites (NFCs). These emerging materials, usually layer-by-layer manufactured, are susceptible to defects or inconsistencies, and often exhibit heterogeneous and anisotropic properties due to the presence of natural fibers. For this reason, to ensure quality and safety is necessary not only to know their discrete mechanical characteristics but rather to approach the problems from a stochastic perspective, for which it is necessary to know the probability distribution that can serve as input in the context of Stochastic Finite Element Models (SFEM). Additionally, DIC could enable real-time monitoring of deformation and failure mechanisms under various load conditions. Tensile tests were performed on PLA-based NFC reinforced with pine fibers specimens, using DIC as a non-contact, full-field measurement technique. The main objective of this work was to demonstrate that it is possible to generate Probability Density Functions (PDFs) for key mechanical properties (specifically Young’s Modulus and Tensile Strength), which are essential for stochastic simulations. An in-house DIC-based setup was applied to obtain the PDF for important mechanical features such as Young’s Modulus and the Tensile Stress, since the high spatial resolution of the DIC enabled the identification of deformation patterns. The results confirm that DIC enables reliable, flexible, and high-resolution testing of NFCs for AM, and can effectively support stochastic modeling approaches by providing accurate probabilistic distributions of material properties.
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1 Introduction
Industry 4.0 is continuously evolving and must consider a wide range of factors, with environmental and social awareness being among the most critical. The growing need for sustainable development seeks to replace traditional materials with biodegradable ones that promote recycling [1, 2].
In recent years, biomaterials, specifically Natural Fiber Composites (NFCs), have been gaining relevance in Additive Manufacturing (AM) [3] mainly due to the growth of the AM technologies [4], and now a wide variety of commercial bio-composite filaments are available [5]. Polylactic Acid (PLA) is a biodegradable polymer that has a high potential to replace thermoplastic polymers in AM [6]. However, due to some of its properties, like low thermal resistance and high brittleness, it is necessary to add reinforcement in order to use it in applications requiring a certain mechanical strength. To improve the mechanical properties, the bio-composites based on PLA and wood fibers have become a focus of attention [7].
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Nevertheless, composites are more complex materials from different points of view [8]. From a numerical approach, the wide range of uncertainties during manufacturing, the anisotropy, and their structure create uncertainty when using them for mechanical design. For example, fiber orientation and size of the fiber are among the most critical factors that affect the mechanical characteristics of bio-composites [9]. Furthermore, these materials have a wide range of properties, so traditional mechanical characterization alone is not sufficient and must be accompanied by robust techniques, even statistical analysis [10].
3D printed bio-composites have an associated problem: during the characterization of the material, there is wide variability in the testing results due to the high number of parameters that provoke variability (most related to process and environment) and the dispersion between them [11]. Some NFCs do not have perfectly defined printing temperatures, and even if they do, other factors, such as lack of uniformity in the internal distribution of the material, can lead to the appearance of internal defects [12]. Furthermore, complexity increases when it increases the amount of fiber used in the composite. This complicates the printing process because of issues with nozzle clogging due to the buildup of material at the nozzle opening [7]. The use of the Finite Element Method (FEM) with a probabilistic approach could be a potential solution [13], which is also known as Stochastic Finite Element Method (SFEM). To be able to use this approach, it is necessary to apply a statistical study of the different mechanical variables to be able to generate their Probabilistic Density Functions (PDFs). In this context, Digital Image Correlation (DIC) offers a reliable alternative to traditional tactile methods for measuring strain in classic compression-loaded carbon fiber composites [14]. By following established guidelines, DIC can provide consistent and reproducible strain data, which is crucial for accurate material characterization.
