Ultrasonic cavitation damage characteristics of materials and a prediction model of cavitation impact load based on size effect

Highlights

• The size effect of materials should be considered in the formation of cavitation pits.

• The prediction models of cavitation impact load, impact pressure and velocity of micro-jet with size effect were established.

• A size effect coefficient $\sqrt{1+\frac{54h_{\text{p}}{\alpha }^2{\mu }^{2}b}{d_{\text{p}}^2{\sigma }_{\text{JC}}^2}}$ was defined.

• The predicted values of parameters increased by about 11%–88% for the ten typical cavitation pits when considering the size effect.

Abstract

High-speed micro-jet produced by cavitation collapse near the wall is the main mechanism of material damage, and cavitation pit is the most typical damage feature. The reason why high-pressure and high-speed micro-jet can only cause nano- and microscale cavitation pit is that the micro-jet is a short-term impact load of nano- and microscale, and the material shows size effect during the formation of pits. To further explore the cavitation damage characteristics and deformation mechanism of materials, the theoretical framework of indentation test and J-C constitutive model were adopted, and the size effect of materials during the process of cavitation pit formation was mainly considered, and the prediction models of cavitation impact load, impact pressure and velocity of micro-jet were established. The results showed that the equivalent stress and strain of cavitation pit and the impact pressure and velocity of micro-jet are only related to the diameter-to-depth ratio of pit without size effect, and also to the diameter of pit with size effect. Larger diameter and deeper depth of the pit infers greater cavitation impact load, and the influence of the pit diameter is more obvious. When considering the size effect, there is an additional size effect coefficient: $\sqrt{1+\frac{54h_{\text{p}}{\alpha }^2{\mu }^{2}b}{d_{\text{p}}^2{\sigma }_{\text{JC}}^2}}$. In the selected size range of pit, the cavitation impact load, impact pressure and velocity of micro-jet predicted with size effect increase by 0.9408%–322.5% compared with those without size effect. The maximum increase ratio appears at the minimum of diameter-to-depth ratio of pit (d_p = 2 μm and d_h = 2 μm), that is, the smaller the pit diameter is and the greater the depth is, the greater the increase ratio is. Ten typical cavitation pits were selected for inversion analysis. The impact pressure and velocity of micro-jet with and without size effect are 473–1131 MPa and 355–848 m/s, and 427–604 MPa and 320–453 m/s, respectively. The predicted values increase by about 11%-88% when considering the size effect, and the micro-jet velocity predicted is closer to that observed by high-speed cameras, which confirms the necessity and rationality of size effect in the inversion analysis of cavitation pits.

Introduction

Cavitation occurs when the local pressure in the liquid is lower than the saturated vapor pressure. It is a complex physical phenomenon, which shows a series of bubble nonlinear disturbance such as growth, expansion, contraction, collapse, etc. There are two most common ways to produce cavitation: ultrasonic induced cavitation and hydraulic cavitation. They reduce the local pressure of liquid through ultrasonic negative pressure and the change of fluid-structure, respectively. Generally speaking, ultrasonic induced cavitation is used to utilize cavitation. The cavitation phenomenon in hydraulic machinery will cause damage and failure of some parts, such as propeller blades, turbines, and centrifugal pumps, which needs to be avoided.

Cavitation collapse is characterized by local extreme physical and chemical phenomena, such as local high temperature, high pressure, micro-jet, shock wave, sonoluminescence, acoustic free radical, etc. [1], [2] Based on this, cavitation can be applied in many fields, such as using ultrasonic cavitation to improve the chemical reaction rate, even using dual- and multi-frequency ultrasound [3], using high temperature and acoustic free radicals to degrade sewage [4], using local impact load generated by bubble collapse for surface peening and modification [5], ultrasonic cleaning [6], etc. Ultrasonic induced cavitation is the main method. This is because the location and intensity of cavitation can be controlled, and the density and intensity of bubbles can also be regulated. Therefore, the optimal process conditions can be selected, which is very conducive to the research and application of cavitation.

For the cavitation damage of materials, micro-jet and shock wave are the two main mechanisms. The collapsed form of the bubble depends on its proximity to the boundary. In practice, the number of bubbles in the cavitation area is extremely large, and the distance from the solid wall is also different, so the cavitation damage is caused by both micro-jet and shock wave, but the former dominates. Therefore, the cavitation pressure exerted on the surface of materials is mainly the impact pressure of micro-jet. Many scholars have done a lot of work on cavitation damage characteristics of materials. In short, long-term cavitation damage is mainly characterized by material degradation, cracks, and fractures. The short-term cavitation damage mainly consists of micro indentation of material called cavitation pit, which is often involved in the cavitation experiment and research. It is characterized by the size of 0.1–10 μm, and its accumulation can lead to material failure. Roy [7] predicted the pressure causing cavitation pit on the surface of aluminum alloy by reverse theory, and results showed that the depth and diameter of most of the cavitation pits were 0.5–2 μm and 1–50 μm respectively, and the predicted peak impact pressure was 1.4–3 GPa. Tzanakis [8] analyzed the geometric characteristics of cavitation pit, and the test showed that the average diameter and depth were 6–7 μm and 0.13–0.15 μm respectively, and the cavitation impact load and the corresponding micro-jet velocity predicted through reverse engineering were 0.4–1 GPa and 200–700 m/s, respectively. In addition, previous experimental and numerical studies of various cavitation sources have shown that the impact pressure generated by the implosion or collapse of bubbles is usually 0.2–2 GPa, but it may be as high as 10 GPa [9], [10], [11] in some cases.

