Document [original]

Nanofatigue behaviour of single struts of cast A356.0 foam: cyclic

deformation, nanoindent characteristics and sub-surface microstructure

M. Schmahl

,A.Märten

, P. Zaslansky

,C.Fleck

⁎

Materials Science & Engineering, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany

Restorative and Preventive Dentistry, Charité - Universitätsmedizin Berlin, Aßmannshauser Straße 4-6, 14197 Berlin, Germany

HIGHLIGHTS

•Millimetre-sized struts of a cast AlSiMg

foam were cyclically nanofatigued up

to 10

cycles.

•Quasi-static nanoindentation revealed

inclusion effects on local properties.

•Silicon inclusions affected cyclic proper-

ties at a distance of 5 to 10 μm.

•Nanocyclic deformation behaviour was

strongly affected by residual stress

release.

•We observed signiﬁcant hardening for

N≦10

. Hardening decreased for N ≧

, sometimes down to saturation.

GRAPHICAL ABSTRACT

abstractarticle info

Article history:

Received 21 October 2019

Received in revised form 27 July 2020

Accepted 28 July 2020

Available online 4 August 2020

Keywords:

Al-Si-Mg alloy

Open-cell metal foam

Nanoindentation

Nano-fatigue

Cyclic deformation behaviour

Phase-contrast enhanced microcomputed to-

mography (PCE-μCT)

Transmission electron microscopy

Indent morphology

Struts are the main load carrying elements in cyclically loaded open cell metal foams. Little is known about the

local fatigue behaviour and the inﬂuence of the microstructure on nanoscale deformation mechanisms. Different

to the bulk counterpart, the millimetre-sized struts in precision-cast AlSi7Mg0.3 foams contain only 1–2

Al-dendrites, Si-Al-eutectic and intermetallic phases. We applied cyclic nanoindentation to N=10

to assess

nanofatigue. The change in minimum depth per cycle and the ratio of minimum to maximum indentation depths

versus the number of cycles correspond to cyclic plastic processes. These and the indent and pile-up morphol-

ogies were correlated with the microstructure and dislocation formations revealed by phase-contrast-

enhanced micro-computed tomography and transmission electron microscopy. Our results reveal that

Si-particles affect deformation within 5 to 10 μm from the indent, and that they favour the formation of fatigue

induced dislocation cells in the affected volume. We believe that this interaction is mediated through residual

stresses. Furthermore, local variations in microstructure strongly inﬂuence the cyclic deformation behaviour

and the indent pile-up size and morphology. Interestingly, the results well coincide with observations during

fatigue of the bulk alloy reported in the literature.

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Metal foams are a modern class of materials that recently gained in-

creasing interest due to their impressive weight-to-stiffness ratios and

excellent damping, insulation and energy absorption properties [1].

They offer design ﬂexibility and make it possible to combine different

functions such as load bearing and media storage. They have particu-

larly promising use for applications in weight-restricted ﬁelds [2], in-

volving complex quasi-static and cyclic loading conditions. An

important route for creating open-cell metal foams is by investment

casting, for example of aluminium silicon (AlSi) alloys. Speciﬁcally,

Materials and Design 195 (2020) 109016

⁎Corresponding author.

E-mail address: claudia.ﬂeck@tu-berlin.de (C. Fleck).

https://doi.org/10.1016/j.matdes.2020.109016

Contents lists available at ScienceDirect

Materials and Design

journal homepage: www.elsevier.com/locate/matdes

near-eutectic compositions containing magnesium (Mg), e.g. the alloy

A356.0 (AlSi7Mg0.3), are easily used for the production of precision

cast open-cell metal foams [3].

The macroscopic fatigue behaviour of cast Al-based foams has been

widely investigated revealing a large scatter in fatigue life [4–6]. A

high scatter is also typical for the quasi-static properties, where it has

been assigned to a statistical distribution of defects on the different

levels of the hierarchical microstructure [7]. The high scatter means

that large numbers of samples must be tested to reliably characterise

the fatigue properties. An alternative approach is to focus on the local

behaviour of the main load carrying elements. Improved knowledge

about the cyclic deformation mechanisms of the single struts may

serve to better predict foam performance. Microstructural characteris-

tics in the single struts are known to strongly inﬂuence the foam behav-

iour under quasi-static loading conditions [7,8] and are likely to

critically inﬂuence the fatigue behaviour as well.

Due to a low cooling rate [9], the microstructure of cast struts of

Al-Si-Mg foams is signiﬁcantly different from bulk alloys with a similar

composition. Struts of Al-Si-Mg foams, made by a modiﬁed investment

casting process, are several millimetres long and about 0.5 mm wide,

and they usually consist of only one or two dendrites with a ﬁne Al-Si

eutectic in the interdendritic spaces. These dendrites have different

orientations of the dendrite backbone with respect to the strut axis and

the crystallographic orientation of the grain. As the eutectic is arranged

in the spaces between the dendrite arms, there is often a higher amount

of eutectic towards the outer strut edges as demonstrated by

synchrotron-based micro-computed tomography with slight phase-

contrast enhancement. Small Mg

Si precipitates and few, relatively

coarseiron-basedintermetallicparticles(Fe-IMP)arefoundinthematrix

and in the interdendritic spaces [8–10].

For bulk Al-Si-alloys, the fatigue failure mechanisms are inﬂuenced

by various microstructural features including the composition of the

phases, the texture, secondary dendrite arm spacing (SDAS) [11,12]

and the presence of precipitates on the sub-micrometre size range

[12,13]. For example, Si-, Mg

Si- and IMP-particles hinder dislocation

movement resulting in cyclic hardening [13]. However, little is known

about how the strikingly different microstructure of the struts inﬂu-

ences the fatigue behaviour. A precise characterisation of the fatigue

mechanisms in the strut material is required for successfully predicting

the fatigue behaviour of open cell foams. However, the small dimen-

sions of the millimetre-sized struts make fatigue testing extremely dif-

ﬁcult. Nanoindentation offers an excellent alternative well suited to

investigate the local mechanical properties under cyclic loading condi-

tions of tiny pillar-shaped specimens. To the best of our knowledge, to

date, such nanofatigue tests in the high cycle regime have not yet

been reported.

Nanoindentation was originally developed to characterise the

mechanical properties of thin ﬁlms [14–16]. Over time, the method

has been increasingly used for a much wider range of bulk and po-

rous materials [17–23]. Commonly, nanoindentation is used under

one of two measurement regimes: i) quasi-static loading, where

hardness and stiffness are calculated from force-depth curves ob-

tained from single, relatively slow indentation events; ii) nano-

DMA (dynamic mechanical analysis) tests, assessing loading-rate de-

pendent stiffness, where the loading amplitude is kept constant dur-

ing frequency sweeps. In nano-DMA tests, the material is indented

repeatedly and elastically at the same point. If higher loads are ap-

plied repeatedly, material fatigue comes into play. Cyclic nanoinden-

tation with such higher loads may reveal fatigue mechanisms at the

micro- and nanoscale. Speciﬁcally, this makes it possible to charac-

terise the inﬂuence of grain boundaries or second phases on the cy-

clic deformation behaviour on the nanoscale. Such information

augments fatigue measurements performed on the macroscale. Ulti-

mately, such knowledge may establish the basis for mechanism-

based predictions of the cyclic deformation behaviour, especially

for hierarchically structured materials.

