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A virtual permeability measurement framework for fiber reinforcements using micro CT generated digital twins
International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
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Original Article
A virtual permeability measurement framework for fiber reinforcements using micro CT generated digital twins M.A. Ali, R. Umer*, K.A. Khan Department of Aerospace Engineering, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 October 2019 Received in revised form 4 December 2019 Accepted 4 December 2019 Available online xxx
Liquid Composite Molding (LCM) is one of the widely used manufacturing techniques for high performance composite parts. In a simple LCM process, a pressurized liquid resin is injected inside a mold containing fibrous reinforcements. In order to create quality components using LCM processes, reinforcement characterization such as permeability and compaction response need to be performed fast and accurately. In this work, a micro CT based experimental-numerical reinforcement compaction and permeability characterization framework has been proposed which can potentially reduce process characterization cost by lowering material consumption and labor time and effort. The framework is non-destructive in nature and uses a miniaturized compression stage that can be housed in an X-ray computed tomography (XCT) system. This in-situ XCT experimental set-up is used to acquire the stress relaxation curve and XCT images of the reinforcement internal structure at multiple fiber volume fractions which are then converted into digital twins of the reinforcements. The virtual permeability of the reinforcement digital twin is computed through numerical flow simulations using realistic voxel models extracted from the stack of XCT images. The proposed approach has the capability of obtaining a plethora of information about the preform including, compaction response, statistical measurements of the internal preform geometry, and voxel models for numerical simulations. The methodology has been successfully demonstrated using two carbon fiber reinforcements with 3D woven architecture. The virtual permeability predictions were benchmarked against experimentally measured values, and were found to be in excellent agreement with the experimental data. © 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
Keywords: Liquid composite molding Permeability Compaction response Micro CT
1. Introduction Fiber reinforced polymer composites are being used in a variety of high performance applications due to their significantly enhanced structural, mechanical, and tribological properties [1]. These composites are produced in the form laminates or sandwich structures through various manufacturing techniques such as autoclave manufacturing, liquid composite molding [2e4], additive manufacturing [5] and automated fiber placement method [6]. In a generic LCM process, the fiber reinforcements are placed inside a mold cavity for subsequent compaction and resin injection [7]. Upon filling the mold cavity completely with catalyzed liquid resin,
* Corresponding author. E-mail address: [email protected] (R. Umer). Peer review under responsibility of Editorial Board of International Journal of Lightweight Materials and Manufacture.
the resin is allowed to cure and the part is then removed from the mold cavity. The fibrous reinforcements used in LCM process exhibit dual-scale flow characteristics as they are often produced from a pre-existing assembly of fine reinforcing filaments, generally produced in the form of yarns or tows, which are then further combined together in various architectures. To manufacture high quality products with consistent thickness and minimum void, the reinforcement compaction behavior and permeability characteristics need to be understood [8e10]. The compaction response and permeability of fiber reinforcements can be determined through analytical relationships, experimental procedures and numerical methods [11e13]. The theoretical models for the compaction response relate the compaction stress to the fiber volume fraction (Vf) through an algebraic relationship which are derived from micro, meso or macro-scale compaction behavior [14,15]. Similarly, predictive permeability models present permeability as a function of fiber diameter and the fiber volume fraction (Vf ) [11,16e18]. However,
https://doi.org/10.1016/j.ijlmm.2019.12.002 2588-8404/© 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: M.A. Ali et al., A virtual permeability measurement framework for fiber reinforcements using micro CT generated digital twins, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.12.002
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these models for both compaction response and permeability predictions are limited to simplified cases and do not capture the complex dual scale behavior of the fiber reinforcements. Experimental procedures for reinforcement compaction and permeability characterization are complex and costly [19e21]. Geometrical models of the complex reinforcement architectures are needed for the characterization of the reinforcements using numerical techniques. Generation of accurate models to represent the complex reinforcement architectures are not in the capability of modeling tools used for this purpose [22e24]. Hence, a robust characterization framework needs to be developed for cost reduction as well as to accurately predict the reinforcement permeability and compaction response. The XCT coupled with computer simulations provide an exceptionally powerful and versatile tool for material characterization
[25e29] and can offer an advanced platform for the reinforcement compaction and permeability characterizations. XCT has been used by a number of researchers to investigate the internal geometry changes due to compaction and other loading conditions typical of those encountered in LCM processes [30e34]. Permeability predictions using XCT based models either use realistic voxel models [35e40] or stochastic virtual models [9,41]. Most of the data presented in these studies either correspond to a single reinforcement state or use multiple samples. In this study, a non-destructive hybrid framework was used to investigate the compaction behavior and to predict the virtual permeability of two 3D reinforcement digital twins. The primary goal of this hybrid framework is to offer a single 2-in-1 platform for reinforcement compaction and permeability characterization which can potentially reduce process characterization cost by
Fig. 1. Overview of the hybrid characterization framework.
