Document [original]

ORIGINAL ARTICLE

Cyclic deformation behavior of Mg–SiC nanocomposites on

the macroscale and nanoscale

Daniela Hübler

1,2

| Kai Winkler

| Ralf Riedel

| Sepideh Kamrani

Claudia Fleck

Chair of Materials Science &

Engineering, Institute of Technology

Berlin, Berlin, Germany

Division Tribology and Wear Protection,

Bundesanstalt für Materialforschung und

-prüfung, Berlin, Germany

Theoretical Biophysics, Institute for

Biology, Humboldt University Berlin,

Berlin, Germany

Fachgebiet Disperse Feststoffe,

Fachbereich Material- und

Geowissenschaften, Technische

Universität Darmstadt, Darmstadt,

Germany

Correspondence

Daniela Hübler and Claudia Fleck, Chair

of Materials Science & Engineering,

Institute of Technology Berlin, Straße des

17. Juni 135, 10623 Berlin, Germany.

Email: [email protected];

claudia.fleck@tu-berlin.de

Funding information

Deutsche Forschungsgemeinschaft

Abstract

Metal-ceramic nanocomposites are promising candidates for applications

necessitating light weight and excellent fatigue resistance. We produced

Mg–SiC nanocomposites from mechanically milled powders, yielding a

homogeneous nanocrystalline structure and excellent quasistatic strength

values. Little is known, however, about the fatigue behavior of such compos-

ites. Here, we used load increase tests on the macroscale to yield estimation

values of the fatigue endurance limit. Fatigue strength increased significantly

for the materials processed by the powder metallurgical route. We further

investigated the cyclic deformation behavior under stress-controlled condi-

tions on the macroscale and nanoscale. Cyclic nanoindentation showed that

indentation depth and cyclic plastic deformation decreased with increasing

reinforcement content, hinting to a higher cyclic strength and corroborating

the results from the macroscopic load increase tests. Our results therefore

show that cyclic nanoindentation reliably determines the plastic deformation

behavior of Mg nanocomposites offering the possibility of fast material

analysis.

KEYWORDS

cyclic deformation behavior, cyclic nanoindentation, fatigue behavior, load increase test,

Mg–SiC nanocomposite

1|INTRODUCTION

There is increasing need for lightweight materials capa-

ble of sustaining cyclic loading over a long lifetime, spe-

cifically in the vehicle or aviation industry. Designing

such materials requires thorough understanding of the

fatigue behavior and cyclic deformation behavior.

Metal-

matrix composites (MMCs) offer a promising way to

combine low weight with high strength and ductility, also

for cyclic loading conditions. In MMCs reinforced with

micron-sized SiC particles, interface debonding and/or

particle cracking are the predominant failure mecha-

nisms, both under quasistatic and fatigue loading.

2,3

Fatigue resistance of MMCs depends on many parame-

ters, comprising grain size, reinforcement geometry, and

distribution as well as coherence between reinforcements

and matrix. The use of nanoparticles in MMCs has high

potential to promote excellent interfacial bonding, and

Sepideh Kamrani and Claudia Fleck contributed equally to the paper.

Received: 20 July 2021 Revised: 29 September 2021 Accepted: 10 October 2021

DOI: 10.1111/ffe.13600

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided

the original work is properly cited.

386 Fatigue Fract Eng Mater Struct. 2022;45:386–399.wileyonlinelibrary.com/journal/ffe

thus excellent load-bearing capability.

4–7

Importantly,

regarding fatigue resistance, nanoparticles promote strain

hardening within nanocomposites as well during

processing as during service loading. This leads to a

higher density of pre-existing dislocations with beneficial

dislocation-nanoparticle as well as dislocation–

dislocation interactions.

One consequence is the activa-

tion of nonbasal slip systems in the Mg matrix, which

can lead to improved fracture strains.

2,9

To provide local information on cyclic plastic zone,

cyclic hardening, and crack propagation,

nanoindentation has been suggested.

The method gives

insights into dynamic processes within a material that

lead to both dislocation generation and annihilation due

to the effective applied stress, and distribution of

internal stresses. So far only one study reports on

the nanofatigue behavior of a Mg alloy using

nanoindentation. Loading was, however, limited to

300 cycles.

Schmahl et al.

presented nanofatigue

experiments on an Al–Si–Mg alloy with loading up to a

much higher cycle number of 10.

In contrast to cyclic nanoindentation, a large num-

ber of macrofatigue tests has been published for Mg

alloy composites, for example, Hassan et al.,

including

Mg alloy-SiC composites,

13,14

and pure Mg

nanocomposites.

3,15–19

On the macro level, constant

amplitude (CAT) and load increase tests (LIT) are

often used to investigate the complex processes during

fatigue loading. Specifically, LIT are useful for

estimating the fatigue endurance limit and cyclic

stress strain curves, when only a small number of sam-

ples is available as previously shown for a variety of

materials, also for Mg alloys.

20,21

While endurance

limits of about 60 MPa (CAT, 2 10

cycles)

and

71 MPa (CAT, 1.2 10

cycles) have been reported for

pure Mg and AZ31, respectively, reinforcement of

AZ31 by Al

nanoparticles improved the fatigue

endurance limit to 91 MPa.

