Global and Local Deformation Analysis of Mg-SiC Nanocomposites: Digital Image Correlation (DIC) and Representative Volume Element (RVE) Techniques

Abstract

Improving the ductile deformation behavior of Mg-SiC nanocomposites without compromising strength is critical to enhancing their mechanical properties. Mg-SiC nanocomposites are produced through mechanical milling, cold isostatic pressing, sintering, and hot extrusion processes. This study investigates the uniaxial stress–strain response and deformation behavior of the Mg-SiC nanocomposite compared to pure Mg samples with and without the milling process. The deformation behavior was investigated by two-dimensional (2D) digital image correlation (DIC) at two macroscopic and microscopic scales, employing light micrographs and in situ loading samples, respectively, in the scanning electron microscope. Compared to the pure Mg samples, the mechanical test results demonstrated a significant improvement in strength (80 MPa) and fracture strain (23.5%) of the Mg-SiC nanocomposite. The three-dimensional (3D) representative volume element (RVE) model revealed the particle dispersion effect on the mechanical properties of the nanocomposite. The RVE results demonstrate ductile deformation behavior in the sample with homogenous dispersion of SiC particles compared with the heterogeneous dispersion of SiC particles in Mg-SiC nanocomposite. The results demonstrated a good agreement between DIC and RVE predictions for Mg-SiC nanocomposites across macro- and microscales.

1. Introduction

The ability to enhance mechanical properties without any adverse effect on their ductility using nano-sized reinforcements makes magnesium (Mg) nanocomposites an attractive choice for lightweight engineering applications [1]. Their increased strength can mainly be attributed to the nanoparticles’ enhanced load-bearing capacity, the greater density of dislocations resulting from the residual plastic strain due to differing thermal expansion coefficients between the matrix and reinforcing nanoparticles, and the Orowan pinning effect induced by the nano-sized particles [2]. Furthermore, nano-sized reinforcements have demonstrated the activation of non-basal slip systems within the Mg matrix at room temperature, along with aiding in grain refinement, resulting in improved ductility [3,4]. The substantial benefits have sparked notable research interest in utilizing sub-micron- and nanoparticles to reinforce magnesium and its alloys in recent years. Nevertheless, the anticipated improvement in properties has not yet been fully achieved, primarily due to the challenge of achieving a homogeneous dispersion of nanoparticles in the matrix, particularly at higher nanoparticle concentrations [5]. Various research studies have identified regions where agglomerated nanoparticles lead to a subsequent reduction in the mechanical properties of the composite [3,6].

Mechanical milling is a promising method to overcome the agglomeration typically observed in nanocomposites [7,8]. In this process, plastic deformation, repetitive cold welding, the fracture of deformed metal particles, and the fragmentation of brittle powder particles lead to a satisfactory dispersion of the reinforcing nanoparticles [9]. However, intensive plastic deformation leads to strain hardening, and the elevated hardness of composite powder particles hinders further deformation during subsequent compaction phases. This introduces challenges in processing milled powders using conventional compaction techniques [10]. Recently, Penther et al. effectively attained a consistent dispersion of SiC nanoparticles, reaching up to 10% volume fraction within a fully dense nanostructured Mg matrix through mechanical milling and hot extrusion [11].

In addition to the significance of nanoparticle distribution, recent studies have placed considerable importance on understanding how nanoparticle reinforcements affect the microstructure and, subsequently, the overall mechanical properties of Mg nanocomposites [11,12].

The mechanical properties of Mg nanocomposites are often determined by phenomena occurring at the microscopic level. These phenomena are significantly influenced by the properties of the constituent materials and the mechanical interactions at the interfaces between the reinforcement and the matrix [13]. Indeed, various micromechanisms of deformation within each phase and debonding of interfaces between the matrix and reinforcement can lead to non-uniform deformation and the consequent formation of microvoids [14]. Therefore, it is essential to investigate the underlying mechanisms at both the macro- and microscales, which can direct us to achieve the expected improvement in the mechanical properties of Mg nanocomposites. Various methods have been proposed to offer insights into the deformation behavior of metal matrix composites (MMCs).