So far, cyclic nanoindentation has mainly been applied to thin ﬁlms

[24,25]. It has rarely been used for assessing the fatigue properties of

materials, usually bulk metals [26,27]. Most of the work characterised

low cycle fatigue, with cycle numbers below 3 × 10

. Nanofatigue

tests with cyclic nanoindentation on magnesium [26] and copper [27]

focused on the development of depth of the indents with cycle number.

For magnesium, crack growth and the inﬂuence of a heat treatment on

plastic deformation mechanisms, twinning and slipping, were also re-

ported [26]. Interestingly, cyclic micro-indentation with up to 10 cycles

was successfully used for fatigue life predictions [28]. Overall, additional

information is still needed for better understanding the local fatigue de-

formation mechanisms on the nano-scale.

Here we report the quasi-static mechanical properties and the fa-

tigue behaviour of single millimetre-sized struts of AlSi7Mg0.3 open-

cell foam. Nano-scale structure and mechanical response are evaluated

for high cycle fatigue nanoindentation up to 10

cycles. The evaluations

of changes in indentation depth over the number of cycles show pre-

dominantly cyclic hardening. We correlate the results with the geome-

try of the indents, observed by scanning probe microscopy, and the

microstructure around them, characterised in 2D and 3D by phase-

contrast enhanced micro-computed tomography and transmission

electron microscopy. We identify important inﬂuences of the micro-

structure below the indents on the cyclic deformation behaviour of

the strut material.

2. Experimental procedures

2.1. Material and sample preparation

Open-cell A356.0 (7 wt% Si, 0.3 wt% Mg) Al-alloy foams with 10 ppi

pore size were fabricated by a modiﬁed investment casting process

(Foundry Institute, RWTH Aachen, [9]). Single millimetre-sized struts

(Fig. 1b) were extracted from the as-cast foam (Fig. 1a) using wire-

Fig. 1. a) Structure of open-cell Al-Si-Mg foam; b) single strut extracted from the foam

structure; c) embedded and indented strut mounted for PCE-μCT (white arrow

highlights the strut within the embedding); d) SEM micrograph of one shown indent on

a strut cross-section (white dashed line source of TEM lamella in (e)); e) SEM

micrograph of FIB extracted TEM lamella cut through the indent tip.

2M. Schmahl et al. / Materials and Design 195 (2020) 109016

cutting pliers while avoiding shearing or bending of the struts. Fig. 1

shows a typical foam sample and illustrates the specimen preparation

steps. To prepare even and smooth cross-sections for nanoindentation,

single struts were embedded upright in EpoFix resin (Struers, Ballerup,

Denmark) and subsequently ground with a series of silicon carbide pa-

pers, polished with diamond suspension down to a grain size of 3 μm

and further polished with a colloidal silica slurry with a particle size of

50 nm. For tomographic imaging following nanoindentation, cylindrical

samples were drilled out of the polished blocks each containing one

strut (Fig. 1c). For transmission electron microscopy (TEM) 100 nm

thick lamellae were milled within longitudinal sections cut through

the tip of the indent with a focused ion beam (FIB) (Fig. 1 d) (FEI Helios

NanoLab 600, Field Electron and Ion Company, Hillsboro, USA) using a

gallium ion beam. To ensure positioning through the indent tip during

thinning, nano-markers were ﬁrst milled around the indent. The speci-

men surface was covered with a thin layer of platinum to protect it from

the gallium ions. In this manner we were able to obtain TEM samples

without any plastic deformation from sample preparation.

2.2. Quasi-static nanoindentation

The mechanical properties of the Al-matrix and the eutectic Si were

determined by quasi-static nanoindentation tests using a trapezoidal

load function in a TI 950 TriboIndenter (Bruker, Billerica, USA) equipped

with a Berkovich tip. Several groups of indents were placed (i) in the α-

Al-matrix (n= 300), (ii) on the Si-particles (n= 50), and, (iii) in the α-

Al-matrix with increasing surface distances from visible Si-particles

employing a constant spacing of 5 μm (n = 50: ten lines with 5 indents

each) (Fig. 2). Indent positioning was planned based on observations of

the different alloy phases, clearly distinguishable by their appearance

following polishing. The distance between indents was at least 2.5

times the size of the indents, mostly 3 μmto4μm apart, to avoid mutual

interactions. The α-Al-matrix and the Si-particles were loaded with a

maximum force of 1000 μN and 5000 μN, respectively. These forces

gave sufﬁcient indentation depths for reproducible determination of

hardness and reduced elastic modulus values. The maximum load was

held for 5 s before unloading to 0 μN. The loading and unloading rates

were 200 μN/s and 1000 μN/s, respectively. Hardness and reduced

elastic modulus were calculated from the load-displacement curves ac-

cording to the standard method described by Oliver and Pharr [29,30].

2.3. Nanoscale fatigue testing

The nano-scale fatigue behaviour was investigated by cyclic nanoin-

dentation with closed-loop force control and a frequency of 201 Hz up

to a maximum number of cycles of 10

. During such relatively fast “load-

ing”cycles, it is not possible to acquire sufﬁcient data to evaluate full

load-displacement hysteresis loops. Therefore, fast loading was

interrupted after every 10

,100

, 1000

and 10,000

cycle, to perform

several (n= 3) slow cycles with a loading frequency of 0.1 Hz, also with

closed-loop force control. These slow indents were used as nanoinden-

tation “measurement cycles".

Two loading regimes were chosen: during slow and fast loading, the

maximum and the minimum forces were P

max

=965μNandP

min

=75

μN(ΔP=890μN) in the ﬁrst case (indents marked with 4-x labels). In

the second case, they were P

max

= 930 μN and P

min

= 120 μN(ΔP=

810 μN: indents marked with 5-x and 7–4 labels). The minimum load

chosen ensured a constant contact between the tip and the sample sur-

face. The load function is displayed in Suppl. Fig. 1. A settle time of 2 h

was used prior to each indentation experiment to minimise thermal

drift. The α-Al was indented: (i) in the matrix, far from Si or IMP on

the surface, (ii) in the matrix near the eutectic, and (iii) within the eu-

tectic. Indents were placed in 6 struts yielding a total of 14 nano-

fatigue tests.

2.4. Microstructural and morphological characterisation

The indents and the surrounding surfaces were imaged using the

scanning probe microscopy (SPM) mode of the nanoindenter. Both to-

pography and gradient images were evaluated qualitatively and quanti-

tatively with Gwyddion [31] and Fiji [32,33]. The projected area and the

outer pile-up area were measured for each of the indents using Fiji

where the best ﬁt for both areas was found by visual inspection. Fig. 3

shows a typical SPM topography image result of a cyclic indent and in-

dicates the deﬁnitions of these areas. The pile-up volume was deter-

mined by integration of all pixels under the area. Indent and pile-up

proﬁles were measured using Gwyddion.

High resolution synchrotron based phase contrast enhanced micro-

computed tomography (PCE-μCT) was used to evaluate the microstruc-

ture in the entire volumes of the struts. Scans with effective pixel reso-

lutions of 438 nm or 876 nm were obtained using an energy of 30 keV

on BAMline, the X-ray imaging beamline of the BESSY II electron storage

ring of the Helmholtz Center of Materials and Energy (HZB, Berlin). The

cylindrical specimens (Fig. 1 c) were mounted upright using a sample to

detector distance of 35 mm to induce moderate phase-contrast en-

hancement. The data obtained from a PCO-4000 camera mounted on

an Optique-Peter imaging system was normalised using customised

code, reconstructed with the software NRecon, visualised using CTVox

(Bruker-microCT, Kontich, Belgium) and further processed using Fiji.

