Atomistic Modeling of Thermomechanical and Microstructural Evolution in Additive Friction Stir Deposition

1. Introduction

Friction Stir Welding (FSW) emerged in the early 1990s as a solid state joining technique that uses frictional heat and mechanical stirring to bond materials without reaching their melting point. The process employs a rotating tool that generates localized heating through friction while applying severe plastic deformation to the workpiece [1,2,3,4,5,6]. This combination softens the material and creates a metallurgical bond between adjacent parts. FSW proved particularly effective for joining aluminum alloys that are difficult to weld using conventional fusion methods, avoiding issues such as porosity, hot cracking, and solidification defects. The success of FSW in producing high quality joints with minimal distortion and superior mechanical properties motivated researchers to explore extensions of the underlying principles to other manufacturing applications.

Additive Friction Stir Deposition (AFSD) represents a direct adaptation of FSW principles to additive manufacturing. Instead of joining two separate pieces, AFSD uses a rotating hollow tool to push a consumable feedstock rod onto a substrate, depositing material layer by layer. The rotating tool generates frictional heat at the interface while imposing severe plastic deformation on the softened feedstock. Material transfers from the feedstock to the substrate, building up three dimensional components through successive deposition passes. AFSD operates entirely in the solid state, avoiding the thermal gradients, residual stresses, and microstructural coarsening associated with fusion based additive techniques [7,8,9,10,11]. The process enables fabrication of large scale components from high strength aluminum alloys, titanium alloys, and other materials that are challenging to process using powder bed or directed energy deposition methods.

Industrial adoption of AFSD has grown rapidly, yet fundamental understanding of the process remains limited. Experimental characterization provides valuable data on temperature fields, deposition rates, and final microstructures, but direct observation of interfacial phenomena during processing is challenging [12,13,14,15]. The deformation zone beneath the tool experiences extreme conditions including strain rates exceeding 10³ per second, temperatures approaching the solidus, and complex three dimensional material flow. Conventional characterization techniques cannot resolve the atomic scale mechanisms governing material transfer, interfacial bonding, and defect formation during deposition. Macroscopic models based on continuum mechanics provide useful predictions of temperature and stress fields but lack the resolution to capture dislocation dynamics, grain boundary evolution, and local structural transformations that determine final material properties.

Atomistic modeling offers a direct approach to investigate deformation mechanisms at length and time scales inaccessible to experimental methods. Molecular dynamics simulations explicitly track individual atoms, computing forces from interatomic potentials and integrating equations of motion to evolve the system. This approach naturally captures plastic deformation through dislocation nucleation and motion, structural phase transformations, and interfacial phenomena without imposed constitutive assumptions. Atomic scale resolution enables quantification of local strain fields, coordination environments, and defect structures throughout the deformation process. Recent advances in computational power and interatomic potential development have made it feasible to simulate systems containing millions of atoms under realistic processing conditions, bridging the gap between quantum mechanical calculations and continuum models.

This work presents the first atomistic investigation of AFSD using molecular dynamics simulations. The study focuses on aluminum deposition to establish baseline understanding of fundamental mechanisms. Simulations reproduce the essential features of AFSD including tool rotation, feedstock feeding, frictional heating, and material deposition. Detailed analysis of atomic trajectories, strain fields, coordination numbers, and defect structures reveals how severe plastic deformation at the tool substrate interface enables material transfer and metallurgical bonding. Results provide direct evidence of deformation localization, dislocation activity, and free volume generation that underlie successful solid state deposition. The atomistic framework developed here establishes a foundation for predicting microstructural evolution and optimizing process parameters in AFSD and related solid state manufacturing technologies.

2. Methodology

An atomistic simulation framework was developed to study the Additive Friction Stir Deposition (AFSD) process show in Figure 1 using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [16] depicted in Figure 2. The simulations were carried out in three dimensions under metal units with periodic boundary conditions in the lateral directions and a free surface along the build direction, enabling realistic material flow and deposition. Aluminum was modeled using an FCC lattice with a lattice constant of 4.05 Å, and atomic interactions were described through an Embedded Atom Method (EAM) alloy potential suitable for aluminum systems. The computational domain consisted of a rigid substrate and a cylindrical feedstock positioned above it, representing the consumable rod used in AFSD. The substrate occupied the lower region of the simulation box, while the feedstock was initialized as a vertical cylinder extending above the substrate.