The digital image correlation (DIC) method has proven effective in measuring strain and visualizing local deformations on the surfaces of metallic materials with heterogeneous microstructures in a 2D, non-contact way [15]. This method involves monitoring changes in the grayscale pattern within small local areas in a series of images as deformation occurs. Kaya et al. [16] and Schüler et al. [17] employed this method at the macroscale to investigate the deformation behavior of open-cell stainless steel and to characterize the deformation behavior and cracking of porous segmented Alumina, respectively. Moreover, the potential of microscale DIC (µDIC) to analyze deformations in composite materials at the microscale was assessed in several studies [18,19]. However, it is still challenging to obtain the necessary spatial resolution to measure the strain field at the micron and submicron scale.

Recently, numerical simulation, based on the microstructure of materials, has been proposed for modeling the mechanical properties of nanocomposites [20,21]. Among the different methods, representative volume element (RVE) models utilize constitutive properties and microstructural characteristics such as the volume fraction, size, shape, and distribution of constitutive material to predict the mechanical properties, especially at a microscale [22]. A simulation based on the RVE model and microstructure has been utilized to predict the deformation behavior in various multiphase materials and metal matrix composites [23,24,25].

This study investigates the effect of mechanical milling and SiC particles on the compressive deformation behavior of Mg-SiC nanocomposites produced through mechanical milling, cold-isostatic pressing, sintering, and hot extrusion. The deformation behavior of the Mg-SiC composite and pure Mg with and without mechanical milling was examined by two-dimensional (2D) DIC to analyze deformation at both macro- and microscales using light microscopy and scanning electron microscopy, respectively. The 2D DIC findings highlight that the nanocomposite’s increased strength and ductile deformation behavior are influenced by grain refinement during extrusion, facilitated by prior mechanical milling, and the presence of SiC particles. Moreover, the importance of the homogenous distribution of SiC particles to ensure ductile deformation behavior in Mg-SiC nanocomposites is emphasized conducting three-dimensional (3D) RVE model analysis.

2. Materials and Methods

2.1. Material

Magnesium (Mg) powder with an average particle size of −325 mesh, and β-SiC powder with an average particle size of ≤1 µm and purity of 99.8%, were bought from Alfa Aesar (Ward Hill, MA, USA). Mg-SiC composites containing 10 vol% submicron SiC particles (M10sµ) were produced by high-energy mechanical milling. Mechanically milled pure Mg (MM) and non-milled pure Mg (Mg) were used as reference materials. For all three samples, consolidation steps, including isostatic cold-pressing, sintering, and hot extrusion, were employed to achieve full-density composite components. We previously [11,26] showed that this processing route leads to a homogeneous distribution of the SiC particles in the matrix. The Mg-SiC composite containing 10 vol% submicron SiC represented the highest density distribution homogeneity compared to the other samples containing 1 vol% and 10 vol% nano-SiC particles [27].

Table 1. Characterization of prepared sample for compression test.

Sample	Content	Milling Time (h)	Subsequent Process
Mg	Mg	0	CIP + sinter + extrusion
MM	Mg	25	CIP + sinter + extrusion
M10Sµ	Mg + 10% SiC (1 µm>)	25	CIP + sinter + extrusion

shows the sample characterization used in this study. More details about the production process are found in this Reference [11].

2.2. Sample Preparation and Speckle Pattern for DIC

The DIC method utilizes random speckle patterns on the specimen’s surface to monitor deformation by comparing digitized images of the specimen in its original and deformed states [28]. Hence, generating suitable patterns for DIC is of the utmost importance to ensure accurate deformation results. In this study, the speckle patterns for DIC at the macroscale were generated using airbrushing on the surface of all samples, Mg, MM, and M10Sµ. At the microscale, the SEM images of the surface features of the M10Sµ served as the speckle patterns for DIC analysis, although the SEM surface features of the Mg and MM were not suitable as the speckle patterns for DIC. To achieve a suitable patterned surface for Mg and MM, the sputter coating technique was utilized. This technique involved depositing a thin layer of gold film onto the specimen surface via magnetron sputter coating [29]. The sputter coating utilized a copper gilder grid with 2000 mesh with a 5 µm bar width of the mesh, G2786C from Plano GmbH, which covered the Mg and MM surface, and the copper gilder grid was removed after the gold spatter coating. Figure 1 represents the prepared sample surfaces for DIC.