For higher resolution characterisation of the microstructure and the

dislocations below the indents, TEM was performed using an FEI Tecnai

20 S-TWIN (Field Electron and Ion Company, Hillsboro, USA),

equipped with an LaB

cathode and an accelerating voltage of 200 kV.

3. Results

3.1. Morphological characteristics

3.1.1. Surface roughness

The topography of the samples was mapped by SPM mode of the in-

denter, in areas surrounding each of the indents (Table 1) and in zones

unaffected by mechanical loading. The average roughness ranges from

1.9 nm for the smoothest specimen to 4.3 nm for the roughest surface.

Fig. 2. Ground and polished cross-section of an A356.0 open-cell foam strut: phases

appearing white and grey are α-Al and Si-particles, respectively. Quasi-static

nanoindentation was performed i) as maps in the α-Al-matrix (marked by a rectangle),

ii) on the Si-particles (marked by black dot), and iii) as line-scans in the α-Al-matrix

with increasing lateral distance from a Si-particle. Dashed rectangle is a magniﬁed view

of the eutectic in region (ii).

3M. Schmahl et al. / Materials and Design 195 (2020) 109016

Such variation was observed both between struts and within the same

struts, regardless of which struts were polished together.

3.1.2. Reference, standard nanoindentation (“quasi-static indentation”)

Nanoindentation (single cycle) in the ɑ-Al-matrix resulted in prom-

inent indentation marks remaining clearly visible after unloading

(Fig. 4). These differed markedly from indents in Si that were barely vis-

ible after unloading (data not shown). The indents in the ɑ-Al-matrix

presented a range of sizes, with some showing pronounced pile-up

while others exhibiting only faint bulging (Fig. 4a-c). Indents with in-

creasing distances from visible Si-particles demarcated the region of

possible inﬂuence of the harder Si-particles on the nanoindentation be-

haviour of the Al-matrix (Fig. 2 iii). No visible differences in indent or

pile-up size and morphology could be identiﬁed with increasing

distance.

3.1.3. Cyclic nanoindentation

Fatigue induced indent morphologies are profoundly different from

quasi-static indents. Indentation depths and sizes of the pile-up are

much higher, and most indents show steps in the pile-up and/or on

the faces of the indents. Typical differences between a quasi-static and

two typical cyclic nanoindents are presented in Fig. 5.

The maximum indentation depth in the ﬁrst cycle (for maximum

load) scales with the applied load: the average value for samples loaded

with a maximum force of 965 μN was 179 nm ± 13 nm whereas the

value for samples loaded to 930 μN was 159 nm ± 10 nm. After cyclic

loading, there was no correlation between the applied force and the in-

dentation depth, highlighting the strong inﬂuence of the underlying mi-

crostructure, as will be shown below.

Fatigue indents were clustered into 5 groups based on indent size,

the presence and the size of pile-up, and the presence and the size of

steps in the pile-up and/or on the faces of the indents (Fig. 6 &Table 2):

•“type S”:small indent size, only minor pile-up,

•“type M”:medium indent size, slightly more pile-up with steps on one

side of the indent,

•“type L”:large indent size, large pile-up with steps on one side of the

indent, steps on at least one face of the indent, position of the step cor-

relates with partial pile-up at the edge of the indent,

•“type P”: very pronounced pile-up with steps on one side of the indent

and partial pile-up on the other sides, but no steps on the faces of the

indent, and very large indent size,

•“type C”:compound group of individual, non-recurring indent

shapes: a) steps visible on the faces of the indent, irregular, pyramidal

pile-up on all sides of the indent. b) non-symmetric elongated indent

with partial pile-up at one end of the indent.

The maximum pile-up point and the dimensions of the steps were

obtained from proﬁles measured in topography images of the indents

as shown in Suppl. Fig. 2. The steps in the pile-up are 100 to 300 nm

wide and 5 to 15 nm high, as compared with 30–40 nm height for

steps across the entire inside in the indent faces. Table 1 lists the maxi-

mum indentation depth, the projected area and the outer pile-up area,

for each of the indents, determined by quantitative image analysis.

The pile-up areas span 1.63 μm

to 3.95 μm

and the volumes span

0.045 μm

to 0.14 μm

. The values correlate with the projected area of

the indent. The pile-ups are not uniformly distributed along the edges

of the indents (best seen in indents of types L and P), and some contain

signiﬁcant local maxima. The linear correlation between the maximum

indentation depth after cyclic loading D

max

(N=10

) and the projected

area was R= 0.81 for indents with hardly any pile-up (type S), and R=

0.61 for indents with signiﬁcant pile-up.

3.2. Microstructure beneath the indents in 3D

To better understand the inﬂuence of the microstructure on the

nanofatigue behaviour, high resolution PCE-μCT was used. Fig. 7

shows examples of the four types of microstructures that we observed

Fig. 3. Evaluation of indent morphological features: a) SPM topography image of a typical cyclic indent; b) typical mask of indent area; c) typical mask of pile-up area.

Table 1

Results of the quantitative analysis of indent and pile-up size and morphology: average

roughness (R

) of the non-deformed surface surrounding the indent, maximum indenta-

tion depth after fatigue loading (D

max

(N=10

)), projected indent area (A

), pile-up area

p-u

), pile-up volume (V

p-u

) and maximum pile-up height (h

p-u, max

Indent Surface Indent Pile-up

max

(N = 10

p-u

p-u,max

(nm) (nm) (μm

)(μm

) (nm)

4-1 a 2.71 ± 0.69 218.88 1.767 2.836 0.129 66.9

4-2 a 2.86 ± 0.62 223.45 1.683 1.902 0.045 46.0

4-2 b 2.86 ± 0.69 222.25 1.720 1.632 0.048 48.2

4-2 d 4.01 ± 0.42 208.02 2.262 3.088 0.105 75.0

4-3 a 2.52 ± 0.28 284.33 2.095 1.988 0.065 58.3

4-3 b 3.87 ± 0.62 259.83 2.112 1.942 0.063 76.8

4-3 c 3.17 ± 0.61 278.84 2.309 2.225 0.075 83.4

4-3 d 4.17 ± 1.72 314.46 3.254 2.838 0.140 107.9

4-3 e 3.30 ± 0.16 319.59 4.082 3.952 0.201 149.6

5-1 a 2.25 ± 0.85 250.06 2.879 3.066 0.131 116.2

5-1 d 1.89 ± 0.64 219.66 1.960 1.869 0.074 100.1

5-3 a 4.25 ± 0.78 284.46 2.966 2.896 0.125 160.7

5-3 d 2.94 ± 0.47 272.95 2.576 2.516 0.095 110.9

7-4 c 2.77 ± 1.05 341.46 3.074 3.351 0.134 143.8

4M. Schmahl et al. / Materials and Design 195 (2020) 109016

in the volumes beneath all cyclic nanoindents. The ɑ-Al-matrix appears

grey. The Si-particles appear slightly darker and only become visible due

to the phase contrast enhancement induced during imaging. The

Fe-IMPs strongly attenuate the X-ray beams and thus appear very

bright. Both sections through the data and projections of maximum

and minimum intensity in the 3D data are shown. The indents are not

visible at this resolution and their approximate position is indicated

by the dotted white line, identiﬁed on the upper surface position by

the white arrowheads. Si-particles are best seen by projection of the

minimum intensity through ~80 μm thickness sub-volumes in the to-

mographic data beneath the indent. Correspondingly, the projections

of the maximum intensity highlight the IMPs. The results are

summarised in Table 2. We discriminated the microstructures according

to their appearance of different phases in a volume of a maximum ra-

dius of 10 μm around the indent according to:

•“type Al”lacks any secondary phases in the ɑ-Al-matrix,

•“type Si”contains few particles in the proximity of the indent,

•“type Eu”is characterised by a high concentration of Si-particles, usu-

ally a eutectic volume,

•“type IMP”contains IMP-particles, relatively large inclusions near the

indent.