Therefore, an increase in

endurance limit can also be assumed for pure-

Mg-nanocomposites. To the best of our knowledge,

there are no studies on the macro-fatigue behavior of

Mg–SiC nanocomposites.

Here, we report on high-cycle nanofatigue and

macrofatigue tests on a Mg–SiC MMC made from

mechanically milled composite powders with nanoscale

reinforcements. Nanofatigue tests were performed up to

cycle numbers of 10

and analyzed using the method pro-

posed previously for Al alloys.

Fatigue mechanisms

were investigated by observations of fracture surfaces of

macrofatigued samples, and texture analysis was

deployed to support our conclusions on the active defor-

mation mechanisms. Comparisons of the plastic deforma-

tion behavior on the nanoscale and macroscale helped us

to evaluate to what extent cyclic nanoindentation tests

can be used to predict the macrofatigue behavior.

2|MATERIALS AND METHODS

2.1 |Sample preparation

Mg–SiC nanocomposites with SiC nanoparticles with vol-

ume fractions of 1 vol% and 3 vol% were produced by

high-energy mechanical milling, cold-isostatic pressing,

sintering, and hot extrusion. Mg powder with an average

particle size of 325 mesh and β-SiC powder with an

average particle size of 50 nm were used. Further details

of the processing are given in Penther et al.

We previ-

ously showed

22,23

that this processing route leads to a

homogeneous distribution of the nanoparticles in the

matrix and to a very fine grain that is retained through-

out all processing steps. Henceforth, these

nanocomposites are referred to as M1S

and M3S

for

samples with reinforcement contents of 1 or 3 vol% SiC

nanoparticles, respectively. Mechanically milled pure Mg

(MM) and nonmilled pure Mg (Mg) were used as refer-

ence materials. One nanoindentation specimen was cut

off from each extruded flat rod with dimensions of

15 2 mm. The cross-sections were then ground step-

wise with SiC paper down to 4000 grit using ethanol as

lubricant, and subsequently polished, using ethanol and

diamond spray down to a particle size of 1/4μm. Three

fatigue specimens of each composition were extracted

from as-extruded flat rods, cut parallel to the extrusion

direction (ED) by wire electrical discharge machining

(EDM; AGIECUT AC Vertex 1 F, GF Machining Solu-

tions GmbH, Geneva, Switzerland). The geometry and

size of the specimens is shown in Figure 1. In order to

remove the oxide layer and the EDM-induced damage,

thus preventing stress raising effects during testing, the

sample surfaces were stepwise polished using diamond

spray down to 1-μm particle size (Struers, Ballerup,

Denmark). We may safely assume a surface roughness in

the range of about 1 μm as bigger scratches were

excluded by light microscopic inspection.

FIGURE 1 Geometry of the fatigue specimens

HÜBLER ET AL.387

2.2 |Mechanical testing

2.2.1 | Nanofatigue behavior

For local fatigue analysis, cyclic nanoindentation was

performed with a Hysitron TI 950 TriboIndenter (Bruker

Corporation, Billerica, Massachusetts, USA) equipped

with a standard Berkovich diamond indenter tip. High-

frequency “loading”cycles (f=201 Hz) were combined

with interspersed low-frequency “measurement”cycles

(f=0.05 Hz) as described in detail elsewhere

at maxi-

mum and minimum loads of 968 and 72 μN, respectively.

Note that, in compliance with the usual notation in

nanoindentation, the loads are given as positive values

even though they are compressive loads. The maximum

number of cycles was 10.

Several areas of each sample

were cyclically indented with a grid arrangement of

45 indents, with all indents in a grid 10 μm apart from

each other

The hysteresis data of at least 20 indents per sample

were evaluated by custom-made code. The calculated

parameters were averaged over all indents, resulting in

average-value-curves. To analyze the plastic deformation

behavior, we evaluated the changes in D

min

during cyclic

loading. Because slight differences in the applied force

could not be avoided (9% in P

min

), D

min

were normal-

ized by the corresponding P

min

ΔDmin=Pmin

ðÞ¼Dmin=Pmin

ðÞNxþ1

ðÞDmin=Pmin

ðÞNx

ðÞ

ð1Þ

with D

min

the minimum displacement at minimum load

min

and N

x+1

the number of cycles in consecutive

measurement cycles, indicated by subscripts “x”and “x

+1”. Because the number of cycles between measure-

ment cycles was not constant, Δ(D

min

) was normal-

ized by the number of cycles between consecutive

measurement cycles:

ΔDminnorm ¼ΔDmin=Pmin

ðÞ=Nxþ1Nx

ðÞð2Þ

To evaluate cyclic plasticity further, the ratio of mini-

mum to maximum displacement within a loading cycle,

min

max

was analyzed. The value correlates with the

amount of irreversible and reversible deformation in a

single loading/unloading cycle: higher values indicate

relatively more plastic (irreversible) deformation, while

lower values indicate the opposite. Changes in this ratio

with Nindicate softening for increasing ratios and hard-

ening for decreasing ratios.

The cyclic indents were imaged by the scanning probe

microscopy (SPM) mode of the nanoindenter. The

topography images of two indents were analyzed for each

material regarding size and volume of the indent and

pile-up using the open-source program Gwyddion.