2.3. In Situ Compression Testing for Macro–Micro DIC Analysis

The mechanical tests were carried out with a Kammrath & Weiss micro-testing stage (Kammrath & Weiss, Düsseldorf, Germany). The machine was equipped with a 10 kN load cell with a resolution of 1 N and a displacement gage with a range of 12 mm and a resolution of 1.2 mm. The cubic specimens were machined with a diamond saw with edge lengths of 4 × 4 × 4 (mm³) and were mounted between two platens that were polished to decrease the friction between them and the specimen. All compression tests were performed with the loading direction parallel to the transversal direction of the cells. Dantec Dynamics Istra 4D (version 4.3.1.460, Nova Instruments, Skovlunde, Denmark) software was used to perform the DIC technique. In situ compression tests for macroscale investigation were carried out in a digital optical microscope (Keyence—100 vhx, Neu-Isenburg, Germany) with a displacement rate of 0.5 µms⁻¹ and, during testing, the images of the specimen surfaces were captured every 15 s.

Compression tests for the microscale investigation were carried out using scanning electron microscopy (SEM; CamScan REM Serie2, Obducat, Lund, Sweden) in the secondary electron mode at an accelerating voltage of 20 KV. The specimen was loaded step by step under the displacement rate of 0.2 µms⁻¹. After each increment, the loading was paused to acquire SEM images at the specific load level with ×1000 magnification. The area of interest was 370 × 290 µm in size and was located near the center of the sample. To minimize the error caused by the spatial distortion of SEM imaging, the imaging area of the specimen was carefully adjusted so that the images were always taken from the same area on the specimen after each loading step. The position adjustment was based on the tracking of some chosen reference markers. Using a higher magnification level, the reference marker was relocated to the same location as the previous SEM image by moving the whole loading-stage assembly inside the SEM chamber. The magnification was then reduced to ×200 to acquire the SEM images, and the brightness and contrast were carefully adjusted so that they remained constant.

2.4. Numerical Modeling; RVE Generation

The numerical analysis of the particle-reinforced composite, M10Sµ, was performed based on the Finite Element Analysis (FEA) of the 3D RVE. The simulation was conducted with the ABAQUS 6.14-4 software (SIMULIA, Providence, RI, USA). A symmetrical boundary condition was exerted on the RVE models for the uniaxial compression test. All nodes on the bottom edge can only move in the X direction, while all nodes on the left edge can only move in the y direction. A cubic RVE with dimensions of 10 (width) × 10 (height) × 0.01 (length) µm³ representing the microstructure of particle-reinforced composite was generated by using Python scripting in Abaqus. To understand the effect of SiC particle dispersion on the Mg-SiC nanocomposite deformation behavior, the RVE model consisting of approximately 10 vol% nonintersecting spherical particles of different sizes in the range of 0.2–0.45 µm was created, in which spatial distribution was determined randomly and based on the microstructure size of constitutive particles. This RVE, consisting of the homogeneous and heterogeneous distribution of 10 vol% SiC reinforcements particles in Mg, is presented in Figure 2a,b.

3. Results

3.1. Mechanical Responses to the Uniaxial Compressive Loading

The mechanical test results conducted with Kammrath & Weiss are shown in Figure 3. The representative compressive stress–strain curves for Mg, MM, and M10Sµ cubic specimens were tested under the same conditions at room temperature in ambient air. These materials exhibit markedly distinct mechanical responses.

Mg demonstrates a compressive yield strength (CYS) of 150 MPa, and MM displays an elevated CYS at 190 MPa, indicating increased strength compared to Mg. M10Sµ stands out with the highest CYS, at 230 MPa, representing a substantial 53% increase over Mg and a significant 21% increase over MM, highlighting its superior strength. The stress difference of 5% before ultimate compressive strength (UCS) and at UCS could reveal that the stress concentration before fracture is 40%, 23%, and 13%, respectively, for Mg, MM, and M10Sµ. Mg demonstrates restricted deformation behavior, experiencing sudden failure after reaching the UCS at 350 MPa with only a 15% strain. Similarly, MM also exhibits abrupt failure at 260 MPa with a 21% strain upon reaching UCS, which indicates a modest level of ductility. In stark contrast, M10Sµ reaches UCS at 320 MPa with an impressive 38.5% strain, underscoring its exceptional ductility compared to Mg and MM.