Fig. 4. Results for quasi-static nanoindentation, showing 3 different quasi-static impressions with different indent morphologies. SPM gradient and topography imagesand 3D surface plots

are displayed. a) Larger indent with pronounced pile-up; b) larger indent without signiﬁcant pile-up; c) small indent without pile-up. The projected area of the indents (A

), the pile-up

area (A

p-u

) and the pile-up volume (V

p-u

) were determined after background subtraction. Note different scale of the z-axis (depth of the indent) as compared to the lateral scale, chosen for

better visibility of the indent in the 3D surface plots.

Fig. 5. 3D comparison of the indents of quasi-static and cyclic indentation in the ɑ-Al-matrix. a) Quasi-static indent with pronounced pile-up compared to other typical quasi-static results;

b) cyclic indent typical for moderate pile-up; c) cyclic indent typical for increased pile-up and indentation depth. Note that the projected area and the pile-up volume are higher for the

cyclic indents compared to the quasi-static indent. The projected area of the indents (A

), the pile-up area (A

p-u

) and the pile-up volume (V

p-u

) were determined after background

subtraction. Note different scale of the z-axis (depth of the indent) as compared to the lateral scale.

5M. Schmahl et al. / Materials and Design 195 (2020) 109016

3.3. Dislocation structure beneath the indents

TEM observations of a non-deformed reference sample (Fig. 8a)

show a relatively homogeneous microstructure below the surface. The

α-Al-matrix is occasionally interrupted by dislocations (straight dark

lines or points). Selected area electron diffraction (SAED) revealed the

presence of a single dendrite. The light grey needles (indicated by

white arrows) are Si-particles. EDX revealed a low amount of Mg, indi-

cating the additional presence of Mg

Si. Near the surface, some artefacts

developed presumably due to the FIB preparation process.

For quasi-static indents placed in the α-Al-matrix, TEM observations

show the microstructure and dislocation density in the volumes below

the indents. The indent shown in Fig. 8b, c extends about 200 nm

deep. SAED conﬁrmed that a single α-Al dendrite is present (data not

shown) with an almost homogeneous microstructure. Only few small

needle-shaped precipitates are visible consisting of Si and Mg, as identi-

ﬁed by EDX. A higher dislocation density is seen in the volume directly

below and around the indent, as compared to the less mechanically af-

fected volume of the specimen, seen in the lower area of the image. The

dislocation motion into the deeper volume of the sample appears to

have been arrested by a horizontally oriented Si-particle located about

400 nm beneath the indent.

Note that, although we cannot be sure that our TEM lamellae are cut

right through the tip, we are certain that they pass very close to it, given

that the depth of the observed triangular proﬁle of the indent matches

the range of typical indent depths in our study (160 to 200 nm).

TEM measurements of specimens cyclically loaded to 965 μNre-

vealed the microstructure beneath the loaded surface and its relation

to the nano-scale fatigue and deformation mechanisms. Fig. 9 shows

TEM longitudinal slices from six of the cyclic indents, representing the

different indent and microstructural types (Table 2). Indents appear as

triangular structures visible at the upper rim of the lamellae. The main

differences visible for the different samples are the dislocation density

and sub grain structures. In the lamella of indent 4–3 d, the overall

Fig. 6. SPM gradient images of 12 cyclic nanoindents, grouped according to indent size, presence and size of pile-up, and presence and size of steps, visible in the pile-up and/or at the

indent faces: type S - small indents with only small pile-up; type M - medium indents with more pile-up and slight steps; type L - large indents with signiﬁcant pile-up and

pronounced steps within the pile-up and on the indent faces; type P - large indents with signiﬁcant pile-up and steps in the pile-up, but no steps on the indent faces; type C -

compound group: relatively small indent with pronounced pile-up and steps (5-3 d); large, irregular indent with signiﬁcant pile-up and steps (7-4 c).

6M. Schmahl et al. / Materials and Design 195 (2020) 109016

lowest dislocation density is shown. We observe a few single disloca-

tions (marked by arrow ①in Fig. 9) and some formation of sub grain

structures (marked by arrow ②in Fig. 9), limited to the faces of the in-

dent, and only rather indistinct sub grain boundaries. The dotted white

arrow without number indicates an artefact caused by the FIB prepara-

tion process. The observations in the volume inﬂuenced by the indenta-

tion process for indent 4–3 a are very similar to 4–3 d, with a slightly

higher overall dislocation density. Arrays of parallel, unidirectional dis-

locations (marked by arrow ①in Fig. 9) are homogeneously distributed

throughout the ﬁeld of view. In a small volume directly beneath the

indent and extending across the width of the indent face, the disloca-

tions are clustered, forming two clearly visible sub grains (marked by

arrow ②in Fig. 9). Some diffraction artefacts caused by the bending of

the lamellae during the FIB preparation process are seen (marked

by white arrows without number in Fig. 9). Elemental mapping

(Fig. 10 a) showed a higher oxygen content at the surface as compared

to the bulk of the specimens which we attribute to the natural formation

of an oxide layer.

Indents 4–3cand4–2 d are examples for a less homogeneous dislo-

cation structure and more clearly developed sub grains. More extended

sub grain structures are visible in a larger volume beneath the indents

and the sub grain boundaries are further developed as compared to

the indents 4–3aand4–3 c. Indent 4–3 b shows a very ﬁne and well-

developed sub grain structure. SAED in the areas between the sub

grain boundaries (positions marked by * and # in Fig. 9)revealedanori-

entation difference between these areas, proving that the features we

see are indeed sub grains (Fig. 10b). In a conﬁned area directly below

these sub grains, the dislocation density is lower, while it is higher

again towards the lower part of the lamella. Further, a eutectic Si-

particle is seen in the vicinity of the indent, which was not visible in

the reconstructed PCE-μCT data (marked by arrow ③in Fig. 9). The cor-

responding EDX analysis is shown in Fig. 10c.

While all other investigated lamellae contained only one dendrite,

the TEM micrographs of indent 4–3 e clearly show a dendrite border

(markedbyarrow④in Fig. 9). Pronounced sub grain structures are

seen in the left dendrite, while only single dislocations are visible in

the right dendrite. The differences in orientation and dislocation density

between the dendrites and the sub grains in the left dendrite are espe-

cially well visible by the pronounced contrast in the STEM image (upper

image of 4–3 e): the left dendrite appears much brighter with the sub

grains visible as darker areas, and the right dendrite appears in rela-

tively uniform, very dark grey.