2.2.2 | Macrofatigue behavior

Stress-controlled stepwise load increase (LIT) tests were

performed in ambient air at room temperature on an Elec-

troPuls E3000 (Instron, Buckinghamshire, UK). The long

axis of the samples was aligned exactly with the loading

axis to avoid bending stresses. Force was measured using

the inbuilt 5-kN load cell (accuracy ±0.005% for F≤50 N

and ±0.5% for F> 50 N). Strain was measured using an

inductive displacement sensor (multi-NCDT Series

300, Micro-Epsilon Messtechnik, Ortenburg, Germany)

with a resolution of 0.4% that was attached to the grips.

Calibration was carried out for an increasing load series in

the elastic regime, using 1-mm-long strain gauges with a

tolerance of ±0.85 μm/m (FLK-1-23, Tokyo Measuring

Instruments Laboratory Co., Ltd., Tokyo, Japan) mounted

on the gauge length of one sample. We note that strain

values are averaged over the whole measurement volume

as soon as strain localization (e.g., as more localized plas-

ticity during cyclic hardening and softening) occurs

Three samples of each composition were tested using

a sinusoidal waveform with completely reversed loading

(R=σ

min

/σ

max

=1) at a frequency of 5 Hz. Loading

started with a stress amplitude of 10 MPa; after a number

of 10

cycles, the stress amplitude was increased by

5 MPa over 10

cycles. These steps were repeated until

specimen failure. From the hysteresis loops, the plastic

strain amplitude, plastic mean strain (ε

m,p

=ε

m,t

σ

/E,

with ε

m,t

=total mean strain, σ

=mean stress,

E=Young's modulus) and minimum and maximum

strain were determined by custom-made code. In order to

precisely determine the stress amplitude for which the

plastic strain amplitude increases significantly, thus esti-

mating the cyclic yield strength and from this the fatigue

endurance limit,

the plastic strain amplitude, plotted

versus the number of cycles, was fitted by a third-degree

polynomial function, and the first derivation of this curve

was used to determine the change in slope. A “signifi-

cant”change was defined as a deviation of the first deri-

vation from a linear progression over the number of

cycles.

Topography of the fracture surfaces was investigated

using a Phenom XL (Thermo Fisher Scientific, Waltham,

USA) scanning electron microscope at an accelerating

voltage of 10 kV. Surface filter with shortest and longest

cut-off wavelengths of λs=223.61 nm and

λc=282.84 μm, respectively, were employed to deter-

mine the mean arithmetic height Sa.

388 HÜBLER ET AL.

2.3 |Texture analysis

In order to investigate the influence of texture as a func-

tion of the reinforcement content, X-ray diffraction

(XRD) measurements were performed on longitudinal

sections (cut parallel to ED), corresponding to the X-ray

direction being orthogonal to ED, using a psi-

diffractometer (Huber) with a position sensitive detector

(PSD-50M, M. Braun GmbH), monochromatic Co K

radiation, an accelerating voltage of 40 kV and a colli-

mated beam diameter of 2 mm. To observe the intensity

distribution of the 1010



, 0002

,1011



,1012



, and

1120



reflections, the samples were tilted (psi axis) and

rotated (phi axis) in 5 deg steps from 0to 55and 0to

355, respectively. The orientation distribution function

was determined from the experimental data after rotation

by 90to analyze the texture in a cross-sectional plane

orthogonal to ED using the ODF program system

and

the Matlab software package MTEX.

3|RESULTS

3.1 |Cyclic nanoindentation

Figure 2 shows SPM topography images and 3D elevation

profiles of cyclic indents in Mg, MM, M1S

, and M3S

Indent and pile-up volumes of all samples are plotted in

Figure 3. The data clearly show decreasing indentation

sizes and depths for mechanically milled MM as

FIGURE 2 SPM topography images (top) and 3D elevation profiles (bottom) of nanoindents, loaded up to N=10

cycles, showing pile-

up in all samples: (A) Mg, (B) MM, (C) M1S

, and (D) M3S

[Colour figure can be viewed at wileyonlinelibrary.com]

HÜBLER ET AL.389

compared to nonmilled Mg, and with increasing rein-

forcement content for the mechanically milled

nanocomposites. Significant pile-up is seen at the edges

of all indents, but no cracks were observed in the vicinity

of any of the indents.

Figure 4A shows the average ratios of D

min

to D

max

plotted versus N. All sample types exhibit a steep increase

within the first ten cycles, followed by smaller increases

with ongoing cyclic loading. While the Mg curve has a

slightly convex shape for higher cycle numbers and a lin-

ear slope for N≥10,

the curves of the nanocomposites

have slightly concave progressions with an increasing

trend for higher cycle numbers. This is most pronounced

for M3S

. Over the investigated range of cycle numbers,

Mg exhibits the highest values of D

min

max

. Mechanical

milling and nanoparticle reinforcement lead to lower

values, with similar ratios for MM and M1S

and much

lower values for M3S

The average values of ΔD

min-norm

are plotted versus

Nin Figure 4B. Two regimes with significantly different

behavior are observed: the “incipient”fatigue regime up

to N=10,

and the “advanced”regime from N=10

N=10.

