Investigation of Thermo-Mechanical Characteristics in Friction Stir Processing of AZ91 Surface Composite: Novel Study Through SPH Analysis

Abstract

The current study examines the influence of tool rotational speed (TRS) and reinforcement volume fraction (%vol.) of SiC on particle distribution in the stir zone (SZ) of AZ91 Mg alloy. Two parameter sets were analyzed: S1 (500 rpm TRS, 13% vol.) and S2 (1500 rpm TRS, 10% vol.), with a constant tool traverse speed (TTS) of 60 mm/min. SPH simulations revealed that in S1, lower TRS resulted in limited SiC displacement, leading to significant agglomeration zones, particularly along the advancing side (AS) and beneath the tool pin. Cross-sectional observations at 15 mm and 20 mm from the plunging phase indicated the formation of reinforcement clusters along the tool path, with inadequate SiC transference to the retreating side (RS). The reduced stirring force in S1 caused poor reinforcement dispersion, with most SiC nodes settling at the SZ bottom due to insufficient upward movement. In contrast, S2 demonstrated enhanced particle mobility due to higher TRS, improving reinforcement homogeneity. Intense stirring facilitated lateral and upward SiC movement, forming an interconnected reinforcement network. SPH nodes exhibited improved dispersion, with particles across the SZ and more evenly deposited on the RS. A comparative assessment of experimental and simulated reinforcement distributions confirmed a strong correlation. Results highlight the pivotal role of TRS in reinforcement movement and agglomeration control. Higher TRS enhances stirring and promotes uniform SiC dispersion, whereas an excessive reinforcement fraction increases matrix viscosity and restricts particle mobility. Thus, optimizing TRS and reinforcement content through numerical analysis using SPH is essential for producing a homogeneous, well-reinforced composite layer with improved surface properties. The findings of this study have significant practical applications, particularly in industrial material selection, improving manufacturing processes, and developing more efficient surface composites, thereby enhancing the overall performance and reliability of Mg alloys in engineering applications.

1. Introduction

Lightweight alloys, particularly aluminium and magnesium, have become increasingly attractive in modern engineering because of their favourable strength-to-weight ratio, corrosion resistance, and applicability in automotive, aerospace, and electric vehicle industries [1]. Within this group, magnesium alloys are being progressively preferred over aluminium to address industrial needs. Despite these advantages, their relatively poor surface characteristics—such as low hardness and limited wear resistance—hinder widespread application. To overcome these limitations, Friction Stir Processing (FSP) has been recognized as a promising technique for developing magnesium-based metal matrix composites (MMCs) [2]. FSP employs a rotating, non-consumable tool that generates frictional heat and plastic deformation, producing refined microstructures and enabling uniform dispersion of reinforcement particles in the processed zone [3,4]. This technique has demonstrated strong potential for improving material properties [5,6,7]. However, due to its three-dimensional nature and dependence on multiple interacting parameters, understanding and optimizing FSP exclusively through experiments is challenging. The process involves non-linear material responses, intricate tool–workpiece interactions, and complex geometries, making mathematical formulations equally difficult [8,9,10,11]. A detailed thermo-mechanical understanding of FSP is crucial, as the process encompasses severe plastic deformation, intense mixing, frictional contact, dynamic structural evolution, and heat generation. Among these, temperature distribution and material flow are regarded as the most critical aspects influencing the process and the final properties of the composite [12]. Experimental measurement of these parameters, particularly at the tool–workpiece interface, remains difficult, and tracking material flow patterns is even more complex [13]. Although numerical modelling has advanced significantly [14], several challenges remain unresolved.

Different computational methods have been introduced to simulate phenomena such as heat transfer, material flow, thermo-mechanical coupling, reinforcement transport, and defect prediction [15,16,17,18,19,20,21,22]. The main modelling frameworks include the Lagrangian, Eulerian, Arbitrary Lagrangian–Eulerian (ALE), Coupled Eulerian–Lagrangian (CEL), and Smoothed Particle Hydrodynamics (SPH) methods. Each approach provides unique strengths and weaknesses depending on the degree of deformation and the complexity of the FSP process. In the Lagrangian framework, material points and nodes move together as deformation progresses, preserving their interconnection [23]. Boundary conditions are easier to impose, and constitutive equations remain consistently evaluated at material points. This method is well-suited for solid mechanics problems with small deformations [24]. However, in FSP, where deformation is severe, mesh distortion becomes excessive, limiting the applicability of traditional FEM-based Lagrangian simulations. Unlike Lagrangian models, Eulerian formulations use a fixed mesh through which material flows. It makes them effective for analyzing flow behaviour but less accurate for thermal simulations. Limitations include difficulty handling free boundaries and higher numerical diffusion near material interfaces [25]. Consequently, the method has rarely been applied to thermal problems, except where deformed boundaries are already known [26].

ALE combines the benefits of Lagrangian and Eulerian approaches. By allowing nodes to move arbitrarily, mesh distortion can be minimized while retaining accurate tracking of deformation. In FSP studies, ALE has been widely applied to preserve mesh quality under high strain conditions, particularly near the tool region [15,27]. Nevertheless, its effectiveness decreases when deformations become excessively large. CEL also merges the strengths of Eulerian and Lagrangian methods, but uses two separate computational domains—Lagrangian for solids and Eulerian for fluids. Thus, it is suitable for fluid–structure interaction (FSI) problems with high deformation. The solid boundary, represented in a Lagrangian frame, acts as a kinematic constraint on the Eulerian calculation, accurately defining the material interface [28,29]. Large deformations often lead to severe mesh distortion, which mesh-free methods like SPH can overcome [30,31]. Unlike grid-based techniques, SPH uses interpolation between discrete particles [32]. Initially proposed for astrophysical simulations by Gingold, Monaghan, and Lucy in 1977 [33,34], SPH has since been extended to manufacturing applications, including brittle solid mechanics [35] and die casting [36]. As a Lagrangian particle-based method, SPH can naturally capture dynamic interfaces, high deformations, and thermo-mechanical histories (temperature and strain) without complex tracking systems. Figure 1 illustrates the frequency of publications using Lagrangian, Eulerian, ALE, CEL, and SPH methods in FSP research between 2004 and February 2024, showing that SPH remains relatively underexplored. Current research highlights the need to further advance SPH by addressing critical issues such as convergence, consistency, stability, adaptivity, boundary condition treatment, and integration with other numerical approaches, as emphasized by SPHERIC members [37,38]. A comparative summary of the modelling techniques and their software capabilities for FSP simulations is provided in Table 1. Although numerous experimental studies have investigated surface composite fabrication through FSP, numerical modelling of monolithic and hybrid composites remains scarce. In particular, the role of reinforcement particles in altering the thermo-mechanical behaviour of processed composites is still not fully understood. Developing reliable numerical models offers several advantages: it reduces the high cost associated with nano-reinforcements, minimizes time-consuming trial-and-error experiments, and provides predictive insights into particle distribution, thereby enabling more effective process optimization. Table 2 summarises notable numerical modelling attempts for composites; however, most involve major assumptions and simplifications regarding reinforcements. In many cases, reinforcement effects are entirely excluded to reduce computational complexity.

Tutunchilar et al. [19] employed a Lagrangian incremental model in DEFORM-3D to simulate LM13/Gr composites. Using point-tracking, they observed material flow within the stir zone (SZ), noting particle movements from the core toward both the advancing side (AS) and retreating side (RS). This approach allowed reinforcement trajectories to be traced, albeit with pre-defined assumptions about their initial positions. Experimentally validated results revealed typical FSP defects such as tunnel cavities and voids behind the pin, as shown in Figure 2. To model reinforcement diffusion, an ALE formulation was used for MWCNTs in polyamide 6 [39]. A point-tracing approach with seven discrete points (three on the AS, one on the centre line, and three on the RS) revealed that temperature decreased with increasing distance from the tool centre. The resulting material flow pattern supported the characteristic jug-shaped SZ profile observed in cross-sections. Machine learning techniques have also been integrated with numerical models. For example, artificial neural networks were applied to predict hardness and grain size in SiC-reinforced AZ91 Mg composites based on tool rotational speed, traverse speed, and region type [40]. Sensitivity analysis identified region type as the dominant factor influencing grain refinement and hardness, with the model outputs strongly correlating with experimental results. Efforts to improve reinforcement uniformity have also been reported. By applying electrical current through the tool shoulder, researchers enhanced particle dispersion in AA5083-H111 composites [41]. Numerical simulations characterized current density and flow behaviour, which matched well with experimental observations of improved particle distribution, increased SZ width and depth, and enhanced bonding to the substrate.

Despite these advances, the numerical investigation of composites lags behind experimental studies. Existing models often focus on isolated aspects such as defect prediction, thermal profiles, or reinforcement motion, but comprehensive models accounting for reinforcement type, volume fraction, and process parameters remain limited [42,43]. Therefore, future research should expand simulation capabilities to explore the coupled effects of reinforcement volume percentage, process parameters, and thermo-mechanical responses in monolithic and hybrid FSP composites.