3.4. Mechanical properties

Typical load-displacement curves from quasi-static nanoindentation

tests on the α-Al-matrix and the Si-particles are shown in Suppl. Fig. 3.

For testing the Si-particles, the load was increased by a factor of ﬁve to

achieve the same indentation depth as in the Al-matrix. While the

curves for the Al-matrix are smooth, the curves for the Si-particles

show the so-called “elbow effect”in the unloading segment. This effect

has been previously related to the formation of an amorphous Si-phase

[34]. None of the curves show severe load serrations which would indi-

cate a pop-in effect or crack nucleation. The α-Al-matrix exhibits much

higher plasticity in comparison with Si, visible from the higher maxi-

mum displacements, perfectly matching the morphological observa-

tions. The differences in the deformation behaviour of the two phases

are also reﬂected in the measured values of the hardness and the re-

duced elastic modulus (Table 3). Both are signiﬁcantly higher for the

Si-particles.

By mapping the α-Al-matrix, indents end up with a variety of dis-

tances to the Si-particles on the surface. To investigate a possible in-

ﬂuence of this variation as well as possible effects of other inclusions

such as IMPs, we placed additional indents in the matrix along lines

orthogonal to the interfaces and with increasing distances from Si-

particles, as indicated in Fig. 2. Close inspection of such indents

with the SPM imaging mode of the nanoindenter did not reveal

any correlation between the distance, the indent shape and size in

the gradient images and the calculated hardness of the material

(Table 4). However, the reduced elastic modulus was roughly 15%

higher near the Si-particles, observed for measurements obtained

within a distance of 5 μm.

For the fatigue investigations, all indentations were performed in the

α-Al-matrix, with different surrounding local microstructures. During

fatigue loading, hysteresis loops develop and the maximum and mini-

mum depth (D

max

min

respectively) reached in every single cycle

change gradually. To evaluate the development of the plastic deforma-

tion, we analysed the change in D

min

from cycle to cycle. ΔD

min

repre-

sents the incremental plastic deformation, induced by the application

of the force amplitude over the entire history of loading. The change

in minimum displacement between consecutive measurement cycles

x+1

and N

is:

ΔDmin Nxþ1

ðÞ¼Dmin Nxþ1

ðÞ−Dmin Nx

ðÞ ð1Þ

Table 2

Results of the microstructural investigations: for each indent, the groups according to indent size and morphology and to PCE-μCT results of the volumes beneath the indents are listed. For

the indents where TEM has been performed, short descriptions and the groups, based on differences in microstructure and dislocation formations, are given.

Indent Size/morphology (Fig. 6) PCE-μCT (Fig. 7) TEM (Fig. 9)

4-1 a M Si - Eu –

4-2 a S Al –

4-2 b S Al –

4-2 d M Eu II: medium-size affected area, pronounced sub grain structures

4-3 a S Si I: small affected area, few indistinct sub grain boundaries

4-3 b M Si III: large affected area, very ﬁne and very pronounced sub grain structure;

Si particle near indent

4-3 c M Si - Eu II: medium-size affected area, pronounced sub grain structures

4-3 d P IMP I: small affected area with few indistinct sub grain boundaries

4-3 e P Eu dendrite border: left dendrite II: medium-size affected area, pronounced sub grain

structures; right dendrite: single dislocations

5-1 a L Al –

5-1 d M Eu –

5-3 a L Al –

5-3 d C: M indent & pile-up, pronounced steps Eu –

7-4 c C: elongated indent, medium pile-up, steps IMP –

Indent size/morphology groups: S: small indent & pile-up; M: medium indent & pile-up, steps; L: large indent & pile-up, many steps; P: very large indent & pronounced pile-up; steps; C:

compound group; PCE-μCT microstructural groups: Eu = eutectic; Al = Al matrix; Si = silicon; IMP = Fe-IMP inclusion.

7M. Schmahl et al. / Materials and Design 195 (2020) 109016

Fig. 7. PCE-μCT data showing typical 3D-microstructures in the volumes below the cyclic nanoindents: distribution of Si-particles and IMPs up to 10 μm beneath the indent: type Al - only

α-Al; type Si - some small Si-Mg-particles; type Eu - Si eutectic; type IMP - IMPs and Si-Mg-particles. “Section”denotes longitudinal sections through the reconstructed volumes, max. and

min. intensity are projections of the maximum and minimum intensity across 20 μm in the volume beneath the indent. Two orthogonal sections (left and right image) are shown for each

type. The white dotted lines and the white arrowhead indicate the indent and surface position. The solid white arrows point to Si-particles which appear in darker grey, and the dotted

white arrows point to IMPs which appear in bright grey/white.

8M. Schmahl et al. / Materials and Design 195 (2020) 109016

and is normalised by the number of cycles over which the change oc-

curred. Since there were slight unavoidable differences in the applied

force (~30% in P

min

) for the different tests, we scale the result by P

min

ΔDmin−norm Nxþ1

ðÞ¼ΔDmin=Nxþ1−Nx

ðÞPmin Nxþ1

ðÞðÞð2Þ

Fig. 11 shows typical curve progressions for ΔD

min-norm

versus N for

two regimes of cycle numbers: up to 10

, and from 10

to 10

. For the

curves of all indents see Suppl. Fig. 4. In the following, we address the

ﬁrst and second regime of cycles as “incipient”and “advanced”fatigue

regime.

We see that the changes of plastic deformation are much lower in

the advanced regime as compared to the incipient one. All tests show

a decrease in the incremental plastic deformation per cycle over N.

The variations in ΔD

min-norm

over the ﬁrst ten cycles and the signiﬁ-

cantly lower variations during the following cycles are partially due to

the averaging performed for the higher cycle numbers, where only

every 100

, 1000

or 10,000

cycles are measured. Different speci-

mens ﬂuctuate differently, suggesting that the changes are also due to

a real decrease in the plastic deformation from cycle to cycle, indicating

some saturation.

For the incipient regime, two main types of cyclic deformation be-

haviour are observed (types A1 and A2, see Table 5): the absolute

value of the ﬂuctuations during the ﬁrst ten cycles is more pronounced

for the “A2”curves. Furthermore, the “A1”curves exhibit an increase be-

tween 10 and 100 cycles followed by a decreasing trend whereas “A2”

curves decrease continuously beyond 10 cycles. The curves vary in

their incline or decline and many “A2”curves show a lower decline

after 10 than after 100 cycles. Some indents are difﬁcult to sort into

groups, due to the high variations in the curve progression. For example,

indents 4–3dand4–3e,both“A2”, show an overall decreasing behav-

iour after 10 cycles, but the decline between 10 and 100 cycles is very

small and almost plateau-like.

With ongoing loading (advanced regime), two main types of behav-

iour are observed. In the ﬁrst case (type B1), ΔD

min-norm

is approxi-

mately constant on a very low level, indicating a pronounced

saturation state. In the second case (type B2), ΔD

min-norm

decreases fur-

ther up to about 20,000 cycles, followed by a nearly steady state with

only slightly decreasing trend. Only three curves (4-1 a, 4-2 a, 4-2 b)

show B1 behaviour in the advanced regime, while nearly all other

curves exhibit B2 behaviour.