To capture the mechanical and thermal behavior during deposition, atoms were categorized into substrate, feedstock, and deposited material based on their type, with dynamic group definitions used to track oxide layers, core tracer atoms, and the evolving interface region. The bottommost substrate layers were fully constrained to emulate a rigid backing plate, while the remaining substrate atoms were allowed to respond dynamically. Initial velocities corresponding to 300 K were assigned to all atoms except the fixed boundary. Temperature control was applied using Nosé–Hoover thermostats, with separate thermal ramps for the substrate and feedstock to reproduce differential heating during processing. A timestep of 1 fs was used to ensure numerical stability given the high strain rates and temperatures involved.

The AFSD process was emulated by superimposing rotational, translational, and downward feed motions on the feedstock atoms. Rotation corresponding to 300 rpm was imposed via body forces derived from angular velocity, while linear traverse and feed velocities controlled lateral movement and material deposition, respectively. Frictional heating at the tool–substrate interface was modeled by dynamically identifying atoms within a predefined contact zone and applying a localized heat flux when contact occurred. Deposition was represented by converting feedstock atoms to deposited material once they crossed a specified height threshold, allowing continuous buildup of material over multiple deposition cycles. This conversion was performed iteratively to mimic steady-state deposition.

Extensive atomistic diagnostics were employed to analyze the evolving microstructure and thermomechanical response. Per-atom quantities such as potential energy, kinetic energy, stress tensor components, coordination number, centro-symmetry parameter, common neighbor analysis, displacement, and Voronoi volumes were computed throughout the simulation. Spatially resolved temperature fields were obtained using three-dimensional binning, and time-averaged quantities were recorded to assess steady-state behavior. Multiple dump files tracked oxide evolution, tracer motion, and interface characteristics. Following active deposition, a controlled cooldown stage using Langevin dynamics reduced the system temperature to ambient conditions. The final atomic configuration was written to a data file, and global metrics such as atom counts, average coordination number, and centro-symmetry parameter were evaluated to quantify the final deposited structure and its structural integrity.

3. Results and Discussion

3.1. Atomic Strain analysis

The localized shear strain observed beneath the feedstock arises from the combined effects of tool rotation, axial feeding, and frictional heating, as implemented in the molecular dynamics model. The local atomic shear strain is computed from the deviatoric component of the strain tensor is computed using Equation 1.

$${\gamma }_i=\sqrt{{\displaystyle \frac{2}{3}}{\epsilon }_i^{\text{'}}}:{\epsilon }_i^{\text{'}}$$

(1)

where ${\epsilon }_i^{\text{'}}$denotes the deviatoric strain tensor. Figure 3 shows that elevated values of ${\gamma }_i$ are concentrated near the tool–substrate interface and directly beneath the rotating feedstock. The concentration of strain at the tool–substrate interface indicates the formation of a severe plastic deformation zone, which is a prerequisite for metallurgical bonding and material transfer in AFSD. The limited penetration of high shear strain into the bulk substrate suggests that deformation is efficiently confined, reducing excessive subsurface damage while promoting interfacial mixing. These atomistic observations provide direct evidence of the mechanisms responsible for layer formation in AFSD, complementing experimental interpretations based on macroscopic force and temperature measurements.

3.2. Local Atomic Coordination Analysis

Figure 4 shows the spatial evolution of the atomic coordination number during tool engagement. The local coordination number $Z_i$ of atom $i$ is defined using Equation 2.

$$Z_i={\sum }_{j\ne 1}H\left(r_c-r_{ij}\right)$$

(2)

where $r_{ij}$ is the interatomic distance $r_c$ is the cutoff radius and $H$ is the Heaviside function. Atoms in the undeformed regions of the substrate and feedstock maintain coordination values close to those of the initial crystalline lattice. A pronounced reduction in $Z_i$ is observed at the tool–substrate interface, as seen in Figure 4(a–c). The three-dimensional view (Figure 4(d)) confirms that coordination loss is spatially confined to a narrow interfacial zone beneath the tool.

