Document [original]

Citation: Rahimi Mehr, F.; Kamrani,

S.; Fleck, C.; Salavati, M. Optimal

Performance of Mg-SiC

Nanocomposite: Unraveling the

Influence of Reinforcement Particle

Size on Compaction and

Densification in Materials Processed

via Mechanical Milling and Cold

Iso-Static Pressing. Appl. Sci. 2023,13,

8909. https://doi.org/10.3390/

app13158909

Academic Editor: Andrea Carpinteri

Received: 13 May 2023

Revised: 29 June 2023

Accepted: 28 July 2023

Published: 2 August 2023

Licensee MDPI, Basel, Switzerland.

This article is an open access article

distributed under the terms and

conditions of the Creative Commons

Attribution (CC BY) license (https://

creativecommons.org/licenses/by/

4.0/).

applied

sciences

Article

Optimal Performance of Mg-SiC Nanocomposite: Unraveling

the Influence of Reinforcement Particle Size on Compaction and

Densification in Materials Processed via Mechanical Milling

and Cold Iso-Static Pressing

Fatemeh Rahimi Mehr , Sepideh Kamrani, Claudia Fleck and Mohammad Salavati *

Faculty III Process Sciences, Institute of Materials Science and Technology, Technische Universität Berlin,

Fachgebiet Werkstofftechnik, Strasse des 17. Juni 135, 10623 Berlin, Germany;

[email protected] (F.R.M.)

*Correspondence: [email protected]

Abstract:

Achieving uniformly distributed reinforcement particles in a dense matrix is crucial for

enhancing the mechanical properties of nanocomposites. This study focuses on fabricating Mg-SiC

nanocomposites with a high-volume fraction of SiC particles (10 vol.%) using cold isostatic pressing

(CIP). The objective is to obtain a fully dense material with a uniform dispersion of nanoparticles. The

SiC particle size impact on the compressibility and density distribution of milled Mg-SiC nanocom-

posites is studied through the elastoplastic Modified Drucker-Prager Cap (MDPC) model and finite

element method (FEM) simulations. The findings demonstrate significant variations in the size and

dispersion of SiC particles within the Mg matrix. Specifically, the Mg-SiC nanocomposite with 10%

submicron-scale SiC content (M10S

) exhibits superior compressibility, higher relative density, in-

creased element volume (EVOL), and more consistent density distribution compared to the composite

containing 10% nanoscale SiC (M10Sn) following CIP simulation. Under 700 MPa, M10S

shows

improvements in both computational and experimental results for volume reduction percentage,

2.31% and 2.81%, respectively, and relative density, 4.14% and 3.73%, respectively, compared to

M10Sn. The relative density and volume reduction outcomes are in qualitative alignment with

experimental findings, emphasizing the significance of particle size in optimizing nanocomposite

characteristics.

Keywords:

Mg-SiC composite; nano and micro-sized SiC particles; density distribution; cold isostatic

press; modified Drucker-Prager Cap model

1. Introduction

Magnesium-based metal matrix composites (MMCs), owing to their advantageous

characteristics such as superior strength-to-weight ratio, enhanced thermal conductivity,

and commendable wear resistance, have elicited significant interest, positioning them as a

material of choice for advanced applications across diverse industries, including automo-

tive, aerospace, and electronics [

]. However, magnesium-based MMCs exhibit limited

strength and ductility. Incorporating reinforcement particles like SiC can significantly

improve these properties [3,4].

The particle size is a critical determinant in shaping the microstructure and thereby in-

fluencing the properties of particle-reinforced magnesium matrix composites (PRMMCs) [

Recent research suggest micron-sized ceramic particles may reduce ductility, and nano-

sized reinforcements can enhance strength and ductility in Mg-composites [6,7].

Despite promising results, achieving uniform density distribution in green compacted

parts during consolidation remains challenging, as inhomogeneous density distribution

can cause nonuniform shrinkage or distortion during subsequent processes [

]. Particle

Appl. Sci. 2023,13, 8909. https://doi.org/10.3390/app13158909 https://www.mdpi.com/journal/applsci

Appl. Sci. 2023,13, 8909 2 of 13

size, shape, and distribution influence the desired density distribution [

]. Mechanical

milling has shown great promise as a method to attain homogeneous dispersion of nano-

reinforcement particles within the matrix [

]. However, mechanical milling can result in

microstructural refinement and strain hardening, hindering further plastic deformation

during compaction. Conventional compaction methods, such as uniaxial pressing, may

need to be revised for consolidating milled powder, leading to high porosity [

]. Cold

isostatic pressing (CIP) is a cost-effective method for producing green ceramic compo-

nents with uniform density and high quality [

]. Optimizing process parameters such as

pressure, time, and change in pressure rate is essential for achieving the desired density

distribution at an affordable price [

]. However, predicting density distribution can be

challenging. While various experimental methods such as Nuclear Magnetic Resonance

(NMR) radioscopy [

], micro-indentation [

], X-ray tomography [

] have been used, they

are not practical for predicting the densification behavior of powders before completing

the experiment.

