**3. Results and discussion**

#### **3.1. Compaction process and property characterization**

In PM production, the relationship between the relative density *ρ* and the pressure *P* during compaction is always firstly concerned. Here, the compaction curves (*ρ − P* relations) for different ordered packings of composite Al/SiC powders are shown in **Figure 3**, where the inset images demonstrate the morphologies of the compacts at different compaction stages (marked by A, B, and C) with honeycomb initial packing structure. As can be seen that before compaction, different ordered packing structures correspond to different initial relative densities. For SC and HCP initial packings, both the relative densities increase smoothly with the compaction pressure to a high value. While for the compaction on honeycomb initial packing, the fluctuation of relative density during pressing can be observed when the pressure is very low. This can be explained by: (1) For SC and HCP initial packings, their structures are stable. During compaction the densification is mainly achieved by plastic deformation of Al component, little relative sliding and rolling between Al/SiC composite particles can be observed. Therefore, the compaction curves evolve smoothly; (2) Compared with SC and HCP, honeycomb initial packing structure is less stable. So at the early stage of compaction, the initial ordered packing structure is destroyed (please refer to the evolution of packing morphology in the inset images of **Figure 3(a)** for details, where the arrows indicate the tendency of movement for corresponding particles and the circled areas illustrate the local dense clusters formed after rearrangement), which leads to the rearrangement of the composite particles through sliding and rolling for densification. And this process continues until all the particles are in a stable state. From **Figure 3(a)** one can also find that even the initial

**Figure 3.** (a) Evolution of relative density with the pressure during compaction of different initial ordered packing structures, where the inset figures are the morphologies of compacts from honeycomb initial packing at different compaction stages; (b) morphologies of final compacts obtained in (a) and corresponding stress distributions.

punch and the die are fixed. During compaction, the relative density of the compact is calculated by the displacement of the upper punch, and it is not influenced by the strain rate because the materials are set to be not sensitive to this parameter. Meanwhile, each Al granular mesh was set to global mesh self-adaptive to guarantee the accuracy of simulation results. Once all the simulation parameters are determined, the job will be submitted to the server for running.

Global mesh self-adaptive division: for

**Contact definition Loading setup Operation conditions**

residual stress control

Friction: modified Coulomb friction

Contact method: segment to segment

Large deformation: updated Lagrange function

model

method

Particles: deformable Iteration method: full Newton-Raphson algorithm

Die and punches: rigid Convergence criteria: displacement or

Al part

In PM production, the relationship between the relative density *ρ* and the pressure *P* during compaction is always firstly concerned. Here, the compaction curves (*ρ − P* relations) for different ordered packings of composite Al/SiC powders are shown in **Figure 3**, where the inset images demonstrate the morphologies of the compacts at different compaction stages (marked by A, B, and C) with honeycomb initial packing structure. As can be seen that before compaction, different ordered packing structures correspond to different initial relative densities. For SC and HCP initial packings, both the relative densities increase smoothly with the compaction pressure to a high value. While for the compaction on honeycomb initial packing, the fluctuation of relative density during pressing can be observed when the pressure is very low. This can be explained by: (1) For SC and HCP initial packings, their structures are stable. During compaction the densification is mainly achieved by plastic deformation of Al component, little relative sliding and rolling between Al/SiC composite particles can be observed. Therefore, the compaction curves evolve smoothly; (2) Compared with SC and HCP, honeycomb initial packing structure is less stable. So at the early stage of compaction, the initial ordered packing structure is destroyed (please refer to the evolution of packing morphology in the inset images of **Figure 3(a)** for details, where the arrows indicate the tendency of movement for corresponding particles and the circled areas illustrate the local dense clusters formed after rearrangement), which leads to the rearrangement of the composite particles through sliding and rolling for densification. And this process continues until all the particles are in a stable state. From **Figure 3(a)** one can also find that even the initial

**3. Results and discussion**

Friction coefficient between

Upper punch: velocity control

**Table 3.** Modeling parameters used in the simulation.

particles: *μ* = 0.2

28 Powder Technology

(*v* = 1 mm/s)

**3.1. Compaction process and property characterization**

packing structures are different, the compaction in each case can reach almost full densification with the relative density of about 1.0 for each compact, which exhibits the advantages of the Al/SiC composite powders with core/shell structures. However, the structures of final compacts and the distributions of stresses therein as indicated in **Figure 3(b)** all demonstrate different features. Especially for the compact obtained from honeycomb initial ordered packing, the shape of each composite particle and the distribution of equivalent Von Mises stresses are all non-uniform compared with the former two cases and more like disordered state, which will determine the final performance of the compact.