The incremental plastic deformation per cycle

decreases over N. Within the first 10 cycles, ΔD

min-norm

decreases by more than 60% for all materials, and hardly

any differences are observed between the different mate-

rials. Subsequently, ΔD

min-norm

continues to decrease, but

with a lower rate, and only small changes can be identi-

fied with increasing cycle number. Up to N=10,

and M3S

exhibit the overall highest and lowest values,

respectively, while the values of MM and M1S

are very

similar and lie between the Mg and M3S

curves. The

same differences between the materials are observed in

the advanced regime. However, while MM exhibits a sat-

uration state with constant values for N≥210,

the

values of all other samples slightly further decrease to

higher cycle numbers, after which they also enter a

saturation state. The numbers of cycles, for which satura-

tion is reached, increase with increasing reinforcement

content, up to N=710

for M3S

. For M3S

, a slightly

increasing trend is observed for higher cycle numbers

beyond this threshold.

3.2 |Estimation of the fatigue

endurance limit from load increase tests

Figure 5A shows typical progressions of plastic strain

amplitude (ε

a,p

) versus Ntogether with fitted polynomial

functions from stress-controlled macrofatigue tests, per-

formed with R=1. The small values and the relatively

high scatter of ε

a,p

make it difficult to extract the cyclic

yield strength from the original curves. Fitting polyno-

mials, and evaluating the first derivative, allows clear

determination of the critical stress amplitude, where ε

a,p

becomes significant.

The first derivatives of the fits of

the plastic strain amplitude versus the number of cycles

highlight the change in ε

a,p

with increasing stress ampli-

tude (Figure 5B). The range where the slope of ε

a,p

shows

a significant change from the initially extremely low

values indicates the estimation value of the cyclic yield

strength and, thus, of the endurance limit. This range of

significant change in ε

a,p

is marked with arrows. From

these graphs, we estimate an endurance limit for MM of

about 95 MPa. Both nanocomposites, M1S

(data not

shown) and M3S

, exhibit a higher value of about

110 MPa. The value for Mg is much lower than for the

mechanically milled materials (60 MPa; data not shown).

3.3 |Cyclic deformation behavior

Figure 6A shows the development of ε

a,p

, averaged

over each loading step, versus Nand versus σ

for the

FIGURE 3 Indent and pile-up volumes after cyclic nanoindentation up to N=10

cycles for two typical indents per material [Colour

figure can be viewed at wileyonlinelibrary.com]

390 HÜBLER ET AL.

same specimens as shown in Figure 5. Averaging over

the loading steps highlights some typical aspects of the

cyclic deformation behavior. In the beginning, all

materials exhibit a linear increase in ε

a,p

with

increasing stress amplitude. In the further course, Mg

shows two steep increases between 40 and 45 MPa as

well as 60 and 90 MPa resulting in the highest overall

a,p

values.

FIGURE 4 Cyclic deformation behavior during nanofatigue loading: (A) average values and standard deviations of D

min

max

plotted

versus N;(B–D) average ΔD

min-norm

/N-curves (B) for the whole test, (C) in the “incipient”regime (N≤10

cycles), (D) in the “advanced”

regime (N≥10

cycles). The regions shown in panels (C) and (D) are marked with dotted rectangles in (B). For standard deviations see

supplementary figure S1 [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 5 Progression of plastic strain amplitude versus number of cycles of mechanically milled Mg (MM) and Mg–SiC

nanocomposites M3S

in LIT: (A) typical examples of ε

a,p

/N-curves (dotted graphs) together with their fitted polynomial functions (full

lines); (B) plots of the differentiated fit functions for ε

a,p

with the estimated fatigue endurance limits, marked by arrows [Colour figure can

be viewed at wileyonlinelibrary.com]

HÜBLER ET AL.391

To better discriminate differences between the

mechanically milled materials, a magnified view of the

lower loading regime (dotted rectangle in Figure 6A) is

shown in Figure 6B. These materials, MM, M1S

, and

M3S

, exhibit similar values of the plastic strain ampli-

tude up to a stress amplitude of 50 MPa. MM shows two

significant cyclic hardening events (blue arrows in

Figure 6B) between 50 and 55 MPa as well as 75 and

80 MPa each followed by strong cyclic softening. After

the second cyclic hardening event, the plastic strain

amplitude for MM steadily increases until it reaches a

saturation state at 135 MPa shortly before fracture in the

next loading step (140 MPa). Overall, M1S

shows cyclic

hardening with only two small plateau regions, between

60 and 65 MPa and at 150 MPa right before fracture at

160 MPa. M3S

exhibits only one plateau between 55 and

65 MPa. In the further course, ε

a,p

shows slight cyclic

hardening at 90 MPa and 115 MPa. From 140 MPa

onwards, ε

a,p

of M3S

almost linearly increases until frac-

ture at 160 MPa.

Figure 6C shows the development of plastic mean

strain over the number of cycles and corresponding stress

amplitude. Mg exhibits pronounced creep in the positive

direction. In some loading steps, namely, 55 to 65 MPa

and 80 MPa, ε

m,p

shows a more pronounced increase,

followed by a decrease over several loading steps. From

90 MPa onwards, only a small further increase in ε

m,p

observed. The decrease in ε

m,p

correlates with the cyclic

hardening phases described above (Figure 6A). MM and

M1S

exhibit almost similar ε

m,p

values up to a stress

amplitude of 95 MPa, and much lower than those

observed for Mg. In the further course, ε

m,p

decreases

slightly for MM, while ε

m,p

of M1S

increases up to a

stress amplitude of 115 MPa and only remains constant

until fracture for higher stress amplitudes. M3S

increases up to a stress amplitude of 95 MPa showing sig-

nificantly more pronounced tensile creep than both, MM

and M1S

. From 95 MPa onwards, ε

m,p

first slightly

decreases until 110 MPa and then remains more or less

constant until fracture.