Figure 1. Pervasiveness of the approaches used for FSP in Science Direct [44].

Figure 1. Pervasiveness of the approaches used for FSP in Science Direct [44].

Table 1. Various modelling approaches used for FSP.

Ref.	BM	Approach	Software	Objective	Outcomes	Merits/Demerits
[45]	AZ91	Lagrangian	DEFORM 3D	Temperature & material flow predictions	Major flow occurs on the AS, with the SZ stretching towards it. The peak temperature for recrystallization was determined. Material deformation and temperature are linked to microstructure.	Automatic re-meshing & point tracking. Distortion in networks & elements.
[46]	AZ91	Lagrangian	ABAQUS Explicit	Small hole drilling analysis on FSP and Friction Stir Vibration Processing (FSVP)	Higher deformation in the stir zone (SZ) of FSVP compared to FSP. Chip formation and its morphology: Discontinuous chips in FSVP have higher hardness than the FSP. Cutting force is reduced in FSP.	JC law was applied, & only the impact of vibration on drilling was modelled.
[47]	Mg alloy; Tool-H13	Lagrangian	ANSYS	FSP tool design and simulation for Mg alloy.	Low stress, long fatigue life, and slight deformation resulted from the tool’s structural and fatigue examination. Maximum force occurs at the tool shoulder and pin tip during plunging and on the pin side during travelling.	Tool designed with 20 mm SD & 4 mm PD must be used for safety operations in Mg alloy.
[48]	SS304L	Eulerian	Forge	Prediction of grains from flow stresses, strain rate, and temperature.	Estimated the recrystallized grains in the SZ using simulated temperatures. Model is favourable for hardness, exhibiting minimal variation of 10%.	Predicted grain size differed by up to 39%. Difficulty was encountered in analyzing material flow at free boundary surfaces.
[49]	AA2024	–	ABAQUS Fluent	Temperature field and plastic material flow in crack repair.	Crack healing occurred in the solid phase, as indicated by the measured temperature. Strength of the repaired zone was restored through grain refinement. Material flow was chaotic in the RS & regular in the AS.	Different FEM tools were used for temperature & material flow predictions.
[50]	Al-12% Si	CEL	–	Effect of process parameters on a temperature gradient	Temperature and plastic strain were directly proportional to TRS. Temperature decreases from the surface through thickness; Less heat is generated & increased dissipation to the backing plate.	Impact of used parameters on material flow was not reported.
[31]	AA6061-T6	SPH	LS-Dyna	Develop an AFSP model using the meshfree technique.	Entire HAZ had a dome shape, with the Tmax. at the filler rod-substrate contact surface reached about 79% of Tmelt. High hardness & stress were observed at the top deposition layer.	JC material law was applied. SPH-SPH contact not defined.

Table 1. Various modelling approaches used for FSP.

Ref.	BM	Approach	Software	Objective	Outcomes	Merits/Demerits
[45]	AZ91	Lagrangian	DEFORM 3D	Temperature & material flow predictions	Major flow occurs on the AS, with the SZ stretching towards it. The peak temperature for recrystallization was determined. Material deformation and temperature are linked to microstructure.	Automatic re-meshing & point tracking. Distortion in networks & elements.
[46]	AZ91	Lagrangian	ABAQUS Explicit	Small hole drilling analysis on FSP and Friction Stir Vibration Processing (FSVP)	Higher deformation in the stir zone (SZ) of FSVP compared to FSP. Chip formation and its morphology: Discontinuous chips in FSVP have higher hardness than the FSP. Cutting force is reduced in FSP.	JC law was applied, & only the impact of vibration on drilling was modelled.
[47]	Mg alloy; Tool-H13	Lagrangian	ANSYS	FSP tool design and simulation for Mg alloy.	Low stress, long fatigue life, and slight deformation resulted from the tool’s structural and fatigue examination. Maximum force occurs at the tool shoulder and pin tip during plunging and on the pin side during travelling.	Tool designed with 20 mm SD & 4 mm PD must be used for safety operations in Mg alloy.
[48]	SS304L	Eulerian	Forge	Prediction of grains from flow stresses, strain rate, and temperature.	Estimated the recrystallized grains in the SZ using simulated temperatures. Model is favourable for hardness, exhibiting minimal variation of 10%.	Predicted grain size differed by up to 39%. Difficulty was encountered in analyzing material flow at free boundary surfaces.
[49]	AA2024	–	ABAQUS Fluent	Temperature field and plastic material flow in crack repair.	Crack healing occurred in the solid phase, as indicated by the measured temperature. Strength of the repaired zone was restored through grain refinement. Material flow was chaotic in the RS & regular in the AS.	Different FEM tools were used for temperature & material flow predictions.
[50]	Al-12% Si	CEL	–	Effect of process parameters on a temperature gradient	Temperature and plastic strain were directly proportional to TRS. Temperature decreases from the surface through thickness; Less heat is generated & increased dissipation to the backing plate.	Impact of used parameters on material flow was not reported.
[31]	AA6061-T6	SPH	LS-Dyna	Develop an AFSP model using the meshfree technique.	Entire HAZ had a dome shape, with the Tmax. at the filler rod-substrate contact surface reached about 79% of Tmelt. High hardness & stress were observed at the top deposition layer.	JC material law was applied. SPH-SPH contact not defined.

Figure 2. (a) Tunnelling cavity formation behind the pin and (b) slot formation at AS behind the pin (c) Comparison of simulated and experimental SZ shape.

Figure 2. (a) Tunnelling cavity formation behind the pin and (b) slot formation at AS behind the pin (c) Comparison of simulated and experimental SZ shape.

Table 2. Numerical analysis of composite models in FSP.

Ref.	BM/Reinf.	Approach	Software	Objective	Outcomes	Merits/Demerits
[51]	A356/ZrO2, B4C, TiC & SiC	–	DEFORM 3D	Material flow simulation for different pin profiles	Material revolution around the threaded pin, a vertical material motion was observed. Vertical motion discontinued the transverse bands formed in the cylindrical pin profile. TiC achieved an increase in hardness due to excellent bonding.	Non-uniform and automatic remeshing. Reinforcing particles are not accounted in the numerical analysis; instead, pointers are assumed.
[18]	A356/B4C	Lagrangian	DEFORM 3D	Impact of tool pin profile on reinforcement distribution	Particle distribution was nearly uniform in threaded pin profiles compared to square, hexagonal, and cylindrical profiles. Material flow patterns closely matched SZ shapes from simulation and experiment.	Reinforcement distribution requires point-tracking adjustment at specific intervals for complex deformations. Network and element distortions necessitate severe re-meshing.
[19]	LM13/Gr	Lagrangian incremental	DEFORM 3D	Simulate the material flow and its behaviour.	Material flow, prediction of SZ shape, and temperature matched the experimental data well. Powder agglomeration and tunnel defects were observed at AS. Moving the FSP tool towards RS, leads to a more even powder distribution.	Reinforcing particles are excluded from the numerical modelling; markers or tracers are assumed.
[39]	Polyamide 6/MWCNT	ALE	DEFORM 3D	Temperature distribution, material flow & plastic strain	Peak Temperature (Tp) is observed at the shoulder/workpiece interface, and the temperature distribution is asymmetric at the surface. Plastic strain shows higher shearing on the AS than the Retreating Side (RS) and decreases towards the edge of the SZ.	Point tracing depicts the concave cross-section of the SZ. Point tracing required adjustment & pre-assumed specific intervals.
[52]	AA6061/SiC	CEL	ABAQUS	Impact of tool pin profile on temperature distribution	Minor temperature variations were observed due to the same shoulder size serving as the primary heat source. Cylindrical tool exhibited higher temperatures in the pin-affected region due to its larger surface area. In contrast, the triangular tool sample experienced lower temperatures in this area due to its smaller surface area.	Reinforcing particles are excluded from the model. Backing plate is not considered.

Table 2. Numerical analysis of composite models in FSP.