In comparison with ordered initial packings, the initial random packings of Al/SiC composite powders are frequently encountered in actual PM production. **Figure 4** gives the compaction curves of five initial random packings with different SiC contents and relative densities as well as corresponding model validation. As indicated in **Figure 4(a)**, the compaction curves are quite different from those in **Figure 3(a)**, which can be ascribed to the difference of initial packing structures. For each *ρ* − *P* curve during compaction on random initial packing, three stages can be identified: (1) At the initial compaction stage with very low pressure, the densification is mainly implemented by particle rearrangement to fill the large voids or pores. Here, the translational motion and rotational motion of the particles are dominant in densification. (2) Once a stable packing is formed in the first stage, the compaction steps into the second stage for large deformation. At this stage, the relative density of the compact increases continuously with the pressure due to the plastic deformation of Al component for adjacent pore filling, which greatly increases the relative density. (3) When the pressure exceeds a critical value, the increasing rate of the relative density decreases, and each *ρ* − *P* curve tends to level off because the large deformation of particles creates work hardening which impedes further

**Figure 4.** (a) Compaction curves for five initial random packings with different SiC contents, where the inset figure shows the local zoom of the compaction curves; (b) validation of the numerical model by fitting the simulation results with the Heckel equation (b).

deformation unless extra high pressure is applied. In this stage, the powder mass shows a bulk behavior. In order to validate the effectiveness of the model used in the simulation, the numerical results are fitted with Heckel equation given by [46, 47]:

$$\ln\left[1/(1-\rho\_{\diamond})\right] = \text{UP} + \text{Z} \tag{4}$$

where *σ*<sup>1</sup>

, *σ*<sup>2</sup> , *σ*<sup>3</sup>

SiC when the compaction pressure is 200 MPa.

are the principal Cauchy stresses along three main axes. It can be seen that the

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compaction on different initial packing structures can lead to different densification behavior and rate. For the same initial packing structure, increasing the SiC content can aid the densification. I.e. with a certain compaction pressure, the relative density of the compact with high SiC content is larger than that with low SiC content. This can be explained by the high efficient stress transmission as indicated in **Figure 5(b)** when *P* = 200 MPa. One can see that larger stresses are mainly concentrated on SiC particles (cores) in the compacts with higher SiC content, which can accelerate the densification through mass transfer by adjacent Al deformation extruded by neighboring SiC cores. Compared with the compacts obtained from SC initial packing, the stresses in corresponding compacts with HCP structure are larger, which implies the higher densification rate for the latter case. Meanwhile, from **Figure 5(b)** one can also find that debonding at the interface between Al and SiC occurs for both cases when the SiC content

**Figure 5.** (a) Compaction on SC and HCP ordered initial packing structures with different SiC contents; (b) equivalent Von Mises stress distributions in the compacts formed from SC and HCP initial packings with respectively 25 and 44.4%

is high, the mechanism of this phenomenon can be discussed in the following section.