Finite element method (FEM) simulations have become reliable for predicting and

analyzing powder densification behavior, reducing costs and time waste [

–

]. Simulat-

ing powder compaction processes numerically necessitates the use of suitable continuum

models capable of accurately depicting densification behaviors, which can be studied and

modeled by examining powder interactions after characterizing the powder based on its

size, hardness, and shap. The Modified Drucker Prager Cap (MDPC) model is frequently

employed to study the densification behavior of powders, treating them as a homogeneous

continuum [

–

]. The MDPC model represents powders as a uniform continuum, con-

sidering input parameters encompassing elastic behavior, shear failure surface definition,

cap shape determination, and the governing hardening law that prescribes alterations in

material strength with plastic deformation [

]. Reiterer et al. employed the MDPC model

to characterize the densification behavior of SiC components. In the prior research [

], the

MDPC model was utilized to estimate the impact of SiC nanoparticle density distribution

on the compressibility of milled powder following CIP. The findings demonstrated a strong

correlation between simulation and experimental outcomes for Mg-SiC nanocomposites

using the MDPC model.

This study investigates how the size of reinforcement particles impacts the densifi-

cation behavior of milled Mg-SiC powders during CIP. The MDPC model was utilized to

simulate the CIP process using FEM. Various tests were conducted, including uniaxial and

Brazilian compressive tests, die compaction test, and CIP experiments, to derive the param-

eters for the modified Drucker-Prager Cap (DPC) model. The study assessed the impact

of nano and submicron-sized SiC reinforcements on the compaction behavior and density

distribution of Mg-SiC nanocomposites within the Cold Isostatic Pressing. Moreover, sim-

ulation results of the CIP process for Mg-SiC composites were analyzed and discussed,

including pressure distribution, relative density distribution, and element volumes.

2. Modified Drucker-Prager Cap Constitutive Model and Related Parameters

The MDPC model assumes that the material is a compressible continuum. This model

is an elastoplastic, volumetric hardening plasticity model. Numerical studies in this paper

are based on the MDPC model implemented in the commercial software ABAQUS 6.14-4

(SIMULIA, Providence, RI, USA). Figure 1shows the yield surface of the MDPC model.

The model operates under the assumption of isotropy, and its yield surface is com-

prised of three segments: a shear failure surface, which predominantly drives shear flow;

Fs, describe as in [24]:

Fs=q−p tanβ−d=0 (1)

where

and dare the friction angle and cohesion of material, respectively, qis deviatoric,

or Mises stress, and, prepresents hydrostatic pressure.

Appl. Sci. 2023,13, 8909 3 of 13

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Figure 1. An illustration of Drucker-Prager Cap model: yield surface in the p-q plane.

The model operates under the assumption of isotropy, and its yield surface is com-

prised of three segments: a shear failure surface, which predominantly drives shear flow;

Fs, describe as in [24]:

𝐹𝑠=𝑞−𝑝 𝑡𝑎𝑛𝛽− 𝑑=0

(1)

where β and d are the friction angle and cohesion of material, respectively, q is deviatoric,

or Mises stress, and, p represents hydrostatic pressure.

A cap, providing an inelastic hardening mechanism to represent plastic compaction

(Fc), is written as [26]:

𝐹𝑐=√(𝑃−𝑃𝑎)2+( 𝑅𝑞

1+𝛼−𝛼 𝑐𝑜𝑠𝛽

⁄)2−𝑅(𝑑+𝑃𝑎 𝑡𝑎𝑛𝛽)=0

(2)

where R denotes the material parameter that manipulates the form of the cap. α represents

a minor coefficient used to delineate the transition yield surface. 𝑃𝑎 acts as an evolution-

ary parameter that signifies the progression of the volumetric plastic strain-induced hard-

ening and is expressed as:

𝑃𝑎=𝑃𝑏−𝑅𝑑

(1+𝑅𝑡𝑎𝑛𝛽)

(3)

Pb is the hydrostatic pressure that determines the cap position and is denoted as:

𝜀𝑣𝑝𝐿=ln(𝜌

𝜌0)

(4)

In this equation, 𝜀𝑣𝑝𝑙 is the volumetric plastic strain, ρ is the current relative density,

while ρ0 denotes the initial relative density. At the end of the cap surface, powders have

been consolidated under high pressure, making the powder challenging to compress [24].

The transient surface (Ft), a transition region between the cap yield and shear failure

surfaces, is introduced to prepare a smooth surface purely for facilitating the numerical

implementation [24] and written as:

𝐹𝑡 = √(𝑃−𝑃𝑎)2+ [𝑞 − (1 − 𝛼

𝑐𝑜𝑠𝛽)(d+𝑃𝑎 𝑡𝑎𝑛𝛽)]2 − α (d + 𝑃𝑎 𝑡𝑎𝑛𝛽) = 0

(5)

These three surfaces can be used to model the three powder compaction stages.