3.2. Deformation Behavior

Figure 4 and Figure 5 show the results of the DIC 2d analysis of plastically deformed Mg, MM, and M10Sµ at the macroscale and microscale, respectively. The surfaces of these samples before compression, along with the scale size, are presented in Table 1, and the stress–strain curves of the samples are shown in Figure 3. Strain field images of the samples are shown at strain rates of 0% (a point), CYS (b point), 5% before UCS (c point), and at UCS (d point) for macro- and microscales in Figure 4 and Figure 5, respectively. To better evaluate the sample deformation behavior up to CYS (b point) the strain scale bars are adjusted from 0 to 10% in the Istra 4D program.

Examining the corresponding deformation behavior of Mg, MM, and M10Sµ at the macroscale in point b, CYS (Figure 3) reveals that, in the case of Mg, highly strained deformed parts are concentrated along an angled line, with some regions remaining relatively undeformed (Figure 4b, Mg). In contrast, for the MM, these highly strained deformed parts are more dispersed throughout the surface, with fewer undeformed areas than Mg (Figure 4b, MM). For M10Sµ, high strains, and deformed parts are predominantly visible on one side of the sample, running parallel to the platen, and almost all parts of M10Sµ contribute to the deformation (Figure 4b, M10Sµ). Shortly before the onset of fracture at point c, 5% before strain (Figure 3), examining the corresponding deformation behavior at the macroscale shows that, in Mg, the high-strain parts are in the form of shear bands with angles of from 30° to 45° to the loading axis (Figure 4c, Mg). The behavior of MM is quite similar, as shear bands form with angles of from 30° to 45° to the loading axis (Figure 4c, MM); however, at this point, for MM, the area with high strain is more visible than Mg. For M10Sµ at the same point, the high-strain parts are on both sides, near and parallel to the platen, and the area between the platens shows the lowest strain (Figure 4c, M10Sµ). Upon further loading of all samples to point d, UCS (Figure 3), for Mg, fractures occur along the shear bands with angles of from 30° to 45° to the loading axis, with insignificant changes in the extent of deformation (Figure 4d, Mg). MM exhibits a similar fracture behavior, with more parts participating in deformation than Mg (Figure 4d, MM). Surprisingly, for M10Sµ in UCS, the areas between the platens reveal a strain decrease while the strain in the areas near the platen continues to increase, suggesting that the crack opens in the Y direction (Figure 4d, M10Sµ).

Examining the corresponding deformation behavior of Mg, MM, and M10Sµ at the microscale in point b, CYS (Figure 3) clarifies that, in the case of Mg, the high-strain parts are almost concentrated on one side (Figure 5b, Mg) however, in MM, the high strain parts are dispersed over the whole surface (Figure 5b, MM) and, in M10Sµ, almost the entire selected area uniformly participates in deformation, and strain localization is only visible in a small region (Figure 5b, M10Sµ). With further load increases to point c, 5% before UCS (Figure 3), insignificant strain is observed in bands perpendicular to the loading direction in Mg (Figure 5c, Mg). In contrast, in MM, the formation of different angled shear bands is visible in the strain of 5% before UCS (Figure 5c, MM). In the case of M10Sµ in point c, as the load increases, strain increases in all parts homogenously, except for one part that shows the strain localization with a decrease in strain in front of it (Figure 5c, M10Sµ). As the load increases to point d, UCS (Figure 3), fracture occurs through increasing the strain in bands perpendicular to the loading direction in the case of Mg (Figure 5d, Mg), and increasing the strain in angled shear bands for MM (Figure 5d, MM). In M10Sµ, the strain localization is increased in one part while the strain in front of that is decreased compared to point c, indicating crack growth in the x direction and crack opening in the y direction (Figure 5d, M10Sµ).