Indirect measurement techniques, where the device does not come into contact with the test material, are used to determine the properties. In this group, the Digital Image Correlation (DIC) has become one of the most relevant methods. DIC refers to a full-field and non-contact technique capable of analyzing a set of images to determine their displacements and strains [15]. While direct measuring devices such as extensometers or strain gauges can only measure a small region, DIC allows a complete field analysis. The fact that it is a full-field technique is beneficial in this type of material, where anisotropy and high variability of results may appear. Furthermore, DIC allows the acquisition of images that do not need to be modified, allowing processing to be carried out as many times as necessary. This method can be applied using two DIC methodologies: the first one corresponds to a two-dimensional approach (2D), and the second one consists of a three-dimensional approach (3D) [16]. Generally, the 2D method allows the measurement of strains and displacements in a single study plane using only one camera and without the need for an external calibration. This makes the setup simpler and the procedure much faster. However, the camera must be oriented fully orthogonal to the plane of the specimen to avoid perspective errors, and the uncertainties that can occur out of the plane can be problematic when using this technique [17]. However, when 3D DIC is used, this problem is minimized, but it requires more preparation and the use of more cameras to guarantee stereoscopy. Some studies suggest that there is no significant difference between 2D and 3D DIC in the results for single flat specimens under controlled conditions [13]. Taking into account that single flat specimens will be used in this work and in order to reduce post-processing time and simplify test preparation, it has been decided to work with the 2D DIC method.
DIC is extremely useful for implementing tests that allow the calculation of PDF for mechanical variables like Young’s modulus and tensile strength. This distribution can be introduced as input in SFEM methods to reiterate simulations and sensible analysis, improving the quality of the result concerning the deterministic FEM [11].
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Given that NFCs are complex materials whose mechanical properties depend on a wide range of factors and therefore require precise study, the combination of SFEM and digital image correlation may provide substantial added value by mitigating such effects and consequently improving material quality. This research work aims to evaluate whether it is feasible to derive PDF functions from DIC data to be incorporated as inputs into SFEM-based model.
Mechanical properties provided by the manufacturer under the following conditions: nozzle 0,6 mm, 100% rectilinear filling, layer height 0,2 mm for more information [18]
Density ρ (g/cm3)
Young’s Modulus E (MPa)*
Tensile strength σb (MPa)*
1.09
2944.4
32.4
Note that E and σb is represented in the X-Y plane
The manufacturing process of the specimens has been carried out according to the following standards: ISO 527-1, ISO 527-2, and ISO/ASTM 52,924 [19‐21]. A commercial and widely known 3D printer (Prusa® i3 MK3s+) was used to manufacture the specimens. In total, 18 specimens were produced using a 100% rectilinear filling according to the printing parameters shown in Table 2. A total of 18 specimens were tested.
Table 2
Printing parameters used for specimen manufacturing
Printing temperature (ºC)
Bed temperature (ºC)
Print speed (mm/s)
Layer height (mm)
Nozzle diameter (mm)
220
60
50
0.2
0.6
For performing the tensile test, a Servosis® ME-405/50/5 test machine was used. A TC50Kn REP (50kN) load cell was used in conjunction with MTS Model XSA304A Grips. All tests performed have been recorded by a camera in order to be able to perform a 2D DIC analysis. To minimize the appearance of uncertainties the camera was placed orthogonal to the piece, guaranteed by the use of high-precision scaled rule and tripod. The acquisition system is configured by a CCD camera, a microcontroller as a synchronization source, and a PC to control all the data and elements. The camera model used was the Manta® G-504. This camera has a Sony ICX 665, Progressive CCD Monochrome sensor type, with a resolution of 2452 (H) x 2056 (V) pixels, with a square size of 3.45 × 3.45 μm and a maximum Frame Rate with full resolution of 9.2 images per second. The attached objective focal length is 5 mm.
For automating the data acquisition, an Arduino ® Uno has been used to control the signals. The microcontroller can simultaneously send a signal to the camera, which captures the images, and send a signal to a Data Acquisition System. This system has been used to synchronize the camera with the machine to ensure that the measurements of the machine are known at all times and can be related to the corresponding image. As shown in Fig. 1, two led spotlights were used to guarantee adequate illumination during the test.