Figure 1. An illustration of Drucker-Prager Cap model: yield surface in the p-q plane.

A cap, providing an inelastic hardening mechanism to represent plastic compaction

(Fc), is written as [26]:

Fc=s(P−Pa)2+ ( Rq

1+α−α/cosβ)

−R(d+Patanβ)=0 (2)

where Rdenotes the material parameter that manipulates the form of the cap.

represents

a minor coefficient used to delineate the transition yield surface.

acts as an evolutionary

parameter that signifies the progression of the volumetric plastic strain-induced hardening

and is expressed as:

Pa=Pb−Rd

(1+Rtanβ)(3)

Pbis the hydrostatic pressure that determines the cap position and is denoted as:

εpL

v=lnρ

ρ0(4)

In this equation,

εpl

is the volumetric plastic strain,

is the current relative density,

while

ρ0

denotes the initial relative density. At the end of the cap surface, powders have

been consolidated under high pressure, making the powder challenging to compress [24].

The transient surface (F

), a transition region between the cap yield and shear failure

surfaces, is introduced to prepare a smooth surface purely for facilitating the numerical

implementation [24] and written as:

Ft=s(P−Pa)2+q−1−α

cosβ(d+Patanβ)]2−α(d+Patanβ)=0 (5)

These three surfaces can be used to model the three powder compaction stages.

3. Materials and Experimental Methods

3.1. Materials

In this study, magnesium (Mg) powder was used as the matrix material, and

-SiC

powder with purity of 99.8% was employed as the reinforcement. The powders were

provided by Alfa Aesar (Ward Hill, MA, USA). Mg-SiC composite mixtures, namely M10S

and M10Sn, containing 10 vol% SiC submicron particles and 10 vol% SiC nanoparticles,

respectively, were prepared through 25 h of high-energy mechanical milling. In order to

govern the milling process and reduce cold welding in the mixture, a milling process control

agent (PCA) in the form of 2 wt% stearic acid was applied [

]. The powder mixtures were

mixed for 20 min on a rolling bank to ensure homogeneity.

Appl. Sci. 2023,13, 8909 4 of 13

The milling process was conducted using a planetary ball mill (Pulverisette 5, Fritsch,

Germany) in a hard PE with zirconia balls vessel for 25 h. The ball-to-powder weight

ratio and rotational speed were maintained 10:1 and 250 rpm, respectively, throughout the

milling process. All handling, mixing, and milling procedures were carried out in a glove

box under an argon atmosphere with high purity.

The average grain sizes of the as-received Mg, SiC, and vol% of SiC in the Mg-SiC

powder composite are listed in Table 1.

Table 1.

The particle sizes of as-received Mg, SiC, and the particles volume percent (Vol%) of the

Mg-SiC powder composites.

Sample Mg Average Particle Size SiC Average Particle Size SiC Particle Vol%

M10Sµ(Mg+ Submicron size SiC) 40 µm/1µm 10%

M10Sn (Mg+ Nano size SiC) 40 µm 50 nm 10%

3.2. Experimental Methods

In order to comprehensively characterize the yield surface, the following parameters

need to be determined:

,d,

,R,

and

[

]. To define the Drucker-Prager shear

failure surface, the internal friction angle

and the cohesion of material dare required; to

specify the cap surface, the cap shape parameter Rand evolution

are needed [

The various experiments shown in Table 2were used to determine the DPC parameters.

Lastly, for the DPC parameters determined from the experiments shown in Table 2, we

have referenced a summary in our current study and provided detailed descriptions in our

previous study [27].

Table 2. The calibration of Modified Drucker-Prager Cap model.

Testing Procedure Description Parameter, Unit

axial compression test cohesion of material d, MPa

Radial compression test friction angle β, degree

Instrumented die compaction test Cap eccentricity R

CIP experiment Pressure (Hardening law) Pb, Mpa

Prior to the main compaction process, the samples were subjected to pre-compaction

using a uniaxial press equipment. The die used for pre-compaction had a circular tube

shape with an external diameter, an internal diameter, and a height of 20 mm,10 mm, and

50 mm, respectively. The punches, and the die utilized in the pre-compaction were made

from 115CrV3 steel, which has a Poisson ratio of 0.3 and Young’s modulus of 210 GPa.

Silicon spray was sprayed in the inner surface of die wall to decrease the friction of particles

and the die surface [28].

Five samples of each composition were subjected to a series of Brazilian and uniaxial

compression tests to determine the shear failure line parameters, the cohesion of material

(d), and the friction angle (

). The specimens with height-to-diameter aspect ratios of 1.5:1

and 0.25 were used for the uniaxial and Brazilian compression tests. Axial loading for

the tests was applied using the Hegewald & Peschke material testing system (Nossen,

Sachsen, Germany).