In addition to the compaction on ordered initial packing structures, the evolutions of morphologies and stresses in the compacts formed by random initial packings with five SiC contents at different compaction stages are also systematically studied. Here, the compaction on the random initial packing with 25% SiC is taken as an example for detailed analysis. **Figure 6** gives the morphology evolution of the compact and corresponding stress transmission/distribution at each compaction stage. As indicated, during compaction both translational motion (including the sliding as indicated by the arrow in the third snapshot of **Figure 6(a)**) and rotational motion are observed, which are mainly occurred in early stage of compaction when the pressure is low. In this case, the densification is mainly due to the rearrangement of the Al/SiC composite particles, and the force chain is formed as a skeleton or network. With the increase of the incremental modeling steps *N*, the particles that form the force network begin to deform when the pressure exceeds their yield limit. Due to the heterogeneity of the force

where *ρ*<sup>c</sup> is the relative density of the compact; *P* is applied pressure; U and Z are constants. **Figure 4(b)** demonstrates that the simulation results agree well with the Heckel equation with high confidence (high R<sup>2</sup> value), which proves the robustness of the numerical model and the accuracy of the simulation results. It needs to note that both the differences of compaction curves as shown in the enlarged zoon of **Figure 4(a)** and of the slopes of the fitting lines as indicated in **Figure 4(b)** can be influenced by the initial packing structure and SiC content. But compared with the compaction on ordered initial packing structures, the influences of SiC content on the densification behavior are less significant, which will be discussed in the subsequent sections.

#### **3.2. Initial packing structure effects**

Previous results have illustrated that the initial packing structure of the composite powder or the SiC content can create effects on the compaction behavior and property of the compact. To further identify their important role in the densification process, the compaction on SC and HCP ordered initial packings with different SiC contents is shown in **Figure 5**, where **Figure 5(a)** gives the compaction curves and **Figure 5(b)** indicates the morphologies of the compacts under the pressure of 200 MPa and the stress distributions therein. Here, the equivalent Von Mises stress is given by:

$$\overline{\sigma} = \left[ (\sigma\_1 - \sigma\_2)^2 + (\sigma\_2 - \sigma\_3)^2 + (\sigma\_3 - \sigma\_1)^2 \right]^{12} / \sqrt{2} \tag{5}$$

MPFEM Modeling on the Compaction of Al/SiC Composite Powders with Core/Shell Structure http://dx.doi.org/10.5772/intechopen.76563 31

**Figure 5.** (a) Compaction on SC and HCP ordered initial packing structures with different SiC contents; (b) equivalent Von Mises stress distributions in the compacts formed from SC and HCP initial packings with respectively 25 and 44.4% SiC when the compaction pressure is 200 MPa.

deformation unless extra high pressure is applied. In this stage, the powder mass shows a bulk behavior. In order to validate the effectiveness of the model used in the simulation, the

**Figure 4.** (a) Compaction curves for five initial random packings with different SiC contents, where the inset figure shows the local zoom of the compaction curves; (b) validation of the numerical model by fitting the simulation results

ln[1/(1 − *ρ*c)] = U*P* + Z (4)

**Figure 4(b)** demonstrates that the simulation results agree well with the Heckel equation with

accuracy of the simulation results. It needs to note that both the differences of compaction curves as shown in the enlarged zoon of **Figure 4(a)** and of the slopes of the fitting lines as indicated in **Figure 4(b)** can be influenced by the initial packing structure and SiC content. But compared with the compaction on ordered initial packing structures, the influences of SiC content on the densification behavior are less significant, which will be discussed in the subsequent sections.

Previous results have illustrated that the initial packing structure of the composite powder or the SiC content can create effects on the compaction behavior and property of the compact. To further identify their important role in the densification process, the compaction on SC and HCP ordered initial packings with different SiC contents is shown in **Figure 5**, where **Figure 5(a)** gives the compaction curves and **Figure 5(b)** indicates the morphologies of the compacts under the pressure of 200 MPa and the stress distributions therein. Here, the equivalent Von

<sup>2</sup> + (*σ*<sup>2</sup> − *σ*3)

<sup>2</sup> + (*σ*<sup>3</sup> − *σ*1)

2 ] 1/2 /√ \_\_

2 (5)

is the relative density of the compact; *P* is applied pressure; U and Z are constants.

value), which proves the robustness of the numerical model and the

numerical results are fitted with Heckel equation given by [46, 47]:

where *ρ*<sup>c</sup>

high confidence (high R<sup>2</sup>

with the Heckel equation (b).