3.4 |Fracture surface morphology

Figure 7 shows roughness profiles, plotted as color maps,

of the fracture surfaces near the fatigue origin (left) and

far from the fatigue origin (right) of MM (A,D), M1S

(B,E), and M3S

(C,F). Fatigue failure generally started

on the surface, at one of the edges of the rectangular sam-

ples. Dark red color is associated with peaks, whereas

blue color indicates valleys. The mean arithmetic height

Sa is denoted in each image. As to be expected, all mate-

rials show lower roughness near the fatigue origin than

further away from it. MM and M1S

exhibit very similar

roughness values, both at the fatigue origin and further

away from it. In contrast, M3S

has a very smooth frac-

ture surface near the fatigue origin but a relatively rough

surface further away. With a value of 1.90 μm near the

fatigue origin and 8.63 μm further away, Sa only reaches

a little bit more than half (60%) the values measured for

MM and M1S

near the fatigue origin, but double the

values of MM and M1S

further away.

3.5 |Textures

Pole figures of Mg, MM, M1S

, and M3S

, illustrating the

density distribution of crystallographic grain orientations

FIGURE 6 Cyclic deformation and cyclic creep behavior of Mg, MM, M1S

and M3S

averaged over each load step: (A) plastic strain

amplitude (ε

a,p

), (B) magnified view of the progression of ε

a,p

in the lower loading regime (marked by the dotted rectangle in panel A),and

m,p

) plotted versus number of cycles (N) and stress amplitude (σ

) [Colour figure can be viewed at

wileyonlinelibrary.com]

392 HÜBLER ET AL.

in the basal 0001ðÞ, prismatic 1010



, and pyramidal

planes 1011



, are represented in Figure 8. As to be

expected, Mg shows a strong texture. The two maxima of

the (0001) plane indicate that the basal planes are parallel

to ED (Figure 8A). The three maxima of the 1010



pole

figure correspond to a preferential orientation of the

prism planes of the hexagonal unit cell. Mechanical mill-

ing of the powders leads to a much weaker texture, both

for the non-reinforced MM and the nanocomposites

(Figure 8B–D). Specifically, we observe weakening of the

texture by rotation of the basal plane from its parallel ori-

entation to the ED. The (0001) pole figure of the

nanocomposites (Figure 8C,D) shows two maxima,

whereby the intensity is slightly higher in M3S

. All

samples also exhibit a strong maximum in the 1010



pole figure, which is associated with the fiber

texture. Here, too, the intensity increases in M3S

compared to M1S

4|DISCUSSION

Cyclic fatigue behavior is one of the most important

properties to be considered when designing parts in

motion. The deformation behavior under fatigue loading

is influenced by the manufacturing processes and the

resulting microstructure. Here, we investigated the cyclic

deformation behavior of Mg–SiC nanocomposites on the

nanoscale using cyclic nanoindentation and on the mac-

roscale using stress-controlled LIT. Due to the small

number of samples available, LIT was a helpful method

to estimate the fatigue endurance limit and to gain

insights into the cyclic deformation behavior. Interest-

ingly, cyclic nanoindentation and macroscopic, fully

reversed cyclic loading lead to similar observations

despite the different loading conditions. Grain size, defect

density, and texture strongly determine the fatigue limit

and the cyclic deformation capability by complex

interactions.

We propose that the interaction of different micro-

structural features and the corresponding strengthening

FIGURE 7 Roughness profiles as color maps near the fatigue

origin (A–C) and far from the fatigue origin (D–F) of (A,D) MM,

(B,E) M1S

, and (C,F) M3S

. Dark red indicates peaks whereas blue

indicates valleys. The mean arithmetic height Sa is denoted in each

profile [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 8 Pole figures of (A) Mg, (B) MM, (C) M1S

, and

(D) M3S

illustrating the density distribution of crystallographic

grain orientations in cross-sections (note: ED is orthogonal to the

viewing plane) for the basal 0001ðÞ, prismatic 1010



, and

pyramidal planes 1011



[Colour figure can be viewed at

wileyonlinelibrary.com]

HÜBLER ET AL.393

mechanisms, including grain boundary strengthening,

work hardening, and precipitation hardening, together

with crack–particle interactions contribute to different

extents to cyclic plastic deformability, leading to different

fatigue failure mechanisms in the different materials.

Figure 9 summarizes the influence of reinforcement con-

tent on microstructural features, that is grain size and

dislocation density, and on plastic deformability. In the

following, we will discuss these connections in detail.

4.1 |Specifics of the microstructure

The deformation behavior under fatigue loading is

influenced by the manufacturing processes and the

resulting microstructural parameters. We previously

showed that mechanical milling leads to nanocrystalline

and nanocomposite powders.

