# Numerical Simulation on Thermal Stresses and Solidification Microstructure for Making Fiber-Reinforced Aluminum Matrix Composites

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## Abstract

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## 1. Introduction

_{4}C

_{3}between carbon fibers and the aluminum matrix, which leads to the degradation of carbon fibers and consequently results in the deterioration of the mechanical properties of the composite and leads to its early failure under load [15]. High-resolution microfractography and transmission electron microscopy show that the mechanical behavior of the carbon-fiber-reinforced Al-based matrix composites is related to the presence of brittle interfacial phases [16]. The most common way to solve this problem is to coat the surface of the carbon fibers using the vapor deposition technique with nickel or copper [15]. This coating not only reduces the reaction at the fiber–melt interface, but also improves the wettability [17,18,19]. By using the nanoindentation technique, A. Urena et al. [19] investigated the interfacial mechanical properties of an AA6061 composite reinforced with short carbon fibers coated with copper and nickel films. The film coating on the carbon fiber surface was applied to control the interfacial reactivity of fibers with molten aluminum during the manufacture of the composite. The results showed that the copper coating produced by electroless increases the hardness and stiffness of the aluminum matrix, and nickel coatings decrease the hardness of the matrix close to the fibers and produce a high dispersion of stiffness values, especially in the own interface and at distances above 5 μm from the fibers. Improving the interfacial bonding between fibers and melt is one of the key factors in improving the properties of the fiber-reinforced composites [15,20]. The coating can play the adhesive role on the interface, leading to an improvement in the load transfer to the fibers. It has also been observed experimentally that the presence of carbon fibers alters the microstructure of the matrix alloy created during solidification. For example, Z.G. Liu et al. [21] studied the interface in the carbon fiber-reinforced Al–Cu alloy composites. The important feature observed in their experiments was that the microstructure of the Al–Cu matrix alloy was altered due to carbon fibers.

^{®}of ESI Group. The effect of nickel coating on the solidification process is also studied. These results should be helpful in controlling and optimizing the solidification process witnessed during the making of MMCs.

## 2. Problem Description and Simulation Method

#### 2.1. Mathematical Model

#### 2.1.1. Energy Equation

#### 2.1.2. Thermal-Elastic-Plastic Model

#### 2.1.3. Nucleation and Growth Model

#### 2.2. Material Properties

#### 2.3. Initial and Boundary Conditions

_{w1}and T

_{w2}represent the surface temperatures of the coating and melt, respectively.

#### 2.4. Numerical Solution

^{−6}. During the presentation of the results, some variables involved in the governing equations are rendered dimensionless, including geometry, temperature, and time equations [17,30]:

_{m}, T

_{0}, and T

_{i}is the temperature of the alloy, the cooling temperature, and the initial temperature, respectively. The symbol t represents the time, and a is the thermal expansion coefficient. The symbol with a bar represents the dimensionless parameters. AR is the aspect ratio of the mold, the dimensionless temperature of the alloy, the dimensionless time, and the dimensionless heat flux.

## 3. Results and Discussion

## 4. Conclusions

- Based on a modified infiltration process by Nguyen et al., the effect of active cooling conditions on temperature distribution was simulated. The predicted results of temperature evolution agreed well with the reported results.
- The distribution of heat flux has a significant influence on the microstructure and thermal stress. The heat flux trend is gradually evolving from the top of the model to the bottom of the fiber due to active cooling through carbon fiber. On the side of the fiber, the heat flux changes smoothly, while it varies drastically at the melt side. Comparing analysis results of the heat flux with and without nickel coating reveals that it is smoother and smaller in the Ni-coating model, which is favorable for preventing debonding at the interface of coating/fiber and alloy and obtaining the finer grains.
- The predicted results of the thermal stress show that there is high thermal stress on the interfaces of fiber–coating, coating–melt, and fiber–melt. These places tend to cause stress concentration. On the one hand, it is easy to generate microcracks in these locations, resulting in interface failure; on the other hand, it tends to lead to debonding of the coating.
- The formation and growth of grains are closely related to the temperature field. The heat is only dissipated from the bottom of the fiber. Therefore, the dendrites obliquely grew along with the model from the lower part of the fiber. The number of grains near the nucleation is more than that of the other places due to the effect of chilling. We also can see that the microstructure is significantly refined, and then the properties of metal matrix composites can be improved when the fiber is wrapped by nickel coating.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Flow chart of the numerical solution procedure adapted for modeling the solidification process of MMCs.