Ref.	BM/Reinf.	Approach	Software	Objective	Outcomes	Merits/Demerits
[51]	A356/ZrO2, B4C, TiC & SiC	–	DEFORM 3D	Material flow simulation for different pin profiles	Material revolution around the threaded pin, a vertical material motion was observed. Vertical motion discontinued the transverse bands formed in the cylindrical pin profile. TiC achieved an increase in hardness due to excellent bonding.	Non-uniform and automatic remeshing. Reinforcing particles are not accounted in the numerical analysis; instead, pointers are assumed.
[18]	A356/B4C	Lagrangian	DEFORM 3D	Impact of tool pin profile on reinforcement distribution	Particle distribution was nearly uniform in threaded pin profiles compared to square, hexagonal, and cylindrical profiles. Material flow patterns closely matched SZ shapes from simulation and experiment.	Reinforcement distribution requires point-tracking adjustment at specific intervals for complex deformations. Network and element distortions necessitate severe re-meshing.
[19]	LM13/Gr	Lagrangian incremental	DEFORM 3D	Simulate the material flow and its behaviour.	Material flow, prediction of SZ shape, and temperature matched the experimental data well. Powder agglomeration and tunnel defects were observed at AS. Moving the FSP tool towards RS, leads to a more even powder distribution.	Reinforcing particles are excluded from the numerical modelling; markers or tracers are assumed.
[39]	Polyamide 6/MWCNT	ALE	DEFORM 3D	Temperature distribution, material flow & plastic strain	Peak Temperature (Tp) is observed at the shoulder/workpiece interface, and the temperature distribution is asymmetric at the surface. Plastic strain shows higher shearing on the AS than the Retreating Side (RS) and decreases towards the edge of the SZ.	Point tracing depicts the concave cross-section of the SZ. Point tracing required adjustment & pre-assumed specific intervals.
[52]	AA6061/SiC	CEL	ABAQUS	Impact of tool pin profile on temperature distribution	Minor temperature variations were observed due to the same shoulder size serving as the primary heat source. Cylindrical tool exhibited higher temperatures in the pin-affected region due to its larger surface area. In contrast, the triangular tool sample experienced lower temperatures in this area due to its smaller surface area.	Reinforcing particles are excluded from the model. Backing plate is not considered.

Altair RADIOSS has been widely applied to simulate demanding scenarios such as vehicle crashes, drop tests, ballistic impacts, and blast events involving severe plastic deformation [53,54,55,56,57]. Its reliability in handling such complex, non-linear problems has established it as a trusted solver in industries including aerospace, defense, automotive, and advanced research organizations, where the HyperWorks framework is used for predictive design and analysis. Similarly, modeling FSP presents unique challenges due to the combined effects of high strain rates, elevated temperatures, and non-linear material flow. To address these, the present study employs the Altair RADIOSS 2021.1 solver, which is particularly effective in capturing intense plastic deformation and dynamic material behavior. The integrated SPH technique further enhances this capability by offering a mesh-free formulation that eliminates issues of mesh distortion while accurately representing thermo-mechanical interactions. SPH has been successfully utilized across solid and fluid mechanics applications such as impact dynamics, metal forming, and high-velocity events. To the best of our knowledge, no prior work has numerically investigated mono-composites developed through FSP using SPH, particularly for AZ91 magnesium alloy reinforced with SiC particles, and this forms the key novelty of the present research.

Thus, the present work is applied to examine particle flow, reinforcement dispersion, and SZ size and shape evolution during FSP of AZ91. It employs SPH to investigate AZ91 magnesium alloy surface composites reinforced with SiC particles. Particular emphasis is placed on the influence of TRS and %vol. on temperature evolution, material flow, and particle dispersion within the SZ. Two process conditions—low TRS with higher reinforcement content (S1) and high TRS with lower reinforcement fraction (S2)—are analyzed and validated through experimental comparison. By integrating advanced SPH simulations with experimental data, this work provides novel insights into reinforcement transport, agglomeration control, and process parameter optimization for developing homogeneous, well-reinforced AZ91/SiC surface composites with superior surface characteristics. These contributions establish the study as the first SPH-based numerical framework tailored for mono-composite FSP, highlighting both its originality and practical relevance.

2. Methodology

Numerical simulations are essential for gaining deeper insights into the complex physics of Friction Stir Processing (FSP). In the present study, Altair RADIOSS 2021.1, a commercial finite element (FE) software, was employed to investigate the thermo-mechanical behaviour of the FSP process. This solver was selected because of its proven capability to handle large plastic deformations typically encountered in extreme engineering applications such as vehicle crashworthiness, impact dynamics, and blast simulations. These capabilities make it particularly well-suited for modelling the severe plastic deformation inherent to FSP. Furthermore, integrating the Smoothed Particle Hydrodynamics (SPH) module within RADIOSS significantly strengthens its ability to simulate coupled solid–fluid mechanics, thereby enhancing its applicability in analyzing the complex material flow and thermal characteristics of FSP [27].

2.1. Experimental Methodology

In the present investigation, AZ91 Mg alloy plates were employed as the base material, alloy contains approximately 9 wt.% aluminium and about 1 wt.% zinc. The plates had standard dimensions of 100 mm in width, 150 mm in length, and 6.35 mm in thickness. For the fabrication, H13 tool steel was selected, featuring a cylindrical flat pin with a diameter of 6 mm, a pin height of 3 mm, and a shoulder diameter of 20 mm. Following best practices reported in earlier works [58,59,60], the pin length was designed to be about half of the plate thickness. The tool plunge depth was set at 3.3 mm, comprising the 3 mm pin length plus an additional 0.3 mm. All processing was carried out on a CNC-controlled FSW machine. The reinforcement, in the form of SiC particles, was introduced through the hole deposition technique at different volume fractions. Based on preliminary trials, 7%, 10%, and 13% vol. reinforcement levels were chosen. These values were determined from the maximum and minimum feasible hole spacing. At the highest reinforcement content (13% vol.), a centre-to-centre distance of 4 mm produced a 2 mm edge-to-edge spacing, which was the minimum practical limit; further reduction would lead to groove formation and particle clustering [1]. At the lowest level (7% vol.), the centre-to-centre distance was 8 mm, resulting in a 6 mm edge-to-edge spacing; larger spacing would lead to poor mixing and incomplete consolidation. The intermediate fraction (10% vol.) was selected to study reinforcement effects systematically. For the present work, two specific parameter sets were adopted from earlier L₉ DOE trials [4,6], namely S1 (500–60–13) and S2 (1500–60–10), based on the highest and lowest microhardness outcomes. S1 represents baseline processing conditions, while S2 reflects an extreme case for comparison. Since this is a mono-composite system, hybrid reinforcement ratios were not considered. The shoulder to pin diameter (D/d) ratio was kept above 3 to obtain defect-free surface composites, per published guidelines [61]. Before clamping, the BM was cleaned thoroughly with acetone to remove contaminants. Temperature measurements during processing were recorded using a Ti32 thermal camera, selected based on prior studies [62,63,64,65]. The Ti32 provides a wide measurement range (–20 °C to +600 °C), a precision of ±2 °C, and eliminates the limitations associated with thermocouples [66]. Thermal images were acquired during plunging, dwelling, and traversing, with temperatures extracted at the shoulder edge and at 15 mm and 20 mm from the plunging location using SmartView Classic 4.4 software. The camera was placed about 100 cm away from the tool and aligned with the processing direction. The material was processed at a plunge speed of 40 mm/min and a tool tilt angle of 2.5°, as recommended by previous studies [42]. To maximize simulation runtime without affecting the accuracy of the results, the backing and BM geometries were shortened compared to the real experiment.

2.2. Meshfree Technique: Smoothed Particle Hydrodynamics (SPH)

The concept of Smoothed Particle Hydrodynamics (SPH) was put forward in 1977 by Gingold, Monaghan, and Lucy, mainly to study astrophysical systems [33]. Over the years, its scope expanded to high-velocity impact studies, volcanic eruptions, multi-phase flows, and large-scale water dynamics [67,68,69]. The absence of a predefined mesh makes SPH different from grid-based numerical schemes. Instead, the method tracks the motion of individual particles, which naturally follows a Lagrangian description. This approach is particularly advantageous in modelling complex processes like FSW/P, where material deformation and boundary conditions are difficult to capture with fixed grids. The formulation of SPH begins by rewriting the governing partial differential equations in an integral form. These integrals are then approximated through interpolation based on a set of discrete particles. Using this framework, any scalar field can be estimated at a given location, as outlined in Equation (1). The kernel function defines how neighbouring particles influence this interpolation, while the smoothing length controls the extent of their effect. $W\left(x-y,h\right)$ serves as kernel function acting as a weighting tool that links a point of evaluation $x$ with its neighbouring point $y$. The parameter $h$, known as the smoothing length, determines how far this influence extends. For the kernel to be mathematically valid, it should act like a Dirac delta function in the limit and also satisfy several conditions, such as being positive, normalized to unity, smooth, and having compact support.

$$\varphi f\left(x\right)={\int }_{\Omega }f\left(y\right)W\left(x-y,h\right)dy$$

(1)

Instead of using a mesh, SPH represents the domain through particles situated at $x_i$. Every particle is assigned values such as density, velocity, stress, or temperature, so together they mimic the material’s properties. These particles serve as the basis for interpolation during computation. For a particle with mass $m_i$ and density ${\rho }_i$, the corresponding smoothed function and derivative expressions are given by:

$${\varphi }_{s}f\left(x\right)=\sum _{i=1,n}{\displaystyle \frac{m_i}{{\rho }_i}}f\left(x_i\right)W\left(x-y,h\right)$$