22,23

Even during the follow-

ing processing steps, comprising cold-isostatic pressing,

sintering, and hot extrusion, nanocrystallinity is pre-

served. Another important microstructural factor

influencing the deformation behavior is texture. Mg

wrought alloys usually develop a pronounced basal fiber

texture during extrusion.

27,28

In contrast, we unexpect-

edly observed a weak, tilted basal fiber texture in the

mechanically milled materials. The weak texture and the

tilting of the c-axis can only be partially explained by the

decrease in grain size and the randomization of grain ori-

entations due to dynamic recrystallization.

17,29

A further

possible explanation is a slight torsional stress exerted

during extrusion due to the shape of the die. A similar

effect of a spiral-shaped basal texture, where the c-axis

deviates outwards instead of being oriented orthogonal to

the extrusion direction, was described by She et al. for

on-line twist extrusion.

Further, the extruded nanocomposites contain a

higher amount of dislocations as compared to the non-

reinforced but mechanically milled pure magnesium vari-

ant MM.

22,31

This is caused by extensive plastic

deformation during mechanical milling, leading to a

higher dislocation density in the nanoparticle reinforced

variants. Defect density is further influenced by the dif-

ference in thermal expansion coefficients between SiC

particles and Mg matrix. All this results in a build-up of

defects around the nanoparticles during the manufactur-

ing process and thus in an increase in defect density in

the nanocomposites. Although the higher dislocation

density that is reached due to the nanoparticles triggers

dynamic recrystallization which explains the small

retained grain size, not all defects are removed during the

process. This observation is in good agreement with

results reported by Koneva et al.,

where strong barriers

such as nanoparticles and grain boundaries lead to the

accumulation of geometrically necessary dislocations (ρ

These retained dislocations significantly influence the

mechanical behavior of the nanocomposites by determin-

ing the plastic deformability. Grain size decreases and

defect density increases with increasing reinforcement

content because interactions between (a lower volume

fraction of) nanoparticles and dislocations lead to less

plastic deformation and less dynamic recrystallization

during extrusion in M1S

as compared to M3S

n.22

As a

result, M1S

also has a lower quasistatic strength but a

higher ductility than M3S

and microhardness increases

as a function of the decrease in grain size and increase in

dislocation density.

4.2 |Microstructural effects on fatigue

endurance

Pure Mg showed a fatigue endurance limit of 60 MPa,

estimated from macro-LIT. This value is comparable with

those commonly reported for pure magnesium.

expected, the estimation values increased by using

mechanically milled powders and, further, by addition of

nanoparticles. Since the main microstructural difference

between Mg and MM is the grain refinement of the latter,

the higher endurance limit of MM compared to Mg is

therefore likely due to Hall–Petch hardening by grain

refinement. Increasing nanoparticle contents in the

nanocomposites lead to even smaller grain sizes

and a

decrease in tension-compression-asymmetry, which

explains the increase in endurance limit when

nanoparticles are added. Compared to Mg, the materials

made from mechanically milled powders, namely, MM,

M1S

, and M3S

, show a higher plastic deformability due

to their extremely small grain size. Concomitantly, grain

boundary strengthening triggers the activation of non-

basal slip. This finding highlights the very positive effect

of mechanical milling as a first process step. Surprisingly,

however, increasing reinforcement contents had no

FIGURE 9 Microstructural features and plastic deformability

dependent on the reinforcement content. Dislocation density ρ

comprises density of statistically stored dislocations (ρ

) and of

geometrically necessary dislocations (ρ

). ρ

increases with

increasing amount of grain boundaries and reinforcement content

394 HÜBLER ET AL.

additional positive effect, despite the decrease in grain

size, and the corresponding higher work hardening capa-

bility and quasistatic strength. An explanation is the

increased dislocation density with increasing reinforce-

ment content due to the pinning-effect of the

nanoparticles, which decreases plastic deformability and

facilitates faster crack growth once a fatigue crack has

been initiated. Relatively lower energy absorption and

faster crack velocities near the fatigue origin, suggesting

a more brittle fracture behavior for small crack lengths,

as compared to MM and M1S

, are supported by the

observation of a very smooth fracture surface of M3S

near the fatigue origin. Similarly, Sattari and Atrian

describe a reduced dimple size, that is a more brittle frac-

ture mode, with increasing SiC content in fatigued Al–

SiC nanocomposites. Further explanation of the very

smooth fracture surface near the fatigue origin in M3S

given by the geometric model for roughness-induced

crack closure.

The authors stated that the extent of

crack closure is a strong function of surface roughness,

mode II crack tip displacement, and grain size. The

model suggests that the plastic zone size exceeds the

grain size during fatigue initiation, especially in case of

M3S

with the smallest grain size of all investigated

materials. This leads to a more planar crack path due to

activation of more than one slip system.

The effect of increasing brittleness with increasing

nanoparticle content is counteracted by a higher propen-

sity to crack deflection and energy absorption due to

microcrack formation at particle–matrix interfaces. We

see this in regions far from the fatigue origin, where

crack deflection leads to a plastic zone that is smaller

than the grain size. Consequently, we measure the

highest roughness on the fracture surfaces in M3S

together with a serrated fracture path due to slip along

one single slip system.

We therefore conclude that the resistance against

crack formation and against crack growth both play

important but different roles for the deformation behav-

ior of M1S

and M3S

thus explaining the similar fatigue

endurance limits.

