*2.2.2.2 Creating a cavity on the surface layer*

Preferential decomposition theory can explain the decrease in mechanical properties of composite materials, but it cannot be used to explain the decrease in mechanical properties of single-phase materials. Some researchers also researched the erosion-corrosion process of single-phase materials. Zhuo and his colleagues [31] investigated the reduction of mechanical properties of pure iron under anodic decomposition conditions in solution by *in situ* nano dentations and found that the surface hardness significantly decreased in the presence of a corrosion current compared with the conditions under cathodic protection. Matsumura et al. [9] reported that in a NaOH slurry, material loss from pure iron in the presence of a corrosion current was 20% higher than in the case without corrosion, although the corrosion current was measured to be very small. Jones et al. [32] proposed the vacancy generation theory to explain this effect for single-phase material. When a material is exposed to anodic decomposition, a supersaturated state of vacancies is formed on the surface of the material by anodic decomposition. A large amount of vacancies leads to the weakening of interatomic bonds on the surface of the metal. The interatomic bonds create a chemical potential gradient between the surface layer and the bulk material, which causes the induced decomposition of anodic and dislocation movement in the surface layer. During the electrochemical decomposition, the vacancies are attracted to the dislocations and increase their kinetic energy. This increase in the kinetic energy of the dislocation reduces the resistance of the surface layer against the change of plastic shape. Others [33] also found that the weakening of interatomic bonds on the surface of the metal leads to the deterioration of the mechanical properties of the material, such as tensile strength, modulus, and fatigue life; hence, it causes a decrease in erosion resistance.

Vacancies also cause corrosion and a chemical mechanical effect. A chemical mechanical effect occurs when a load is applied to the surface of a material while a chemical reaction is taking place. As a result, the mechanical properties are affected by this process. Gutman [34] found that on the surface of a metal, electrochemical or chemical decomposition can lead to a decrease in free energy and an increase in the kinetic power of the dislocations produced in this process. Therefore, the resistance to plastic deformation decreases. Jones et al. [32], and Zhu et al. [35] suggested that anodic decomposition can create a supersaturation of vacancies on the metal surface. These voids penetrate the grain boundaries and isolated voids, causing acceleration of infiltration creep and the ascent of dislocations.

#### **2.3 Factors affecting the erosion-corrosion process**

As mentioned above, erosion-corrosion is defined as the interaction of solid particles, fluid medium, and corrosion. This process is considered an interdisciplinary study between materials, hydrodynamics, and electrochemical properties. Therefore, the factors that affect each of these processes also affect erosion-corrosion.

#### *2.3.1 Material properties*

#### *2.3.1.1 Microstructure*

Resistance to erosion-corrosion is almost dependent on phase composition and particle size [36–39]. Wang et al. [36] investigated the erosion-corrosion behavior of carbon steel and found that the lower bainite microstructure can increase the erosioncorrosion resistance of carbon steel. Patterson and his colleagues [37] investigated the effect of different microstructures on carbon steels in most of the impact angles and found that their erosion resistance is based on the increase of erosion speed in the following order:

Spherodized, pearlite, tempered martensite, and martensite.

Lindsley et al. [38] reported that in spheroidized Fe-C alloys, the wear resistance increased when the mean path between carbides and grain boundaries decreased. Berglozzi [39] reported that erosion resistance is also dependent on the particle size and the erosion resistance increased with decreasing particle size.

#### *2.3.1.2 Composition*

The resistance of metals and alloys against erosion-corrosion depends on their chemical composition, corrosion resistance, hardness, and metallurgical history. The corrosion resistance of metals and alloys is mainly determined by the chemical composition. If it is an active metal, or an alloy that consists of active elements, its corrosion resistance mainly depends on the ability to form and maintains a protective shell. If the metal is nobler, it has good inherent corrosion resistance. Therefore, if all other factors are equal, a metal with higher intrinsic resistance will be more resistant to erosion-corrosion [40].

In general, the increase of carbon in carbon steels increases the resistance to erosion, but the resistance to corrosion decreases [28]. For alloy steels, the addition of alloying elements such as Ni, Mn, Mo, and Cr improves the corrosion resistance of the alloy. Samy [41] reported that alloy steels with higher Cr have better erosioncorrosion resistance because increasing Cr increases both corrosion resistance and mechanical properties.

#### *2.3.1.3 Surface shells*

The nature and properties of surface protective shells that are formed on some metals and alloys are very important in terms of resistance to erosion-corrosion. The ability of these shells to protect the metal depends on quickly or easily forming them in the early stages of contact with the corrosive environment, their resistance against mechanical damage or erosion, and the speed of their re-formation in case of damage or destruction. A surface shell that is hard, dense, sticky, and continuous is better protection than when the shell is easily worn or peeled off. If the shell is brittle and cracks and crumbles under stress, it will no longer be protective. Sometimes, the nature of the protective shell that forms on the surface of the metal will depend on the corrosive environment in which the metal is located, which is a determining factor.