(2)

$$\nabla f\left(x\right)=\sum _{i=1,n}{\displaystyle \frac{m_i}{{\rho }_i}}f\left(x_i\right)\nabla W\left(x-y,h\right)$$

(3)

The selected kernel approximates the Gaussian kernel using cubic splines [70]. Figure 3 presents a visual insight into this interpolation technique.

$$\mathrm{for} r\le h; W\left(r,h\right)={\displaystyle \frac{3}{2\pi h^3}}\left[{\displaystyle \frac{2}{3}}-{\left({\displaystyle \frac{r}{h}}\right)}^2+{\left({\displaystyle \frac{r}{h}}\right)}^3\right]$$

(4)

$$\mathrm{for} h\le r\le 2h; W\left(r,h\right)={\displaystyle \frac{1}{4\pi h^3}}{\left(2-{\displaystyle \frac{r}{h}}\right)}^3$$

(5)

$$\mathrm{for} 2h\le r; W\left(r,h\right)=0$$

(6)

Equations (7)–(9) express the governing principles for conserving mass, moment, and energy in SPH form concerning solid deformation [71].

$${\displaystyle \frac{d{\rho }_i}{dt}}={\rho }_i\sum _{j=1}^{N_i}{\displaystyle \frac{m_j}{{\rho }_j}}\left(v_i-v_j\right){\displaystyle \frac{\partial W_{ij}}{\partial x_i}}$$

(7)

$${\displaystyle \frac{d{v}_i}{dt}}=\sum _{j=1}^{N_i}{m}_j\left({\displaystyle \frac{P_i}{{\rho }_i^2}}+{\displaystyle \frac{P_j}{{\rho }_j^2}}+{\varphi }_{ij}\right){\displaystyle \frac{\partial W_{ij}}{\partial x_i}}$$

(8)

$${\displaystyle \frac{d{T}_i}{dt}}={\displaystyle \frac{1}{{\rho }_i{C}_{pi}}}\left[\sum _{j=1}^{N_i}{\displaystyle \frac{m_j}{{\rho }_j}}{\displaystyle \frac{4k_i{k}_j}{k_i+k_j}}{\displaystyle \frac{{(T}_i-T_j)}{{\left|x_i\right|}^2}}{x}_{ij}{\displaystyle \frac{\partial W_{ij}}{\partial x_i}}+{\dot{q}}_i\right]$$

(9)

The densities of particles $i$ and $j$ are represented by ${\rho }_i$, and ${\rho }_j$, respectively; the mass of particle $j$ is indicated by $m_j$; and the relative velocity between particles $i$ and $j$ is shown by $v_i-v_j$. $P_i$ and $P_j$ represent the pressures of particles $i$ and $j$, respectively, while $W_{ij}$ describes the smoothing kernel for point $i$ at point $j$. The artificial viscosity term that characterizes the viscosity effects between particles $i$ and $j$ is captured by ${\varphi }_{ij}$. Furthermore, particle $i$’s specific heat capacity is denoted by $C_{pi}$, while particles $i$ and $j$’s respective thermal conductivities are denoted by $k_i$ and $k_j$. The temperature differential between particles $i$ and $j$ is denoted by $T_i-T_j$, and the internal heat production rate per unit volume at particle $i$’s location is denoted by ${\dot{q}}_i$. SPH requires much more processing power than standard mesh-based techniques since it searches for the kernel function and finds the node-to-surface contact by looking for neighboring particles.

SPH methodology is best suited for several situations where the precision and efficiency of the Finite Element approach are lost in both the ALE and Lagrangian formulations. Numerous procedures may take advantage of the SPH technique that the RADIOSS code implements. It is possible to interact between two discretized objects: one using particles, the other using finite elements. The SPH formulation supports only 3D analysis. It is recommended that particles be constructed in Altair-RADIOSS using a face-centred cubic or cubic net packing. Figure 4 shows the simple cubic net packing utilized in the current study. The relationship between the particle mass ($m_p$), the material density ($\rho$), and the net size ($c$) may be found in Equation (10).

$$m_p=c^3.\rho$$

(10)

2.3. Numerical Model for AZ91 Surface Composites

A numerical model for AZ91 surface composites reinforced with SiC particles has been developed, marking a substantial advancement in numerical analysis within the field of FSP. Leveraging the unique capabilities of SPH, this study effectively captures the complex interactions within the composite materials during FSP, specifically examining reinforcement effects on temperature, material flow in both (AZ91)SPH and (SiC)SPH elements, and SZ characteristics. Altair-RADIOSS, known for handling high plastic deformation and impact analysis, is employed to address the non-linear thermo-mechanical challenges presented by FSP, making it an ideal tool for simulating these complex interactions.

2.3.1. Geometric Model

CATIA V5 R21 was utilized to create the geometries of the tool, workpiece, backing plate, and reinforcements, integrating them into an assembly. These assembled components were imported into Altair RADIOSS in *.stp file format. In line with the experimental setup, the hole deposition technique was applied in numerical analysis. The holes, measuring 2 mm in diameter and 3 mm in depth, were spaced variably based on the volume percentage. Reinforcement particles were assumed to be cylindrical, and these holes were filled to ensure continuity for SPH particle application. The complex interactions between (AZ91)SPH and (SiC)SPH notably increased computational demands and costs. Pre-optimized parameters were employed from experimentation to develop the numerical model, selecting higher and lower surface property parameters. These parameters are included as TRS-TTS-%vol. sequence as 500-60-13 (S1) and 1500-60-10 (S2) with a constant plunging speed of 40 mm/min. The holes were inter-spaced at 4 mm and 5.5 mm, corresponding to 13% and 10% volume, respectively. The model was run to a 20 mm traversing distance to streamline the process; it encompasses three and four holes for two respective models, aiming to extract and validate results against experimental data. Both models with dimensions are highlighted in Figure 5. The AZ91/SiC surface composite models in Figure 6 illustrate the incorporation of tool tilt, enabling comprehensive visualization.

2.3.2. Particle Independence Study

Selecting an appropriate SPH particle configuration is crucial for achieving numerical accuracy while balancing the limitations of available computational resources. In SPH, particle density is similar to mesh resolution in traditional grid-based methods, affecting simulation accuracy and computational cost. Higher particle density increases the accuracy of the simulation but also significantly raises the computational cost and simulation time. On the other hand, lower particle density reduces simulation costs but risks sacrificing result accuracy. A particle independence study uses four distinct particle configurations to ensure optimal balance, as shown in Figure 7a–d. These configurations vary in particle pitch, meaning the spacing between individual SPH particles, and aim to identify the particle configuration that meets accuracy requirements without tremendous computational resources.

Four different pitch sizes and their combinations were chosen to adjust particle coverage and facilitate interaction between the tool, supporting plate, and the upper and lower SPH particle layers, ensuring accurate tracking of material movement. Similarly, the reinforcement particles were arranged cylindrically within the holes, with pitch sizes adjusted to align with the upper surface of BM and penetrate the full depth of the hole.

Table 3. SPH particles count from coarse (Type 1) to fine (Type 4).

Configuration Type	Base Material Pitch (mm)	Reinforcement Pitch (mm)	Particle Count (Nos.)
1	1.05	0.58	47,520
2	0.975	0.53	55,212
3	0.901	0.495	75,302
4	0.81	0.43	92,841

presents the particle configurations used in the SPH simulation, ranging from coarse (Type 1) to fine (Type 4) particle resolutions. Each configuration shows base material as AZ91 and reinforcement as SiC pitches, and the corresponding total particle counts required for each setup. A finer particle distribution increases the particle count and computational cost, requiring a careful balance between achieving higher accuracy and managing resource limitations.

The particle independence study was conducted during the traversing phase, focusing on the advancing side temperature due to its representation of steady-state conditions with significant material flow and deformation. This phase experiences higher friction and shear forces, leading to pronounced temperature gradients, making it ideal for analyzing the impact of varying particle counts. In contrast, other phases are less suitable; plunging is transient with the restricted flow and unstable temperatures, while dwelling with heat build-up lacks dynamic interactions. The temperature variation analysis during the traversing phase with different particle counts is shown in Figure 8.

The temperature rises as the particle count increases due to enhanced heat transfer efficiency and better representation of thermal gradients with finer resolution. This improved interaction among closely spaced particles facilitates more accurate thermal exchange. For instance, 47,520 particles yield 525.7 K, while 92,841 particles result in 589.8 K, demonstrating that higher particle density captures the thermal dynamics of the process more effectively. Results revealed that particle configurations 3 and 4 produced similar temperature values, suggesting convergence in accuracy. In contrast, configurations 1 and 2 displayed more significant deviations, indicating lower accuracy. Ultimately, particle configuration 3, with an SPH particle count of approximately 75,302 particles, was chosen over configuration 4. This selection balances between maintaining simulation accuracy and optimizing computational efficiency, allowing high-quality results without excessive resource demands. From the particle independence study, the same pitch size for the workpiece and reinforcement was implemented for the S1 model, resulting in a total particle count of 75,352. The meshing scheme for both S1 and S2 models during the FSP process is outlined in detail in Figure 9. Further, the tool and the backing have meshed using approximately 3192 tetra components and 2700 quad elements, employing a rigid body model.