Two curves do not ﬁt the described behaviours: indent 4–2d

exhibits extreme ﬂuctuations of ΔD

min-norm

during the ﬁrst 10 cycles,

with signiﬁcantly negative values, and a further decrease for the ad-

vanced regime with consistently negative changes of ΔD

min-norm

, indi-

cating a decrease in the minimum depth over the number of cycles.

The second special case is indent 7–4 c where we observe a slight in-

crease in ΔD

min-norm

from 40,000 to 100,000 cycles, indicating continu-

ous softening.

The ratios of D

min

to D

max

versus the number of cycles are shown in

Fig. 11 and Suppl. Fig. 5. Whereas this value increases if the indented

volume behaves increasingly more elastic, it decreases, if a higher

amount of plastic deformation occurs or a crack is formed. Here we

also observe four different types of behaviour (Table 5): three indents

have very similar courses of D

min

max

versus N, with a low ﬂuctuation

and a clearly visible saturation state following an initial increase in

min

max

up to N= 100 (type I). The second group (type II) shows

more pronounced ﬂuctuations and a steady increase over N. This

increase in D

min

max

over N is even more pronounced for the “type

III”behaviour. The three remaining specimens exhibit the opposite

behaviour (type IV): D

min

max

decreases over the last 50,000 to

90,000 cycles, following a range with nearly constant values up to

10 cycles, and an increase afterwards.

4. Discussion

By cyclically indenting up to N=10

,wewereabletoinducefatigue

characteristics in the Al-matrix of open-cell A356.0 foam struts, similar

to those usually seen in bulk Al alloys. The combination of very high res-

olution localised 2D microstructural analysis (e.g. TEM, Fig. 9)andhigh

resolution 3D analysis of a larger volume (PCE-μCT, Fig. 7), allowed us to

develop a comprehensive understanding of the microstructural pro-

cesses on different length scales. Our results reveal a range of local inter-

actions of the indenter with the microstructure. Signiﬁcant hardening is

observed during the ﬁrst few cycles, followed by either saturation or

further hardening. Local microstructural inhomogeneities, such as Si-

particles, inﬂuence the matrix behaviour in an interaction volume of 5

to 10 μm. On the nanoscale, we observed typical fatigue induced dislo-

cation structures. The variation in the data suggests that the different in-

dents are in different fatigue states, depending on the secondary phases

beneath the area where the force was applied. An important observa-

tion was of ﬂuctuations in the cyclic deformation behaviour following

repeated loading which we assign to interactions with and the release

of residual stresses. Interpretation of our fatigue results requires consid-

ering the initial interactions between the indenter and the strut and the

changes that evolve over time.

Fig. 8. Bright-ﬁeld TEM micrographs showing FIB sections through: a) a non-deformed reference sample, and b, c) a quasistatic indent (“triangle”, delineated by the dotted line in b). a) The

non-deformed state exhibits a very low dislocation density in the ɑ-Al-matrix. Note that the dark areas marked by the black arrow ①are preparation and imaging artefacts as

demonstrated by tilting the specimen during TEM observation. An elongated Si-Mg-particle is visible in darker grey (white arrow ②). b, c) Following quasi-static nanoindentation, the

dislocation density in the volume below the indent has increased signiﬁcantly (white arrow ③). With higher magniﬁcation (c; area marked in (b) by the white dotted rectangle), a Si-

Mg-particle (white arrow ②) is visible, seemingly hindering further dislocation movements into the lower part of the specimen.

9M. Schmahl et al. / Materials and Design 195 (2020) 109016

Fig. 9. Typical TEM and STEM images of lamellae prepared through the tips ofsixcyclic indents.The upper and lower image ofeachindentshow surveys and magniﬁed views, respectively.

Microstructural features are indicated by white or black arrows and numbers: dislocations ①, dislocation cells ②, a Si-Mg-particle ③and a dendrite border ④. SAED was performed on the

lamella of indent 4-3 b in two areas next to a sub grain boundary (marked with * and #). The white arrows without numbers in the micrographs of indent 4-3 d and 4-3 a point to

preparation and diffraction artefacts, respectively.

10 M. Schmahl et al. / Materials and Design 195 (2020) 109016

Our quasi-static nanoindentation hardness results (1.0 ± 0.1 GPa)

for the α-Al-matrix show values that are only slightly lower than values

reported for a nickel coated AlSi7Mg0.3 hybrid foam by Jung et al.

(2015) [22]. The slightly higher values that they report for the matrix

(1.4 ± 0.1 GPa) might be due to the lower indentation force of their ex-

periment (500 μN) or a different manufacturing process of the foam that

they used. Those authors also studied the hardness values for the Si

phase using the same indentation force as we used in our study (5000

μN). They report a value of 10.3 ± 0.4 GPa, which corresponds well

with our own results (11.2 ± 1.5 GPa). Importantly, both previous

and our own measurements reveal some variance over the indented

surface which we attribute to locally varying microstructure. Speciﬁ-

cally, the sub-surface microstructure, Si- or IMP-particles, will inﬂuence

the deformation resistance and hence the indenter imprint. Our TEM

observations around an example quasi-static indent clearly show an in-

teraction of the indent with the Si-particles that hinder dislocation

movements into deeper parts of the specimen (see Fig. 8c).

The variations in the local properties affecting the quasi-static

indentations naturally also affect the cyclic loading experiments.

During the onset of loading, we see a clear inﬂuence of the applied

load on the indentation depth, in addition to the variation caused

by the microstructure. With increasing numbers of cycles, the

differences between indents no longer uniquely correspond to dif-

ferences in the applied load. This is seen by the average maximum

depth values. Speciﬁcally, some of the indents with lower loads

showed higher indentation depths whereas other indents with

higher loads showed lower indentation depths. These differences

can only be explained by local variations in microstructure that

take control over the deformation processes with increasing num-

bers of cycles. These observations are mirrored by the dimensions

and morphology of the pile-up of these indents. Small cyclic indents

with very little pile-up and no steps (type S, Fig. 6) are usually ob-

served in areas with no or only few, very small Si-particles. Smaller

indent sizes in the advanced regime suggest a relatively high resis-

tance to cyclic plastic deformation with pronounced cyclic harden-

ing. Unexpectedly, when the volume beneath the indent contains

hard secondary phases often larger imprints are seen (types M, L,

P, Fig. 6). A possible explanation is the release of tensile residual

stresses in the Al-matrix coupled with reduction of compressive re-

sidual stresses in the Si-particles. We propose that residual stresses

arising during cooling after casting due to differences in the thermal

shrinkage of the main phases (ɑ

th,Al

≅2

th,Si

) decrease the energy

necessary for dislocation slippage in the Al-matrix. It has been

shown for quasi-static indentation that residual stresses strongly

inﬂuence the amount of pile-up [35].

We note that, with increasing indent size, the pile-up volume in-

creases. We propose that blockage of dislocation motion into deeper

areas beneath the surface leads to excessive material being pushed out

above the surface. Evidence for this is seen in TEM images where dislo-

cations are often not seen in regions below Si-particles (see Fig. 9). Fur-

ther work is needed to fully clarify the exact mechanisms involved in

these processes.

The ﬁnal resulting cyclic-indentation imprint is inﬂuenced by both

the plastic strain history and by the extent of strain hardening. We see

two very different outcomes for the pure ɑ-Al-matrix:

•There are cases where we observe an early onset of strain hardening.