30 Powder Technology

Mises stress is given by:

**3.2. Initial packing structure effects**

*σ*¯ = [(*σ*<sup>1</sup> − *σ*2)

where *σ*<sup>1</sup> , *σ*<sup>2</sup> , *σ*<sup>3</sup> are the principal Cauchy stresses along three main axes. It can be seen that the compaction on different initial packing structures can lead to different densification behavior and rate. For the same initial packing structure, increasing the SiC content can aid the densification. I.e. with a certain compaction pressure, the relative density of the compact with high SiC content is larger than that with low SiC content. This can be explained by the high efficient stress transmission as indicated in **Figure 5(b)** when *P* = 200 MPa. One can see that larger stresses are mainly concentrated on SiC particles (cores) in the compacts with higher SiC content, which can accelerate the densification through mass transfer by adjacent Al deformation extruded by neighboring SiC cores. Compared with the compacts obtained from SC initial packing, the stresses in corresponding compacts with HCP structure are larger, which implies the higher densification rate for the latter case. Meanwhile, from **Figure 5(b)** one can also find that debonding at the interface between Al and SiC occurs for both cases when the SiC content is high, the mechanism of this phenomenon can be discussed in the following section.

In addition to the compaction on ordered initial packing structures, the evolutions of morphologies and stresses in the compacts formed by random initial packings with five SiC contents at different compaction stages are also systematically studied. Here, the compaction on the random initial packing with 25% SiC is taken as an example for detailed analysis. **Figure 6** gives the morphology evolution of the compact and corresponding stress transmission/distribution at each compaction stage. As indicated, during compaction both translational motion (including the sliding as indicated by the arrow in the third snapshot of **Figure 6(a)**) and rotational motion are observed, which are mainly occurred in early stage of compaction when the pressure is low. In this case, the densification is mainly due to the rearrangement of the Al/SiC composite particles, and the force chain is formed as a skeleton or network. With the increase of the incremental modeling steps *N*, the particles that form the force network begin to deform when the pressure exceeds their yield limit. Due to the heterogeneity of the force

schematically illustrates the particle (here two nodes adjacent to SiC core in Al is selected as the research target) relative position before (e.g. ΔOAB) and after (e.g. ΔOA′B′) rotation, here the coordinates of (*x*A, *y*A) for point A, (*x*B, *y*B) for point B, (*x*A′, *y*A′) for point A′, (*x*B′, *y*B′) for point B′ are known at each time step. Therefore, the rotational angle *θ* can be calculated by:

MPFEM Modeling on the Compaction of Al/SiC Composite Powders with Core/Shell Structure

*θ* = *α* + *β* (6)

( *yB* <sup>−</sup> *<sup>y</sup>* \_\_\_\_\_*<sup>A</sup>*

( *yB* ' − *yA* '

To further study the effects of initial packing structures, three packings with the similar relative densities (≈ 0.74) and SiC (25%) but different structures as shown in **Figure 7(b)** were chosen for analysis. The results are shown in **Figure 8**, where **Figure 8(a)** gives the evolution of average rational angle with the relative density of each initial packing structure during compaction and **Figure 8(b)** indicates the quantitative statistics on the distribution of rotational angles. As can be seen from **Figure 8(a)** that with each case, the average rotational angle increases with the relative density but the increasing rate decreases. And different initial packing structures

**Figure 7.** (a) Schematic diagram to calculate the rotation of one particle during compaction; (b) three initial packing structures with similar relative density and SiC content (25%) but different packing structures used for quantitative

\_\_\_\_\_\_ *xB* ' − *xA* '

*xB* <sup>−</sup> *xA*) (7)

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) (8)

where:

and

*α* = tan<sup>−</sup><sup>1</sup>

*β* = tan<sup>−</sup><sup>1</sup>

particle rotation calculation during compaction.