Figure 2a,b present the failure mode of the Brazilian and uniaxial compression tests,

respectively. During the Brazilian compression test, the samples underwent compression

diametrically. The resulting radial strength for Brazilian compression test

σT

of the samples

can be determined using the following equation:

σT=2PT

ΠDt (6)

Appl. Sci. 2023,13, 8909 5 of 13

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Figure 2. (a) the failure mode of the Brazilian compression test mode of failure, (b) the failure mode

of the uniaxial compression test, (c) the die compaction set-up, and (d) the die compaction schematic

with four strain gauges.

Finite element analysis was conducted to calculate the hoop strains on the die outer

surface under various uniform interior pressures at different heights. Moreover, a histo-

gram was generated according to the calculated finite element outcomes for radial stress,

hoop strain, and compact height on the outer surface of the die [23]. The hoop strains

resulting from the die compaction test at different compact heights are depicted in Figure

Figure 3. The measured hoop strain εθ for the upper and lower strain gauges versus various com-

pacts height under an interior pressure of 700 MPa for M10Sn and M10Sµ.

Figure 2.

(

) the failure mode of the Brazilian compression test mode of failure, (

) the failure mode

of the uniaxial compression test, (

) the die compaction set-up, and (

) the die compaction schematic

with four strain gauges.

The failure load

and the dimensions of the cylindrical sample, including diameter D

and thickness t, are used to calculate tensile strength for Brazilian compression test

σT

. The

sample stress state experienced by diametrical loading can be mathematically represented

by the following equations:

σC=PC

A(7)

where

and Arepresent the uniaxial breaking force and the sample cross-section area [

From this stress state, the cohesion of material dand friction angle

can be defined

as follows:

d=σCσT(√13 −2)

σC−2σT

(8)

β=tan−13(σC−d)

σC(9)

The cap shape parameters

and Pb

were obtained using the die compaction test.

The similar die used in the uniaxial and Brazilian compaction experiments was utilized for

this test. Figure 2c depicts the die compaction set-up, while Figure 2d illustrates the die

compaction test schematic, which includes four strain gauges on the outer wall of the die

for measuring hoop strains.

The die was carefully filled with the powders to ensure consistent packing. The load

and unload procedures were conducted at a consistent speed of 2 mm/min, which was

controlled by the movement of the upper punch, while the bottom punch stayed unmoved.

Within the die compaction test, the height of the compact underwent continuous changes

in response to the applied pressure. To determine the radial stress, the measured hoop

strains by the strain gauges pasted on the die wall were analyzed.

Finite element analysis was conducted to calculate the hoop strains on the die outer

surface under various uniform interior pressures at different heights. Moreover, a histogram

was generated according to the calculated finite element outcomes for radial stress, hoop

strain, and compact height on the outer surface of the die [

]. The hoop strains resulting

from the die compaction test at different compact heights are depicted in Figure 3.

Appl. Sci. 2023,13, 8909 6 of 13

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Figure 2. (a) the failure mode of the Brazilian compression test mode of failure, (b) the failure mode

of the uniaxial compression test, (c) the die compaction set-up, and (d) the die compaction schematic

with four strain gauges.

Finite element analysis was conducted to calculate the hoop strains on the die outer

surface under various uniform interior pressures at different heights. Moreover, a histo-

gram was generated according to the calculated finite element outcomes for radial stress,

hoop strain, and compact height on the outer surface of the die [23]. The hoop strains

resulting from the die compaction test at different compact heights are depicted in Figure

Figure 3. The measured hoop strain εθ for the upper and lower strain gauges versus various com-

pacts height under an interior pressure of 700 MPa for M10Sn and M10Sµ.

Figure 3.

The measured hoop strain

εθ

for the upper and lower strain gauges versus various compacts

height under an interior pressure of 700 MPa for M10Sn and M10Sµ.

By utilizing the experimental data of a particular height of compaction and the cor-

responding hoop strain, the radial stress was determined by resourcing the histogram

provided from the simulation results. Finally, the cap eccentricity (R) was determined by

utilizing the maximal amount of radial stress, as calculated using Equation (10).

R=1

3√6v

t1+α−α

cos(β)2(p−pa)

q(10)

where

was assumed to be 0.01 for both samples, and the evolution parameter

was

defined from Equation (3) in Section 2[

], and the hydrostatic pressure (p) and deviatoric

stress (q) were determined utilizing Equation (11).

P=1

3(σz+σr)(11)

q=|σz+σr|(12)

where

σz

and

σr

represent the maximal magnitudes of the axial and radial stresses during

loading, respectively.

as a function of the volumetric plastic strain is needed to determine

the cap hardening/softening rule [

]. A series of CIP experiments under pressures ranging

from 100 to 700 MPa and with 10 min holding time in a latex cover was performed for

every sample. All samples were hand-pressed prior to the CIP experiment for 5 min

under 89 MPa pressure in a glove box under an atmosphere with high purity argon. To

mitigate the friction between the particles and the die wall, silicone spray was applied. The

volumetric plastic strain is derived from the relative density as:

εpl

v=lnρ

ρ0(13)

where

represents the sample’s relative density after cold isostatic press, and

ρ0

is the

sample’s relative density after hand press. The Archimedes method in ethanol was applied

to determine the relative density of samples. Figure 4c depicts the plotted curves of

volumetric plastic strain versus pressure, which were utilized to derive the equation for the

hardening law of the samples. Table 3represents the accomplished tests results and the

used DPC model parameters in this work.