2.3.3. Material Model and Properties

In RADIOSS, the material laws are developed to be applicable for several physical scenarios, including isotropic elasticity, isotropic elasto-plasticity, composites and anisotropy, viscous behaviour, hydrodynamics, and explosives. To accurately depict the material characteristics in FSP, a generative law that appropriately considers the interaction between flow-generated stress, temperature, strain rate, and plastic strain must be chosen. The Johnson-Cook model is commonly employed in solid-state processes due to its integrated factors such as temperature, strain, and strain rate [15,72,73]. Equation (11) defines the Johnson-Cook flow stress model.

$$\sigma =\left(A+B{\epsilon }^n\right)\left[1+Cln\left(1+{\displaystyle \frac{\dot{\epsilon }}{\dot{{\epsilon }_0}}}\right)\right]\left(1-\widehat{T}\right)$$

(11)

$$\because \widehat{T}={\left[{\displaystyle \frac{T-T_{room}}{T_{melt}-T_{room}}}\right]}^m$$

where $\sigma$ represents the material flow stress, $\epsilon$ is the equivalent plastic strain, $\dot{\epsilon }$ and $\dot{{\epsilon }_0}$ are plastic and reference strain rates, $T_{melt}$ the melting, and $T_{room}$ the ambient reference temperature. The quasi-static yield strength of material $A$, the strain hardening constant $B$, the strain hardening coefficient $n$, and the thermal softening coefficient $m$ are the material constants derived at the reference strain rate. For the strain-rate dependence, $C$ stands for the strengthening coefficient. In this study, the tool and backing are assumed to remain non-deformable and isotropic, following the material law referred to as MAT/LAW1, whereas the BM is a homogeneous and isotropic model represented by an elastoplastic material defined by MAT/LAW4. The model assumes a 90% heat generation efficiency from strain [73]. The material properties for AZ91, H13 tool steel, and SiC nano-powder are outlined in

Table 4. Material properties for AZ9, H13 tool steel, and SiC nano-powder [15,46,73,75,76,77,78,79,80,81,82,83].

Material Properties	AZ91	H13	SiC
Density $\rho$ (Tonne/mm3)	1.81 × 10−9	7.8 × 10−9	3.1 × 10−9
Young’s modulus E (MPa)	46,000	210,000	438,000
Poisson’s ratio ($\mu$)	0.33	0.3	0.15
Specific heat per unit volume (N/mm2. K)	1.9	3.56	2.08
Reference temperature $T_{room}$ (K)	298	298	298
Melting temperature $T_{melt}$ (K)	803	1700	2970
Thermal Conductivity (W/mK)	72.7	24.5	360

from the previous study [46]. MAT/LAW4 was also used to specify the reinforcement in the same way as the workpiece. The JC coefficient values and specific material characteristics selected for AZ91 and SiC are included in

Table 5. Johnson-Cook constants for AZ91 and SiC [46,74].

Parameters	Initial Yield Stress [MPa]	Hardening Modulus [MPa]	Coefficient Depending on the Strain Rate	Work-Hardening Exponent	Thermal Softening Coefficient
Symbolized	$A$	$B$	$C$	$n$	$m$
AZ91	164	343	0.021	0.283	1.768
SiC	200	400	0.01	0.2	0.3

[46,74].

2.3.4. Contact, Boundary Conditions, and Friction Model

During the process, both the leading and trailing edges of the tool need to be fully engaged with the workpiece to achieve the desired impact of heat from the friction and plastic deformation. Ensuring this full engagement facilitates the effective control of the process along the global vertical axis by accurately calculating and accounting for movements in the Z direction. This precision enables the tool to maintain consistent continuous contact with the workpiece. These hypotheses were provided in this current study to describe the boundary condition of the complex link at the tilt of the tool and workpiece interface. A master node is a central control entity that oversees and manages the activities of other nodes within a network or system. In the context of the tool and backing functioning as rigid bodies, their respective master nodes facilitate the application of motion and constraints. An interface contact of type 7 (node-to-surface) was established between the tool’s main segment and the workpiece’s secondary nodes in Altair-RADIOSS. This interface type facilitates the consideration of heat generation resulting from friction. Figure 10 illustrates the implemented boundary conditions and contact types. The global axis system serves as the reference point for all IMPDISP boundary conditions, including those for tool plunging in the Z direction and traverse movement in the X direction.

Friction between the rotating tool and the workpiece, along with the plastic deformation of the workpiece, stands as the main contributor to heat generation during FSP. Coulomb’s law of friction governs the frictional contact between the tool and the workpiece; thus, Equation (12) defines the amount of force generated by friction.

$$F_{frict}=\mu F_n$$

(12)

Here, $F_{frict}$ indicates the frictional shear stress, $F_n$ is the contact pressure at the tool-workpiece interface, and the COF as $\mu$. Approximately 10% of the total heat generated in FSP can be attributed to plastic deformation, while the remaining heat is primarily due to frictional effects [84,85,86].

To evaluate the effect of a constant COF on temperature, values reported in the literature were considered to examine their applicability to SPH, as they have been primarily used in grid-based approaches. Accordingly, constant COF values of 0.25, 0.3, and 0.4 from the literature [15,45,77] were employed to assess their suitability for SPH. However, it was observed that these values deviated significantly from the predicted temperatures for the previously optimized process parameters (1000 rpm and 40 mm plunging speed with zero defects) [42] when compared with the experimental measurements in FSP. Typically, during FSP, the process temperatures remain between 50% and 90% of the material’s melting point [87]. Applying consistent COF values for SPH may lead to notable differences in temperature measurements. Figure 11 clearly illustrates that the simulated values exceed the prescribed temperature range. The divergence was expected to occur in close proximity to the experimental temperature of around 500.5 K, as recorded on the AS near the tool shoulder edge.

Furthermore, materials often exhibit lower friction at higher temperatures due to thermal softening. However, constant COF leads to inaccuracies, as it should decrease after a specific temperature range [77]. A temperature-dependent friction coefficient was also recommended to counter tool slippage [88,89,90]. Therefore, a Coulomb COF dependent on the interface temperature (T_int) was utilized and detailed in

Table 6. Temperature-dependent COF with interface temperature.

Tint (K)	273	285.5	504	521	530	>803
($\mu$)	0.45	0.35	0.25	0.001	0.0001	0

. The interface temperature refers to the average of temperatures observed on the main (T_m) and secondary sides (T_s) of the interface.

Figure 12 depicts the integration of values from Table 6, emphasizing the agreement between the experimental temperature values during the plunging stage and those acquired from the simulation, with just a 1.78% difference. The phase diagram of the Mg-Al binary system supports these values, showing that strengthening precipitates dissolve as the COF thermally softens the material, facilitating more effortless material flow.

The friction model is also applied for tool-reinforcement contact to ensure that the tool accommodates the newly introduced reinforcement within the workpiece. Thus, a Type 7 contact was specifically implemented between the tool and SiC particles, as illustrated in Figure 10. In the plunging phase of AZ91 surface composites, the tool operates until reaching the required depth within a duration of 4.95 s. The subsequent dwelling phase lasts 5 s. Following this is the traversing step, lasting for approximately 20 s out of a total process duration of 30 s. The tool advances in the X-direction for 20 mm at a specified speed during this time.

2.4. High-Performance Computing (HPC)

Compared to conventional mesh-based techniques, SPH requires much more processing power since it must find the kernel function, explore nearby particles, and determine node-to-surface contact. The time step is crucial in reducing the computational time without compromising accuracy. In this case, a time step of 5 × 10⁻⁷ s was utilized. HPC is employed to solve the models because of the longer FSP process time with the SPH. HPC systems are designed to perform parallel processing, allowing them to tackle large-scale calculations and simulations much faster than traditional computers. In the domain of HPC, solutions for extensive Altair-RADIOSS problems encompass various parallelization avenues: Serial processing, SMP, MPI, and Hybrid MPI. Serial execution refers to running a program or simulation sequentially on a single computing core. In the absence of parallelization, computations proceed one after the other. This approach suits simpler simulations and tasks that do not demand extensive computational resources. SMP is a parallel computing architecture where multiple processors coordinate on a singular task by accessing a shared memory pool [91,92]. It illustrates a scenario where a program or simulation is optimized to utilize multiple cores within a single computing node. MPI is a widely adopted framework for enabling parallelization through shared memory, facilitating information sharing and message transmission among multiple nodes in clusters or distributed computing setups. When pairing MPI with another method like SMP or GPU computing for parallelization, it is referred to as hybrid MPI [93]. This technique, which divides simulations into smaller subdomains using MPI, is often used to speed up simulations that need the simultaneous usage of MPI and SMP at a larger scale. These are then distributed across multiple computers. Within each node, SMP techniques parallelize computations across all available CPU cores. This hybrid strategy harnesses the speed advantages of both distributed and shared-memory parallelism, utilized extensively to solve all numerical models. Every numerical model was solved using hybrid MPI. Models were processed using a single node equipped with 48 cores and one thread, with 90 GB of RAM. Depending on the available wall time budget, a setup with 96 cores, two threads, and 160 GB of RAM could also be utilized.