**Figure 6.** (a) Evolution of equivalent Von Mises stresses during compaction on random initial packing with 25% SiC; (b) force chain structure and stress transmission in the compact when the incremental modeling step is *N* = 400, where the circled local structures are the clusters surrounded by the force chains, within which no or only small stresses can be identified in these particles.

structure, the shape of each composite particle in the final compact is irregular. In the whole process, the force chain structure varies, which dominates the deformation of the particles and the stresses are mainly concentrated on SiC particles. To more clearly demonstrate the force chain structure and explain the irregular deformation of the composite Al/SiC particles, the compact obtained at the incremental modeling step *N* = 400 in **Figure 6(a)** is redisplayed while the scale of the legend is reduced as shown in **Figure 6(b)**. From the figure one can see that not all of the particles in the compact are involved in the force chain, some local clusters as circled are shielded by the force chain which makes them free from deformation, because the forces or stresses on these particles are very small or even nil, which will impede the densification process. On the other hand, the particles in the force chain are easily moved or deformed by the large forces acted on them, which will enhance the densification. On the whole, due to the non-uniformity of the force chain and stress distributions, even though the final compact can be fully dense, the deformation of the composite particles therein is not uniform. This phenomenon has been identified in the MPFEM modeling on the compaction of Fe-Al composite powders [42]. While unlike the compaction on mixed binary Al and SiC composite powders, the reinforced SiC particles are uniformly distributed in the fully dense final compact and the stress distributions are also homogeneous, which indicates the advantages of current process applied in PM production.

#### **3.3. Quantitative analysis on particle rearrangement during compaction**

It is known that the densification of composite powders during early stage of compaction is mainly due to the rearrangement of particles through translational motion and rotational motion, while systematic analysis on the particle rotation in the compaction process is less studied because this behavior is difficult to be quantitatively characterized. To achieve this, an algorithm is proposed to calculate the rotation of particles during compaction. **Figure 7(a)**

schematically illustrates the particle (here two nodes adjacent to SiC core in Al is selected as the research target) relative position before (e.g. ΔOAB) and after (e.g. ΔOA′B′) rotation, here the coordinates of (*x*A, *y*A) for point A, (*x*B, *y*B) for point B, (*x*A′, *y*A′) for point A′, (*x*B′, *y*B′) for point B′ are known at each time step. Therefore, the rotational angle *θ* can be calculated by:

$$
\theta = a + \beta \tag{6}
$$

where:

$$\alpha = \tan^{-1} \left( \frac{y\_s - y\_A}{\overline{x\_s - \overline{x\_A}}} \right) \tag{7}$$

and

structure, the shape of each composite particle in the final compact is irregular. In the whole process, the force chain structure varies, which dominates the deformation of the particles and the stresses are mainly concentrated on SiC particles. To more clearly demonstrate the force chain structure and explain the irregular deformation of the composite Al/SiC particles, the compact obtained at the incremental modeling step *N* = 400 in **Figure 6(a)** is redisplayed while the scale of the legend is reduced as shown in **Figure 6(b)**. From the figure one can see that not all of the particles in the compact are involved in the force chain, some local clusters as circled are shielded by the force chain which makes them free from deformation, because the forces or stresses on these particles are very small or even nil, which will impede the densification process. On the other hand, the particles in the force chain are easily moved or deformed by the large forces acted on them, which will enhance the densification. On the whole, due to the non-uniformity of the force chain and stress distributions, even though the final compact can be fully dense, the deformation of the composite particles therein is not uniform. This phenomenon has been identified in the MPFEM modeling on the compaction of Fe-Al composite powders [42]. While unlike the compaction on mixed binary Al and SiC composite powders, the reinforced SiC particles are uniformly distributed in the fully dense final compact and the stress distributions are also homogeneous, which indicates the advan-

**Figure 6.** (a) Evolution of equivalent Von Mises stresses during compaction on random initial packing with 25% SiC; (b) force chain structure and stress transmission in the compact when the incremental modeling step is *N* = 400, where the circled local structures are the clusters surrounded by the force chains, within which no or only small stresses can

tages of current process applied in PM production.

be identified in these particles.

