Abrasive waterjet machining (AWJM) is a typical high-energy fluid jet machining technology. The abrasive particles are entrained within the high-velocity waterjet and accelerated inside the nozzle head . It offers superior processing performance, such as negligible heat-affected zone, low specific cutting force, and high flexibilities over other conventional (e.g., milling, turning) or non-conventional machining techniques (e.g., electrical discharge machining, laser). Thus, it is being widely and increasingly utilized to machine hard-to-cut materials like engineered ceramics , composites , and high strength steel , for instance. Despite all the advantages mentioned above, there are some challenges in the AWJM fields. The cutting qualities, especially the kerf geometrical characteristics and surface integrities, are susceptible to energetic, kinematic, and constructive parameters, which result in the difficulties of controlling the AWJM process.
Plenty of academics devote themselves to exploring the influence of process parameters on cutting quality. Hashish  divided the parameters involved in the AWJM operation into two categories. The first group was related to the AWJM itself, including the hydraulic, abrasive, and mixing parameters. And the second group mainly included kinematic parameters such as standoff distance and traverse speed etc. Wang et al. established empirical models to predict the kerf geometry and surface roughness based on extensive experimental data. Additionally, there were different kinds of intelligent optimization algorithms, such as multi-objective artificial bee colony algorithm , extreme learning machine (ELM) , and artificial neural networks (ANNs)  implanted to achieve a higher quality of AWJM. But a large number of experiments are required to build an accurate optimization model, which is labor-intensive. And some essential outputs like the uniformity of abrasive particles mixed with waterjet inside the nozzle are hard to be acquired by measurements because of the extreme operating conditions.
It is well known that high-fidelity numerical simulations play a critical role in assisting in understanding the complex mechanisms, which could significantly save cost and time. Hence, various numerical strategies are adopted to build the AWJM models to study the flow characteristics inside the nozzle [10–12] and the high-speed impact erosion mechanism on the target [13–17]. Computational fluid dynamics (CFD) methods were mainly employed to investigate jet flow characteristics. Qiang et al.  carried out CFD simulations of three-phase flow to analyze the mixing and accelerating process of the abrasive particles inside the nozzle head. The effects of constructive parameters (i.e., abrasive inlet angle, abrasive inlet position, and focusing tube converging angle) on the nozzle wear were also discussed in detail. The knowledge of the energy distribution across the water jet is one of the most crucial factors affecting the cutting quality. Liu et al.  and Wang  attempted to establish a CFD model of ultra-high pressure AWJM to study the dynamic characteristics of waterjet outside the nozzle. The results indicated that the waterjet velocities at a given cross-section of the outflow formed a top-hat profile where the velocity at the jet center was higher than the boundaries.
Although CFD based models show the detailed features of the internal and external flow field, it is unable to demonstrate the particle erosion process on the workpiece. Consequently, numerous researches in the literature have concentrated on modeling high-speed particle impact damages on the target using finite element analysis (FEA) [13–15] and smoothed particle hydrodynamics (SPH) [16, 17]. Eltobgy et al.  conducted the explicit FEM simulations of the single-particle erosion process at different velocities and impact angles, which was proven to be consistent with the research by Finnie Bitter, and Hashish. Furthermore, Anwar et al. [14, 15] extended the simulations into multiple-particle situations. The abrasive particles were presented in non-spherical shapes with sharp cutting edges. Besides, the SPH method is also widely used in modeling AWJM. Wang et al.  firstly advocated that the waterjet containing abrasives could be established in SPH particles. Then Dong et al.  further modeled abrasive particles into arbitrarily shaped rigid bodies and considered the interaction between fluid and abrasives. However, the above models adopted the simplified motion laws of the internal flow field inside the nozzle head. The velocity distribution at a given cross-section of the jet beam was assumed to be the same. Thus, the previous models are unable to predict the kerf profiles accurately. It is necessary to develop the simulation models of the whole AWJM process which takes both internal and external flow fields into consideration.
To address the requirements, Gong et al.  built a numerical model to simulate the whole process stage of AWJM using the coupled ALE-FEM method. The water flow, which had large deformation during processing, was expressed by the arbitrary lagrangian eulerian (ALE) method. The mixture of water and abrasives was achieved by setting a keyword defining the volume fraction of different materials in the initial ALE elements. The lagrangian elements were used for the target. But there were no discrete abrasive particles in the model. The momentum transfer between the abrasives and the waterjet was ignored. Feng et al. attempted to use the coupled SPH-FEM method to establish the whole process model of AWJM. In their study, one abrasive particle in low velocity was accelerated by the high-speed water stream escaped from the fine orifice and eventually impacted the target. The dynamic characteristics of the mixing and acceleration of particles inside the nozzle head were discussed in detail. Nevertheless, there was only one abrasive particle in the model. The contact between abrasive particles was neglected. Besides, the abrasive particles and water flow particles were pre-established in the model, which could not only increase the model size but also limit the simulated cutting depth.
Although there have been some pioneer researchers [21, 22] who put much effort into the whole stage simulations of AWJM, the established models are still far different from the actual processing situations. The complexities, such as the mixing and accelerating process between particles and waterjet, the collisions among particles, and the high-speed particle erosions on the target, etc., have greatly increased the difficulties in modeling. On account of this, the coupled SPH-DEM-FEM modeling strategy is applied to the whole-stage AWJM model. The fluid with extra-large deformation is modeled by the SPH method; the multiple abrasive particles are expressed by the discrete element method (DEM), and the nozzle head and the workpiece are meshed by FEM grids. Besides, a large number of SPH and DEM particles are continuously injected from the inlet, which is much more alike to the actual cutting operations. To evaluate the scalability of the newly developed model for various operating conditions on metal specimens, the dynamic characteristics of the internal flow field, the nozzle wear induced by abrasives, and the impact stress of the target are discussed in detail. In addition, experiments are carried out to verify the correctness of this model.