The changes in the corrosion rate of steel by static water at different pH are dependent on the nature and composition of the surface shells that are formed. **Figure 3** shows the effect of the pH of distilled water at 50°C on the erosion-corrosion of carbon steel. Corrosion speed is low at pH 6 and 10, and corrosion speed is high at pH 8 and less than 6. At pH less than 5, the shell cracks, which is probably due to internal stresses, and the surface of the metal is exposed to the environment. In the areas where the corrosion rate is low, the corrosion products are Fe(OH)2 and Fe(OH) 3, which are more protective because they have prevented the transfer of oxygen and

ions. Erosion-corrosion tests in a boiler at 250°F using different equipment, as well as the experiences of power plants, confirm the results of high corrosion rate at pH = 8. The behavior of steel pipes and low-alloy steels against petroleum materials at high temperatures in refineries depends on the sulfide shell formed on the surface of the pipes. When the shell is worn, high corrosion occurs. For example, in organic systems, if cyanides are present, the sulfide shell, which is solid and integrated, became porous and will no longer be protected. The correct and effective use of inhibitors in reducing erosive corrosion in most cases depends on the nature and type of shell on the metal and, as a result, the reaction between the metal and the inhibitor [40].

#### *2.3.1.4 Mechanical properties*

Mechanical properties such as hardness, toughness, strength, and strain hardness can influence the rate of erosion-corrosion by changing the erosion behavior. Many erosion models are mainly created by eliminating these mechanical features. Hardness is one of the important parameters that has attracted many researchers in the field of erosion-corrosion. It is generally said that increasing hardness leads to decreasing erosion. Many researchers who built erosion models have all shown that the erosion rate has an inverse relationship with the hardness of the material [42]. The following equation was created in this regard:

$$e^{\circ} = k\_H H\_v^{-n\_H} \tag{2}$$

That *kH* and *nH* are laboratory constants that are related to hydrodynamic conditions. *Hv* is the hardness of the bulk material. Oka and his colleagues [43] found that it is not the initial hardness of the material that affects the erosion process, but the hardness that affects it during the erosion process, that is, the effect of hardening. Hutchings [28] investigated the erosion behavior of a wide range of materials and found that the erosion rate is strongly dependent on the hardness difference between the target material and the impacting particles. Finnie [44] also investigated a range of materials and found that the erosion rate is inversely proportional to the hardness if the power constant is equal to 1.

When there is corrosion, the mechanical properties of the material change. Guo [31] and his colleagues investigated the degradation of the mechanical properties of the pure iron surface in a solution with current density of 0.5 mA/(cm<sup>2</sup> ) and 1 mA/ (cm2 ) and found that the mechanical properties of corrosion flow are reduced. Based on this, it can be concluded that the reduction of erosion resistance in the erosioncorrosion process is probably due to the loss of the surface mechanical properties of the material caused by the corrosion flow. Gottman [34] also performed the necessary experiments and theoretical analysis and found that the hardness and strength of the surface layer decrease with the increase in the density of the anodic decomposition current. Lu and Liu [45] have shown a theoretical prediction of the relationship between the increased erosion rate with the presence of a corrosion current and surface degradation. This relationship is as follows:

$$\frac{\mathcal{e}\_c}{\mathcal{e}\_\*} = -n \frac{\Delta H\_v}{H\_v} \tag{3}$$

Where *Δ Η <sup>v</sup>* is the difference between the hardness in the corrosion process and the hardness without the corrosion process, and *n* is the laboratory constant, which is the difference between the erosion systems.

#### *2.3.2 Hydrodynamic properties*

#### *2.3.2.1 Flow rate*

The slurry is a two-phase fluid system including liquid and solid. Contrary to a single-phase system, the collision of particles should be considered. Meng and his colleagues [46] found that the speed of particle collision is an important parameter in determining the wear rate, and this parameter is directly dependent on the speed of the slurry. Postlewaite and his colleagues [47] have shown the relationship between the erosion-corrosion rate and the flow rate in Eq. (4):

$$w = m\_1 \mathcal{M}\_p f(\theta) U^{m\_2} \tag{4}$$

Where *Mp* is the weight of particles per unit volume of solution, *f*ð Þ*θ* is a dependent function that determines the rate of erosion according to the angle of impact, and *m*<sup>1</sup> and *m*<sup>2</sup> are constants dependent on erosion-corrosion systems. Some researchers also found a power law between erosion-corrosion speed and flow speed and found that the power value of this law is between 1 and 4 [2].