Appl. Sci. 2023,13, 8909 7 of 13

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Figure 4. (a) Compressibility-relative density [%] over 100, 300, 500, and 700 [MPa] after CIP for

M10Sµ and M10Sn from Exp. and FEM outcomes. (b) The FEM predicted value of element volume

EVOL [mm3] in the pressure certain domain for M10sµ and M10Sn. (c) Volumetric plastic strain-

Pressure (Hardening law) for M10Sn and M10Sµ (d) FEM and Exp magnitude of e reduction in

volume for M10Sµ and M10Sn under 700 MPa CIP.

Table 3. Modified Drucker-Prager Cap model obtained parameters for M10Sµ and M10Sn.

Sample

Parameter

(Cohesion of

Material,

MPa)

β,

(Friction An-

gle, Degree)

(Cap Shape

Parameter)

Hardening Law

M10Sµ

0.375

76.67

1.77

p = 30.071 𝑒 14.508 𝜀𝑣𝑝

M10Sn

0.36

76.6

0.53

p = 33.434 𝑒 14.508 𝜀𝑣𝑝

3.3. CIP Simulation

The CIP process simulation was conducted using ABAQUS 6.14-4 software (SIM-

ULIA, Providence, RI, USA). The computations were executed on North-German Super-

computing Alliance hardware (HLRN, Zuse Institute, Berlin, Germany). The material was

modeled utilizing the modified Drucker-Prager-Cap model. In the simulation, symmetry

was considered, and due to geometric symmetry, only one-eighth of a cylindrical sample

with a diameter and height of 12 mm and 3 mm was modeled, respectively. Moreover,

Figure 4.

(

) Compressibility-relative density [%] over 100, 300, 500, and 700 [MPa] after CIP for

M10S

and M10Sn from Exp. and FEM outcomes. (

) The FEM predicted value of element volume

EVOL [mm

] in the pressure certain domain for M10s

and M10Sn. (

) Volumetric plastic strain-

Pressure (Hardening law) for M10Sn and M10S

(

) FEM and Exp magnitude of e reduction in

volume for M10Sµand M10Sn under 700 MPa CIP.

Table 3. Modified Drucker-Prager Cap model obtained parameters for M10Sµand M10Sn.

Sample

Parameter

(Cohesion of Material,

MPa)

β,

(Friction Angle, Degree)

(Cap Shape Parameter) Hardening Law

M10Sµ0.375 76.67 1.77 p= 30.071 e14.508 εp

M10Sn 0.36 76.6 0.53 p= 33.434 e14.508 εp

3.3. CIP Simulation

The CIP process simulation was conducted using ABAQUS 6.14-4 software (SIMULIA,

Providence, RI, USA). The computations were executed on North-German Supercomputing

Alliance hardware (HLRN, Zuse Institute, Berlin, Germany). The material was modeled

utilizing the modified Drucker-Prager-Cap model. In the simulation, symmetry was

considered, and due to geometric symmetry, only one-eighth of a cylindrical sample with

a diameter and height of 12 mm and 3 mm was modeled, respectively. Moreover, three

Appl. Sci. 2023,13, 8909 8 of 13

symmetry boundary conditions were applied along the X, Y, and Z planes. Furthermore,

linear brick mesh elements, each consisting of 8 nodes, were utilized for Finite

Element Method. A pressure of 700 MPa was applied to the free surface of 1/8th of the

FEM model.

To compute the relative density after the CIP process from the simulated data, the

hardening law equations were modified in the form of both the initial relative density (

ρ0

)

and the pressure at each step (p) and then incorporated into the output field of the ABAQUS

software. The following formulas were entered for M10S

and M10Sn, respectively:

ρ0

(0.33 P)

0.069

and

ρ0

(0.028 P)

0.072

. The initial relative density of the samples

(

ρ0

) in the formulas was equal to the after hand press relative density, which was 74.62%

and 71.8%, respectively, for M10Sµand M10Sn.

To assess the homogeneity of density distribution and calculate the element volume

(EVol), a Python script was employed. This script analyzed the samples after simulating

the CIP process using ABAQUS CAE software. Furthermore, the volume reduction was

determined by comparing the volume of samples before and after CIP, considering both

experimental and computational results.