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lowering material consumption and labor time. The originality of this approach lies in the in-situ compaction characterization followed by generation of digital twins for virtual permeability computations, thus providing a combined compaction and permeability characterization framework. A single test sample of each reinforcement was used to characterize the reinforcements at multiple fiber volume fractions (Vf). In the hybrid method, realistic voxel models were generated from a stack of XCT images obtained under various compaction levels. The compaction data in the form of load and displacement measurements were also acquired through the load cell of an in-situ compression stage. The realistic voxel models were then used to predict the virtual permeability through digital flow simulations. 2. The hybrid framework As discussed in the previous section, XCT has been used to investigate the internal geometry changes due to compaction as well as to compute virtual permeability and investigate infusion processes. XCT is widely used to provide the geometry of reinforcements as input into finite element simulations for compaction characterization and evaluation of mechanical properties of the composites [23,42e45]. Naouar et al. [42,43] used a method to automatically build meso-scale finite element models of a 3D woven fabric from XCT images in which the most critical part of the process is the separation of warp, weft, and binder yarns with a segmentation process. To address the challenges associated with the segmentation process, Straumit et al. [46] used the structure tensor approach for generating voxel models. Moreover, Joaquim et al. [47] established the ability of XCT to analyze the details of micro-flow and void transport within a single tow through in-situ vacuum-assisted infiltration experiments using synchrotron X-ray computed tomography. Schmidt et al. [48] proposed a novel simulative-experimental approach to determine the permeability of fibrous reinforcements using experimentally calibrated digital twins mapped with XCT images. In all the studies discussed above, the non-destructive capability of the XCT has not been used to its full potential yet and the XCT data is used in a limited capacity. Moreover, the compaction and permeability characterization has not been performed on a single platform. These shortcomings can be addressed by employing the hybrid characterization framework which has a mixture of experimental and numerical procedures. In the experimental permeability measurements, a number of test samples are used in fluid injection experiments in which flow rates and pressure gradients are measured using several transducers. On the other hand, in the numerical approach, the reinforcement geometrical models are used in a digital flow simulation to predict the reinforcement permeability. Here, in the proposed hybrid approach, the initial steps of the experimental procedure are combined with the final
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steps of the numerical approach. An overview of the hybrid framework is illustrated in Fig. 1, outlining the various steps involved. In the hybrid framework, the load and displacement data is obtained from the load cell of the in-situ compression stage. The load and displacement data obtained is then converted into the stress relaxation curves. Once the compaction stress on the test sample reaches to a quasi-steady-state level, radiographic projections of the test sample are acquired using an XCT machine. After the acquisition of the radiographic projections, the sample is subjected to the next level of loading and the process of scanning is repeated. The radiographic projections are stored on a computer and reconstructed into 3D volumes using post processing software. The reconstructed 3D volume can be sliced in all three principle directions, or along any arbitrary cutting plane, to obtain 2D crosssectional images. Geometrical features of the internal structure, such as tow cross sections and inter-two gaps, can be visualized as well as quantified through manual or automated measurements form these 2D cross-sectional images. Additionally, the reconstructed 3D volume can be converted into computational voxel models. These voxel models can then be used in numerical simulations for both compaction studies and virtual permeability prediction.
3. Materials and methods 3.1. Materials In this study, two different types of 3D carbon fiber reinforcements, supplied by Sigmatex UK, were used. The reinforcements were used in there dry state without any resin to enable in-situ compaction. One of the reinforcements has orthogonal architecture whereas the other one has angle interlock architecture. The two reinforcements are different in terms of their weaving patterns, hence possessing different mechanical response under compaction loading. The z-binder yarns in both fabrics run through the thickness in a different pattern to hold the warp and weft tows together. The basic difference between the two reinforcements is the interlacing angle between the binder and weft yarns. The interlacing angles are 90 and 45 in the orthogonal and angle inter-lock architectures respectively. In both cases, the binder yarns penetrate all the way through the thickness. Both reinforcements have eight layers of warp tows and nine layers of weft tows. The warp and weft tows are made from 12K carbon fibers and the z-binder yarns are made from 6K carbon fibers. As per the specifications provided by the supplier, the orthogonal and angle inter-lock reinforcements have an areal density of 3353 g/m2 and 3045 g/m2 respectively. Both the reinforcements are shown in Fig. 2.
Fig. 2. Experimental materials (a) orthogonal and (b) angle inter-lock 3D fabrics.
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Fig. 3. The hybrid characterization set-up in the XCT machine.
3.2. In-situ XCT system The in-situ XCT system consists of an X-ray machine (GE Phoenix Nanotom) and a number of software packages. The compaction stage is supplied by DEBEN, UK model CT5000 in-situ compression fixture with 5 kN load cell. The XCT system is used for both scientific and industrial computed tomography and 3D metrology. The maximum sample size that can be accommodated in this machine is 240 mm diameter and 250 mm height. The power rating of the X-ray tube is 180 kV/15 W. The resolution that can be achieved is 300 nm. The DEBEN CT5000 in-situ testing stage can be placed inside the GE Nanotom XCT machine, as shown in Fig. 3. In the compression mode, the stage has two compression platens
vertically aligned inside a 3 mm thick glass tube. The glass tube encloses the test sample. The upper platen is fixed at the top of the tube whereas the lower platen is connected to a motorized gearbox and a 5 kN load cell. The software packages used for data acquisition in the hybrid framework are the Phoenix Datosx and the MICROTEST control software. The Phoenix Datosx is fully automated XCT data acquisition software that minimizes operator time and influence, while highly increasing the repeatability and reproducibility of XCT results. The user interface for this software is shown in Fig. 4 (a). The DEBEN CT5000 in-situ testing stage is controlled through the MICROTEST control software giving a wide range of control functions. The load and displacement
Fig. 4. (a) The screenshot of live user interface of Phoenix Datosx XCT data acquisition software, (b) DEBEN MICROTEST software environment showing load vs. time graph.
Fig. 5. Tow details as resolved at voxel sizes (a) 25 mm, (b) 12.5 and (c) 5.667 mm.
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Fig. 6. The different levels of compaction.
data is continuously displayed on the screen as shown in Fig. 4 (b). The user can setup various types of loading conditions. A target displacement or force is defined, which is then achieved by moving the lower platen of the compression stage. 3.3. XCT scan settings Test samples of 40 mm diameter of both the orthogonal and angle interlock 3D reinforcements were used in this study.
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From this test sample, approximately 8 and 4 digital twins can be extracted for both 3D fabrics respectively. The compression stage was placed inside the GE Nanotom machine carefully. A series of radiographic projections, each with a resolution of 2400 1600 pixels, were captured by rotating the sample to full 360 in 1500 steps. This gives an angle increment of 0.24 per step. The number of steps should be according to the size of the scanned image and affects the quality and noise level of the scans. For 3D fabrics, angle increment of 0.1e0.4 has been reported to be appropriate [49,50]. The applied voltage on the X-ray tube was 120 kV with a current of 200 mA. A preliminary study was conducted to choose the optimum voxel size by scanning test samples at resolutions of 25, 12.5 and 5.667 mm. Samples of scanned images at each resolution are shown in Fig. 5. The voxel size of 25 mm was found to be appropriate for adequately resolving the meso-scale structure of 3D reinforcements [40,51]. The selection of an appropriate voxel size was based on a hit-and-trail approach in the current study. However, this can be chosen systematically to avoid excessive scans by using the known geometrical attributes of the reinforcement architecture (diameter of fiber, tow dimensions, tows interlacements, etc.) and modeling approach in the subsequent analysis. For example, if the microstructure of a fabric is to be resolved, the voxel size should be approximately 1/5th of the fiber diameter. In case, where meso-structure is to be resolved, the resolution could be taken as 5e10 times that of a single fiber diameter [28].