4.3 |Macroscale cyclic deformation

behavior

We further evaluated stress-controlled LIT regarding

deformation and creep behavior Our observation of ten-

sile cyclic creep is in good agreement with our quasistatic

results where we observed higher compressive than ten-

sile strength.

35,36

This is surprising in light of the other

reports on extruded magnesium materials. Generally, a

strong ring-fiber texture is observed which leads to lower

strength in compression as compared to tension.

37,38

This

asymmetric deformation behavior, the so-called strength

difference effect (SDE), is due to inhibition of basal slip

and activation of twinning under compression.

39,40

Rea-

sons for the low and inverse tension-compression asym-

metric behavior that we see in our mechanically milled

Mg–SiC nanocomposites may be:

i) weakening of the texture due to an increase in

dynamic recrystallization with increasing reinforce-

ment content,

ii) the slightly tilted texture, since the tension-

compression yield asymmetry is orientation-

dependent,

and

iii) the low total strain amplitudes of less than 0.2%

resulting in an overall decreased asymmetry.

Texture strongly influences the activation of certain

slip systems and/or twinning. A weak texture involves a

significant number of randomly oriented grains that

exhibit a lower Schmid factor for extension twinning.

Thus, activation of twinning is hindered, leading to more

pronounced work hardening. Hassan and Lewandowski

ascribed the work hardening to a higher density of pre-

existing dislocations, dislocation–dislocation interaction,

and interactions of mobile dislocations with

nanoparticles leading to forest dislocations. The small

grain sizes (<1 μm) and the tilted, weak fiber texture sug-

gest that negligible or no twinning took place

and that

consequently, secondary deformation modes such as

non-basal dislocation slip, are more prominent.

This

conjecture is confirmed by the observation of Lin et al.,

who reported for equal channel angular extrusion of an

AZ31 alloy easier slip in tensile testing than in compres-

sion testing, resulting in lower yield strength and ulti-

mate tensile strength, due to the preferred orientation of

the basal planes.

Maxima in the pole figures can be associated with the

activity of different slip systems. Based on observations

by Min

arik et al.

on the influence of texture in the Mg

alloy LAE442 on the deformation mechanisms we deduce

that prismatic slip, associated with maxima in the (0001)

pole figure and additional texture intensities in the

1010



pole figure, is the predominant deformation

mechanism in our Mg material. Accordingly, basal

slip predominates in the nanocomposites, as it is

associated with maxima in the (0001) pole figures.

We therefore assume that activation of prismatic

slip in the nanocomposites can be a reason for the

significantly higher endurance limit compared to

pure Mg.

Comparison of ε

m,p

of Mg with MM, M1S

, and

M3S

indicates reduced cyclic creep for the latter

HÜBLER ET AL.395

(see Figure 6C). These observations well match the

findings of Dieringa,

who reported improved creep

resistance in mechanically milled composites. A reason

for higher cyclic creep under tension of M3S

compared

to MM and M1S

may be hindered twinning due to a

small grain size and the pinning-effect of the

nanoparticles resulting in faster crack initiation.

We further conclude that the relatively high plastic

deformation indicated by a steep increase in ε

a,p

over

several loading steps of M3S

(Figure 6A) is due to

microcrack formation and growth and less to real plastic

deformation.

This conclusion is corroborated by the

observation of decreasing slopes of the hysteresis loops,

with cyclic loading (Figure S2).

4.4 |Nanoscale cyclic deformation

behavior

High cycle fatigue tests on the nanoscale, performed by

cyclic nanoindentation, are still very scarce. For the first

time, we characterized the nanofatigue behavior of

Mg–SiC nanocomposites by repeatedly nanoindenting

the same position up to 10

cycles. The load-indentation

curves yield information on the cyclic deformation

behavior, and quantitative evaluation of indent and pile-

up volumes reflects the plastic deformation capability of

the different nanocomposites.

As to be expected, the largest indents and the highest

pile-up were observed for Mg. This is associated with its

relatively low strength and its low potential for work

hardening.

The latter allows relatively high amounts of

plastic deformation and easy propagation of the plastic

zone. Conversely, in the case of nanoparticle reinforced

composites, the regions of higher defect density

surrounding the nanoparticles, and the extremely small

grain size of the nanocomposites hinder dislocation

movement and thus hamper the propagation of the

plastic zone developing beneath the indenter tip. This

leads to less plastic deformation and, concurrently, to

smaller indent and pile-up sizes with increasing

reinforcement contents.

The significant change in D

min

max

over the course

of loading hints to significant plastic deformation and

cyclic hardening in all materials. Interestingly, we see

only little local variation in the behavior between indents

performed at different positions in one material, in con-

trast to what we observed for an Al–Si–Mg alloy.

This is

due to the much finer, homogeneous microstructure of

the materials investigated here. Thus, the nanoindents

are much larger than the typical microstructural unit,

and we probe volumes of interest that represent the bulk

material. In materials with a coarser microstructure, the

nanocyclic deformation behavior varies to a great extent

depending on indent position. This applies when the

mean distance between particles or precipitates in the

volume beneath the indent is relatively large as compared

to indent size or when grain size is so large that single

grains are indented and differences in grain orientation

become crucial for plastic deformation (e.g., Schmahl

et al.

and Bocˇan et al.