**Figure 3.**Temperature profile in axial section of the model without coating (

**a**,

**b**) and with coating (

**c**,

**d**) at different dimensionless times (

**a**,

**c**) Fo = 0.156, (

**b**,

**d**) Fo = 0.234.

**Figure 4.**Comparison of the results from the present simulation with that reported in the literature [30] on the evolution of temperature without the nickel coating: (

**a**) $\overline{\mathrm{r}}$ = 0.25, (

**b**) $\overline{\mathrm{z}}$ = 0.1.

**Figure 5.**Effect of different distances on dimensionless heat flux without the nickel coating: (

**a**) at Fo = 0.195; (

**b**) at $\overline{\mathrm{z}}$ = 0.2.

**Figure 6.**Changes in the dimensionless heat flux (without the nickel coating) along the fiber-axis direction at (

**a**) $\overline{\mathrm{r}}$ = 0.19, (

**b**) $\overline{\mathrm{r}}$ = 0.26.

**Figure 8.**Variation in von Mises stress along the radial direction for the no-nickel-coating case at dimensionless time Fo = 0.195.

**Figure 9.**Radial changes in von Mises stress with and without nickel coating $\overline{\mathrm{z}}$ = 0.1.

**Figure 10.**Distributions of radial deformation: (

**a**) Fo = 0.156, without coating; (

**b**) Fo = 0.234, without coating; (

**c**) Fo = 0.156, with coating; (

**d**) Fo = 0.234, with coating.

**Figure 11.**Distributions of axial deformation: (

**a**) Fo = 0.156, without coating; (

**b**) Fo = 0.234, without coating; (

**c**) Fo = 0.156, with coating; (

**d**) Fo = 0.234, with coating.

**Figure 12.**Deformation with and without nickel coating: (

**a**) at $\overline{\mathrm{z}}$ = 0.2, (

**b**) at $\overline{\mathrm{r}}$ = 0.19 and $\overline{\mathrm{r}}$ = 0.4.

**Figure 13.**Microstructure predicted at the different sections: (

**a**) axial sections, (

**b**) radial sections.

**Figure 14.**Microstructure morphology predicted of different axial sections with the cooling temperature of 25 °C (

**a**–

**e**) without nickel coating; (

**a1**–

**e1**) with nickel coating.

**Figure 15.**Microstructure morphology predicted of different axial sections with the cooling temperature of −78 °C (

**a**–

**e**) without nickel coating; (

**a1**–

**e1**) with nickel coating.

**Figure 17.**Microstructure morphology predicted of different radial sections with the cooling temperature of 25 °C (

**a**–

**e**) without nickel coating; (

**a1**–

**e1**) with nickel coating.

**Figure 18.**Microstructure morphology predicted of different radial sections with the cooling temperature of −78 °C (

**a**–

**e**) without nickel coating; (

**a1**–

**e1**) with nickel coating.

**Figure 20.**Solidifying microstructure of thermally managed Al-9% Cu alloy composite (

**a**) with external cooling of graphite rod extending out of the melt and (

**b**) without external cooling of the graphite rod [27].

**Table 1.**Material parameters gleaned from [35] and used in ProCast’s CAFE simulation.

Property | Carbon Fiber | Nickel | Al-2014 |
---|---|---|---|

Thermal conductivity (W/m C) | 54 | 60.7 | 193 |

Specific heat capacity (J/kg K) | 921 | 460 | 880 |

Density (kg/m^{3}) | 1800 | 8880 | 2800 |

Thermal expansion coefficient (m/m °C) | −10^{−7} | 13 × 10^{−6} | 23 × 10^{−6} |

Young’s modulus (GPa) | 217 | 207 | 71 |

Poisson’s ratio | 0.3 | 0.31 | 0.33 |

Property | Value | |
---|---|---|

a2(First coefficient of the growth kinetics) | 4.7 × 10^{−6} | |

a3(Second coefficient of the growth kinetics) | 2.5 × 10^{−7} | |

Nucleation parameters in the bulk of the liquid (Gaussian distribution) | DTm (Average undercooling) | 2.5 |

DTs (Standard deviation) | 1 | |

Nmax (Maximum number of nuclei) | 7 × 10^{10} | |

Nucleation parameters at the surface (Gaussian distribution) | dTm (Average undercooling) | 0.5 |

dTs (Standard deviation) | 0.1 | |

Gmax (Maximum number of nuclei) | 5.0 × 10^{10} |

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**MDPI and ACS Style**

Xing, C.; Etemadi, R.; Pillai, K.M.; Wang, Q.; Wang, B. Numerical Simulation on Thermal Stresses and Solidification Microstructure for Making Fiber-Reinforced Aluminum Matrix Composites. *Materials* **2022**, *15*, 4166.
https://doi.org/10.3390/ma15124166

**AMA Style**

Xing C, Etemadi R, Pillai KM, Wang Q, Wang B. Numerical Simulation on Thermal Stresses and Solidification Microstructure for Making Fiber-Reinforced Aluminum Matrix Composites. *Materials*. 2022; 15(12):4166.
https://doi.org/10.3390/ma15124166

**Chicago/Turabian Style**

Xing, Chenyang, Reihaneh Etemadi, Krishna M. Pillai, Qian Wang, and Bo Wang. 2022. "Numerical Simulation on Thermal Stresses and Solidification Microstructure for Making Fiber-Reinforced Aluminum Matrix Composites" *Materials* 15, no. 12: 4166.
https://doi.org/10.3390/ma15124166