4. Results

The behavior of Mg-SiC nanocomposites during compaction was examined utilizing

the MDPC model in FEM simulation to study the impact of submicron and nano-size SiC

reinforcement particles. Figure 5a illustrates the distribution of equivalent pressure stress

for Mg-10% SiC composite mixtures containing both submicron and nano reinforcement

particles at applied pressures of 100, 300, 500, and 700 Mpa. According to these results,

inhomogeneous pressure distribution within the samples was predicted under different

applied pressures, despite the uniformly applied isostatic pressure. The larger equiva-

lent pressure, indicating harder compressibility, is visible in the Mg-SiC nanocomposite

containing nanoparticles reinforcement.

The relative density distributions in M10S

and M10Sn composites are shown in

Figure 5b after CIP simulation under applied pressure values of 100, 300, 500, and 700 Mpa.

As shown in Figure 5b, different relative density distributions were predicted within

M10S

and M10Sn composites after CIP simulation under 100, 300, 500, and 700 MPa

pressure values. The relative density was estimated as described in Section 3.3, and under

the same pressure, M10S

indicated a higher magnitude of relative density compared to

M10Sn. Correspondingly, the higher magnitudes of relative density were predicted as

82.36%, 87.6%, 90.84%, and 92.81% for M10S

and as 79.50%, 84.75%, 87.46%, and 88.67%

for M10Sn.

Figure 4a compares the FEM and experimental approaches for determining relative

density under 100, 300, 500, and 700 MPa uniform isostatic pressure for M10S

and M10Sn.

The computational and experimental outcomes are in good agreement, and M10S

exhibits the maximum magnitude of relative density under different pressures. The element

volume (EVOL) in certain pressure ranges was also calculated in Figure 4b to investigate

the density distribution after CIP. Consequently, the maximum EVOL values computed for

M10S

are considerably higher than those for M10Sn, with values of 28.46 and 18.95 es-

timated within the 690.5 to 717 MPa pressure ranges for M10S

and M10Sn, respectively.

This outcome provides evidence for a higher homogeneous density distribution of the

Mg-SiC composite containing submicron particles. Figure 4c shows the volumetric plastic

strain changes with pressure for M10Sn and M10S

. The volume reduction percentage

under 700 MPa for computational and experimental outcomes was compared in Figure 4d.

It can be observed that M10S

exhibits 2.13% and 2.81% enhancement in volume reduc-

tion percentage for FEM and experimental results, respectively, compared to the values

for M10Sn.

Appl. Sci. 2023,13, 8909 9 of 13

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Figure 5. (a) the contour plots of pressure distribution for M10Sµ and M10Sn after the CIP process

under different applied pressures of 100, 300, 500, and 700 Mpa, (b) the contour plots of Relative

density distribution for M10Sµ and M10Sn after CIP under 100, 300, 500 and 700 MPa.

As shown in Figure 5b, different relative density distributions were predicted within

M10Sµ and M10Sn composites after CIP simulation under 100, 300, 500, and 700 MPa

pressure values. The relative density was estimated as described in Section 3.3, and under

the same pressure, M10Sµ indicated a higher magnitude of relative density compared to

M10Sn. Correspondingly, the higher magnitudes of relative density were predicted as

82.36%, 87.6%, 90.84%, and 92.81% for M10Sµ and as 79.50%, 84.75%, 87.46%, and 88.67%

for M10Sn.

Figure 4a compares the FEM and experimental approaches for determining relative

density under 100, 300, 500, and 700 MPa uniform isostatic pressure for M10Sµ and

M10Sn.

The computational and experimental outcomes are in good agreement, and M10Sµ

exhibits the maximum magnitude of relative density under different pressures. The ele-

ment volume (EVOL) in certain pressure ranges was also calculated in Figure 4b to inves-

tigate the density distribution after CIP. Consequently, the maximum EVOL values com-

puted for M10Sµ are considerably higher than those for M10Sn, with values of 28.46 and

18.95 estimated within the 690.5 to 717 MPa pressure ranges for M10Sµ and M10Sn, re-

spectively. This outcome provides evidence for a higher homogeneous density distribu-

tion of the Mg-SiC composite containing submicron particles. Figure 4c shows the volu-

metric plastic strain changes with pressure for M10Sn and M10Sµ. The volume reduction

Figure 5.

(

) the contour plots of pressure distribution for M10S

and M10Sn after the CIP process

under different applied pressures of 100, 300, 500, and 700 Mpa, (

) the contour plots of Relative

density distribution for M10Sµand M10Sn after CIP under 100, 300, 500 and 700 MPa.

5. Discussion

This study aimed to investigate the effect of SiC particle size on the densification

behavior, specifically the homogeneity of density distribution in Mg-SiC nanocomposites

following the CIP process, which is critical for achieving uniform density distribution. To

meet this, a modified Drucker-Prager Cap (DPC) elastoplastic continuum finite element

method (FEM) model was employed, previously utilized and validated for analyzing

the impact of SiC volume fraction on the Mg-SiC nanocomposites’ density distribution

homogeneity after cold isostatic pressing [

]. The previous study’s results demonstrated

that as the SiC volume fraction increased, the Mg-SiC nanocomposites’ density distribution

homogeneity decreased.

