Investigations for Design Estimation of an Anisotropic Polymer Matrix Composite Plate with a Central Circular Hole under Uniaxial Tension
Abstract
:1. Introduction
2. Modeling and Analysis
2.1. Modeling
2.2. Analysis of Macro Plate
2.2.1. Theoretical Formulations
2.2.2. Analysis Validation
3. Results and Discussion
4. Conclusions
- Hoop stress variation is like a Z curve shape around the central circular hole.
- The SCF is varied like a concave curve, decreasing while increasing plate width to hole diameter ratio (w/d).
- FSDT calculates 37, 56, and 70 percent less maximum transverse shear stress than HSDT and elasticity theory for thin, moderately thick, and thick plates for a braided polymer plate. Thus, FSDT cannot calculate accurate transverse stress, but HSDT (Reissner–Mindlin) is as accurate as the elasticity theory.
- The change in theory does not affect the circumferential stress, radial stress, and SCF. However, HSDT has higher accuracy than FSDT because FSDT has an approximate 3 percent error from elasticity theory to calculate SCF, but HSDT has an approximate 0.5 percent error. Additionally, the error difference is not significant and can be under a considerable limit. Therefore, after knowing the time and modeling cost of HSDT and elasticity theory, which is 3–4 and 15–20 times higher than FSDT, if transverse shear stress is not under consideration, FSDT is suggested; otherwise, HSDT is required.
- The formulation of SCF of a braided polymer plate showing less curve variation means less stress concentration than the equivalent isotropic/orthotropic plate with a center hole.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
E | Longitudinal modulus |
G | Shear modulus |
Poisson ratio | |
V | Volume fraction |
σ, and ꞇ | Longitudinal and shear stress |
ε, and γ | Longitudinal and shear strain |
Compliance matrix | |
C | Stiffness matrix |
Reinforcing efficiency | |
Stress partitioning factor | |
Linear displacement field in the periodic composites | |
Thickness of plate | |
Width of plate | |
Applied force | |
Radial | |
Circumferential | |
Radial–circumferential | |
K | Young’s modulus |
d | Shear modulus |
ꞇrz, and σθz | Transverse shear stress in cylindrical coordiantes |
, and | Rotations of the cross-section about the x and y axes |
θx, and θy | Angles of the rotation for xz and yz plane |
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Constituent. ↓ | Properties→ | Young Modulus (GPa) | Shear Modulus (GPa) | Poisson Ratio | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Ex | Ey | Ez | Gxy | Gxz | Gyz | νxy | νxz | νyz | ||
Fiber | Carbon T300 | 230 | 40 | 40 | 24 | 24 | 14.3 | 0.26 | 0.26 | 0.399 |
matrix | Epoxy resin | 3.5 | 0.35 | |||||||
Yarn (fiber volume fraction (0.52)) | Microscale homogenizations (microscale unit cell) | 121.28 | 10.16 | 10.16 | 7.93 | 7.93 | 4.36 | 0.303 | 0.303 | 0.375 |
Braided polymer plate with a center hole | Mesoscale homogenizations (mesoscale unit cell) |
Analysis Conditions (Plate Thickness_Analysis Theory) | Maximum Transverse Shear Stress (MPa) | Stress Concentration Factor (Maximum) | ||
---|---|---|---|---|
(ꞇrz) (0,w/2,0) | (ꞇθz) (l/2,0,0) | |||
Thin plate (aspect ratio 0.008) | FSDT | 13.61 | 3.78 | 2.53 |
HSDT (Reissner–Mindlin theory) | 21.50 | 5.90 | 2.60 | |
Elasticity theory | 21.74 | 6.06 | 2.61 | |
Moderate thick plate (aspect ratio 0.04) | FSDT | 5.63 | 2.06 | 2.53 |
HSDT (Reissner–Mindlin theory) | 12.78 | 4.50 | 2.60 | |
Elasticity theory | 12.82 | 4.75 | 2.61 | |
Thick plate (aspect ratio 0.1) | FSDT | 3.14 | 0.95 | 2.53 |
HSDT (Reissner–Mindlin theory) | 10.56 | 3.08 | 2.60 | |
Elasticity theory | 9.30 | 3.1 | 2.61 |
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Lim, S.; Dhimole, V.K.; Kim, Y.; Cho, C. Investigations for Design Estimation of an Anisotropic Polymer Matrix Composite Plate with a Central Circular Hole under Uniaxial Tension. Polymers 2022, 14, 1977. https://doi.org/10.3390/polym14101977
Lim S, Dhimole VK, Kim Y, Cho C. Investigations for Design Estimation of an Anisotropic Polymer Matrix Composite Plate with a Central Circular Hole under Uniaxial Tension. Polymers. 2022; 14(10):1977. https://doi.org/10.3390/polym14101977
Chicago/Turabian StyleLim, Seongsik, Vivek Kumar Dhimole, Yongbae Kim, and Chongdu Cho. 2022. "Investigations for Design Estimation of an Anisotropic Polymer Matrix Composite Plate with a Central Circular Hole under Uniaxial Tension" Polymers 14, no. 10: 1977. https://doi.org/10.3390/polym14101977