2.5. Assumptions

The physical processes involved in the FSP process are complex to model. As a result, the model has been given several simplifying assumptions.

➢

The initial temperatures assumed for the tool, workpiece, backing, and confined reinforcement within the holes are 298K for all simulations.

➢

The tool and backing are assumed to be rigid bodies, while the workpiece and reinforcement are considered homogeneous, isotropic, and elastoplastic.

➢

It is assumed that uniform boundary conditions persist consistently across the processed part in all simulations. No heat is transferred into the workpiece if local temperatures reach the melting point.

➢

Reinforcement particles are assumed to be cylindrical and packed into the hole to maintain a continuum and facilitate the application of SPH particles.

➢

Assuming capping during the experiment, the temperature-dependent COF used for the workpiece is expected to extend to the tool’s interaction with the reinforcement, as it covers the holes with the base material.

3. Results and Discussion

The distribution of reinforcements during FSP has not been successfully interpreted using experimental or conventional meshing techniques. The ability of SPH to handle complex interactions and dynamic interfaces makes it a prominent tool for studying FSP phenomena in MMCs. The mesh-free-based SPH numerical model is developed for AZ91 surface composites, including plunging, dwelling, and traversing. SPH’s node tracking capability has proven effective in predicting reinforcement dispersion, the impact of its volume content on temperature and material flow distribution, and in comparing the predicted shape of the friction stir-processed zone. During the experiment, the ambient temperature was maintained at 298 K, and the same temperature was subsequently employed as the reference temperature for the numerical analysis. The heat generated during the process is attributed to the friction at the edges and plastic deformation. The temperature distribution within and around the SZ directly influences the microstructure of the processed material, affecting grain size, particle distribution, grain boundary character, precipitate coarsening, dissolution, and the resultant properties. Therefore, obtaining information about the temperature distribution in FSP is crucial. The unique characteristics of SPH are applied to examine the temperature variations within the composite material throughout three phases. SPH provides excellent insights into the effect of reinforcement volume and process parameters on temperature profiles by capturing the dynamic interaction between the tool and reinforcement particles. The temperature distribution history for S1 and S2 was numerically analyzed, as shown in Figure 13 and Figure 14. The analysis was further validated through experimentally recorded temperatures, as shown in Figure 15 and Figure 16.

During the plunging phase of the FSP, the tool penetrates the BM with a plunge rate of 40 mm/min after starting to rotate. The whole plunging movement is predicted to take 4.95 sec, and once the desired depth is reached, the shoulder almost contacts the top surface of the metal. Although the shoulder is near the material, its contact area is less than the dwelling and traversing phases. Maintaining restricted contact minimizes friction and heat production, leading to the lowest temperatures recorded during FSP for S1 and S2 composites. Figure 13a and Figure 14a show the temperature distribution at the nodes acquired from the simulation at the end of the 4.95 sec plunging phase. The simulated temperatures at nodes 10 mm from the centre of the SZ were 443.3 K and 550.8 K on the AS for S1 and S2, respectively. The considerable temperature difference is due to variations in process parameters: S1 runs at 500 rpm TRS and 60 mm/min TTS with 13 vol%, while S2 operates at 1500 rpm TRS and 60 mm/min TTS with 10 vol% of SiC.

Four holes were assumed and analyzed for S1 due to the higher SiC vol% of 13%, while three holes were analyzed for S2 due to the 10% SiC volume, which was covered during the traversing of the 20 mm tool from the plunging. The temperature distribution solely on the reinforcement for both the S1 and S2 runs during the plunging stage is depicted in the same figures. For S2, SiC in all three holes was observed to be affected due to higher TRS and frictional temperatures from the tool. In contrast, in S1, the fourth hole of SiC was noticed to remain unaffected due to the lower TRS and its distance from the tool pin. The closest reinforcement material hole for S1 and S2 was observed to be more affected than other respective holes, even without the contribution of shoulder heat during plunging. This is considered the sole effect of the tool pin heat on the reinforcement material during the plunging stage. However, the most affected first-hole reinforcement is observed in the case of S2. Moreover, the larger temperature “pool” observed in S2 is attributed to the higher TRS. A faster rotating tool stirs the material more vigorously during plunging, potentially distributing the heat over a wider zone than that for S1. Irrespective of the SiC vol%, these findings indicate that S2 generates more heat during the plunging phase than S1.

Following the initial penetration achieved during plunging, the FSP process transitions to the dwelling phase. In contrast to the restricted contact area in the plunging stage between the tool shoulder and the BM, the dwelling stage is characterized by complete contact due to a controlled pause of the tool at a certain depth. This results in greater frictional forces between the tool and the material. As such, the dwelling stage has higher temperatures during the process for both S1 and S2 composites, as illustrated in Figure 13b and Figure 14b. The simulated temperatures at nodes 10 mm from the centre of the SZ for S1 and S2 were 495.7 K and 624.9 K, respectively. Even though the two composites had a consistent TTS of 60 mm/min in both scenarios, there was a significant temperature difference. Notably, while dwelling, the TRS is regarded as the most significant element owing to the absence of lateral movement at this stage. The difference in TRS between S1 (500 rpm) and S2 (1500 rpm) leads to the generation of a bigger and hotter temperature pool in S2 that was extended to the side sections of the BM towards the trailing edge due to the tool tilt for the same dwelling duration (5 s). This greater rotational energy corresponds to a more pronounced frictional engagement between the tool and the material at 1500 rpm, resulting in the observed temperature rise.

The dwelling temperature distribution, concentrating primarily on the S1 and S2 reinforcement, is presented in Figure 13b and Figure 14b. The dwelling causes the temperature in S1 to approach the fourth hole, which was not detected during the plunging phase. Similarly, with S2, the greater TRS causes the peak temperatures to be attained at the first two holes. Despite more reinforcement in S1 than S2, this tends to reduce the peak temperature during FSP owing to several factors. The reinforcement particles replace a specific volume of the metallic matrix to deposit nearly comparable SiC volume. Therefore, the available matrix material for plasticization is limited, and the SiC particles do not undergo plasticization during FSP but instead just flow together with the plasticized matrix material. Frictional heating and plasticization develop heat together, but the heat developed during plasticization is decreased by the presence of reinforcement and the unavailability of the matrix. A higher vol% of SiC was expected to enhance heat transfer within the SZ and create more effective heat distribution. However, the peak temperature reached in S1 is lower due to the lower TRS. Nevertheless, elevated temperatures are observed during dwelling compared to the plunging phase due to increased heat accumulation by non-traversing of the tool, allowing heat to accumulate more efficiently at a specific location.

After the dwelling stage, the FSP process enters the traversing stage, and the tool continues to rotate but travels laterally across the BM surface. Unlike dwelling with its complete tool contact, the traversing stage exhibits a continuously changing contact area between the tool and the material. Temperature distribution during traversing is illustrated in Figure 13c,d for S1 and Figure 14c,d for S2, showing temperature profiles at 15 mm and 20 mm of tool travel from the plunging stage. As discussed, the TRS is the function of frictional heat between the tool and the BM, which remains relevant during traversing. The TTS is consistent for S1 and S2; the higher TRS of 1500 rpm used in S2 led to a more pronounced frictional interaction than the TRS of 500 rpm in S1. Thus, in S1 at 10 mm from the SZ, the nodal temperatures at 15 mm from the plunging point are 467.6 K on the AS and 456.6 K on the RS. As the tool moves forward and reaches 20 mm from the plunging point, the temperatures are 454.7 K on AS and 449.5 K on RS. Similarly, for S2, the nodal temperatures at 15 mm from the plunging point are 584.5 K on AS and 582.4 K on RS, and at 20 mm further from the plunging point, the temperatures are 574.7 K on AS and 570.5 K on RS.

Material points closer to the leading edge in the direction of tool motion, which experiences a shorter period under the region of high temperature because of the tool’s forward movement. Conversely, material at the trailing edge benefits from the tool tilt, basically being “scooped” and kept under the heat for a prolonged period. This difference in residence time translates to a temperature gradient. Thus, during traversing, the rear end of the tool shows a broader temperature pool than the leading edge, even as the tool moves ahead as a heat source. Figure 13c,d and Figure 14c,d presumably show greater temperatures near the trailing edge and a steady decline towards the leading edge. In other words, dynamic thermal conditions evolve inside the SZ as the tool advances because previously stirred material leaves the high-temperature zone, and new material comes into contact with heat for the first time.