3.3. RVE Modeling Results for M10Sµ Sample

The simulated compressive stress–strain curve of the M10Sµ RVE model is shown in Figure 6. The stress–strain curves show no differences for homogeneous and heterogeneous SiC particle distributions in M10Sµ since the curve shows the average results of stress and strain. The simulated curve reveals about a 50 MPa lower CYS and a 2.5% higher fracture strain than the experimental results (Figure 3). The details of the RVE simulation deformation of M10Sµ with the homogeneous and heterogeneous dispersion of SiC particle in magnesium matrix at different strains 10%, 25%, and 40% during compression are given in Figure 7a and Figure 7b, respectively.

In Figure 7a,b (homogeneous M10Sµ and heterogeneous M10Sµ), as the strain reaches 10%, strain concentration is visible around hard SiC particles. However, in the heterogeneous M10Sµ case, some particles are observed without strain concentration. Furthermore, in the case of homogeneous SiC dispersion, there is less strain discrepancy between the Mg matrix and SiC particles compared to the case of heterogeneous dispersion. With a further increase in strain to 25%, in the case of heterogeneous M10Sµ, the strain predominantly increases around the SiC particles. In contrast, in the homogeneous M10Sµ, not only does the strain increase around the SiC particles, but it also extends more into the surrounding matrix. This deformation behavior persists up to a strain of 40% in both homogeneous and heterogeneous M10Sµ. As a result, a more uniform strain distribution is notably evident in the homogeneous M10Sµ compared to the heterogeneous M10Sµ in this strain.

4. Discussion

Previous research has demonstrated that a dense Mg-SiC nanocomposite with uniformly distributed SiC particles in the Mg matrix can be produced through mechanical milling, followed by cold-isostatic pressing, sintering, and hot extrusion [11]. This study examines the specific influence of mechanical milling and SiC particle dispersion on the deformation behavior of the dense nanocomposite samples. Specifically, M10Sµ compared to pure Mg samples with and without mechanical milling, labeled as MM and Mg samples.

A significant increase in the CYS of M10Sµ compared to Mg and MM was observed in the compressive stress–strain curves (Figure 3), which can be attributed to the mechanical milling effect and treatment of SiC particles. Mechanical milling promotes grain refinement and the amount of dislocations in the milled powders through severe plastic deformation [9]. The corresponding refined grains, large grain boundaries, and the higher dislocation density are the places for new grain nucleation during the following hot extrusion process [30]. Indeed, upon deformation during hot extrusion, dynamic recrystallization (DRX) takes place [31], which is defined as the development of a new grain structure in a deformed material through the formation and movement of high-angle grain boundaries, driven by the stored deformation energy [32,33]. In M10Sµ, SiC particles enhance local plastic deformation during mechanical milling, introducing more dislocation density into the Mg matrix [34]. This increased defect density drives DRX during hot extrusion, resulting in finer grain sizes of M10Sµ after extrusion compared to MM and Mg.

Moreover, in the case of M10Sµ, the SiC nanoparticles effectively restrict grain growth during extrusion due to their Smith–Zener pinning effect on grain boundaries, which can more effectively inhibit or delay the recrystallization and lead to grain refinement of the matrix during DRX [32,35]. It is well-known that the grain-size refinement strengthening mechanism, the Hall–Petch mechanism, is the only mechanism that increases the strength and ductility of metals. In this mechanism, grain boundaries act as obstacles for dislocations, requiring extra energy for dislocations to change direction and cross into adjacent grains due to their different lattice orientations. The disordered nature of grain boundaries also disrupts the dislocation movement along continuous slip planes. This hindrance delays the onset of plasticity, increasing the CYS of the material [36]. This mechanism explains that MM has a greater capacity for plastic deformation up to CYS compared to Mg (Figure 4b, Mg, MM). Moreover, the higher grain boundaries in MM compared to Mg means there are a higher number of barriers to dislocation movement, which leads to the greater dispersion of deformed regions in MM than Mg (Figure 5b, Mg, MM). As discussed above, the combined effects of SiC pinning and mechanical milling result in finer grains after extrusion in M10Sµ compared with MM and Mg, and higher deformation toleration up to CYS (Figure 4b, M10Sµ), leading to a greater number of barriers to deformation and a more uniform strain dispersion than Mg and MM (Figure 5b, M10Sµ).

