## 3.1 Redisual stress results of SiC/Al composites

Figure 2 illustrates the results of the stress relief treatment on SiC/Al composite material. After quenching, the SiC/Al composite exhibits substantial compressive stress on the surface, with higher stress observed in the Y-direction compared to the X-direction. The application of TSR, VSR, and TVSR treatments effectively reduces the stress. However, it is noted that the stress reduction in SiC/Al is significantly lower than that in 2024Al[6]. In terms of directional stress, the TVSR process demonstrates a remarkable reduction in stress in the X-direction compared to the Y-direction, while the differences between TSR and VSR processes in directional stress reduction are less pronounced. When considering the von Mises stress, the effectiveness of stress reduction is observed as TSR > TVSR (#2, #3) > VSR.

It can be explained in this way, the shape of the sample can lead to differences in the direction of TSR stress relief. For the TVSR process, the first-order modal frequency of the vibration platform is used, and the vibration mode at this modal frequency is a first-order bending vibration mode. The dynamic stress in the X direction is more obvious, so the residual stress in the dynamic stress coupling makes the stress in the X direction greater. Therefore, the residual stress in this direction is more easily relaxed, as confirmed by previous research [6].

## 3.2 Stress evolution mechanism

A Macro-micro FE model was developed to analyze the quenching process of 20 vol.% SiC/Al composites, as shown in Fig. 3(a). The model was divided into macroscopic and microscopic levels. The macroscopic model simulated the macro residual stresses generated during quenching from 490°C to 25°C, while the microscopic model calculated the microscopic stresses during quenching. The properties for SiC and Al alloy were referenced from the reference [10], while the properties for SiC/Al composites were obtained through homogenization method [10].

The surface of the specimen exhibited compressive stress, while the core region experienced tensile stress, as shown in Fig. 3(b). The stress state at the surface center of the specimen was − 112 MPa in the X-direction and − 125 MPa in the Y-direction. The FE simulation results also indicated that the residual stress in the Y direction was relatively large, which is consistent with the results in the literature [11]. The orientation difference in the residual stress is mainly related to the dimension of the specimen. The stress results obtained from both the macroscopic and microscopic models showed good consistency, as depicted in Fig. 3(c). After quenching, the average stress in the Al alloy matrix approached zero, while the average stress in the SiC reinforcement phase was approximately − 480 MPa. The distribution and contour map of microscopic stress after quenching are shown in Fig. 3(e)-(g). Only a small number of regions exhibited high stress levels, mainly in the vicinity of the matrix around the particles, especially between closely spaced particles.

When the temperature increases from room temperature (25°C) to the aging temperature of 175°C, the macroscopic stress shows little change, but the microscopic stress undergoes significant variations. The average stress in the Al matrix is approximately − 50 MPa, while the average stress in the SiC reinforcement phase is around − 240 MPa. This indicates that the temperature increase leads to an increase in compressive stress in the Al matrix, while the compressive stress in the SiC reinforcement phase decreases, and the dispersion of stress also decreases. Due to the difference in thermal expansion coefficient and elastic modulus between the matrix phase and the reinforcing phase[12], when the temperature changes, the thermal expansion between the matrix phase and the reinforcing phase is different, the thermal expansion coefficient of Al alloy is several times that of SiC [13], during heating, Al expands more, resulting in mismatch phenomenon. Generally, during the heating process, the thermal expansion of the matrix is greater than that of the reinforcing phase, causing tensile stress on the matrix and compressive stress on the reinforcing phase. But this microscopic thermal mismatch stress does not cause changes in macroscopic stress. The simulation results also proved this point.

The reduction of stress during the thermal aging treatment is primarily attributed to the stress relaxation at high temperatures. The stress relaxation process can be approximately described by the following quation[11].

$${\dot {\varepsilon }_c}=A{\sigma ^n}{t^m}\exp \left( { - \frac{Q}{{RT}}} \right)$$

1

Where, *A*, n, m, *Q*, R are the material constant, *σ* is the stress, *t* is the time, and *T* is the relaxation temperature.

In SiC/Al composites, SiC remains stable at the aging temperature without stress relaxation [14]. Therefore, stress reduction in SiC/Al composites primarily occurs due to Al matrix relaxation. After quenching, the Al matrix is subjected to low compressive stress, resulting in a lower relaxation rate during the TSR process compared to matrix Al alloy, this result is consistent with previous experimental results[6]. The effectiveness of stress relief in SiC/Al composites during the VSR process is also influenced by the microscopic stress state. Previous harmonic response analysis results indicate that during the TVSR treatment, there is higher dynamic stress in the X-direction and lower dynamic stress in the Y-direction[6]. When the stress of the Al matrix is superimposed with the dynamic stress, the stress in the X-direction increases, thereby promoting the relaxation of the Al matrix. Therefore, during the TVSR process, the relaxation rate in the X-direction is higher than that in the Y-direction. In other words, TVSR helps to eliminate residual stress in the direction with higher dynamic stress. It is expected that if two directions of vibration stress relief are adopted, TVSR will have a higher stress relief rate.