Many metals and alloys have oxide films on their surface, such as *Al*2*O*3, *Cr*2*O*3, *TiO*2, *Fe*2*O*3, *Fe*3*O*4, and *NiO*, and erosion leads to the removal of these films. If the flow rate is not high, the oxide films can reappear every time after being peeled off from the metal surface. If the flow rate exceeds some critical limits, there will not be enough time for the protective films to reestablish and remove the ions that will occur from the metal grid without the outer protective layer. In other words, the speed of removing the film is faster than the speed of its reproduction. Therefore, it may be easy to find different critical limits for water flow velocity for different metals and alloys on paper, but these limits must be used very carefully because the slightest change in the flow pattern, temperature, and chemical content of liquids and Alloys can lead to a change in the intensity of the critical flow rate [48].

In general, it can be said that increasing the flow rate, depending on its effect on the corrosion mechanism, may increase or decrease the corrosion rate. It can increase the rate of steel corrosion by bringing more oxygen, carbon dioxide, or hydrogen sulfide to the surface, and in the presence of corrosion inhibitors, increasing the flow rate can reduce the corrosion rate by bringing the inhibitors to the metal surface at a higher speed. It has been shown that to protect steel in drinking water at high flow rates, a small amount of sodium nitrite (inhibitor) is needed. Similar mechanisms have been proposed for other types of inhibitors.

The studies [40] of erosion-corrosion of aluminum and stainless steel alloys in fuming nitric acid have produced unexpected and interesting results, and with the increase of the flow rate, the corrosion of aluminum increased and the corrosion of stainless steel 347 decreased. The reason for this behavior was that the corrosion mechanisms in the two cases were different. **Figure 4** shows the increase in the corrosion rate of aluminum with an increase in the flow rate. In nitric acid that fumes aluminum, it forms aluminum nitrate and aluminum oxide. In a static state or at very low speeds, the corrosion rate is low or zero. At moderate velocities of 1–4 ft./sec, the nitrate shell is removed but not enough to remove the sticky oxide shell. Velocities above 4 ft./sec also destroy most of the oxide shell, and erosion-corrosion occurs at a faster rate.

**Figure 5** shows the reduction of the corrosion rate of 347 stainless steel with an increasing flow rate. Under static conditions, this steel is auto-catalytically corroded

#### **Figure 4.**

*Erosion corrosion of aluminum 3003 by fuming nitric acid at 108°F. Corrosion rate based on the average of four periods of 24 hours [40].*

#### **Figure 5.**

*Erosion corrosion of 347 stainless steel by white fuming nitric acid at 108°F. Corrosion rate based on the average of four periods of 24 hours [40].*

by nitric acid because the cathodic reaction forms nitro acid. Increasing the flow rate causes nitro acid to leave the environment and reduces corrosion. It means at higher rates, the corrosion rate reduces by preventing sludge deposition, which would cause crevice corrosion in the absence of high rates.

Most stainless steels are prone to pitting and crevice corrosion in seawater and other chlorides, but some of these steels have been used successfully in seawater at high flow rates. This mode prevents the formation of sediments and prevents the initiation of cavities. Rate changes can also produce strange galvanic effects. In slowmoving seawater, the corrosion of steel does not change appreciably when in contact with stainless steel, copper, nickel, or titanium. At high flow rates, the corrosion of steel in contact with stainless steel and titanium is much less than when it is in contact with copper and nickel. This property is attributed to the more effective cathodic polarization of stainless steel and titanium at high rates [40].

### *2.3.2.2 Particle concentration*

In low particle concentrations, an increase in the erosion rate has been observed linearly with increasing particle concentration. For high-concentration slurry, the erosion rate will also increase with increasing particle concentration, but it will be exponential and progressive rather than linear. Hutchings [28] found that this exponential movement in higher concentrations of particles is due to the interference of particles among each other. In lower particle concentrations, because the particles are almost independent of each other, the erosion rate increases linearly. He investigated the material loss behavior of mild steel in a slurry of silica particles and found that the lower the particle volume concentration from 12%, the material loss increases linearly.

When corrosion is present, the situation becomes more complicated. Zhu and his colleagues [18, 26] investigated the effect of particle concentration on corrosion current density in both active and inactive system states. For active systems [26], he studied the concentration effect on AISI 1045 low carbon steel at different rotation speeds with weight concentrations of 0, 20, and 35% and found that the current density significantly does not change with different concentrations of solid particles. For passive systems [18], the corrosion current density is highly dependent on the particle concentration, so the current density increases with the increase of the particle concentration.

#### *2.3.2.3 Particle properties*

The erosion-corrosion process depends on the properties of the particles. The rate of erosion is strongly affected by the hardness, size, and shape of the particles. Hutchings [42] found that particles that are 1.2–1.5 times harder than the surface of the target material produce a higher erosion rate than other particles. Oka and his colleagues [49] investigated the dependence of the particle size on the erosion rate of steel when its surface was hit by quartz particles and found that the erosion rate tends to increase up to a critical value, and after that, the erosion rate decreases to a relatively stable state.