Additionally, according to the Hall–Petch mechanism, the accumulation of more dislocations in large grains creates a stronger driving force, initiating dislocation movement in adjacent grains due to the longer paths, greater dislocation buildup, and higher stress concentration. Consequently, smaller grain sizes more effectively hinder dislocation motion. However, more grains increase the likelihood of favorably oriented neighboring grains, allowing for dislocations to continue their movement and increasing their ductility [36,37]. The lower stress increase from point c (5% before UCS) to point d (UCS) and higher fracture strain at point d (UCS) (Figure 3) for M10Sµ, at 13%, in comparison to MM and Mg, at 23% and 40%, respectively, shows the ductile deformation behavior of M10Sµ compared to MM and Mg, resulting from the lower stress concentration caused by the smaller grain size during deformation.

Indeed, a fracture could occur due to plastic instability, such as the formation of shear bands in particle-free materials along a 45-degree line and in particle-containing ductile materials due to void formation around the particles, parallel to the loading direction [38]. The brittle behavior of Mg and MM is visible in 2D macro-DIC results, where the shear band in Mg and MM formed along a 45-degree line in 5% before UCS in both samples (Figure 4c, Mg and MM) with insignificant changes in the deformed parts, especially for Mg, where the fracture occurred (Figure 4d, Mg and MM). Scientifically, an emerging consensus is that the poor processing behavior and anisotropic mechanical behavior of Mg alloys are due to their hexagonal crystal structure (HCP), and their asymmetric crystallographic nature [39], where slips upon their non-basal systems have a considerable critically resolved shear stress (CRSS) that refrains them from being activated at room temperature, and hence from satisfying the five slip systems required by the Von Mises law [40]. In general, it is believed that the deformation behavior of Mg alloys is governed by deformation twinning and basal slip at room temperature [41]. Moreover, at room temperature, the (CRSS) for slip is higher than twinning, which dominates the deformation at lower temperatures [42]. The distinctive upward concave compression curve of extruded Mg might be due to twinning being the main deformation mechanism (Figure 3). Indeed, twinning introduces additional barriers to dislocation movement [43]: when the twins reach saturation in the grains, they induce the crack source there, and once the crack appears, it will rapidly result in Mg fracture. The formation of shear bands containing a group of parallel compression twins is visible in Figure 5c, Mg. The strain increased insignificantly up to fracture in these bands (Figure 5d, Mg).

Furthermore, Meyers et al. [44] have demonstrated that the twinning stress often increases more rapidly with decreasing grain size compared to the stress needed to initiate slip. Decreasing the grain size is analogous to increasing the temperature in that a grain size is eventually reached below which slip can proceed under lower stresses than those required to initiate twin and dominate deformation under these conditions [43]. The effect of grain size refinement using mechanical milling in the activation of the slip system is clear in MM, and the participation of a high number of angled shear bands in point 5% before UCS (Figure 5c, MM). Consequently, fracture occurs with an insignificant increase in these deformed parts (Figure 5d, MM); however, the strain in these parts is more comparable to Mg.

In the case of M10Sµ, distinct ductile fracture behavior is visible compared to Mg and MM. Indeed, in ductile fracture upon uniaxial compression, crack propagation runs parallel to the load direction, and crack-opening occurs in the direction perpendicular to the load direction [45]. The strain increased on both sides of the sample near the platens perpendicular to load direction, along with a decrease in strain in the area between the platens at point 5% before UCS (Figure 4c, M10Sµ), and the extension of the increase and decrease in strain in the same areas, up to UCS (Figure 4d, M10Sµ) suggests potential crack growth and crack-opening in M10Sµ at the macroscale. A strain distribution analysis of M10Sµ in the y direction using the Istra 4D program at the macroscale represents the crack propagation and crack-opening in this sample (see Figure 8a). The ductile fracture behavior of M10Sµ is attributed to the presence of SiC particles. The large elastic module contrast between Mg as the matrix and SiC as reinforcement will lead to inhomogeneous deformation fields and strain localization around the hard SiC particles [46]. This strain localization may lead to crack initiation via microvoid formation and its coalescence in the matrix material, or by debonding the interfaces between the matrix and the reinforcements preceding the actual failure event [40]. The strain localization in (Figure 5c, M10Sµ) indicates that a crack was initiated in M10Sµ. As the load in the x-direction increases, the strain ahead of the crack tip also increases, indicating crack growth and a ductile fracture in M10Sµ (Figure 5d, M10Sµ). A strain distribution analysis of M10Sµ in the y-direction at the macroscale using the Istra 4D program clearly illustrates crack propagation and opening, as depicted in Figure 8b.

