Characterization of Pultruded Glass-Fiber Reinforced Polymers with Two-Step Homogenization

Vianna, Rafael da S.; Pereira, André M.B.; Leiderman, Ricardo; Vieira, Janine D.

doi:10.1590/1980-5373-MR-2022-0252

Rafael da S. Vianna ^**e-mail: rafaelvianna@id.uff.br

Universidade Federal Fluminense, Instituto de Computação, Niterói, RJ, Brasil.

https://orcid.org/0000-0001-7856-6811

André M.B. Pereira

Universidade Federal Fluminense, Instituto de Computação, Niterói, RJ, Brasil.

Ricardo Leiderman

Universidade Federal Fluminense, Instituto de Computação, Niterói, RJ, Brasil.

Janine D. Vieira

Universidade Federal Fluminense, Departamento de Engenharia Civil, Niterói, RJ, Brasil.

*e-mail: rafaelvianna@id.uff.br

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Figure 1
Workflow from sample extraction to micro-CT scanning: (a) C-shape pultruded GFRP profile; (b) extracted samples; (c) micro-CT image. The cut in the sample presented in (b) was made to facilitate the sample positioning in the support for the micro-CT acquisition.

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Figure 2
Relation between image quality and size of ROI for a micro-CT image with fixed number of voxels. In the left, a small region can be digitalized with small voxels obtaining a good quality to represent the details. On the other hand, the image on the right represents a bigger region with bigger voxels resulting in lower quality.

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Figure 3
Micro-CT acquisition of the profile sample, roving layer and CSM layer.

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Figure 4
Micro-CT image of a pultruded GFRP sample with different 2D slices to emphasize the heterogeneity of the sample and its constituents, i.e., to show how difficult it is to separate the layers.

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Figure 5
Different processing operations for highlighting fibers and voids for subsequent segmentation.

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Figure 6
Segmentation workflow of fiber, voids and resin.

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Figure 7
Response of different Gabor filters: (a) original image; (b) Gabor 1 with theta equal to 0; (c) Gabor 1 with theta equal to π/2; (d) Gabor 2 with theta equal to 0; (e) Gabor 3 with theta equal to 0; and (f) Gabor 4 with theta equal to 0.

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Figure 8
Result of the classification model and the post-processing step applied to a slice of Tomo 1: (a) original image in the XZ-plane; (b) result from segmentation with the created classification model; (c) final segmentation after the post-processing steps.

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Figure 9
Results of the segmentation (of roving in blue) in different slices (different orthogonal planes) of a pultruded GFRP sample.

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Figure 10
Combination of segmentations A and B to generate segmentation C.

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Figure 11
Slices of Tomo 2 and their respective segmentations: (a), (b) and (c) original images; (d), (e) and (f) the respective segmentations of fibers without considering the fillers.

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Figure 12
Result of segmentation of the roving layer: (a) original image; (b) segmented image.

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Figure 13
Result of segmentation of Tomo 3 using Trainable Weka Segmentation: (a) original image; (b) segmented image.

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Figure 14
Homogenization procedure of a heterogeneous material: Application of a unitary deformation at the macro scale; computation of a stress field in the micro scale; computation of the average stress; and calculation of the effective tensor in the macro scale using the Hooke’s law.

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Figure 15
Pultruded GFRP at different scales.

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Figure 16
Two-step homogenization methodology.

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Figure 17
Convergence of effective properties in X, Y and Z directions in the roving layer.

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Figure 18
Convergence of effective properties of CSM layer in all directions.

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Table 1
Parameters of micro-CT scanning used to digitalize the samples of pultruded GFRP.

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Table 2
Segmentations for the correspondent micro-CT images and the respective labeled phases.

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Table 3
Parameters used for the creation of the Gabor filter bank.

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Table 4
Accuracy of the tests in the stratified 10-fold cross-validation.

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Table 5
Content of fibers for CSM and roving layer from each sample compared to the experimental results.

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Table 6
Content of roving layers and CSM layers in each sample.

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Table 7
Phase’s content (in volume) in CSM and roving layer for the samples.

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Table 8
Effective elastic properties of samples obtained by two-step homogenization (CoV in parenthesis).

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Table 9
Comparison between the experimental results and the Rule of Mixture for laminates with the results obtained in this work (CoV in parenthesis).