Fig. 7. Graphical user interface of VGStudio.
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Fig. 8. Generating voxel models by applying thresholding on the stack of XCT images.
Fig. 9. Generation of digital twins, (a) segmented volume and (b) a digital twin extracted from the segmented volume.
3.4. Compaction tests The compaction and XCT scanning data was acquired at four different compaction levels. Initially, the test samples were
scanned in their pristine state. A load of only 10 N was applied during the initial scan. This initial compaction level is referred as h0. After the initial scan, the test samples were compacted to a target Vf by setting a target thickness in the MICROTEST
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Fig. 10. Boundary conditions used for the (a) through-thickness and (b) in-plane flows.
Fig. 11. (a) Changes in thickness during compaction experiments, (b) tow aspect ratio changes after compaction at each thickness, (c) tow deformations at h0 and h1.
software. Once the target thickness was reached, the position of the lower platen was fixed, and the stress was allowed to relax until a quasi-steady-state was achieved. XCT images were again acquired at this compaction level denoted by (h1). The
same steps were repeated for two more compaction levels (h2 and h3). All the four levels of compaction are schematically shown in Fig. 6. The rate of compression was kept at 0.5 mm/min for all the compaction tests.
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Fig. 12. Resin flow paths in all three directions at thickness h1 for, (a) K11 , (b) K22 and (c) K33 .
3.5. Data analysis and tow visualization The radiographic projections were reconstructed into 3D volumes which were then visualized using VGStudio Max software, as shown in Fig. 7. The VGStudio Max software processes the scanned images to generate 3D volume models which can be visualized in 3D or 2D image slices. A range of different rendering methods provide unique functionality for precise and fast analysis of the XCT image data. The software also allows volume data to be imported and exported in various commonly used formats. In the current application, the XCT volume data was exported as a stack of images to be used in further processing. The reconstructed 3D volumes were inspected for documenting the tow deformations and gap reductions in the test samples as a result of transverse compaction. The tow deformations and gap reductions were also quantified by taking manual measurements using hand-picked tools in the VGStudio Max UGI. 3.6. Generation of digital twins The ImportGeo module of Math2Market's GeoDict software package was used to import 3D images for further analysis. In the ImportGeo, images scanned using XCT machine were imported, and then segmented. ImportGeo creates three-dimensional digital twins, which are well-suited to perform simulations, characterization and modeling operations. The extraction of gray value images was completed by segmentation, a procedure that converts gray values to index values. The index values are the material labels assigned to each voxel after segmentation. Segmentation is performed on the basis of gray value of each voxel. The loading of images and segmenting procedure is shown in Fig. 8. Several digital twins were extracted from the segmented volume by recognizing the periodic pattern of the reinforcement
structure, and were then used in the digital flow simulations. The digital twin extraction was achieved by cropping the stack of images, as shown in Fig. 9. For virtual permeability computation of the 3D reinforcements, a total number of 4 digital twins were extracted from different locations.
3.7. Digital flow simulations The digital flow simulation for virtual permeability predictions is based on the mass and momentum conservation laws of fluid dynamics. Typically, these laws are presented as a set of partial differential equations known as the Navier-Stokes equations. These equations describe how the velocity, pressure and density of a moving Newtonian fluid are related. These equations are applicable to all types of the flow of a Newtonian fluid. However, in case of resin injection through a fiber bed, Navier-Stokes equations can be simplified so that flow is considered as incompressible, isothermal and laminar flow. Moreover, Reynold's number for such flows are considered to be much less than unity. With these assumptions, the simplified equations are known as Stokes equations [7] and are given as,
V$v ¼ 0
(1)
mV2 v Vp ¼ 0
(2)
where, v is the velocity vector, m is the viscosity of the fluid and p is the pressure. The symbol V is the differential operator. The solution of these equations is a three dimensional flow velocity field. The velocity field thus obtained is used in conjunction with Darcy's law to compute the permeability.
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Fig. 13. Comparisons of predicted permeability values with the experimentally measured values, (a) K11 , (b) K22 and (c) K33 .
3.8. Boundary conditions for flow modeling The digital flow simulation for virtual permeability prediction is the solution of boundary value problem using governing equations of fluid dynamics. The working fluid was assumed to be a Newtonian fluid with a constant density (879 kg/m3) and viscosity (0.105 Pa.s). The digital flow simulation was carried out on a digital twin which is a representative volume element with three sets of
faces. An appropriate boundary condition need to be defined on all faces as well as at the interface at the tow surfaces. Here, due to negligible contributions by the micro scale flow, the fiber tows were assumed to be solid and flow through them was completely neglected. Hence a no-slip impermeable wall condition was imposed on the tow surfaces. For computing the through-thickness permeability (K33 .), flow through the thickness was simulated by applying periodic boundary conditions at the top and bottom faces
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Fig. 14. The variation in the predicted permeability values among various digital twins.
Table 1 Numerical values of coefficients in the modified Kozeny-Carman correlation. Reinforcement Type
Coefficients C22
C11 Orthogonal Angle Interlock
8
1.42 10 1.32 108
C33 9
7.42 10 8.50 109
1.65 109 2.09 109
The tows of the angle interlock fabric had thick elliptical cross sections before compaction. As a result of compaction, they were flattened and became more elongated. The deformed tows and the change in the shape of the binder yarn after compaction, is shown in Fig. 11 (c). The shape of z-binder yarn shows “step-like” shape navigating through the thickness of the preform. 4.2. Fluid flow field analysis
with a pressure gradient of 100 kPa. Simple periodic boundary conditions were applied on the remaining two sets of faces. For computing the in-plane permeability (K11 and K22 ), the top and bottom faces were considered as no-slip walls. Periodic boundary conditions with a pressure gradient of 100 kPa applied across the faces which were normal to the flow directions. Simple periodic boundary conditions were imposed on the remaining set of inplane tangential faces. Details of the applied boundary conditions for both the through-thickness and in-plane flows are illustrated in Fig. 10.
