Stress Evolution of Amorphous Thermoplastic Plate during Forming Process
Abstract
:1. Introduction
2. Theory
2.1. Polyetherimide
2.2. Thermal Analysis
2.3. Mechanical Analysis
3. Finite Element Analysis
3.1. Model
3.2. Program Validation
4. Thermally-Induced Mechanical Change
4.1. Temperature Profile
4.2. Volume Shrinkage
4.3. Modulus and Shift Factor
5. Stress Evolution
5.1. Residual Stress Distribution
5.2. Temperature Distribution Through Plate Thickness
5.3. Thermal Strain and Rate of Strain
5.4. Stress in Stage 1
5.5. Stress in Stage 2
5.6. Stress in Stage 3
5.7. Stress Evolution Process
6. Forming Mechanism of Residuals Stress
7. Conclusions
- Stage 1:
- When the temperature of the whole plate is greater than Tg, stress barely forms.
- Stage 2:
- When the plate cools to Tg from one side to the other side, a large portion of the residual stress forms in a relatively short time, although the duration of this stage is typically short.
- Stage 3:
- Until the whole plate cools to room temperature, the residual stress changes further, and finally a parabolic-shaped residual stress forms.
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
T | Temperature, K |
Tg | Glass transition temperature, 483 K |
Troom | Room temperature, 298 K |
Tt | Pressure-dependent Tg |
T | Time, s |
V | Volume, m3 |
V0 | Reference volume, m3 |
P | Pressure, MPa |
ρ | Density, kg/m3 |
Cp | Specific heat, kJ/(kg·K) |
k | Thermal conductivity, W/(m·K) |
B | Material coefficients |
C | Constant in Tait equation, 0.0894 |
AT | Shift factor |
E | Young’s modulus, MPa |
τ | Stress relaxation time, s |
ε | Strain |
σ | Stress, MPa |
b | Fitting parameter |
Appendix A. Cooling Rate
Appendix B. Plate Thickness
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Wu, Q.; Ogasawara, T.; Yoshikawa, N.; Zhai, H. Stress Evolution of Amorphous Thermoplastic Plate during Forming Process. Materials 2018, 11, 464. https://doi.org/10.3390/ma11040464
Wu Q, Ogasawara T, Yoshikawa N, Zhai H. Stress Evolution of Amorphous Thermoplastic Plate during Forming Process. Materials. 2018; 11(4):464. https://doi.org/10.3390/ma11040464
Chicago/Turabian StyleWu, Qi, Tomotaka Ogasawara, Nobuhiro Yoshikawa, and Hongzhou Zhai. 2018. "Stress Evolution of Amorphous Thermoplastic Plate during Forming Process" Materials 11, no. 4: 464. https://doi.org/10.3390/ma11040464