32 Powder Technology

**3.3. Quantitative analysis on particle rearrangement during compaction**

It is known that the densification of composite powders during early stage of compaction is mainly due to the rearrangement of particles through translational motion and rotational motion, while systematic analysis on the particle rotation in the compaction process is less studied because this behavior is difficult to be quantitatively characterized. To achieve this, an algorithm is proposed to calculate the rotation of particles during compaction. **Figure 7(a)**

$$\beta = \tan^{-1} \left( \frac{y\_a^{\prime} - y\_A^{\prime}}{x\_a^{\prime} - x\_A^{\prime}} \right) \tag{8}$$

To further study the effects of initial packing structures, three packings with the similar relative densities (≈ 0.74) and SiC (25%) but different structures as shown in **Figure 7(b)** were chosen for analysis. The results are shown in **Figure 8**, where **Figure 8(a)** gives the evolution of average rational angle with the relative density of each initial packing structure during compaction and **Figure 8(b)** indicates the quantitative statistics on the distribution of rotational angles. As can be seen from **Figure 8(a)** that with each case, the average rotational angle increases with the relative density but the increasing rate decreases. And different initial packing structures

**Figure 7.** (a) Schematic diagram to calculate the rotation of one particle during compaction; (b) three initial packing structures with similar relative density and SiC content (25%) but different packing structures used for quantitative particle rotation calculation during compaction.

can result in different rotation behavior even the relative density and the composition of the composite powder are similar. Meanwhile, one can also find that the fast increasing region of rational angle is mainly located in the region where the relative density is lower than about 0.82. Previous researches [48] have demonstrated that 0.82 is the relative density of random close packing state with stable structure for 2D disks, beyond which both the translational motion and rotational motion during compaction become difficult. This variation has similar trend with previous results from other packing systems [31]. Besides, the distribution of average rotation angle in **Figure 8(b)** indicate that during compaction most particles rotate with the angle of 1–5°. Large scale particle rotation is mainly formed at the initial rearrangement stage of the compaction when the pressure is low. Because after deformation under high pressure the contact between neighboring particles changes from point to face, which restrains the further rotation of composite particles. From **Figure 8(b)** one can also find that different initial packing structures can lead to different rotation behavior, which will further determine the densification process as well as the resultant properties of the final compacts.

#### **3.4. Debonding and rebonding phenomena**

During compaction on composite powders with core/shell structures, a common phenomenon, i.e. debonding can be occurred, which has also been observed at the Al/SiC interface in current MPFEM simulation. Interestingly, after debonding, the separated Al and SiC in a composite particle can rebond again to form a good cohesion and combination at the interface. It needs to clarify that in current simulation only physical interaction at the interface is considered, chemical reactions are not included. Previous results in this chapter have shown that some composite particles are debonded during compaction. Especially for those particles that are close to the punches or close to the large voids, the debonding is more probable. Those composite particles that form local ordered dense packing structure are not likely to

debond unless the SiC content is very large. In order to explain the mechanisms of debonding and rebonding phenomena, a single Al/SiC composite particle in initial random packing is selected for analysis. The evolution of normal stresses and shear stresses in this particle at different stages of compaction is shown in **Figure 9**. As can be imagined from the figure that at the early stage of compaction, composite particles are fully rearranged with the help of relatively low pressure from the upper punch. In this case, no matter the tangential forces or the normal forces between particles or between Al and SiC at the interface are all very small. With the increase of the compaction pressure, the contact forces between composite particles increase. The large extrusion deformation or the shear due to relative sliding induces large tangential stresses at the interface between Al shell and SiC core, when the normal

incremental modeling steps.

**Figure 9.** Evolution of (a): normal stress (a–d) and (b): shear stress (A–D) at the interface between Al and SiC of a given core/shell particle when SiC content is 25%. And (a–d)/(A–D) respectively correspond to 800, 1500, 1900, and 2160

MPFEM Modeling on the Compaction of Al/SiC Composite Powders with Core/Shell Structure

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**Figure 8.** (a) Evolution of average rotational angle with the relative density for each initial packing structure during compaction when the SiC content is 25%; (b) distribution of average rotational angle in the final compacts formed by different initial packing structures.

