**2. Simulation method and conditions**

### **2.1. Simulation method**

Al/SiC nanocomposites (with 1.5 vol.% SiC) exhibited the best mechanical and thermal per-

Aforementioned researches in physical experiments indicate that most of the previous work was mainly focusing on the sintering stage or the forming stage, comprehensive studies on the compaction of Al/SiC composite powders are less conducted. Actually, most of the densification takes place in the compaction stage by rate-independent plasticity [1]. And the relative density (defined as the volume of the powder divided by the volume occupied by the die) and corresponding packing structure of the compact can determine the subsequent sintering process as well as the final properties of the sintered component. Therefore, the researches on the compaction of Al/SiC composite powders when subjected to external energy have increasingly attracted the materials scientists and engineers' interests in the past few years. Nevertheless, even though physical experiments can reproduce the relationship between relative density and compaction pressure and/or temperature, they are unable to quantitatively characterize the local density distribution, stress distribution, and particle motion behavior for pore (or void) filling in situ, especially the nonlinearity features in geometry, materials, and contact during compaction all increase the difficulties of physical experiments [18–22]. Most importantly, it's really hard for researchers to accurately control the uniform distribution (ordered or disordered) of reinforcement (SiC) in the metal (Al) matrix, these disadvantages in physical experiments can be conquered by the so called numerical simulations.

Numerically, various models or methods were proposed or used to simulate powder compaction densification in PM process. For example, a traditional macro continuous FEM (finite element method) simulation model, in which the powder mass is regarded as a continuum with uniform void distribution, was proposed to solve the problems arising from physical experiments. In addition to the relationship between overall relative density and compaction pressure, this method can also be used to analyze local relative density and distribution, stress distribution, and powder displacement in the compact upon compaction from macro continuous scale. Therefore, as reported in the authors' previous researches, the single-action die compaction of pure metal powders [23, 24] and composite powders [25] has been systematically investigated by this method. Even though the traditional FEM can to some extent solve the problems in physical experiments, it is really hard to deal with the important issues like dynamics and contact mechanics from particulate scale based on the aforementioned continuum assumptions. However, this will be overcome by molecular dynamics based DEM (discrete element method) simulation. DEM has been widely applied to generate various packing structures of spherical and non-spherical particles [26–29], but its effectiveness in modeling the compaction of powders is restricted to limited relative density (e.g. *ρ* < 0.85) [30]. For higher relative density and extra large plastic deformation in PM compaction, a new method MPFEM (multi-particle FEM) has been developed and successfully applied in modeling this process [31–43], but less work was conducted on the compaction of Al/SiC composite powders from particulate scale. Recently, using MPFEM the authors successfully modeled the single action die compaction of Al/SiC composite mixtures [44], and the results show that the packing state, size and number of SiC particles in the initial packing structure can significantly influence not only the densification of the Al/SiC composite powders upon compaction but also the properties of the compacts. Even though our previous numerical simulation can reproduce the compaction of

formance as compared to the other developed Al/SiC nanocomposites.

24 Powder Technology

The simulation method used in current work is MPFEM. In this method, the initial random powder packing is firstly generated by DEM and then imported into FEM model, where each particle is fully discretized into finite element meshes. **Figure 1** respectively gives the schematic diagram of an individual composite particle with core/shell structure and corresponding mesh division as well as the numerically generated initial packing structure in the closed die before compaction when the SiC content is 25 vol.%, where each core (SiC)/shell (Al) composite particle includes respectively 200/1700 nodes and 173/1552 elements. After all the parameters and conditions are determined, the program will be complied and run in the commercialized MSC.Marc software. For simplicity, the details of DEM model are not given here, interested readers can refer to [26–29, 45] for more information. In comparison, each initial ordered binary packing is generated by the intrinsic function in MSC.Marc software based on geometry. The initial random or ordered packing structure was then imported into MPFEM model as the input. **Figure 2** shows the packing morphologies of Al/SiC composite powders before compaction. Here three initial ordered packings, i.e. simple cubic (SC), hexagonal close packed (HCP) and honeycomb structures are considered. The composition of the composite powder can be adjusted by the thickness of Al shell, which is represented by *R* – *r*, where *R* and *r* are respectively the radius of the composite Al/SiC particle and the radius of SiC particle therein. It needs to clarify that the SiC content used in this chapter all refers to volume fraction. For each initial packing structure before compaction, corresponding parameters such as the size ratio between the radius of SiC particle and the radius of the whole composite particle (*r*/*R*), SiC content (vol.%), and packing density (or relative density) are listed in **Table 1**.

