# Residual Stress Analysis of an Orthotropic Composite Cylinder under Thermal Loading and Unloading

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## Abstract

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## 1. Introduction

## 2. Theoretical and Numerical Considerations

## 3. Results and Discussion

#### 3.1. Residual Stress Analysis Under Elastic-Perfectly Plastic Assumption

#### 3.2. Effects of Selective Temperature Dependent Material Properties on Residual Stress

#### 3.3. Residual Stress Analysis with Linear Hardening

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic of the composite cylinder, with $a=0.3$ m and $b=1$ m, confined on the outer rim, $r=1$ m, and (

**b**) representative quasi-static temperature loading profile.

**Figure 2.**(

**a**) Temperature functions for the material properties and (

**b**) representative finite element mesh used in this study.

**Figure 3.**Von Mises residual stress at $r=0.35$ m in the temperature-dependent (TD) case with the polar angle (

**a**) $\theta ={0}^{\xb0}$ and (

**b**) $\theta ={45}^{\xb0}$. Dashed lines indicate the applied temperature difference.

**Figure 4.**Von Mises residual stress at $r=0.35$ m in the temperature-independent (TI) case with the polar angle (

**a**) $\theta ={0}^{\xb0}$ and (

**b**) $\theta ={45}^{\xb0}$. Dashed lines indicate the applied temperature difference.

**Figure 5.**Residual stress distribution for (

**a**) all material parameters being temperature dependent, (

**b**) only yield stress being temperature dependent and (

**c**) all material parameters being temperature independent.

**Figure 6.**Residual stress near the inclusion-matrix interface at $r=0.35$ for the (

**a**) TD and (

**b**) TI case.

**Figure 7.**Von Mises residual stress in the orthotropic composite cylinder with the (

**a**) TD and (

**b**) TI material properties.

**Figure 8.**Von Mises residual stress in the isotropic composite cylinder with the (

**a**) TD and (

**b**) TI material properties.

**Figure 9.**Von Mises residual stress at $r=0.35$ m around the polar angle in the orthotropic cylinder for the (

**a**) TD and (

**b**) TI case.

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**MDPI and ACS Style**

Zarandi, S.B.; Lai, H.-W.; Wang, Y.-C.; Aizikovich, S.
Residual Stress Analysis of an Orthotropic Composite Cylinder under Thermal Loading and Unloading. *Symmetry* **2019**, *11*, 320.
https://doi.org/10.3390/sym11030320

**AMA Style**

Zarandi SB, Lai H-W, Wang Y-C, Aizikovich S.
Residual Stress Analysis of an Orthotropic Composite Cylinder under Thermal Loading and Unloading. *Symmetry*. 2019; 11(3):320.
https://doi.org/10.3390/sym11030320

**Chicago/Turabian Style**

Zarandi, Somayeh Bagherinejad, Hsiang-Wei Lai, Yun-Che Wang, and Sergey Aizikovich.
2019. "Residual Stress Analysis of an Orthotropic Composite Cylinder under Thermal Loading and Unloading" *Symmetry* 11, no. 3: 320.
https://doi.org/10.3390/sym11030320