The densification process occurs in three distinct stages. Initially, there is a rearrange-

ment of powder particles, leading to an increase in packing density [

]. In the second stage,

elastic-plastic deformation takes place at the contact areas between particles, resulting in

a higher coordination number and a reduction in porosity as pressure is applied [

]. As

the pressure further increases, the phenomenon of cold welding and/or mechanical inter-

locking becomes prominent. This causes brittle powder particles to fracture and rearrange,

contributing to enhanced densification [

]. The process of densification is influenced

by several factors, including material properties such as hardness, work-hardening, and

cold-welding response, as well as geometric characteristics like particle shape, size, and

Appl. Sci. 2023,13, 8909 10 of 13

distribution [

]. The higher maximal relative density and improved compressibility ob-

served in the Mg-SiC nanocomposite containing submicron-sized SiC particles, as estimated

through FEM calculations under various pressures, can be attributed to the input model

parameters used in the simulation. Higher values of cohesion of material (d) and friction

angle (

) for M10S

compared to M10Sn (see Table 3) indicated enhanced interlocking of

M10S

constituent particles [

], which can be traced back to the microstructural char-

acterization of the powder composite. M10Sn exhibited finer and equiaxed morphology

after 25 h of mechanical milling (Figure 6a), while M10S

powder particles displayed a

more irregular, flake-like morphology (Figure 6b) [

]. The presence of flakes and irregular-

shaped particles creates an asymmetrical local stress field characterized by a significant

shear component. This shear component contributes to the entanglement and cohesion

of the material [

]. The size and shape of the powder particles also influence the friction

angle (

) of a powder composite. Powder composites with fine and equiaxed particles,

such as M10Sn, tended to have a lower friction angle and reduced interlocking between

the powder particles [

]. The cap eccentricity (R) in the MDPC model reflects the prop-

agation of plastic flow among particles and their resistance to deformation or deflection

under applied loads. It provides information about how the particles resist deformation

or deflection under the given load [

]. The significantly lower cap parameter value for

M10Sn, 0.53, compared to M10S

, 1.77, reveals the lower deflection and higher stiffness,

i.e., higher resistance to permanent plastic deformation [

] of the composite containing

the nanoparticles under the same load. Although the volume fraction of SiC reinforcement

in both M10S

and M10Sn is the same at 10%, the smaller grains in M10Sn containing

nanosized SiC compared to M10S

containing submicron-sized SiC result in an increase

in grain boundaries, thereby increasing resistance to plastic deformation and densifica-

tion of M10Sn [

]. The higher value of relative density and volumetric plastic strain of

M10S

under 100, 300, 500, and 700 MPa compared to M10Sn, as shown in (Figure 5b) and

(

Figure 4c

), respectively, confirm the superior densification of Mg-SiC composite containing

the submicron size reinforcement.

In addition to particle size, particle distribution is another crucial parameter affecting

the densification behavior of powder composites [

]. Cross-sections of M10Sn and M10S

milled powders are displayed in (Figure 6c,d), with the Mg matrix in light grey and the SiC

particles as white dots [

]. These Figures indicate a significantly finer nano SiC distribution

than submicron SiC in the Mg matrix. Reducing SiC reinforcement size increases the

reinforcement particles’ perimeter and, consequently, a larger contact surface between the

matrix and reinforcement. In composites containing nano SiC, the increased total contact

surface results in higher pressure transfer to the SiC, which in turn causes a nonuniform

distribution of pressure and, accordingly, a nonuniform density distribution [5,36].

As evidenced by the FEM-predicted results (Figures 4b and 5b), the M10S

exhibits a

more homogeneous relative density distribution, which is attributed to its more homoge-

neous pressure distribution (Figure 5a).

In conclusion, the Drucker-Prager cap (DPC) model effectively predicts the compaction

behavior of powder composites containing different reinforcement sizes. However, there

was an observed relative error of approximately 2% between the computational and experi-

mental outcomes for relative density (Figure 4a) and also a reduction in volume (Figure 4d).

As detailed in the previous work [

], the observed error is attributable to several influenc-

ing factors, such as spring back [

], the use of silicon spray as a lubricant during the CIP

experiment [

], the assumed constant material parameters in the DPC model [

], and the

omission of friction between the particles and die wall during the tests to obtain the DPC

parameters [

]. The present study offers a solid foundation for understanding the intricate

relationship between SiC particle size and the resulting composite properties in Mg-SiC

nanocomposites under Cold Isostatic Pressing. The findings empower materials scientists

and engineers to develop tailored strategies for enhancing Mg-SiC nanocomposite perfor-

mance by shedding light on the underlying mechanisms and key parameters. Ultimately,

Appl. Sci. 2023,13, 8909 11 of 13

this will pave the way for advanced materials with superior characteristics, catering to the

ever-growing demands of various high-performance applications across industries.

