*2.2.1 Erosion particle size and shape*

The influence of erosion particle size on materials with different properties is different. For ductile materials, the "size effect" of erosion particles [13], determines the erosion rate of the material, that is, the particle size increases, the erosion rate increases, but the critical size no longer meets the "size effect". The secondary erosion theory also believes that when the brittle particles reach a certain scale, they are easy to be broken in the erosion process. After the particles are broken, the erosion energy decreases, which is not enough to cause secondary erosion of materials, and the erosion rate will tend to be stable. For brittle materials, the erosion rate of small angle gradually increases with the decrease of particle size; Under the condition of large angle erosion, the erosion wear caused by large particles is more serious, which is usually a typical brittle fracture erosion mechanism. In addition, under the condition of the same particle size, the impact of particle shape on the material erosion rate is also not the same. Levy et al. [14], studied the influence of Al2O3 particles with different shapes on the erosion wear behavior of carbon steel. The results showed that the weight loss of irregular angular Al2O3 particles was much larger than that of spherical Al2O3 particles. Levy et al. believed that when angular Al2O3 particles impact the material surface, the contact area between the spherical particles and the matrix is much smaller, so the contact stress on the material surface is much larger under the same erosion conditions. The high stress

concentration on the surface of the material makes it easier to initiate cracks, and then crack, resulting in a large amount of wear [11].

### *2.2.2 Impact of erosion parameters*

When evaluating the erosion resistance of materials, erosion parameters (erosion angle, velocity, time, etc.) are the key factors affecting the erosion process of materials. For example, Finnie et al. [15], studied the erosion behavior of two representative materials, Al (ductile material) and Al2O3 (brittle material). It can be seen from **Figure 3** that the erosion rate of ductile material (Al) first increases with the increase of erosion angle and reaches the maximum value at about 15°, and then decreases with the increase of erosion angle. For brittle materials (Al2O3), the erosion rate increases with the increase of erosion angle. The results show that the erosion rate of brittle materials is lower at small angle of attack, while that of ductile materials is lower at large angle of attack. The analysis shows that the plowing effect of ductile materials with low surface hardness is significant in small angle erosion. Under the condition of large angle, the ductile material has a better inhibition effect on the generation of internal fatigue cracks, and the erosion rate is significantly reduced. On the contrary, the high hardness of brittle materials can resist the plowing effect of erosion at small angles of attack, but the high brittleness makes them vulnerable to impact fracture at large angles of attack, resulting in a large number of fatigue cracks and failure. Therefore, ductile materials and brittle materials are two distinct erosion behaviors under the same conditions.

In addition, particle velocity and erosion time are also the key factors affecting the erosion rate of materials. The general rule shows that the erosion rate increases gradually with the extension of erosion time. However, in the early stage of erosion, namely the so-called incubation period, the material will not suffer mass loss, and even a small amount of weight gain may occur. After initial erosion inoculation, the material enters a stable mass loss state. The length of incubation period is affected by erosion angle, erosion rate and material properties. The incubation period will be prolonged with the increase of erosion attack angle and the decrease of particle velocity. In addition, plastic materials usually have a longer incubation period than brittle materials [17]. For erosion particle velocity, lower velocity means lower impact energy, which makes it difficult to introduce high impact stress and reach the stress threshold of plastic deformation or crack initiation. Higher speed can cause surface

**Figure 3.** *Relationship between erosion rate and angle [16].*

damage of materials. Therefore, there is a critical velocity for erosion particles. Below this speed, the particles will be bounced away without damage. Only after exceeding this speed, the material will start to suffer from erosion wear [16].

### **2.3 Methods of SPE protection**

In order to enhance the erosion resistance of materials and prolong their service life, the erosion resistance can be improved by changing the overall structure of materials, but it is difficult to achieve for parts with more complex structures. As the erosion behavior first and mainly acts on the material surface, the surface quality of the material is the key to affect its erosion resistance. Adding protective coatings on the material surface to improve the erosion resistance is easier to achieve, and has been widely used. Surface coating technology is to obtain the required surface morphology, material composition, microstructure, etc. of parts and components through surface pretreatment, coating and other means. Therefore, it is of great significance to adopt modern surface modification technology for surface protection of related components.