Fig. 1
(a) Set up of the performed test and (b) computer-designed Speckle pattern used for DIC analysis
Once the tests have been carried out and a dataset of the main mechanical characteristics has been obtained, PDFs are constructed to further characterize the behavior of this material, taking into account the intrinsic variability of the material. In this work, the fit to normal (N), log-normal (LN), Weibull (W), and Gamma (G) distribution was studied. To assess the adequacy of the adjustment function (model) to the data, different goodness-of-fit tests have been used, which have already been employed in previous works [11, 13] and have provided good results. Specifically, the tests applied for validate the fit were the Chi Square (Chi), Kolmogorov-Smirnov (KS), and Anderson Darling (AD) Goodness-of-Fit (GoF) In this context, the tests are used in such a way that if the result obtained is a value equal to 0, it indicates that the fit is valid, while if the result is equal to 1, the function cannot be fitted to that type of distribution.
3 Results
After the DIC analysis, six strain gauges (three along the vertical direction and three along the horizontal direction) are set up to measure longitudinal and transverse displacements locally. The first one was placed in the center of the ROI, and the rest at a distance of 2 mm for the verticals and 30 mm for the horizontals, as shown in Fig. 2. Note that since the DIC analysis has been performed in 2D instead of 3D, it is possible that angular deviations may appear and cause minor errors during post-processing. However, according to literature [13], specimens with a flat surface are simple enough to obtain good results with the 2D method, which allows much faster processing and easier setup preparation without loss of accuracy.
Fig. 2
Results of the virtual extensometer. The image on the left shows the six virtual extensometers (three longitudinal in green and three transversals in blue) over the region of interest (ROI) in red. On the right, the distribution of deformations obtained after DIC analysis is shown
2D DIC analysis, as mentioned in previous sections, allows obtaining the full field of displacements and strains. Table 3 shows the values for Young’s Modulus (E) and Tensile Strain (σb) obtained from the DIC analysis.
Table 3
Results of the test obtained using 2D DIC. The table reports descriptive statistical indicators for both young’s modulus and tensile strength. These statistical metrics are used to assess variability and serve as a basis for defining probabilistic distributions for stochastic simulation of mechanical behavior
Young’s Modulus E (MPa)
Tensile strength σb (MPa)
Mean
2267.05
23.26
Lower Bound
1439.9
16.39
Upper Bound
3677.3
28.08
Median
2197.6
24.13
SD
514.34
3.48
IQR
508.6
6.25
The PDF of each mechanical variable has been determined to obtain the model that best fits each of them. Table 4 shows the results of using the Chi, KS, and AD tests. Based on this Table, Young’s Modulus (E) has been adapted to a Log-Normal function (LN) and the Tensile Strength (T) to a Weibull function (W). The graphic representation of the PDFs of each parameter is shown in Fig. 3, as well as the principal values of the PDF distributions. For Young’s Modulus E, the Log-Normal distribution has parameters µ = 2267.05 and σ = 514.34. On the other hand, the Weibull function distribution for the Tensile Strength has parameters β = 24.6961 and α = 8.7081.
Table 4
Goodness of fit (GOF) probability from the data obtained by DIC; N (Normal), W (Weibull), G (Gamma); 0 – Accept and 1 – Reject. Chi, KS, and AD test of the young’s modulus (E) and tensile strength (T)
PDF
N
LN
W
G
GOF
Chi
KS
AD
Chi
KS
AD
Chi
KS
AD
Chi
KS
AD
E
0
0
0
0
0
0
0
0
0
0
0
0
T
1
0
0
1
1
1
0
0
0
1
0
1
Fig. 3
Graphical representation of the PDFs obtained by DIC. (a) Log-normal distribution of the young’s modulus (E) and (b) Weibull distribution of the tensile strength (T)
As the reader can observe in Fig. 3, several probability distributions could be applied to model the Young’s Modulus and the Tensile Strength, and not only the classical normal distribution which is not suitable when data are affected by bias or outliers. The parameters of the distributions can be included within SFEM applications in order to include within the analysis the probability function of each variable and, in this manner, make the analysis more accurate, robust, and reliable.