Appl. Sci. 2023, 13, x FOR PEER REVIEW 12 of 15

M10Sµ milled powders are displayed in (Figure 6c,d), with the Mg matrix in light grey

and the SiC particles as white dots [33]. These Figures indicate a significantly finer nano

SiC distribution than submicron SiC in the Mg matrix. Reducing SiC reinforcement size

increases the reinforcement particles’ perimeter and, consequently, a larger contact sur-

face between the matrix and reinforcement. In composites containing nano SiC, the in-

creased total contact surface results in higher pressure transfer to the SiC, which in turn

causes a nonuniform distribution of pressure and, accordingly, a nonuniform density dis-

tribution [5,36].

Figure 6. Morphology of milled powders (a) M10Sn and (b) M10Sµ. The Backscattered electron im-

age of (c) M10Sn and (d) M10Sµ displays the dispersion of SiC particles (white) in the magnesium

matrix (light grey) homogeneously [33].

As evidenced by the FEM-predicted results (Figures 4b and 5b), the M10Sµ exhibits

a more homogeneous relative density distribution, which is attributed to its more homo-

geneous pressure distribution (Figure 5a).

In conclusion, the Drucker-Prager cap (DPC) model effectively predicts the compac-

tion behavior of powder composites containing different reinforcement sizes. However,

there was an observed relative error of approximately 2% between the computational and

experimental outcomes for relative density (Figure 4a) and also a reduction in volume

(Figure 4d). As detailed in the previous work [27], the observed error is attributable to

several influencing factors, such as spring back [37], the use of silicon spray as a lubricant

during the CIP experiment [25], the assumed constant material parameters in the DPC

model [11], and the omission of friction between the particles and die wall during the tests

to obtain the DPC parameters [38]. The present study offers a solid foundation for under-

standing the intricate relationship between SiC particle size and the resulting composite

properties in Mg-SiC nanocomposites under Cold Isostatic Pressing. The findings em-

power materials scientists and engineers to develop tailored strategies for enhancing Mg-

SiC nanocomposite performance by shedding light on the underlying mechanisms and

key parameters. Ultimately, this will pave the way for advanced materials with superior

Figure 6.

Morphology of milled powders (

) M10Sn and (

) M10S

. The Backscattered electron

image of (

) M10Sn and (

) M10S

displays the dispersion of SiC particles (white) in the magnesium

matrix (light grey) homogeneously [33].

6. Conclusions

This study comprehensively investigates the critical role of SiC particle size, specifically

nano and submicron-sized particles, on the compressibility and density distribution of

Mg-SiC composites under Cold Isostatic Pressing. The research unveils valuable insights

that pave the way for optimized processing techniques and superior composite properties

by leveraging an advanced elastoplastic-modified Drucker-Prager Cap constitutive model.

The findings underscore three key aspects:

Particle morphology plays a pivotal role in material cohesion and friction angle. The

presence of fine and equiaxed particles in M10Sn decreases compressibility and densi-

fication compared to M10S

, which exhibits flake-like and irregular-shaped particles.

The smaller grain size in M10Sn, relative to M10S

, introduces more grain boundaries,

contributing to increased resistance to plastic deformation. Consequently, M10Sn

exhibits lower cap eccentricity and faces more significant densification challenges.

The distribution of reinforcement particles profoundly influences pressure and density

distribution. Nano-sized SiC particles in M10Sn foster a more extensive contact surface

area with the Mg matrix, leading to heterogeneous pressure distribution and density

distribution compared to the M10Sµcomposite.

Furthermore, this study underscores the utility of employing a modified Drucker-

Prager-Cap (DPC) model in simulating the Cold Isostatic Pressing (CIP) process. This

approach offers a practical and dependable method for predicting the compaction behavior

of Magnesium Silicon Carbide nanocomposite powders, potentially informing and guiding

future research in this area.

Appl. Sci. 2023,13, 8909 12 of 13

Author Contributions:

Conceptualization, F.R.M., S.K., C.F. and M.S.; methodology, F.R.M. and

M.S.; software, F.R.M. and M.S.; validation, F.R.M. and M.S.; formal analysis, F.R.M.; investigation,

F.R.M.; resources, F.R.M., S.K., C.F. and M.S.; data curation, F.R.M. and M.S.; writing—original draft

preparation, F.R.M. and M.S.; writing—review and editing, F.R.M., S.K., C.F. and M.S.; visualization,

F.R.M. and M.S.; supervision, C.F. and M.S.; project administration, F.R.M., C.F. and M.S.; fund-

ing acquisition, S.K., C.F. and M.S. All authors have read and agreed to the published version of

the manuscript.

Funding: This research received no external funding.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: Not applicable.

Acknowledgments:

The authors would like to express their gratitude to the North-German Super-

computing Alliance (HLRN) for providing the necessary computation facilities for this research.

Conflicts of Interest: The authors declare no conflict of interest.

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