Indeed, the formation of cracks is a primary issue in discussions of the failure of the composite. As discussed before, strain localization around the SiC particles causes crack formation. Moreover, the geometry of reinforcement particles, i.e., the interface region with the matrix and their dispersion state, significantly influences the strain localization and, consequently, crack nucleation and coalescence inside a composite material [40].

In the case of M10Sµ, mechanical milling before extrusion led to grain refinement and significantly increased the homogeneity of SiC particle dispersion in M10Sµ and the coherency between the SiC particles and Mg matrix. As a result, the crack formation and growth were impeded, and the ductility was increased in M10Sµ.

Moreover, an investigation of the predicted RVE results of the homogenous and heterogeneous dispersion of SiC particles in M10Sµ (Figure 7a,b) revealed the key role of uniform particle dispersion and confirmed that the homogenous dispersion of SiC particles in M10Sµ led to a more uniform strain around SiC particles (strain of 10%), more strain transfer to the Mg matrix (strain of 25%) and, consequently, less strain disparity between SiC particles and Mg matrix (strain of 40%), reducing the likelihood of rapid crack growth comparison to heterogeneous M10Sµ. Indeed, a plastic zone exists near the crack tip in situations involving interfacial cracks. The soft phase, Mg, effectively mitigates nearby stress concentration by undergoing plastic deformation, further inhibiting crack growth [45]. Additionally, as predicted by Goodier, plastic deformation concentrates at the poles of the particles along the loading axis [47] and in regions where particles are closely spaced, while limited plasticity occurs due to significant constraints on the matrix in these areas [24]. The microstructure examination of the surface of M10Sµ before fracture at the microscale reveals that the crack originates from a region where the particle dispersion homogeneity is lower (see Figure 1; M10Sµ prepared sample for microscale investigation).

In conclusion, using DIC2d and RVE effectively predicts the effect of mechanical milling and distribution of SiC particles on the deformation behavior of Mg-SiC nanocomposites. A consistent agreement was observed between the modeling predictions and experimental results. However, the underestimated values of CYS and fracture strain observed in the case of M10Sµ in the RVE results compared to the experimental results may be attributed to the presence of magnesium oxide (MgO). Since Mg is a material with a high tendency toward oxidation, during the milling process, the density of the oxide layer on the Mg surface, which is broken down, can interfere with the experimental result. These magnesium oxides can be located at the grain boundaries of the Mg matrix in the SiC-free regions and can inhibit or delay the recrystallization and grain growth of the matrix during DRX, resulting in increasing strength and ductility, as discussed above. Furthermore, it is evident that the adhesion strength of the SiC particles to the matrix in the experimental setup is less strong than the adhesion strength assumed in the RVE simulation. The weaker adhesion in the experiment increases the likelihood of interfacial cracks and, consequently, reduces ductility compared to the results obtained from the RVE simulation. The findings of this study provide materials scientists and engineers with valuable insights into the deformation behavior of Mg-SiC nanocomposites and empower them to develop customized strategies for enhancing the performance of these materials.

5. Conclusions

This study investigated the effect of mechanical milling and SiC particles on the deformation behavior of Mg-SiC nanocomposites under quasistatic load, at both macro- and microscales, using DIC 2d and 3d RVE.

The investigation reveals that the intense localized plastic deformation induced by SiC particles during the mechanical milling process promotes the matrix’s dynamic recrystallization (DRX) during extrusion. Moreover, due to the Smith–Zener pinning effect, the SiC nanoparticles effectively restrict the grain growth of the matrix during extrusion and lead to grain refinement and, consequently, an improvement in the strength and ductile deformation behavior of tbe composite containing micro-SiC. The significantly increased ductility of M10Sµ can be attributed to the homogenous dispersion of SiC particles and their significant adherence to the Mg matrix. This research finding underscores the efficacy of employing DIC and RVE for exploring the deformation behavior of Mg-SiC nanocomposites, offering valuable insights for future studies in this domain.