The results of the digital flow simulation are primarily the three dimensional velocity fields which can be easily visualized as well as analyzed. The velocity fields can be visualized to assess the flow paths, and is used to compute the permeability. As an example, the velocity fields and streamlines passing through the 3D structure during the flow in all three directions at thickness h1 are shown in Fig. 12. From Fig. 12, it can be observed that the fluid predominantly flows through the meso channels. The connectivity between the channels is found to be good at low Vf , however the connectivity between the flow channels is lost at higher Vf .
4. Results and discussion
4.3. Permeability predictions
4.1. Compaction response
The computed permeability values were compared with benchmark experimental measurements [52]. The comparison is shown in Fig. 13, for both the orthogonal and angle interlock reinforcements. The permeability value of the angle interlock reinforcement at initial thickness h0 was not compared as the experimental data at this compaction level was not available. The figure shows that the overall computed permeability values agree well with the experimental values, except the in-plane permeability values at low Vf . The in-plane permeability values at low Vf differ significantly for both the orthogonal and angle interlock reinforcements. The discrepancy at low Vf is mainly due to differences in the sizes of the test samples, used in the experimental measurement, and the hybrid method, as well as because of neglecting the micro-scale flow. Such discrepancies were also reported by other researchers [53e55].
The load and displacement data from the in-situ compression stage was continuously recorded during the XCT data acquisition. The load and displacement data was then converted into stress relaxation curves. The multi-stage stress relaxation curve of the angle interlock reinforcement is shown in Fig. 11 (a). At each thickness, the multi-stage stress relaxation curves showed very similar trends where the stress reached to a peak values and then dropped instantaneously. The drop in the compaction stress was very rapid in the beginning but eventually faded out. After sometime, the compaction stress reached a quasi-steady-state value, where no significant change was observed. The binder yarn influenced the deformation of neighboring tows in both the reinforcements. Under transverse compaction, the inter-tow gaps were reduced; as a result the tows were flattened. The height and width of several tow cross sections were measured using handpicked tools in VGStudio Max UGI. The aspect ratio (width/ height) of the tow cross sections were calculated to quantify the flattening of the tows. The changes in aspect ratio of the tow cross sections of the angle interlock reinforcement are presented in Fig. 11 (b). The figure indicates that the tow aspect ratio increases as the reinforcement is subjected to higher level of compaction.
4.4. Variability in permeability predictions The permeability of fiber reinforcements is not deterministic rather a stochastic value with significant scatter in both experimental measurements and numerical predictions. This scatter is primarily a result of inherent geometrical variability in the reinforcements at all scales (micro, meso and macro). Through the
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Fig. 15. Fitting parameter for Kozeny-Carman predicted permeability vs. simulated values for, (a) K11 , (b) K22 and (c) K33 .
hybrid framework, the macro scale variability can be studied by considering multiple digital twins. The digital twins can be extracted from different locations in the test sample; hence the solid volume fraction (Vs ) of each digital twin differs from that of others. The values of Vs for all digital twins were obtained from the GeoDict software. To illustrate the variability in the computed permeability values, the computed permeability values for all four digital twins of the angle interlock reinforcement are shown in Fig. 14. In Fig. 14 the computed permeability values at h1, h2 and h3
are presented. In this case, at a given compaction level, the variation of Vs among the digital twins was less than 2%. However, the coefficients of variance in the computed permeability values were 8%, 15% and 23% for K11, K22 and K33 respectively. The predicted permeability values were correlated to the Vs of the digital twins by using a modified Kozeny-Carman correlation [16], as explained in the next section. The permeability values are strongly correlated with the Vs of each digital twin. This relationship is further investigated here by
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adopting a modified Kozeny-Carman (K-C) correlation [16]. The original K-C correlation relates the permeability with the fiber volume fraction (Vf ). The Vf in the original K-C correlation can be replaced by Vs to get the modified K-C correlation given as,
2
3 2 3 K11 C11 3 4 K22 5 ¼ 4 C22 5 ð1 Vs Þ 2 Vs K33 C33
(4)
where C11 , C22 and C33 are coefficients from the curve fitting. The values of the coefficients can be obtained from the regression of available data. These coefficients purely reflect the variability in the internal structure. In the current study, the permeability values were computed for a number of digital twins for both 3D reinforcements. This data can be used to obtain numerical values of the coefficients in Equation (4), through least squares regression. The calculated values of the coefficients for both the orthogonal and angle interlock reinforcements are given in Table 1 below. The permeability values predicted by the modified K-C correlation were compared with the original values in Fig. 15. The predicted values are in a reasonable agreement with the original values. Hence, using appropriate coefficients, the modified K-C correlation may also be used to estimate the permeability as a function of Vs .
5. Conclusions An advanced hybrid framework for fiber reinforcement characterization was proposed, which involved both experimental and numerical procedures. The hybrid characterization framework provides a single 2-in-1 platform to obtain the compaction response, and compute the permeability of fiber reinforcements. The compaction response of the reinforcements can be determined at multiple fiber volume fractions from a single test sample, as the framework fully utilizes the non-destructive capability of the XCT. In this study, the hybrid framework was employed to investigate the compaction behavior and compute virtual permeability of two different types of 3D fabrics. As a result of the transverse compaction of the reinforcements, the inter-tow gaps were reduced, and the warp and weft tows were flattened for both 3D fabrics. The z-binder yarn deformed into a more stable shape as well as influenced the deformation of neighboring warp and weft tows. The computed permeability values of fiber reinforcements at different Vf agreed well with the benchmark experimental measurements. The computed principle permeability values were strongly correlated to the solid volume fraction of the individual digital twins which was expressed as a modified Kozeny-Carman correlation. The work presented here, shows the utility of the data obtained from the proposed characterization method over traditional laborious experimental techniques. This technique requires further investigations using various kinds of reinforcements, digital twins with different sizes, and at a number of scanning resolutions.
Conflict of interest The authors declare that there is no conflicts of interest.
Acknowledgements The authors acknowledge Khalifa University for providing PhD scholarship for Mr. MA Ali.