MM showed a steeper incline in D

min

max

in the

advanced regime compared to Mg. This can be related to

a higher degree of work hardening, due to the smaller

grain size and higher defect density. These two parame-

ters lead to an internal reaction stress that lowers the

energy gap to the critical resolved shear stress (CRSS).

Thus, in the case of MM, nonbasal slip is activated more

easily. Compared to the other compositions, M3S

exhibits the smallest grain size and highest defect density.

It further shows the least plastic deformation with

increasing number of cycles, which is mainly attributed

to the greater restriction of plastic flow by the higher con-

tent of nanoparticles and the resulting smaller distances

between them.

This observation is also reflected in the progressions

of ΔD

min-norm

with the number of cycles: MM shows the

highest incremental plastic deformation. Surprisingly,

Mg and M1S

exhibit very similar curves with almost the

same plastic deformation range. Possible reasons are the

low number of independent slip systems in the case of

Mg and the nanoparticle-dislocation interaction in the

case of M1S

. As compared to M1S

, the higher nanopar-

ticle content in M3S

leads to a significant decrease in

ΔD

min-norm

with increasing numbers of cycles. In the late

advanced regime, however, the incremental plastic defor-

mation of M3S

increases, which may possibly be

explained by the activation of nonbasal slip.

4.5 |Comparison of nanofatigue and

macrofatigue behavior

MM, M1S

, and M3S

show similar plastic deformation

behavior in both nanofatigue and macrofatigue tests up

to 210

and 10

cycles, respectively. Surprisingly, Mg

exhibited lower ε

a,p

values than MM in the nanofatigue

tests but higher values in the macrofatigue tests. We

attribute this observation to the absence of microcrack

formation in the nanofatigue tests. Similar to the

macrofatigue tests, we hypothesize that the main plastic

deformation mechanism in cyclic nanoindentation is

dislocation sliding and that no or only minimal twin-

ning is induced.

396 HÜBLER ET AL.

5|CONCLUSIONS

This study contributes in several ways to our understand-

ing of the cyclic fatigue behavior of Mg–SiC

nanocomposites on both the nanoscale and macroscale.

Macrofatigue tests showed that mechanical milling of the

powders leads to a tremendous increase in the fatigue

endurance limit. This is due to the higher amount of

grain boundaries restricting dislocation movements.

Dislocation movements are additionally hindered by

nanoparticles in the nanocomposites. The results further

indicate that the plastic deformation behavior deter-

mined through cyclic nanoindentation tests is compara-

ble to the behavior observed in macrofatigue tests. Thus,

using cyclic nanoindentation allows fast and easy assess-

ment of material performance with a small number of

samples and with minimal material consumption, thus

saving time and cost intensive macrofatigue tests.

We conclude that nanofatigue tests directly predict

the plastic deformation behavior on the macroscale if the

interaction volume below the cyclic nanoindent is repre-

sentative for the bulk microstructure.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support

by the DFG (Deutsche Forschungsgemeinschaft), and we

are grateful to Fraunhofer Institute for Ceramic Technol-

ogies and Systems (IKTS, Dresden) for performing the

hot isostatic pressing. The authors thank Rigerta Tola for

sample preparation, Reinhard Meinke for support with

macrofatigue testing, and Merle Schmahl for assistance

during cyclic nanoindentation testing. The authors fur-

ther thank Sören Müller and René Nitschke, Extrusion

Research and Development Center (FZS), Metallic Mate-

rials, TU Berlin for execution and support during hot

extrusion, and Jonas Schmidt, Metallic Materials, TU

Berlin for the texture measurements. Thanks go to

Fraunhofer Institute for Production Systems and Design

Technology (IPK) for cutting the fatigue specimens using

EDM. We are further grateful to Christoph Fahrenson,

Central Electron Microscopy Unit (ZELMI), TU Berlin,

for his support during SEM analyses. Open Access

funding is provided by Projekt DEAL.

CONFLICT OF INTEREST

The authors declare that there is no conflict of interest.

AUTHOR CONTRIBUTIONS

D. Hübler: Conceptualization (supporting), Formal anal-

ysis, Investigation, Validation, Visualization, Writing –

Original Draft Preparation, Writing –Review & Editing;

K. Winkler: Software, Data curation, Validation, Writ-

ing –Review & Editing; R. Riedel: Resources, Writing –

Review & Editing; S. Kamrani: Conceptualization (lead),

Project Administration, Funding acquisition, Writing –

Review & Editing; C. Fleck: Conceptualization

(supporting), Methodology, Resources, Supervision,

Writing –Review & Editing.

DATA AVAILABILITY STATEMENT

Data are available upon request from the authors.

ORCID

Daniela Hübler https://orcid.org/0000-0002-0272-9343

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SUPPORTING INFORMATION

Additional supporting information may be found in the

online version of the article at the publisher's website.

How to cite this article: Hübler D, Winkler K,

Riedel R, Kamrani S, Fleck C. Cyclic deformation

behavior of Mg–SiC nanocomposites on the

macroscale and nanoscale. Fatigue Fract Eng Mater

Struct. 2022;45(2):386-399. doi:10.1111/ffe.13600

HÜBLER ET AL.399