This is seen by a pronounced decrease in ΔD

min-norm

and increase in

min

max

in the incipient regime, and plateaus or negligible changes

of both curves in the advanced regime. Ultimately, this leads to small

indent imprints with small pile-up (4-2 a, 4-2 b).

•In other cases (5-1 a, 5-3 a), the strain hardening rate appears to be

lower, indicated by a slower decrease in ΔD

min-norm

up to about

N ~ 20,000 and a decrease in D

min

max

in the advanced regime. Re-

peated indentation leads to signiﬁcant plastic deformation, larger in-

dents and larger pile-up.

Fig. 10. Analysis performed on the TEM slices for microstructural characterisation; a) EDX map of oxygen on a TEM lamella revealing a higher oxygen content in the surface-near volume

(top) compared to the bulk (border denoted by the white arrows); b) results for SAED performed at positions * and # in Fig. 9 (4-3 b), showing a misorientation of 3.1° between the two

areas, thus clearly indicating two adjacent sub grain structures; c) EDX spectrum obtained from the particle ③in the lamella through the indent 4-3 b in Fig. 9.

Table 3

Results of quasi-static nanoindentation: hardness and reduced elastic modulus

(mean ± standard deviation) from 300 measurements in the α-Al-matrix (P

max

=1000

μN) and 50 measurements in the eutectic Si-phase (P

max

= 5000 μN).

H (GPa) E

(GPa)

α-Al-matrix 1.0 ± 0.1 83.6 ± 4.6

Eutectic Si 11.2 ± 1.5 129.5 ± 12.5

Table 4

Results of quasi-static nanoindentation: hardness and reduced elastic modulus

(mean ± standard deviation) measured in the α-Al-matrix with increasing distance to

Si-particles, from 10 “lines”placed in the same way as the example indicated in Fig. 2 iii).

Lateral distance (μm) H (GPa) E

(GPa)

0 0.9 ± 0.1 79.9 ± 3.2

5 1.0 ± 0.1 68.9 ± 7.1

10 0.9 ± 0.1 68.4 ± 5.8

15 0.9 ± 0.1 66.6 ± 4.2

20 1.0 ± 0.2 70.3 ± 4.9

11M. Schmahl et al. / Materials and Design 195 (2020) 109016

The appearance of pile-up in an initially soft, ductile material merits

further consideration. Repeated loading cycles lead to hardening of the

affected volume due to repeated activation of dislocations, dislocation

multiplication and, eventually, the development of dislocation struc-

tures. Subsequently, dislocation motion takes place with plastic defor-

mation propagating into neighbouring volumes. Thus, the material

volume affected by indentation increases with increasing cycle number.

In this way initially soft volumes, able to accommodate relatively large

plastic deformation, become hardened and continuous indentation re-

sults in an increase in pile-up. It is worth mentioning, that literature re-

ports of quasi-static nanoindentation experiments on strain-hardened

metals found more pile-up as compared to indentations performed in

the soft states [36–38]. In those works, however, the indent sizes were

smaller. In contrast, under our cyclic loading conditions, higher pile-up

correlates with bigger indent sizes. The reason must be that we initially

indent a soft material and hardening develops during thousands of load-

ing cycles. Similar observations have been reported for fatigue of a cast

AlSiMg alloy with large dendrites. The authors remark that large den-

drite cells with tight interdendritic spaces behave like single grains,

and that the blocking of dislocations at the boundaries between the

dendrite and the eutectic leads to large plastic deformations in these

areas. We deduce that in this way hardening can be combined with

large amounts of plasticity [39].

An explanation for the differences in the amount of pile-up for

similar microstructures might be the orientation of the indenter with

respect to the ɑ-Al-dendrite. Correspondingly, if the preferred slip sys-

tems in the Al-crystal are oriented such that they experience the highest

shear stress during indentation, plastic deformation is extensive. The in-

ﬂuence of dendrite orientation on the development of pile-up and of

sub grain structures is nicely demonstrated by indent 4-3 e where we

cyclically loaded a volume with a dendrite border. While one dendrite

clearly shows sub grain structures, the other dendrite exhibits a very

low dislocation density. For quasi-static nanoindentation it is well

known that the pile-up strongly correlates with the orientation of the

slip systems, hence the crystallographic orientation [40,41]. Detailed

investigations of the relation between dendrite orientation and the

cyclic indentation behaviour are a topic of ongoing work and beyond

the scope of this paper.

Larger indents and pile-up come with an increased appearance of

steps both in the pile-up material and on the exposed faces of the

indents. We assume that these are fatigue slip lines because of their

typical morphology. Such steps emerge as a result of dislocation based

cyclic plastic deformation in the affected volume. In some areas, exten-

sive localised deformation leads to high peaks in the pile-up. The occur-

rence of the slip lines does not correlate with the development of sub

grain boundaries and a dislocation cell structure. We therefore assume

that the slip lines are not associated with persistent slip band formation.

The cyclic deformation curves contain information that provides ad-

ditional insights into how the ﬁnal indent morphology is reached. All in-

dents exhibit pronounced plastic deformation at the beginning of

loading and a subsequent hardening trend. This is seen in the overall

decrease in ΔD

min-norm

and increase in D

min

max

followed by constant

saturation values or by additional changes emerging at a much lower

rate. The hardening is not continuous: relatively large spikes are seen

in the ΔD

min-norm

-N-curves revealing alternating softening and harden-

ing of the material around the indenter tip. Such pronounced ﬂuctua-

tions are seen for nearly all cyclically loaded specimens at the onset of

the experiments. Additional ﬂuctuations are seen in the advanced cycle

regime for many of the samples albeit with a smaller amplitude. The

lower amplitudes for higher cycle numbers have two very different ex-

planations: spikes are either not visible due to averaging across many in-

dentation cycles or the material approaches a saturation fatigue state.

We hypothesize that some spikes/ﬂuctuations are caused by the re-

lease of residual stresses from the Si-inclusions during cyclic loading.

Usually, indents showing more pronounced ﬂuctuations in the ad-

vanced regime are those placed in regions with Si in the volume

below the indent. The ﬂuctuations of ΔD

min-norm

and speciﬁcally, ﬂuctu-

ations to negative values, suggest that pushing-out of the indenter takes

place. We also see a cross-over of some hysteresis loops, with an unex-

pected large decrease in the displacement during unloading (data not

shown). Similar observations regarding the interactions of residual

stresses with the nanoindentation results have been reported for

quasi-static loading [35]. Those authors found that the extent of residual

stresses correlated with the ratio of the ﬁnal depth after unloading to

the maximum depth reached during one loading event.

Generally, indents in pure Al (4-2 a, 4-2 b, 5-1 a, 5-3 a) exhibit pro-

nounced hardening in the incipient regime (A1), but they differ regard-

ing the advanced regime. Indents 4-2 a and 4-2 b enter a pronounced

saturation state while indents 5-1 a and 5-3 a harden with a slower

rate and exhibit more ﬂuctuations in the ΔD

min-norm

-N-curves. These

differences between indents correlate with the indent and pile up

sizes. The higher capability of plastic deformation of the two latter in-

dents correlates with the decrease in D

min

max

during much of the ad-

vanced regime (N ~ 30,000 to 90,000, note the logarithmic scale). More

pronounced ﬂuctuations are seen for indents placed on surfaces with Si-

or IMP-particles in the volume beneath the indents which we assign to

the release of residual stresses. Indents in such regions also differ re-

garding their hardening behaviour. For example, indent 4-1 a, shows

signiﬁcant hardening in the incipient regime (type A1), just like the

Fig. 11. Typical examples of ΔD

min-norm

-N-curves in the “incipient regime”(N ≦10

ΔD

min-norm

-N-curves in the “advanced regime”(N ≧10

), and D

min

max

-N-curves.