**Figure 1.** (a) Schematic diagram of an individual Al/SiC composite particle with core/shell structure and mesh division used in MPFEM simulation; (b) DEM generated initial packing structure in a closed die before compaction with 25% SiC.

mesh adaptability, and loading cases etc. were then set. In the simulation, the power law model is used to describe the properties of aluminum materials and the yield stress is given by:

**Table 1.** Corresponding parameters for initial packing structures of composite powders before compaction.

**Initial packing structure Size ratio (***r***/***R***) SiC content, vol.% Packing density**

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

SC 1/2 25 0.7841 SC 2/3 44.4 0.7842 HCP 1/2 25 0.8782 HCP 2/3 44.4 0.8783 Honeycomb 1/2 25 0.6045 Random 1/√10 10 0.7516 Random √15/10 15 0.7526 Random 1/√5 20 0.7544 Random 1/2 25 0.7424 Random √3/√10 30 0.7515

> ¯) <sup>m</sup> + B *ε* ¯ .n

*ε*<sup>0</sup> = (*E*/A)1/(m−1) (2)

. <sup>=</sup> [2/3(*ε*ij *<sup>ε</sup>*ij)]

where *ε*ij is the strain tensor. The material parameters and modeling parameters are respectively given in **Tables 2** and **3**. Here, SiC material was assumed to be elastomer due to its high hardness compared with Al. In the simulation, the upper punch is movable, while the lower

**MPa**

is the initial yield strain; *ε*

are assumed to be zero. Therefore, the initial yield strain can

(1)

27

¯ . is

¯ is the equivalent strain; *ε*

http://dx.doi.org/10.5772/intechopen.76563

1/2 (3)

**Work hardening index, m**

*σ<sup>y</sup>* = A (*ε*<sup>0</sup> + *ε*

¯ and *ε* ¯ .

**Materials Young's modulus,** *E***/GPa Poisson's ratio, ν Strength coefficient, A/**

SiC 470.00 0.142 Elastic-perfectly

Al 70.00 0.33 225.90 0.05

¯

where *E* is Young's modulus. The equivalent strain rate is:

where A, B, m, n are material constants; *ε*<sup>0</sup>

*ε*

**Table 2.** Materials parameters used in the simulation.

equivalent strain rate. Initially, *ε*

be expressed as:

**Figure 2.** Initial packing structures of Al/SiC composite particles before compaction, where: (a) SC packing; (b) HCP packing; (c) honeycomb packing; (d)–(h) represent random packings with the SiC content of 10, 15, 20, 25, and 30% in volume fraction.

#### **2.2. Simulation conditions**

After the generated binary initial packing structure was imported into the MPFEM model in MSC. Marc software, the simulation conditions including material properties, definition of contact, MPFEM Modeling on the Compaction of Al/SiC Composite Powders with Core/Shell Structure http://dx.doi.org/10.5772/intechopen.76563 27


**Table 1.** Corresponding parameters for initial packing structures of composite powders before compaction.

mesh adaptability, and loading cases etc. were then set. In the simulation, the power law model is used to describe the properties of aluminum materials and the yield stress is given by:

$$
\sigma\_y = \text{A}\left(\varepsilon\_0 + \overline{\varepsilon}\right)^{\text{m}} + \text{B}\,\overline{\overline{\varepsilon}}^{\text{n}} \tag{1}
$$

where A, B, m, n are material constants; *ε*<sup>0</sup> is the initial yield strain; *ε* ¯ is the equivalent strain; *ε* ¯ . is equivalent strain rate. Initially, *ε* ¯ and *ε* ¯ . are assumed to be zero. Therefore, the initial yield strain can be expressed as:

$$
\varepsilon\_0 = \text{ (E/A)}^{1/(m-1)} \tag{2}
$$

where *E* is Young's modulus. The equivalent strain rate is:

$$
\vec{\overline{\varepsilon}}^{\cdot} = \begin{bmatrix} \mathfrak{Z}/\mathfrak{Z}\_{\left[\varepsilon\_{\parallel}\right]} \varepsilon\_{\parallel} \end{bmatrix}^{1/2} \tag{3}
$$

where *ε*ij is the strain tensor. The material parameters and modeling parameters are respectively given in **Tables 2** and **3**. Here, SiC material was assumed to be elastomer due to its high hardness compared with Al. In the simulation, the upper punch is movable, while the lower


**Table 2.** Materials parameters used in the simulation.

**2.2. Simulation conditions**

volume fraction.

26 Powder Technology

After the generated binary initial packing structure was imported into the MPFEM model in MSC. Marc software, the simulation conditions including material properties, definition of contact,

**Figure 2.** Initial packing structures of Al/SiC composite particles before compaction, where: (a) SC packing; (b) HCP packing; (c) honeycomb packing; (d)–(h) represent random packings with the SiC content of 10, 15, 20, 25, and 30% in

**Figure 1.** (a) Schematic diagram of an individual Al/SiC composite particle with core/shell structure and mesh division used in MPFEM simulation; (b) DEM generated initial packing structure in a closed die before compaction with 25% SiC.


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

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.

> 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

> **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.

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

http://dx.doi.org/10.5772/intechopen.76563

29

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

state, which will determine the final performance of the compact.
