Elastic Properties of Jute Fiber Reinforced Polymer Composites with Different Hierarchical Structures
Abstract
:1. Introduction
2. Material and Methods
3. Analytical Studies of Jute Fiber Reinforced Composites
3.1. Estimation of Elastic Properties of Selected RVE
3.1.1. Longitudinal Modulus E1
3.1.2. Transverse Modulus
4. Simulation Studies of Jute Fiber Using Micromechanics Approach
4.1. First Stage of Homogenization
4.2. Second Stage of Homogenization
4.3. Validation of Simulation Studies
5. Results and Discussions
5.1. Simulation Results of JF Using Micromechanics Approach (First Stage of Homogenization)
5.2. Simulation Results of JFR Polypropylene Using Micromechanics Approach (Second Stage of Homogenization)
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
F | Force on the RVE |
Fα | Force taken by Lumen |
Fβ | Force taken by lignin |
Fγ | Force taken by hemi cellulose |
Fδ | Force taken by cellulose |
Fm | Force taken by the Matrix |
σ | RVE stress under longitudinal loading |
σα | Lumen stress under longitudinal loading |
σβ | Lignin stress under longitudinal loading |
σγ | Hemi cellulose stress under longitudinal loading |
σδ | Cellulose stress under longitudinal loading |
A | cross-sectional area of the composite |
A | cross-sectional area of the Lumen |
Aβ | cross-sectional area of the lignin |
Aγ | cross-sectional area of the hemi cellulose |
Aδ | cross-sectional area of the cellulose |
Am | cross-sectional area of the Matrix |
σ | RVE stress under longitudinal loading |
σα | Lumen stress under longitudinal loading |
σβ | Lignin stress under longitudinal loading |
σγ | Hemi cellulose stress under longitudinal loading |
σδ | Cellulose stress under longitudinal loading |
E1 | Longitudinal Elastic modulus of RVE |
E1α | Elastic modulus of Lumen |
E1β | Elastic modulus of Lignin |
E1γ | Elastic modulus of Hemi cellulose |
E1δ | Elastic modulus of Cellulose |
HS | Hierarchical Structures |
JF | Jute Fiber |
JFR | Jute Fiber Reinforced |
NF | Natural Fiber |
NFR | Natural Fiber Reinforced |
RVE | Representative Volume Element |
ε1 | Longitudinal Strain of RVE |
ε1α | Longitudinal strain of Lumen |
Transverse deformation of RVE | |
α | Transverse deformation of Lumen |
β | Transverse deformation of Lignin |
γ | Transverse deformation of Hemi cellulose |
δ | Transverse deformation of Cellulose |
m | Transverse deformation of matrix |
ε2 | Transverse Strain of RVE |
ε2α | Transverse strain of Lumen |
ε2β | Transverse strain of Lignin |
ε2γ | Transverse strain of Hemi cellulose |
ε2δ | Transverse strain of Cellulose |
ε2m | Transverse strain of matrix |
ε2 | Transverse Strain of RVE |
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Weight Fraction of Jute Fiber (%) | Young’s Modulus in GPa | ||||||
---|---|---|---|---|---|---|---|
Specimen 1 | Specimen 2 | Specimen 3 | Specimen 4 | Specimen 5 | Mean | SD | |
12.95 | 12.648 | 10.113 | 15.698 | 15.169 | 15.169 | 13.759 | 1.055 |
36.47 | 22.755 | 19.698 | 20.226 | 25.283 | 18.689 | 21.330 | 1.194 |
Model | Volume Fraction of Cellulose Vc (%) | Volume Fraction of Hemicelluloses Vhc (%) | Hierarchical Structure Volume Fraction of lignin Vl (%) | Volume Fraction of Lumen Vlm (%) |
---|---|---|---|---|
HS-1 | 61 | 14 | 12 | 13 |
HS-2 | 59 | 14 | 12 | 15 |
HS-3 | 54 | 14 | 12 | 20 |
HS-4 | 49 | 14 | 12 | 25 |
HS-5 | 44 | 14 | 12 | 30 |
HS-6 | 39 | 14 | 12 | 35 |
Constituent | E1 [Gpa] | E2 [Gpa] | E2 = E3 [Gpa] | G12 [Gpa] | ν12 [–] |
---|---|---|---|---|---|
Cellulose | 134 | 27.2 | 27.2 | 4.4 | 0.10 |
Hemicellulose | 8 | 4.0 | 4.0 | 2.0 | 0.20 |
Lignin | 4 | 4.0 | 4.0 | 1.5 | 0.33 |
Constituent | Model | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
HS-1 | HS-2 | HS-3 | HS-4 | HS-5 | HS-6 | |||||||
ri (nm) | ro (nm) | ri (nm) | ro (nm) | ri (nm) | ro (nm) | ri (nm) | ro (nm) | ri (nm) | ro (nm) | ri (nm) | ro (nm) | |
Lumen | 2.03 | 2.03 | 2.18 | 2.18 | 2.52 | 2.52 | 2.82 | 2.82 | 3.09 | 3.09 | 3.33 | 3.335 |
Lignin | 2.03 | 2.82 | 2.18 | 2.93 | 2.52 | 3.19 | 2.82 | 3.43 | 3.09 | 3.65 | 3.33 | 3.865 |
Hemicellulose | 2.82 | 3.51 | 2.93 | 3.61 | 3.19 | 3.82 | 3.43 | 4.02 | 3.65 | 4.22 | 3.86 | 4.4 |
Cellulose area [nm2] | 61.295 | 59.058 | 54.036 | 49.028 | 44.013 | 39.178 |
Weight Fraction of Jute Fiber (%) | Young’s Modulus in Gpa | % Error of FEM Results with Experimental Results | ||
---|---|---|---|---|
Experimental | Analytical | FEM | ||
12.95 | 13.759 | 13.88 | 13.98 | 1.64% |
36.47 | 21.330 | 21.42 | 22.62 | 6.04% |
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Prasanthi, P.; Kondapalli, S.B.; Morampudi, N.K.S.R.; Vallabhaneni, V.V.M.; Saxena, K.K.; Mohammed, K.A.; Linul, E.; Prakash, C.; Buddhi, D. Elastic Properties of Jute Fiber Reinforced Polymer Composites with Different Hierarchical Structures. Materials 2022, 15, 7032. https://doi.org/10.3390/ma15197032
Prasanthi P, Kondapalli SB, Morampudi NKSR, Vallabhaneni VVM, Saxena KK, Mohammed KA, Linul E, Prakash C, Buddhi D. Elastic Properties of Jute Fiber Reinforced Polymer Composites with Different Hierarchical Structures. Materials. 2022; 15(19):7032. https://doi.org/10.3390/ma15197032
Chicago/Turabian StylePrasanthi, Phani, Sivaji Babu Kondapalli, Niranjan Kumar Sita Rama Morampudi, Venkata Venu Madhav Vallabhaneni, Kuldeep Kumar Saxena, Kahtan Adnan Mohammed, Emanoil Linul, Chander Prakash, and Dharam Buddhi. 2022. "Elastic Properties of Jute Fiber Reinforced Polymer Composites with Different Hierarchical Structures" Materials 15, no. 19: 7032. https://doi.org/10.3390/ma15197032