The tool and reinforcement temperature interaction for S1 and S2 are highlighted in the same figure. It can be interpreted that at 500 rpm in S1 with a higher %vol of SiC, lumps are formed on the AS and the bottom part of the tool pin due to less intense plasticization, as shown in Figure 13c. As the tool advances, the material in front of the tool is deposited at the back and left behind the rear end, causing the temperature of the reinforcement material to drop as the tool moves forward, as seen in Figure 13d. In contrast, for S2, higher plasticization at 1500 rpm and the lower %vol of SiC particles result in a leaner reinforcement structure, as shown in Figure 14c. As the tool moves forward, the temperature at the rear side reinforcements remains uniform, reflecting this consistency in Figure 14d.

Figure 15 and Figure 16 illustrates the recorded experimental temperatures throughout the plunging, dwelling, and traversing phases during the FSP of the AZ91/SiC composites for S1 and S2, respectively. It can be observed that there is minimal temperature difference between the AS and RS during the plunging and dwelling stages for both S1 and S2 composites, with a temperature variation of no more than 2.2 K within each composite. Although the tool does not divide the plate into AS and RS portions during the plunging and dwelling phases, this division occurs when the tool advances in the processing direction. However, these designations are used for consistency.

During the plunging phase, the tool uniformly distributes heat along the sides. In a dwelling, the material remains in one place, resulting in nearly identical temperatures on both sides as the material continuously rotates. The temperatures at the end of the dwelling phase for S1 and S2 composites at point 2 show the highest temperatures, reaching a maximum of 488.5 K in S1 and 612.2 K in S2. As the tool reaches its midpoint at 40 mm of travel, temperatures on both the AS and RS are nearly identical, approximately 310.8 K and 309 K in S1, measured at 80 mm of tool travel. In S2, temperatures were around 319.5 K and 318.6 K under similar conditions. The lower temperatures at point 5 result from the tool acting as the primary heat source distant from the measurement point. As the distance from the processed zone increases, the temperature naturally decreases.

The accuracy of SPH composite models for temperature prediction was evaluated by comparing experimental data with model simulations at critical points for S1 and S2, as shown in Figure 17 and Figure 18, respectively. These points corresponded to the end of plunging and dwelling, and specific distances traversed along the FSPed composites along AS and RS. The difference between the measured and predicted temperatures served as the error metric. It was found that there was good agreement between the simulated and experimental temperatures in the S1 and S2 composite models. The closest agreement for S1 had a temperature difference of around 5.5 K at the plunging, with a maximum difference of 8.9 K on AS at a traversing distance of 15 mm. This resulted in an inaccuracy below 2%. With an inaccuracy of less than 3%, the closest agreement for S2 was around 6 K at plunging, and the largest discrepancy was 15 K on the RS when the tool travelled 15 mm. These minor discrepancies highlight the SPH model’s ability to accurately predict temperature fields, especially at the surface level where the measurements were taken. Furthermore, the performance criteria based on temperature differences were calculated for S1 and S2, resulting in values of 1.43% and 1.86%, respectively. These minimal values further reinforce the model’s precision in forecasting temperature profiles.

Predicting material flow is essential for understanding material dynamics during FSP [94], as it aids in anticipating microstructural transformations. Additionally, it helps predict the shape and size of the SZ, thereby enhancing and controlling material flow. SPH numerical analysis has successfully predicted temperature profiles in this study. However, a promising avenue lies in incorporating reinforcement material flow. Optimizing the surface characteristics of MMCs requires a thorough understanding of the movement and distribution of reinforcing particles during FSP. Thus, this section aims to provide a detailed and accurate representation of the reinforcement distribution and interaction within the matrix, offering new insights into the processing and performance of MMCs. Figure 19 and Figure 22 depict the initial positions of reinforcement particles (SiC) represented by SPH nodes in S1 and S2 composites, respectively. Isometric and side views are shown in the subfigures. As predicted, due to the higher volume fraction (13% compared to 10% in S2), S1 has more SiC particles distributed across four holes. During the plunging and dwelling stages, the SiC particles remain stationary and away from the tool pin. Therefore, the only influence on the reinforcement during these stages is the thermal effect from the shoulder-BM interaction that affects the temperature of the SiC particles according to the process parameters, as discussed previously. Thus, the tool pin only directly interacts with the reinforcements during the traversing phase. Figure 20a,b and Figure 23a,b illustrate the displacement of the SPH nodes representing these particles at two distinct halt positions: 15 mm and 20 mm away from the plunging point for S1 and S2, respectively.

Following plunging and dwelling, the tool first traverses the processed zone at 15 mm from the plunging, as shown in Figure 20a. The specific tool components interacting with the SiC particles depend on their location within each hole. When the tool comes in contact with the first SiC shole, the shoulder most significantly displaces the SiC particles closest to the top surface due to direct contact. The tool shoulder pushes a few nodes downward, such as nodes 82,771, 82,758, and 82,764, while a couple of nodes move upward, such as 82,769, 82,748, 82,755, and 82,753. Specific reinforcement nodes, like 82,761, 82,760, 82,768, 82,757, 82,762, and 82,759, are restricted in their vertical movement due to compaction from the tool shoulder, causing them to be displaced laterally and move along with the shoulder edge.

Reinforcement SPH nodes located deeper within the hole experience a combined influence from the pin and shoulder of the tool [95]. The influence of the shoulder weakens with increasing depth. The pin exerts an advancing force, pushing them forward, and thus nodes 82,741, 82,746, 82,720, 82,738, and 82,729 are seen to move from their original position towards the traversing X direction. Additionally, the poor tool’s rotation with higher SiC %vol, as a greater number of reinforcement nodes, causes them to be displaced slightly towards the RS. More nodes are found sideways in the AS through the lateral side of the tool pin, as observed from nodes 82,763, 82,761, 82,743, 82,770, 82,748, and 82,750. Nodes at the bottom of the hole experience minimal movement during the initial interaction at 15 mm due to their deeper location and minimal interaction with the tool at this stage, which can be observed through nodes 82,710, 87,709, 82,711, 82,706, and 82,708.

Generally, the reinforcement nodes closer to the AS, where the pin makes first contact, experience a more decisive influence than those on the RS. However, the lower TRS and higher reinforcement %vol make it difficult to deliver sufficient force, making it unable to scoop the particles from AS to RS. Hence, most nodes 82,747, 82,712, 82,754, 82,740, 82,751, and 82,749 remain largely undisturbed. In experimentation, the accumulation of reinforcement was observed due to this phenomenon. Similarly, there is still an uneven distribution for the second and third holes due to the process parameter combination. The majority of nodes, such as 82,798, 82,821, 82,813, 82,808, and 82,811 from the second hole and 82,887, 82,899, 82,889, 82,892, and 82,851 from the third hole, are found to accumulate at the AS. It can also be observed that the first hole reinforcement is the only set of nodes found mostly at the rear bottom side of the tool pin and the upper side near the beneath of the tool shoulder. Compared to the subsequent second and third holes, the reinforcement nodes from the first hole were observed to displace more on the RS, such as 82,755, 82,769, and 82,742. However, in comparison to its respective AS, it is lower. More nodes from this hole on the RS are due to the combined effect of the tool shoulder and pin from the plunging and dwelling. As the tool moved 15 mm from the starting point, minimal effect was observed on the fourth hole of the reinforcement, as the tool did not fully interact with the fourth hole. Thus, as the tool progresses to 20 mm, it achieves deeper interaction with the reinforcement, as seen in Figure 20b. The remaining SPH nodes of SiC particles in the fourth hole, which were not affected at 15 mm, particularly those in the lateral and lower part of the tool pin, now experience significant movement due to the advancing and rotational stirring forces exerted by the pin with further movement.

At this position of the tool, a few nodes, such as 82,823, 82,819, and 82,836 from the second hole and 82,878 and 82,902 from the third hole, are seen to be pulled out farther and deposited on the RS. It supports the expectation that if the reinforcement volume is kept lower and the TRS is increased for the same TTS, the reinforcement distribution in the surface composites can be improved. Even at this stage, too many particle lumps are seen to form groups along the edge of the tool pin, indicating agglomeration. This phenomenon was observed for all four holes, forming an agglomerated zone. Based on this prediction, if there is further movement and a fifth hole, the same phenomenon should appear due to the lower TRS, which is inadequate to cause sufficient reinforcement particle movement from AS to RS.