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Original Article
A virtual permeability measurement framework for fiber reinforcements using micro CT generated digital twins M.A. Ali, R. Umer*, K.A. Khan Department of Aerospace Engineering, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 October 2019 Received in revised form 4 December 2019 Accepted 4 December 2019 Available online xxx
Liquid Composite Molding (LCM) is one of the widely used manufacturing techniques for high performance composite parts. In a simple LCM process, a pressurized liquid resin is injected inside a mold containing fibrous reinforcements. In order to create quality components using LCM processes, reinforcement characterization such as permeability and compaction response need to be performed fast and accurately. In this work, a micro CT based experimental-numerical reinforcement compaction and permeability characterization framework has been proposed which can potentially reduce process characterization cost by lowering material consumption and labor time and effort. The framework is non-destructive in nature and uses a miniaturized compression stage that can be housed in an X-ray computed tomography (XCT) system. This in-situ XCT experimental set-up is used to acquire the stress relaxation curve and XCT images of the reinforcement internal structure at multiple fiber volume fractions which are then converted into digital twins of the reinforcements. The virtual permeability of the reinforcement digital twin is computed through numerical flow simulations using realistic voxel models extracted from the stack of XCT images. The proposed approach has the capability of obtaining a plethora of information about the preform including, compaction response, statistical measurements of the internal preform geometry, and voxel models for numerical simulations. The methodology has been successfully demonstrated using two carbon fiber reinforcements with 3D woven architecture. The virtual permeability predictions were benchmarked against experimentally measured values, and were found to be in excellent agreement with the experimental data. © 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
Keywords: Liquid composite molding Permeability Compaction response Micro CT
1. Introduction Fiber reinforced polymer composites are being used in a variety of high performance applications due to their significantly enhanced structural, mechanical, and tribological properties [1]. These composites are produced in the form laminates or sandwich structures through various manufacturing techniques such as autoclave manufacturing, liquid composite molding [2e4], additive manufacturing [5] and automated fiber placement method [6]. In a generic LCM process, the fiber reinforcements are placed inside a mold cavity for subsequent compaction and resin injection [7]. Upon filling the mold cavity completely with catalyzed liquid resin,
* Corresponding author. E-mail address: [email protected] (R. Umer). Peer review under responsibility of Editorial Board of International Journal of Lightweight Materials and Manufacture.
the resin is allowed to cure and the part is then removed from the mold cavity. The fibrous reinforcements used in LCM process exhibit dual-scale flow characteristics as they are often produced from a pre-existing assembly of fine reinforcing filaments, generally produced in the form of yarns or tows, which are then further combined together in various architectures. To manufacture high quality products with consistent thickness and minimum void, the reinforcement compaction behavior and permeability characteristics need to be understood [8e10]. The compaction response and permeability of fiber reinforcements can be determined through analytical relationships, experimental procedures and numerical methods [11e13]. The theoretical models for the compaction response relate the compaction stress to the fiber volume fraction (Vf) through an algebraic relationship which are derived from micro, meso or macro-scale compaction behavior [14,15]. Similarly, predictive permeability models present permeability as a function of fiber diameter and the fiber volume fraction (Vf ) [11,16e18]. However,
https://doi.org/10.1016/j.ijlmm.2019.12.002 2588-8404/© 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: M.A. Ali et al., A virtual permeability measurement framework for fiber reinforcements using micro CT generated digital twins, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.12.002
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these models for both compaction response and permeability predictions are limited to simplified cases and do not capture the complex dual scale behavior of the fiber reinforcements. Experimental procedures for reinforcement compaction and permeability characterization are complex and costly [19e21]. Geometrical models of the complex reinforcement architectures are needed for the characterization of the reinforcements using numerical techniques. Generation of accurate models to represent the complex reinforcement architectures are not in the capability of modeling tools used for this purpose [22e24]. Hence, a robust characterization framework needs to be developed for cost reduction as well as to accurately predict the reinforcement permeability and compaction response. The XCT coupled with computer simulations provide an exceptionally powerful and versatile tool for material characterization
[25e29] and can offer an advanced platform for the reinforcement compaction and permeability characterizations. XCT has been used by a number of researchers to investigate the internal geometry changes due to compaction and other loading conditions typical of those encountered in LCM processes [30e34]. Permeability predictions using XCT based models either use realistic voxel models [35e40] or stochastic virtual models [9,41]. Most of the data presented in these studies either correspond to a single reinforcement state or use multiple samples. In this study, a non-destructive hybrid framework was used to investigate the compaction behavior and to predict the virtual permeability of two 3D reinforcement digital twins. The primary goal of this hybrid framework is to offer a single 2-in-1 platform for reinforcement compaction and permeability characterization which can potentially reduce process characterization cost by
Fig. 1. Overview of the hybrid characterization framework.