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*Micro-CT*	*Source-sample distance (mm)*	*Detector-sample distance (mm)*	*Lens*	*Binning*	*Power (W)*	*Source Voltage (kV)*	*Exposure Time (s)*	*Voxel Size (µm)*
Tomo 1	30	158	0.4X	2048×2048	4	50	30	5.5
Tomo 2	30	172	4X	1024×1024	7	80	30	1.0
Tomo 3	33	78	4X	1024×1024	4	50	33	2.0

*Segmentation*	*Micro-CT*	*Segmented Phases (Labels)*
A	Tomo 1	Resin, fibers and voids
B	Tomo 1	Roving layers and CSM layers
C	Tomo 1	Roving fibers, CSM fibers, resin and voids
D	Tomo 2	Resin, fibers and voids
E	Tomo 3	Resin, fibers and voids

*Filter*	*Kernel size*	σ	λ	γ	θ
Gabor 1	10	5	10π/3	5	0, π/8, π/4, 3π/8, π/2, 5π/8, 2π/ 3, π
Gabor 2	150	1	π/8	0.05	0, π/8, π/4, 3π/8, π/2, 5π/8, 2π/ 3, π
Gabor 3	50	1.5	π/2	0.05	0, π/8, π/4, 3π/8, π/2, 5π/8, 2π/ 3, π
Gabor 4	50	50	2π	0.05	0, π/8, π/4, 3π/8, π/2, 5π/8, 2π/ 3, π

*Test*	1	2	3	4	5	6	7	8	9	10	*Average*
Accuracy	0.92	0.96	0.95	0.94	0.96	0.95	0.94	0.93	0.94	0.94	0.94

*Phase*	*Volume Fraction (%)*
*Phase*	*Experimental results*	*Sample 1*	*Sample 2*	*Sample 3*
CSM fibers	22.05	23.60	23.78	27.20
Roving fibers	25.49	24.14	24.18	23.42

*Layer*	*Sample 1*	*Sample 2*	*Sample 3*	*Average*
CSM	58.86%	64.36%	60.11%	61.11%
Roving	41.14%	35.64%	39.89%	38.89%

*Sample*	*Layer*	*% Fiber*	*% Resin*	*% Void*
1	CSM	23.78	30.12	4.95
1	Roving	24.18	16.92	0.05
2	CSM	27.20	31.36	5.80
2	Roving	23.42	12.15	0.07
3	CSM	23.60	28.50	7.97
3	Roving	24.14	15.70	0.09

*Effective Property*	*Sample 1*	*Sample 2*	*Sample 3*	*Average*
E_X (GPa)	16.56	15.73	16.36	16.22 (2.20)
E_Y (GPa)	9.55	9.14	9.46	9.38 (1.86)
E_Z (GPa)	11.59	11.69	11.61	11.63 (0.36)
ν_YZ	0.19	0.20	0.20	0.20 (1.19)
ν_XZ	0.25	0.25	0.25	0.25 (0.35)
ν_XY	0.22	0.21	0.22	0.22 (1.81)
ν_ZY	0.11	0.11	0.11	0.11 (1.19)
ν_ZX	0.17	0.18	0.17	0.17 (2.06)
ν_YZ	0.26	0.26	0.26	0.26 (0.12)
G_YZ (GPa)	4.36	4.38	4.37	4.37 (0.18)
G_XZ (GPa)	3.46	3.39	3.45	3.43 (0.93)
G_XY (GPa)	4.41	4.19	4.35	4.32 (2.15)

*Effective Property (GPa)*	*Experimental Results (* ^{Vieira et al., 2018}30 Vieira PR, Carvalho EML, Vieira JD, Toledo Filho RD. Experimental fatigue behavior of pultruded glass fibre reinforced polymer composite materials. Compos, Part B Eng. 2018;146:69-75. http://dx.doi.org/10.1016/j.compositesb.2018.03.040. http://dx.doi.org/10.1016/j.compositesb.... )	*Rule of Mixture for Laminates*	*Weighted Average*	*Homogenization in two Steps (this work)*
E_X	17.2 (0.043)	21.99	21.63 (2.80)	16.22 (2.20)
E_Y	-	-	9.30 (1.82)	9.38 (1.86)
E_Z	-	-	11.63 (0.36)	11.63 (0.36)

[1] *e-mail: rafaelvianna@id.uff.br

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Characterization of Pultruded Glass-Fiber Reinforced Polymers with Two-Step Homogenization

Abstract