Figure 21 depicts a non-uniform distribution of SiC reinforcement particles across the processed zone in S1. The AS exhibits a significantly higher concentration due to two key factors. A lower TRS reduces frictional heating and stirring action, limiting particle movement, particularly towards the RS. A higher SiC volume fraction also increases material viscosity, further hindering effective particle transport. The presence of agglomeration zones, confirmed by the magnified view showing entangled particles, suggests uneven reinforcement distribution at the tool pin base and shoulder edge Figure 22. The central SZ exhibits a significant void lacking with only one node (82,968) present from the fourth hole due to the insufficient stirring force generated by the low TRS, causing most SPH nodes of reinforcements to settle and accumulate at the bottom. The limited upward movement of SPH nodes results in seemingly separated and unconnected nodes at the surface layer, as evidenced by the presence of only three nodes, 82,903, 82,959, and 82,894, at the top. These observations highlight the need for optimizing processing parameters, such as increasing TRS or reducing SiC volume fraction, to achieve a more uniform and well-distributed reinforcement within the processed zone.

Figure 21. Cross-sectional final side view for S1.

Figure 21. Cross-sectional final side view for S1.

Figure 22. Initial positions of reinforcement’s SPH nodes and tool in S2 (a) Iso view and (b) Left-hand side view.

Figure 22. Initial positions of reinforcement’s SPH nodes and tool in S2 (a) Iso view and (b) Left-hand side view.

Figure 23 shows the traversing of the tool over the reinforcement SPH nodes for S2 processing parameters, characterized by a significantly higher TRS and a reduced SiC volume fraction compared to S1. When the tool traverses 15 mm from the starting position, as depicted in Figure 23a, the higher rotating tool moves over the first hole of reinforcement, and intense shearing within the material causes vigorous movement. As can be seen from nodes 54,155, 54,154, and 54,158, the upper layer of the first hole moved farther from its original position, stretched by the tool shoulder. Nodes 54,161 and 54,143 are pushed deep through the shoulder and moved downward, and 54,153 and 54,152 nodes are observed to move backwards, while nodes 54,133 and 54,130 are observed to move upward, which was rarely seen in S1. Moreover, this phenomenon helped increase the number of particles observed to move in the central SZ compared to S1. Thus, nodes 54,152, 54,130, 54,099, and 54,136 from the first hole itself are found to be in the middle.

Figure 23. Location of reinforcement nodes in S2 after traversing (a) 15 mm and (b) 20 mm from plunging.

Figure 23. Location of reinforcement nodes in S2 after traversing (a) 15 mm and (b) 20 mm from plunging.

SPH nodes situated at greater depths within the hole exhibit substantial lateral movement as a result of the rapid rotation of the tool pin. Hence, the nodes in this portion are stretched out and have been strongly pushed back to the rear end of the tool pin, as observed from nodes 54,114, 54,122, 54,156, 54,125, and 54,120. Additionally, the enhanced stirring action associated with the higher TRS is anticipated to reduce the accumulation of particles at the bottom layer directly beneath the tool pin. The majority of nodes from the 2nd and 3rd holes and a few nodes from the first hole are seen to be deposited at the bottom end of the tool pin with little thickness. This reduction might be attributed to a combination of factors, including increased particle mobility within the material matrix and potentially altered inter-particle frictional forces. Consequently, a thinner layer with less particle clustering might be observed behind the tool pin in S2 compared to S1.

As can be observed from the traversing of 15 mm, approximately all of the reinforcement from two holes and 50% of the nodes from the 3rd hole are turbulent from the tool. The remaining SPH nodes from the 3rd hole and some passing distance for the tool were covered in the second phase of the traversing, moving around 20 mm from the start. The reinforcement nodes closer to the AS, where the pin makes first contact, experience a stronger influence than those on the RS. Thus, due to the higher TRS and lower reinforcement %vol, it becomes possible to deliver sufficient force and face fewer obstacles than S1, which had a higher volume fraction of the SiC reinforcement SPH nodes. Thus, nodes 54,217, 54,227, 54,206, 54,210, 54,293, 54,276, 54,265, and 54,281, even from the second and third holes, are found to be delivered to the RS, indicating the flow is switching towards a uniform distribution. This observation was attributed to experimentation, indicating an even and packed distribution of reinforcement.

In the second traversing stage, most of the SPH nodes from the 3rd hole are found to be delivered to the rear side of the tool pin. As noted from nodes 54,276, 54,269, 54,261, 54,253, and 54,267 from the 3rd hole, they fill any cavity left behind the rear of the tool, forming a uniform composite layer by depositing the reinforcement at the rear end as the tool advances further. Furthermore, the upward movement of reinforcement particles facilitated by the higher TRS is expected to form a more interconnected network of particles at the surface layer. This interconnected network, potentially resembling a bridge-like structure, could improve the overall mechanical properties of the final composite. Finally, combining a lower SiC volume fraction and higher TRS mitigates agglomeration zone formation. The enhanced stirring action from the higher TRS might further disrupt potential agglomeration sites by promoting particle movement and dispersion.

After traversing, a side cross-sectional view of the S2 composites is shown in Figure 24. It demonstrates significant improvement in the dispersion of SiC particles compared to S1. While some particles remain concentrated on the AS, more nodes are now visible inside the central SZ (54,253, 54,152, 54,130, 54,099, 54,136) due to the increased TRS of 1500 rpm. The combination of higher TRS and a lower SiC volume fraction in S2 enhances the upward migration of SPH nodes. This rotational motion also reduces the accumulation of SPH nodes at the bottom layer under the tool pin compared to S1, resulting in less clustering of particles behind the tool pin and a thinner layer in that area. The upward movement of SPH nodes contributes to a bridge-like structure composed of interconnected particles at the surface layer. This is supported by observing nodes such as 54,293, 54,227, 54,206, 54,292, 54,186, and 54,210 at the top. These findings demonstrate that the S2 processing parameters have successfully created a more homogeneous and well-reinforced surface composite layer.

Figure 24. Cross-sectional final side view for S2.

Figure 24. Cross-sectional final side view for S2.

Figure 25 and Figure 26 depict the reinforcement distribution for S1 and S2 at the end of the traversing process, compared with simulated and experimentally obtained results from OM. Mapping the displaced SPH nodes with the experimental macrostructure at 20 mm shows a close correlation despite minor disparities due to lower SPH node availability. S1 exhibits groups of SiC reinforcement particles on the top of the AS, at the rear and bottom sides of the SZ. The AS has a significantly higher concentration due to two factors: lower TRS translates to reduced particle movement, particularly towards the RS, and a higher SiC volume fraction increases material viscosity, hindering effective particle transport, as discussed earlier.

In contrast, S2 shows a significant improvement in SiC particle dispersion. While some particle groups remain on the AS, the intense stirring from the tool pin rotating at a higher TRS of 1500 rpm prevents cluster formation below the tool pin, resulting in a thinner reinforcement layer than in S1. Additionally, a larger number of nodes are now visible inside the central processed zone, closely meeting experimental results. The upward movement of reinforcement is also observed, with interconnected particles at the surface of the matrix top layer, indicating a more homogeneous and well-reinforced surface composite layer in S2. The comparative isometric view for S1 and S2 highlights the difference in Figure 25c and Figure 26c. Despite the lower SiC volume fraction, S2 exhibits a more even and homogeneous distribution, with some particles concentrated towards the RS than S1.

Additionally, the first hole in S2 shows a higher deposition of reinforcement particles at the rear side of the RS, which was nearly absent in S1. The increased TRS in S2 leads to a broader visualization of the tool shoulder impression, causing an ironing-like effect on particles and the matrix, with more reinforcement materials found in the central zone due to the intense tool action. These findings emphasize that S2 processing parameters lead to a more homogeneous and well-reinforced surface composite layer than S1, as evidenced by closer alignment between numerical and experimental observations and higher surface microhardness despite lower reinforcement volume.

4. Conclusions

The present study investigated the thermo-mechanical characteristics of FSP in AZ91/SiC surface composites using a SPH numerical approach. The influence of TRS and reinforcement volume fraction on SiC particle distribution, temperature evolution, and material flow was analyzed and validated against experimental data. Based on the results, the following conclusions can be drawn:

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SPH effectively captured complex FSP interactions, accurately predicting temperature distribution and material flow.

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TRS significantly influenced heat generation and thermal distribution:

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Higher TRS (S2: 1500 rpm, 10% SiC) produced a wider, more uniform thermal field.

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Lower TRS (S1: 500 rpm, 13% SiC) caused reinforcement agglomeration and uneven particle distribution.

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Particle distribution varied across the SZ:

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AS had a higher particle concentration at lower TRS.

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Higher TRS improved SiC dispersion, reduced defects, and enhanced homogeneity.

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Reinforcement mobility increased with TRS, but excessive SiC content raised matrix viscosity, limiting material flow.

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Optimizing TRS and reinforcement fraction is crucial for achieving uniform composite microstructure and improved properties.

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SPH provides valuable insights for parameter selection and refining FSP strategies for AZ91/SiC composites.

Future research may investigate hybrid reinforcements, SPH models that include temperature-dependent material characteristics, and the impact of tool geometry on reinforcement distribution to enhance composite processing and broaden its industrial and commercial applications.