4 Discussion
The variability of results is mainly due to the nature of the material and the printing method itself. The material used is based on natural fiber, so the fiber quality and structure are very influential on the behavior of each specimen. Additionally, the 3D printer used was an open printer, so temperature changes due to ventilation currents are very influential in the project. For this reason, test protocols and stochastic approaches are necessary to ensure integrity and safety in service conditions of the parts made using this type of material. In this way, comparing the values with those provided by the manufacturer, it can be seen that the specimens actually have lower mechanical properties than those provided in the datasheet. The manufacturer’s specifications (E and T) are much more optimistic than the results obtained. Please note that for these materials, as normally indicated by the manufacturers, a significant variability is expected in these specifications due to the anisotropy, heterogeneity of the fibers, environmental conditions, AM configuration, etc. For Young’s Modulus, the data provided by the manufacturer was 29.9% higher than the data obtained, and for tensile strength, it was 39.3% higher. It is important to mention that this is the case for the average value, as some specimens individually equaled and exceeded the manufacturer’s value.
Applying the PDF calculated, the probability that the results are below the manufacturer’s values is 90.66% for E and 99.58% for T. One of the main reasons for the lower values than those of the manufacturer may be the manufacturing process configuration and the working environment.
Despite this, the results obtained from other studies on PLA and pine fiber bio-composites are analyzed [26, 27], and it is easy to see that the results are lower than might be expected. While other studies have observed an improvement in the mechanical properties of the material compared to pure PLA, this improvement was not observed in the present study. As mentioned above, one of the reasons behind this may be the use of an open printer. Environmental conditions, especially variations in temperature and humidity, have been shown to significantly influence the mechanical performance of PLA parts manufactured using AM [28]. Additionally, It has been demostrated that internal printing parameters such as extrusion temperature, bed temperature, and printing speed have a direct impact on both thermal and mechanical behavior of PLA, further highlighting the sensitivity of this material to process variability [29]. Tensile strength and Young’s modulus deteriorate in hot and humid environments, while cold and dry conditions sometimes improve performance. This demonstrates that environmental conditions significantly affect material performance and reinforces the importance of controlling ambient temperature and avoiding cooling fluctuations induced by air currents in open-frame printers.
5 Conclusion
This work aims to use a 2D DIC analysis to determine the properties of a bio-composite material based on PLA and pine wood. These materials are state of the art at the present time [5]. To this end and for this research, a total of 18 specimens were manufactured using 3D printing and tested using a tensile test. Since 3 virtual extensometers were used for each specimen (3 longitudinal for Young’s Modulus and 3 transverse for Poisson’s ratio), a sufficient number of data was obtained (54 data). In addition, this number is in accordance with the standard specified for this type of material [21]. This statistical method has been used in previous works [4], and the results obtained have been optimal, so there is no need to use more validation methods.
The mechanical properties of the bio-composite were obtained using virtual extensometers in each one of the samples and by extracting the Young’s Modulus. The results were compatible with the initial hypothesis that NFC have a high variability that is often not considered by the manufacturer’s data because the final result is highly affected by the printing process. DIC analysis has proven to be highly adaptable for capturing the intrinsic variability of composite materials made from natural fibers, confirming that the printing process significantly influences their properties, beyond what is indicated by the manufacturer’s data.
It is possible to state that through a statistical mechanical characterization, the NFCs of this type can be characterized more comprehensively. The use of DIC analysis has been of great importance in the development of the work as it has allowed obtaining variations within the same specimen, which has been taken into account in the variability of the results for new research works. Additionally, from the experimental data, the more optimal PDFs have been generated (for Young’s Modulus and Tensile Strength). This approach was used to estimate the probability that the material properties fall within the manufacturer’s specifications. The results align with the empirical expectations typically observed when characterizing materials of this type.
Regarding future works, it is expected to use this same analysis method to characterize other NFCs composites: PLA reinforced with flax, hemp, and chestnut shell waste. In addition, in order to improve the results obtained, the 3D printer will be closed. This will make the printing environment much more stable, and it is expected that the results will be closer to the manufacturer’s data and other reference works.
Acknowledgements
This research has been funded by the European research project NaturFAB (Interreg-POCTEP) with code 0049_NATUR_FAB_2_E.
Declarations
Competing interests
The authors declare that there is no conflict of interest.
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