12 M. Schmahl et al. / Materials and Design 195 (2020) 109016

pure Al-indents. The signiﬁcant amounts of Si-particles in the vicinity of

the indent correlate with the further progression of the cyclic deforma-

tion curves and a higher pile-up.

We see dislocation cells as predominant dislocation structures in the

Al-matrix. Interestingly, dislocation cells have also been identiﬁed as

main fatigue induced dislocation structures during multiaxial fatigue

of A356 bulk materials [39,42]. In those works, the authors note that

the cell formation and the extent to which they develop strongly de-

pend on the exact loading path and hence the precise stress conditions

[39], as well as on the strain amplitude [42].

We clearly pick up the inﬂuence of the secondary phases on the dis-

location movement and the cyclic deformation behaviour, even though

we indent the matrix extremely locally, with an interaction volume in

the range of 10 μm diameter. Si-particles in the volume affected by cyclic

indentation clearly hinder the dislocation movement. By conﬁning the

available volume, dislocation cells seem to develop earlier in the fatigue

process. The mechanism is schematically summarised in Fig. 12 a. In

cases with no Si-particles in the vicinity of the indent as shown in

Fig. 12 b, we observe a high dislocation density, homogeneously distrib-

uted in the volumebeneath theindent (4–3 a). If Si-particles are present

we see the formation of dislocation cells above the particle, and a very

low dislocation density below the particle (4–3 b). We conclude that

the microstructural fatigue response is a complex function of the multi-

axial loading state, the local microstructure with or without hard pre-

cipitates, and the relative orientation of the indenter and the ɑ-Al-

dendrite.

5. Conclusions

We investigated the inﬂuence of the microstructure on the nanoin-

dentation behaviour of open-cell A356.0 foam struts under quasi-

static and cyclic loading conditions. Our ﬁndings lead to the following

main conclusions:

1. Local variations in microstructure strongly inﬂuence the measured

quasi-static and cyclic indentation data as well as the indent and

the pile-up size and morphology. Indent size after cyclic loading

correlates with the pile-up volume.

2. Our quasi-static investigations proved an interaction distance of the

Si-particles of 5 μm. The interaction volume during cyclic loading

seems to be bigger, in the range of up to 10 μm, where Si- and IMP-

particles signiﬁcantly inﬂuence the cyclic deformation behaviour of

the matrix.

3. We observed slip bands after cyclic loading in many indent imprints,

in both the pile-up and on the indent faces. The extent of slip band

formation (size and density) strongly depends on the local micro-

structure in the volume affected by the indentation.

4. Si-particles act as barriers for the dislocation movement. Under

fatigue conditions, they favour the formation of dislocation cells.

The formation of the dislocation structures further strongly depends

on the dendrite orientation. Interestingly, the pile-up volume and the

formation of slip bands in the pile-up does not correlate with the for-

mation of dislocation cells beneath the indent.

Table 5

Types of cyclic deformation behaviour of the indents: two regions of numbers of cycles

have been evaluated separately for the ΔD

min-norm

curves, the “incipient regime”with N

≦10

,andthe“advanced regime”with N ≧10

. For each regime, the curves could be clus-

tered in two groups: A1: lower spikes; A2: higher spikes with overall hardening; B1: sat-

uration; B2: further hardening with lower rate, ﬂuctuations. Indent 4–2 d no group -

special curves with pronounced spikes and negative values. For the courses of D

min

max

versus the number of cycles, four different types of behaviour were distinguished: I: initial

increase, followed by saturation, ﬂuctuations; II: steady increase, more pronounced ﬂuctu-

ations; III: as II, but even more pronounced; IV: increase followed by decrease over the last

~50,000 cycles.

Indent ΔD

min-norm

“incipient regime”

ΔD

min-norm

“advanced regime”

min

max

4-1 a A1 B1 I

4-2 a A1 B1 I

4-2 b A1 B1 I

4-2 d –– IV

4-3 a A2 B2 II

4-3 b A2 B2 II

4-3 c A2 B2 II

4-3 d A2 B2 II

4-3 e A2 B2 II

5-1 a A2 B2 IV

5-1 d A2 B2 II

5-3 a A1 B2 IV

5-3 d A1 B2 III

7-4 c A2 B2 III

Fig. 12. Schematic illustration of thedislocation distribution and dislocation structures in the volume below the indent a) affected by Si-particle and b) surrounded by the homogeneous α-

Al-matrix only. (1 = indent, 2 = high dislocation density and dislocation cells, 3 = low dislocation density, 4 = Si-particle, 5 = high dislocation density, dislocations homogeneously

distributed).

13M. Schmahl et al. / Materials and Design 195 (2020) 109016

5. Importantly, the fatigued volumes below the indents seem to reach

different fatigue states, depending on the local microstructure.

6. The results well coincide with observations during fatigue of the bulk

alloy reported in the literature. They are therefore an ideal basis for

the future development of models predicting the fatigue behaviour

of A356.0 open-cell foams.

Our insights into the inﬂuence of microstructure on the local cyclic

deformation behaviour will help to tailor the fatigue properties to spe-

ciﬁc applications, for example by using heat treatments or by adding

modiﬁers, thereby changing the distribution, size and morphology of

secondary phases. Another important aspect is the relation between

dendrite orientation and the cyclic indentation behaviour. Further

work is needed to fully elucidate these topics.

Supplementary data to this article can be found online at https://doi.

org/10.1016/j.matdes.2020.109016.

Declaration of Competing Interest

The authors declare that they have no known competing ﬁnancial

interests or personal relationships that could have appeared to inﬂu-

ence the work reported in this paper.

Acknowledgement

The authors thank Prof. Andreas Bührig-Polaczek and Dr. Sebastian

Fischer, Foundry Institute of RWTH Aachen University, for sample cast-

ing and fruitful collaborations within SPP 1420, funded by the DFG. We

further thank Martina Schaube and Ralf Engelmayer (Materials Science

& Engineering, Technische Universität Berlin) for metallographic and

specimen preparation, Dr. Dirk Berger and Sören Selve (Central Electron

Microscopy Unit ZELMI, Technische Universität Berlin) for HR-SEM, FIB

preparation and TEM, and Ana Prates Soares and Andreia Sousa da

Silveira (Restorative and Preventive Dentistry, Charité –Universität-

smedizin Berlin) for their help in PCE-μCT data processing. We thank

the Helmholtz Zentrum Berlin for the allocation of synchrotron radia-

tion beamtime and the beamtime scientist Dr. Christian Gollwitzer for

his excellent support. We are speciﬁcally grateful to Prof. Peter Fratzl

and Petra Leibner (Max-Planck-Institute of Colloids and Interfaces,

Potsdam-Golm) for technical assistance with the nanoindenter. We ac-

knowledge support by the German Research Foundation and the Open

Access Publication Fund of TU Berlin.

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