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lowering material consumption and labor time. The originality of this approach lies in the in-situ compaction characterization followed by generation of digital twins for virtual permeability computations, thus providing a combined compaction and permeability characterization framework. A single test sample of each reinforcement was used to characterize the reinforcements at multiple fiber volume fractions (Vf). In the hybrid method, realistic voxel models were generated from a stack of XCT images obtained under various compaction levels. The compaction data in the form of load and displacement measurements were also acquired through the load cell of an in-situ compression stage. The realistic voxel models were then used to predict the virtual permeability through digital flow simulations. 2. The hybrid framework As discussed in the previous section, XCT has been used to investigate the internal geometry changes due to compaction as well as to compute virtual permeability and investigate infusion processes. XCT is widely used to provide the geometry of reinforcements as input into finite element simulations for compaction characterization and evaluation of mechanical properties of the composites [23,42e45]. Naouar et al. [42,43] used a method to automatically build meso-scale finite element models of a 3D woven fabric from XCT images in which the most critical part of the process is the separation of warp, weft, and binder yarns with a segmentation process. To address the challenges associated with the segmentation process, Straumit et al. [46] used the structure tensor approach for generating voxel models. Moreover, Joaquim et al. [47] established the ability of XCT to analyze the details of micro-flow and void transport within a single tow through in-situ vacuum-assisted infiltration experiments using synchrotron X-ray computed tomography. Schmidt et al. [48] proposed a novel simulative-experimental approach to determine the permeability of fibrous reinforcements using experimentally calibrated digital twins mapped with XCT images. In all the studies discussed above, the non-destructive capability of the XCT has not been used to its full potential yet and the XCT data is used in a limited capacity. Moreover, the compaction and permeability characterization has not been performed on a single platform. These shortcomings can be addressed by employing the hybrid characterization framework which has a mixture of experimental and numerical procedures. In the experimental permeability measurements, a number of test samples are used in fluid injection experiments in which flow rates and pressure gradients are measured using several transducers. On the other hand, in the numerical approach, the reinforcement geometrical models are used in a digital flow simulation to predict the reinforcement permeability. Here, in the proposed hybrid approach, the initial steps of the experimental procedure are combined with the final
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steps of the numerical approach. An overview of the hybrid framework is illustrated in Fig. 1, outlining the various steps involved. In the hybrid framework, the load and displacement data is obtained from the load cell of the in-situ compression stage. The load and displacement data obtained is then converted into the stress relaxation curves. Once the compaction stress on the test sample reaches to a quasi-steady-state level, radiographic projections of the test sample are acquired using an XCT machine. After the acquisition of the radiographic projections, the sample is subjected to the next level of loading and the process of scanning is repeated. The radiographic projections are stored on a computer and reconstructed into 3D volumes using post processing software. The reconstructed 3D volume can be sliced in all three principle directions, or along any arbitrary cutting plane, to obtain 2D crosssectional images. Geometrical features of the internal structure, such as tow cross sections and inter-two gaps, can be visualized as well as quantified through manual or automated measurements form these 2D cross-sectional images. Additionally, the reconstructed 3D volume can be converted into computational voxel models. These voxel models can then be used in numerical simulations for both compaction studies and virtual permeability prediction.
3. Materials and methods 3.1. Materials In this study, two different types of 3D carbon fiber reinforcements, supplied by Sigmatex UK, were used. The reinforcements were used in there dry state without any resin to enable in-situ compaction. One of the reinforcements has orthogonal architecture whereas the other one has angle interlock architecture. The two reinforcements are different in terms of their weaving patterns, hence possessing different mechanical response under compaction loading. The z-binder yarns in both fabrics run through the thickness in a different pattern to hold the warp and weft tows together. The basic difference between the two reinforcements is the interlacing angle between the binder and weft yarns. The interlacing angles are 90 and 45 in the orthogonal and angle inter-lock architectures respectively. In both cases, the binder yarns penetrate all the way through the thickness. Both reinforcements have eight layers of warp tows and nine layers of weft tows. The warp and weft tows are made from 12K carbon fibers and the z-binder yarns are made from 6K carbon fibers. As per the specifications provided by the supplier, the orthogonal and angle inter-lock reinforcements have an areal density of 3353 g/m2 and 3045 g/m2 respectively. Both the reinforcements are shown in Fig. 2.
Fig. 2. Experimental materials (a) orthogonal and (b) angle inter-lock 3D fabrics.
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Fig. 3. The hybrid characterization set-up in the XCT machine.
3.2. In-situ XCT system The in-situ XCT system consists of an X-ray machine (GE Phoenix Nanotom) and a number of software packages. The compaction stage is supplied by DEBEN, UK model CT5000 in-situ compression fixture with 5 kN load cell. The XCT system is used for both scientific and industrial computed tomography and 3D metrology. The maximum sample size that can be accommodated in this machine is 240 mm diameter and 250 mm height. The power rating of the X-ray tube is 180 kV/15 W. The resolution that can be achieved is 300 nm. The DEBEN CT5000 in-situ testing stage can be placed inside the GE Nanotom XCT machine, as shown in Fig. 3. In the compression mode, the stage has two compression platens
vertically aligned inside a 3 mm thick glass tube. The glass tube encloses the test sample. The upper platen is fixed at the top of the tube whereas the lower platen is connected to a motorized gearbox and a 5 kN load cell. The software packages used for data acquisition in the hybrid framework are the Phoenix Datosx and the MICROTEST control software. The Phoenix Datosx is fully automated XCT data acquisition software that minimizes operator time and influence, while highly increasing the repeatability and reproducibility of XCT results. The user interface for this software is shown in Fig. 4 (a). The DEBEN CT5000 in-situ testing stage is controlled through the MICROTEST control software giving a wide range of control functions. The load and displacement
Fig. 4. (a) The screenshot of live user interface of Phoenix Datosx XCT data acquisition software, (b) DEBEN MICROTEST software environment showing load vs. time graph.
Fig. 5. Tow details as resolved at voxel sizes (a) 25 mm, (b) 12.5 and (c) 5.667 mm.
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Fig. 6. The different levels of compaction.
data is continuously displayed on the screen as shown in Fig. 4 (b). The user can setup various types of loading conditions. A target displacement or force is defined, which is then achieved by moving the lower platen of the compression stage. 3.3. XCT scan settings Test samples of 40 mm diameter of both the orthogonal and angle interlock 3D reinforcements were used in this study.
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From this test sample, approximately 8 and 4 digital twins can be extracted for both 3D fabrics respectively. The compression stage was placed inside the GE Nanotom machine carefully. A series of radiographic projections, each with a resolution of 2400 1600 pixels, were captured by rotating the sample to full 360 in 1500 steps. This gives an angle increment of 0.24 per step. The number of steps should be according to the size of the scanned image and affects the quality and noise level of the scans. For 3D fabrics, angle increment of 0.1e0.4 has been reported to be appropriate [49,50]. The applied voltage on the X-ray tube was 120 kV with a current of 200 mA. A preliminary study was conducted to choose the optimum voxel size by scanning test samples at resolutions of 25, 12.5 and 5.667 mm. Samples of scanned images at each resolution are shown in Fig. 5. The voxel size of 25 mm was found to be appropriate for adequately resolving the meso-scale structure of 3D reinforcements [40,51]. The selection of an appropriate voxel size was based on a hit-and-trail approach in the current study. However, this can be chosen systematically to avoid excessive scans by using the known geometrical attributes of the reinforcement architecture (diameter of fiber, tow dimensions, tows interlacements, etc.) and modeling approach in the subsequent analysis. For example, if the microstructure of a fabric is to be resolved, the voxel size should be approximately 1/5th of the fiber diameter. In case, where meso-structure is to be resolved, the resolution could be taken as 5e10 times that of a single fiber diameter [28].