### *2.3.2.4 Angle of impact*

Finnie [50] investigated the erosion behavior of aluminum and its oxide at contact angles from nearly 0 to 90 degrees and found that for aluminum, as a soft material, the maximum erosion rate occurs between 15 and 30 degrees, while for aluminum oxide, as a hard material, the highest erosion rate occurs at 90 degrees. He explained that this angle change is due to the change in the erosion mechanism from soft to hard material. Erosive weight loss of soft materials is mainly done by grooving and cutting.

The reduction in the weight of hard materials is due to failure mechanisms because at 90 degrees, hard materials have the lowest resistance to failure; hence, we have the highest erosion rate.

Collision angles will also affect the corrosion process. Burstein and his colleagues [51] investigated the effect of collision angles on the increase of corrosion current, which is due to the breakdown or removal of the oxide layer on the surface.

#### *2.3.3 Electrochemical parameters*

#### *2.3.3.1 The PH of the slurry*

The PH of the slurry can greatly change the erosive corrosion behavior. As hydrogen ions are highly reactive, they can rapidly react with metal ions, resulting in severe surface erosion and reduced erosive resistance in anodic solutions. Guo and his colleagues [52] investigated the erosion-corrosion behavior of low carbon steel in abrasive slurries with pH 4, 7, and 10, and they found that the erosion rate was the highest in the solution with pH = 4 and the lowest in the solution with pH = 7 and at PH = 10, and our speed was between these two. Zhou et al. [53] also studied the effect of pH on the erosive corrosion characteristics of ductile cast iron under an open-circuit potential and obtained similar results. They explained that slurry with lower pH results in a higher corrosion current density under an open-circuit potential; hence, the erosion resistance will be lower.

#### *2.3.3.2 Corrosion current density*

Usually, the rate of erosion, in the case of corrosion, increases with the corrosion current density. Lu and his colleagues [45] investigated the effect of corrosion current density on the erosion-corrosion rate and found that the erosion rate increases linearly with the logarithm of the anodic current density. He also proposed an equation to calculate the theory of increased erosion rate due to corrosion with a given anodic current density.

$$\frac{\varepsilon\_c}{\varepsilon^\*} = z \log \left( \frac{i\_a}{i\_{th}} \right) \tag{5}$$

Where *ia* and *ith* are the actual anode current density and the threshold density that causes mechanical destruction of the surface, respectively. Z is a constant that varies between erosion-corrosion systems.

#### **2.4 Erosion corrosion mechanism**

If liquids and gases containing solid particles or gases containing liquid droplets flow on the surface of the metal, the abrasive agent causes mechanical wear of the metal. As a result, the metal decomposes in the form of ions or the formation of corrosion products.

The erosion-corrosion mechanism depends on the following components:

1.Flow speed and its characteristics: flow geometry (turbulent or smooth), the presence of obstacles in front of the flow, the angle of the flow to the metal surface, etc.


In general, there are two main reasons for the occurrence of erosion-corrosion. The first reason is "Erosion" due to the impact of certain materials or the impact of certain drops on the surface of metals. Since ancient times, humans have learned to cut "weak" materials such as wood and leather using "hard" materials such as stone and metal. The same phenomenon occurs on the surface of metals. If two solid materials that have hardness are different (metals and corroded particles) and come into contact with each other and move in opposite directions, the material with higher hardness will scratch the other surface.

The kinetic energy of certain materials (solid particles) and liquid droplets that move at high speed carries the necessary energy to cut or break the outer layer of metals. "Erosion" is a mechanical action of "wearing" metal. Corrosion is a chemical action of metal dissolution. Increasing the current speed increases the speed of transferring aggressive components to the metal surface and corrosion products in the opposite direction from the metal surface to the environment; as a result, the penetration speed of the components participating in the cathode and anode of corrosion reactions increases. The use of electrochemical methods for monitoring and controlling erosion-corrosion shows an aspect of the electrochemical mechanism in this complex phenomenon.

The second reason for the occurrence of erosive corrosion is cavitation, which is the formation and collapse of bubbles in the liquid (the first type of cavitation), or the condensation of vapor molecules (the second type of cavitation) on the metal surface during the flow. In the first type of cavitation phenomenon, the turbulent flow of liquids (strong flow under turbulence) causes a change in the pressure in the liquid flow near the metal surface. This condition can occur on the surface of a ship propeller or in centrifugal pumps. The collapse of vapor molecules forms local stresses on the surface of the metal due to the released shock wave. These stresses have higher energy and forces than the chemical electrostatic forces between atoms in the metal lattice. The surface of the metal is not uniform and forms surface pits such as cavities. These holes are called the pitting phenomenon. Chemical factors (if corrosive chemicals are present in the liquid or the vapor stream) can accelerate pitting [54].