MPFEM Modeling on the Compaction of Al/SiC Composite Powders with Core/Shell Structure http://dx.doi.org/10.5772/intechopen.76563 35

can result in different rotation behavior even the relative density and the composition of the composite powder are similar. Meanwhile, one can also find that the fast increasing region of rational angle is mainly located in the region where the relative density is lower than about 0.82. Previous researches [48] have demonstrated that 0.82 is the relative density of random close packing state with stable structure for 2D disks, beyond which both the translational motion and rotational motion during compaction become difficult. This variation has similar trend with previous results from other packing systems [31]. Besides, the distribution of average rotation angle in **Figure 8(b)** indicate that during compaction most particles rotate with the angle of 1–5°. Large scale particle rotation is mainly formed at the initial rearrangement stage of the compaction when the pressure is low. Because after deformation under high pressure the contact between neighboring particles changes from point to face, which restrains the further rotation of composite particles. From **Figure 8(b)** one can also find that different initial packing structures can lead to different rotation behavior, which will further determine the

densification process as well as the resultant properties of the final compacts.

During compaction on composite powders with core/shell structures, a common phenomenon, i.e. debonding can be occurred, which has also been observed at the Al/SiC interface in current MPFEM simulation. Interestingly, after debonding, the separated Al and SiC in a composite particle can rebond again to form a good cohesion and combination at the interface. It needs to clarify that in current simulation only physical interaction at the interface is considered, chemical reactions are not included. Previous results in this chapter have shown that some composite particles are debonded during compaction. Especially for those particles that are close to the punches or close to the large voids, the debonding is more probable. Those composite particles that form local ordered dense packing structure are not likely to

**Figure 8.** (a) Evolution of average rotational angle with the relative density for each initial packing structure during compaction when the SiC content is 25%; (b) distribution of average rotational angle in the final compacts formed by

**3.4. Debonding and rebonding phenomena**

34 Powder Technology

different initial packing structures.

**Figure 9.** Evolution of (a): normal stress (a–d) and (b): shear stress (A–D) at the interface between Al and SiC of a given core/shell particle when SiC content is 25%. And (a–d)/(A–D) respectively correspond to 800, 1500, 1900, and 2160 incremental modeling steps.

debond unless the SiC content is very large. In order to explain the mechanisms of debonding and rebonding phenomena, a single Al/SiC composite particle in initial random packing is selected for analysis. The evolution of normal stresses and shear stresses in this particle at different stages of compaction is shown in **Figure 9**. As can be imagined from the figure that at the early stage of compaction, composite particles are fully rearranged with the help of relatively low pressure from the upper punch. In this case, no matter the tangential forces or the normal forces between particles or between Al and SiC at the interface are all very small. With the increase of the compaction pressure, the contact forces between composite particles increase. The large extrusion deformation or the shear due to relative sliding induces large tangential stresses at the interface between Al shell and SiC core, when the normal contact forces or stresses are very small at this region, the debonding occurs. While with the further increase of the compaction pressure, the bulk density of the compact increases. The normal contact forces or stresses at the debonding region increase due to the extrusion from neighboring particles, leading to the rebonding at the interface. Through comparison, one can conclude that the occurrence of debonding phenomenon, which has also been identified in others' work [49], is mainly caused by sufficient tangential forces but insufficient normal forces at the interface. Therefore, the interface should have a certain shear strength and relatively large normal strength, which can not only effectively avoid the possible debonding, but also make the distribution of equivalent strain in the matrix more uniform.

also provide the materials scientists and engineers with valuable references for the realization

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The authors are grateful to National Natural Science Foundation of China (No. 51374070) and Fundamental Research Funds for the Central Universities of China (No. N162505001) for the

of high performance Al/SiC compact in future PM production.

We declare that we have no conflicts of interest to this work.

**Acknowledgements**

**Conflict of interest**

**Nomenclature**

**Scalars**

financial support of current work.

A strength coefficient B material constant *E* Young's modulus

m work hardening index

n material constant O center of a circle

*P* compaction pressure *r* radius of SiC particle

R<sup>2</sup> relative coefficient

*x* coordinate on X axis *y* coordinate on Y axis

U constant *v* velocity

Z constant

*N* incremental modeling step

*R* radius of Al/SiC composite particle