Fig. 7. Graphical user interface of VGStudio.
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Fig. 8. Generating voxel models by applying thresholding on the stack of XCT images.
Fig. 9. Generation of digital twins, (a) segmented volume and (b) a digital twin extracted from the segmented volume.
3.4. Compaction tests The compaction and XCT scanning data was acquired at four different compaction levels. Initially, the test samples were
scanned in their pristine state. A load of only 10 N was applied during the initial scan. This initial compaction level is referred as h0. After the initial scan, the test samples were compacted to a target Vf by setting a target thickness in the MICROTEST
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Fig. 10. Boundary conditions used for the (a) through-thickness and (b) in-plane flows.
Fig. 11. (a) Changes in thickness during compaction experiments, (b) tow aspect ratio changes after compaction at each thickness, (c) tow deformations at h0 and h1.
software. Once the target thickness was reached, the position of the lower platen was fixed, and the stress was allowed to relax until a quasi-steady-state was achieved. XCT images were again acquired at this compaction level denoted by (h1). The
same steps were repeated for two more compaction levels (h2 and h3). All the four levels of compaction are schematically shown in Fig. 6. The rate of compression was kept at 0.5 mm/min for all the compaction tests.
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Fig. 12. Resin flow paths in all three directions at thickness h1 for, (a) K11 , (b) K22 and (c) K33 .
3.5. Data analysis and tow visualization The radiographic projections were reconstructed into 3D volumes which were then visualized using VGStudio Max software, as shown in Fig. 7. The VGStudio Max software processes the scanned images to generate 3D volume models which can be visualized in 3D or 2D image slices. A range of different rendering methods provide unique functionality for precise and fast analysis of the XCT image data. The software also allows volume data to be imported and exported in various commonly used formats. In the current application, the XCT volume data was exported as a stack of images to be used in further processing. The reconstructed 3D volumes were inspected for documenting the tow deformations and gap reductions in the test samples as a result of transverse compaction. The tow deformations and gap reductions were also quantified by taking manual measurements using hand-picked tools in the VGStudio Max UGI. 3.6. Generation of digital twins The ImportGeo module of Math2Market's GeoDict software package was used to import 3D images for further analysis. In the ImportGeo, images scanned using XCT machine were imported, and then segmented. ImportGeo creates three-dimensional digital twins, which are well-suited to perform simulations, characterization and modeling operations. The extraction of gray value images was completed by segmentation, a procedure that converts gray values to index values. The index values are the material labels assigned to each voxel after segmentation. Segmentation is performed on the basis of gray value of each voxel. The loading of images and segmenting procedure is shown in Fig. 8. Several digital twins were extracted from the segmented volume by recognizing the periodic pattern of the reinforcement
structure, and were then used in the digital flow simulations. The digital twin extraction was achieved by cropping the stack of images, as shown in Fig. 9. For virtual permeability computation of the 3D reinforcements, a total number of 4 digital twins were extracted from different locations.
3.7. Digital flow simulations The digital flow simulation for virtual permeability predictions is based on the mass and momentum conservation laws of fluid dynamics. Typically, these laws are presented as a set of partial differential equations known as the Navier-Stokes equations. These equations describe how the velocity, pressure and density of a moving Newtonian fluid are related. These equations are applicable to all types of the flow of a Newtonian fluid. However, in case of resin injection through a fiber bed, Navier-Stokes equations can be simplified so that flow is considered as incompressible, isothermal and laminar flow. Moreover, Reynold's number for such flows are considered to be much less than unity. With these assumptions, the simplified equations are known as Stokes equations [7] and are given as,
V$v ¼ 0
(1)
mV2 v Vp ¼ 0
(2)
where, v is the velocity vector, m is the viscosity of the fluid and p is the pressure. The symbol V is the differential operator. The solution of these equations is a three dimensional flow velocity field. The velocity field thus obtained is used in conjunction with Darcy's law to compute the permeability.
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Fig. 13. Comparisons of predicted permeability values with the experimentally measured values, (a) K11 , (b) K22 and (c) K33 .
3.8. Boundary conditions for flow modeling The digital flow simulation for virtual permeability prediction is the solution of boundary value problem using governing equations of fluid dynamics. The working fluid was assumed to be a Newtonian fluid with a constant density (879 kg/m3) and viscosity (0.105 Pa.s). The digital flow simulation was carried out on a digital twin which is a representative volume element with three sets of
faces. An appropriate boundary condition need to be defined on all faces as well as at the interface at the tow surfaces. Here, due to negligible contributions by the micro scale flow, the fiber tows were assumed to be solid and flow through them was completely neglected. Hence a no-slip impermeable wall condition was imposed on the tow surfaces. For computing the through-thickness permeability (K33 .), flow through the thickness was simulated by applying periodic boundary conditions at the top and bottom faces
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Fig. 14. The variation in the predicted permeability values among various digital twins.
Table 1 Numerical values of coefficients in the modified Kozeny-Carman correlation. Reinforcement Type
Coefficients C22
C11 Orthogonal Angle Interlock
8
1.42 10 1.32 108
C33 9
7.42 10 8.50 109
1.65 109 2.09 109
The tows of the angle interlock fabric had thick elliptical cross sections before compaction. As a result of compaction, they were flattened and became more elongated. The deformed tows and the change in the shape of the binder yarn after compaction, is shown in Fig. 11 (c). The shape of z-binder yarn shows “step-like” shape navigating through the thickness of the preform. 4.2. Fluid flow field analysis
with a pressure gradient of 100 kPa. Simple periodic boundary conditions were applied on the remaining two sets of faces. For computing the in-plane permeability (K11 and K22 ), the top and bottom faces were considered as no-slip walls. Periodic boundary conditions with a pressure gradient of 100 kPa applied across the faces which were normal to the flow directions. Simple periodic boundary conditions were imposed on the remaining set of inplane tangential faces. Details of the applied boundary conditions for both the through-thickness and in-plane flows are illustrated in Fig. 10.