3.3. Dislocation Structures Analysis

Figure 5 shows the spatial distribution of atomic clusters and defect structures formed during AFSD. Clusters are identified by grouping atoms based on local structural similarity and connectivity. The observed clustering behavior is associated with the accumulation and interaction of dislocations generated by severe plastic deformation. As deformation progresses, dislocations nucleate and interact, leading to the formation of stable defect structures. The local defect density ${\rho }_d$ can be qualitatively related to plastic strain accumulation using Equation 3.

$${\rho }_d\propto {\displaystyle \frac{{\gamma }_p}{b}}$$

(3)

where ${\gamma }_p$ is the local plastic shear strain and $b$ is the Burgers vector magnitude. The confinement of defect clusters to the interfacial region suggests that AFSD promotes localized strain accommodation through dislocation activity, enabling material mixing and bonding while limiting damage to the surrounding substrate.

3.4. Voronoi-Based Local Atomic Volume

Figure 6 shows the spatial distribution of local atomic environments quantified using Voronoi tessellation. Each atom is assigned a Voronoi polyhedron, whose volume and face count characterize its local neighborhood. The effective coordination number can be expressed using Equation 4.

$$Z_i^{Vor}=N_f$$

(4)

where $N_f$ is the number of faces of the Voronoi polyhedron associated with atom $i$. Most atoms in the bulk substrate and feedstock exhibit uniform Voronoi coordination consistent with the initial crystalline structure. Localized deviations in Voronoi coordination are observed beneath the rotating feedstock, as seen in Figure 6(a–c), indicating heterogeneous atomic packing in the interfacial region.

The localized increase and spread in atomic volume reflect dilation and packing inefficiency caused by intense shear deformation and atomic rearrangement as depicted in Figure 7. Variations in atomic volume correlate spatially with regions of high displacement magnitude and reduced coordination, indicating that plastic flow in AFSD is accompanied by transient local free-volume generation. This localized volumetric heterogeneity facilitates atomic mobility and interfacial mixing while preserving dense packing in the surrounding substrate. A qualitative relationship between atomic volume and deformation can be expressed using Equation 5.

$$V_i=V_0+∆V\left({\gamma }_i\right)$$

(5)

Figure 8 presents the cavity radius field computed from Voronoi tessellation. For each atom $i$, the cavity radius $r_i^{cav}$ is defined as the radius of the largest empty sphere that fits within the local Voronoi polyhedron computed using Equation 8.

$$r_i^{cav}=max\left(r\left|sphere\right(r)\subset {\mathsf{{\rm P}}}_i\right)$$

(8)

where ${\mathsf{{\rm P}}}_i$ denotes the Voronoi cell of atom $i$. The results show that most atoms in the bulk substrate exhibit small cavity radii characteristic of dense crystalline packing. A localized increase in$r_i^{cav}$ is observed beneath the feedstock and at the interface (Figure 8(a–c)), with the three-dimensional view (Figure 8(d)) confirming that free-volume accumulation is confined to the active deformation zone.

4. Conclusion

This study presents the first atomistic modeling investigation of Additive Friction Stir Deposition using molecular dynamics simulations. The computational framework successfully captured the essential thermomechanical processes during aluminum deposition, including tool rotation, frictional heating, and severe plastic deformation at the tool substrate interface. Atomic scale analysis revealed that shear strain localizes beneath the rotating feedstock, creating a confined deformation zone that facilitates material transfer while preserving the integrity of the surrounding substrate.

Detailed characterization of microstructural evolution demonstrated significant reduction in atomic coordination numbers at the interface, indicating lattice distortion and disorder induced by intense plastic flow. Dislocation structure analysis identified defect clustering in regions experiencing severe deformation, consistent with the high strain rates imposed during processing. Voronoi tessellation based metrics quantified heterogeneous atomic packing, free volume generation, and cavity formation, all spatially correlated with the active deformation zone. These findings confirm that AFSD achieves metallurgical bonding through localized interfacial mixing driven by severe plastic deformation under solid state conditions.

The atomistic framework developed here provides a foundation for understanding deformation mechanisms in AFSD at length and time scales inaccessible to experimental characterization. Future work will extend these simulations to investigate multi-layer deposition, thermal cycling effects, and processing of alternative alloy systems. Integration of atomistic insights with continuum scale models will enable optimization of process parameters for improved mechanical properties and deposition efficiency in solid state additive manufacturing applications.