Comparing the extreme conditions (very high pressure and high-speed micro-jet) of cavitation collapse with the characteristics of cavitation pit (nano- and microscale), two questions are raised: (1) why the deformation or damage of materials is not as strong as imagined under such high cavitation pressure or micro-jet impact speed; (2) how much the cavitation impact load or the micro-jet velocity is acting on the material surface, and how to effectively predict their magnitudes.

For the first problem, we think that although the cavitation impact pressure (generated by high-speed micro-jet) is very high, its duration is very short and its action scale is at the micro or nano level. On the other hand, more importantly, the response of materials under cavitation impact may involve the size effect, which is ignored by most scholars. In the process of micro forming or micro deformation, when the overall size or deformation size of the material is reduced from macro scale to nano- or micro-scale, some properties of the material, such as shear modulus, initial yield strength, hardness, and the deformation mechanism will change, which is called the size effect, when the macro scale theory is no longer applicable, and a new micro plasticity theory is needed [12]. In the past few decades, Fleck [13], Zhu [14] and Zbib [15] have invested a lot of research in this field. Most typical, metal materials show obvious and representative size effect in the micro-nano indentation test, which is commonly known as the indentation size effect (ISE). Its typical performance is that when the indentation depth is less than about 10 μm, the hardness increases with the decrease of indentation size [16]. This is caused by the change of deformation conditions and deformation mechanisms when the size of plastic deformation area is reduced. It is generally believed that the main contribution of the characteristic size of internal structure (average grain size of polycrystalline, average cell size of dislocation structure, film thickness, superlattice period of polycrystalline coating on the substrate surface, volume of deformation area, etc.) to the size effect is 0.1–10 μm.

To further explore the physical nature of size effect, Ma [17], Nix and Gao [18] proposed a strain gradient plasticity (SGP) theory based on Taylor dislocation theory. According to the work hardening theory of Taylor dislocation of crystalline materials, the statistically stored dislocations (SSDs) caused by homogeneous strain and the geometrically necessary dislocations (GNDs) related to strain gradient all contribute to the hardness [16]. It should be recognized that the laws of SSDs and GNDS are based on the Taylor relation [19], [20], [21]. From the perspective of dislocation dynamics, materials deform and harden due to the formation, movement, and interaction of dislocations. Golovin [22] used a micro-nano indentation test to study the size effect of three FCC metals (nickel, copper and aluminum) in terms of hardness and determined the regional boundaries and characteristics of different types of size effect. Manika [16] studied the size effect in single-crystal and polycrystalline materials by the Vickers hardness method and concluded that the surface hardness can reach the theoretical shear strength by extrapolating the hardness-indentation depth curve of the test. The size characteristics of cavitation pits are in the micro-nano scale and similar to micro-nano indentation, so it can be inferred that the size effect of materials will also be involved in the formation of cavitation pits.

For the second problem, the measurement of cavitation strength or cavitation impact load is the most important in cavitation research, because it can provide a lot of important information. The most direct way is to arrange the pressure sensor on the surface of the target material subjected to cavitation. Although many efforts have been made to develop reliable direct measurement means in recent years, there are still some problems, such as the size of the sensor is too large to measure accurately compared with the micro-nano scale of cavitation impact load, and it is easy to be damaged by cavitation. Another method is to predict the cavitation impact load according to the deformation characteristics of the material surface, but this requires a deep and appropriate understanding of the response of the material under the cavitation impact load to establish a reliable mathematical model. The most widely used theoretical basis is the indentation test theory initiated by Tabor [8].

The precise quantification of cavitation damage and the accurate prediction of cavitation load have great research value. Berchiche [23] proposed an analytical model for cavitation damage prediction, which is characterized by the stress-strain relationship and the microhardness of the cross-section of the eroded surface. Jayaprakash [24] conducted a cavitation pit test on aluminum alloy, nickel aluminum bronze, and duplex stainless steel and analyzed the pit characteristics measured, and proposed that the cumulative distribution of pits can be represented by a Weibull three-parameter function. Hattori and Maeda [25] proposed a logic model to express the cavitation damage process of metal materials. Franc [26] carried out cavitation tests on three kinds of materials and analyzed the cavitation pits, and pointed out that the material damage was closely related to the material strain rate. Roy [7], [27] used the static and dynamic finite element method to predict the cavitation load, which was verified by the inversion analysis of cavitation test. However, in the process of cavitation inversion analysis, few scholars considered the size effect of materials, but it does exist.

In order to study the cavitation damage characteristics and deformation mechanism of materials, the theoretical framework of indentation test is used to analyze the size characteristics of cavitation pits. Then the size effect of materials during the formation of cavitation pits is considered and the material constitutive model is constructed. According to the characteristics of cavitation impact load, the prediction models of cavitation impact load, impact pressure and velocity of micro-jet with size effect are built. Finally, the influence of size effect is compared and analyzed, and the cavitation impact load, impact pressure and velocity of micro-jet are predicted. This paper provides a new suitable method for the prediction of cavitation impact load.