The results of the digital flow simulation are primarily the three dimensional velocity fields which can be easily visualized as well as analyzed. The velocity fields can be visualized to assess the flow paths, and is used to compute the permeability. As an example, the velocity fields and streamlines passing through the 3D structure during the flow in all three directions at thickness h1 are shown in Fig. 12. From Fig. 12, it can be observed that the fluid predominantly flows through the meso channels. The connectivity between the channels is found to be good at low Vf , however the connectivity between the flow channels is lost at higher Vf .
4. Results and discussion
4.3. Permeability predictions
4.1. Compaction response
The computed permeability values were compared with benchmark experimental measurements [52]. The comparison is shown in Fig. 13, for both the orthogonal and angle interlock reinforcements. The permeability value of the angle interlock reinforcement at initial thickness h0 was not compared as the experimental data at this compaction level was not available. The figure shows that the overall computed permeability values agree well with the experimental values, except the in-plane permeability values at low Vf . The in-plane permeability values at low Vf differ significantly for both the orthogonal and angle interlock reinforcements. The discrepancy at low Vf is mainly due to differences in the sizes of the test samples, used in the experimental measurement, and the hybrid method, as well as because of neglecting the micro-scale flow. Such discrepancies were also reported by other researchers [53e55].
The load and displacement data from the in-situ compression stage was continuously recorded during the XCT data acquisition. The load and displacement data was then converted into stress relaxation curves. The multi-stage stress relaxation curve of the angle interlock reinforcement is shown in Fig. 11 (a). At each thickness, the multi-stage stress relaxation curves showed very similar trends where the stress reached to a peak values and then dropped instantaneously. The drop in the compaction stress was very rapid in the beginning but eventually faded out. After sometime, the compaction stress reached a quasi-steady-state value, where no significant change was observed. The binder yarn influenced the deformation of neighboring tows in both the reinforcements. Under transverse compaction, the inter-tow gaps were reduced; as a result the tows were flattened. The height and width of several tow cross sections were measured using handpicked tools in VGStudio Max UGI. The aspect ratio (width/ height) of the tow cross sections were calculated to quantify the flattening of the tows. The changes in aspect ratio of the tow cross sections of the angle interlock reinforcement are presented in Fig. 11 (b). The figure indicates that the tow aspect ratio increases as the reinforcement is subjected to higher level of compaction.
4.4. Variability in permeability predictions The permeability of fiber reinforcements is not deterministic rather a stochastic value with significant scatter in both experimental measurements and numerical predictions. This scatter is primarily a result of inherent geometrical variability in the reinforcements at all scales (micro, meso and macro). Through the
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Fig. 15. Fitting parameter for Kozeny-Carman predicted permeability vs. simulated values for, (a) K11 , (b) K22 and (c) K33 .
hybrid framework, the macro scale variability can be studied by considering multiple digital twins. The digital twins can be extracted from different locations in the test sample; hence the solid volume fraction (Vs ) of each digital twin differs from that of others. The values of Vs for all digital twins were obtained from the GeoDict software. To illustrate the variability in the computed permeability values, the computed permeability values for all four digital twins of the angle interlock reinforcement are shown in Fig. 14. In Fig. 14 the computed permeability values at h1, h2 and h3
are presented. In this case, at a given compaction level, the variation of Vs among the digital twins was less than 2%. However, the coefficients of variance in the computed permeability values were 8%, 15% and 23% for K11, K22 and K33 respectively. The predicted permeability values were correlated to the Vs of the digital twins by using a modified Kozeny-Carman correlation [16], as explained in the next section. The permeability values are strongly correlated with the Vs of each digital twin. This relationship is further investigated here by
Please cite this article as: M.A. Ali et al., A virtual permeability measurement framework for fiber reinforcements using micro CT generated digital twins, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.12.002
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adopting a modified Kozeny-Carman (K-C) correlation [16]. The original K-C correlation relates the permeability with the fiber volume fraction (Vf ). The Vf in the original K-C correlation can be replaced by Vs to get the modified K-C correlation given as,
2
3 2 3 K11 C11 3 4 K22 5 ¼ 4 C22 5 ð1 Vs Þ 2 Vs K33 C33
(4)
where C11 , C22 and C33 are coefficients from the curve fitting. The values of the coefficients can be obtained from the regression of available data. These coefficients purely reflect the variability in the internal structure. In the current study, the permeability values were computed for a number of digital twins for both 3D reinforcements. This data can be used to obtain numerical values of the coefficients in Equation (4), through least squares regression. The calculated values of the coefficients for both the orthogonal and angle interlock reinforcements are given in Table 1 below. The permeability values predicted by the modified K-C correlation were compared with the original values in Fig. 15. The predicted values are in a reasonable agreement with the original values. Hence, using appropriate coefficients, the modified K-C correlation may also be used to estimate the permeability as a function of Vs .
5. Conclusions An advanced hybrid framework for fiber reinforcement characterization was proposed, which involved both experimental and numerical procedures. The hybrid characterization framework provides a single 2-in-1 platform to obtain the compaction response, and compute the permeability of fiber reinforcements. The compaction response of the reinforcements can be determined at multiple fiber volume fractions from a single test sample, as the framework fully utilizes the non-destructive capability of the XCT. In this study, the hybrid framework was employed to investigate the compaction behavior and compute virtual permeability of two different types of 3D fabrics. As a result of the transverse compaction of the reinforcements, the inter-tow gaps were reduced, and the warp and weft tows were flattened for both 3D fabrics. The z-binder yarn deformed into a more stable shape as well as influenced the deformation of neighboring warp and weft tows. The computed permeability values of fiber reinforcements at different Vf agreed well with the benchmark experimental measurements. The computed principle permeability values were strongly correlated to the solid volume fraction of the individual digital twins which was expressed as a modified Kozeny-Carman correlation. The work presented here, shows the utility of the data obtained from the proposed characterization method over traditional laborious experimental techniques. This technique requires further investigations using various kinds of reinforcements, digital twins with different sizes, and at a number of scanning resolutions.
Conflict of interest The authors declare that there is no conflicts of interest.
Acknowledgements The authors acknowledge Khalifa University for providing PhD scholarship for Mr. MA Ali.
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Please cite this article as: M.A. Ali et al., A virtual permeability measurement framework for fiber reinforcements using micro CT generated digital twins, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.12.002