Microstructure and compression behavior of Ag–W metal matrix composite produced from core–shell powder by spark plasma sintering: case study

Vol.:(0123456789)
The In e na ional Jou nal o Ad anced Manu ac u ing Technology (2025) 139:1571–1580
h ps://doi.o g/10.1007/s00170-025-15944-7
ORIGINAL ARTICLE
Mic os uc u e andcomp ession beha io o Ag–W me al ma ix
composi e p oduced omco e–shell powde byspa k plasma
sin e ing: case s udy
AngelinaS akošo á1· D ahomí D o ský1· FilipP ůša2· O solyaMolná o á1· S anisla Hab 1· JakubS oboda3·
I onaSedlářo á2· Dalibo Voj ěch2· Pa elLejček1
Recei ed: 19 Ma ch 2025 / Accep ed: 5 June 2025 / Published online: 24 June 2025
© The Au ho (s) 2025
Abs ac
Me al ma ix composi es ep esen an in e es ing class o ma e ials wi h an exclusi e combina ion o p ope ies. In his s udy,
a unique Ag–W me as able me al ma ix composi e was p oduced om W@Ag co e–shell powde s using a spa k plasma
sin e ing echnique a a empe a u e o 700°C and a p essu e o 80MPa. The mic os uc u es o a de aul powde and as-
p oduced composi e we e obse ed by scanning elec on mic oscopy equipped wi h ene gy-dispe si e X- ay spec oscopy
and elec on backsca e di ac ion. As expec ed, he composi e is cha ac e ized by a dual mic os uc u e: a so ma ix o
pu e Ag wi h a submic ome e g ain size ein o ced by W pa icula es wi h a g ain size o up o 30μm. In addi ion, ensile
and comp ession es s we e pe o med wi h a de o ma ion a e o 10–3 s−1 a ambien empe a u e. The alue o he comp es-
sion yield s ess o Ag–W MMC is highe han he comp ession yield s ess o pu e Ag by app oxima ely 467%. Obse a ion
o he mic os uc u e o he de o med composi e ma e ial e ealed ha he in e ace be ween he ma ix and he ein o ced
pa icles is he weakes place, which is a key ac o in luencing he pe o mance and p ope ies o he composi e ma e ial.
Keywo ds Co e–shell powde · Sil e · Tungs en· Spa k plasma sin e ing· Me al ma ix composi e· Comp ession
de o ma ion
1 In oduc ion
Me al ma ix composi es (MMCs) ep esen a class o highly
sophis ica ed ma e ials wi h a unique combina ion o p ope -
ies, including, e.g., enhanced s eng h, wea esis ance, and
educed he mal expansion [1, 2], ha a e well-sui ed o a
di e se a ay o applica ions such as ae ospace, mili a y,
spo s, and elec onics [3, 4]. MMCs include a con inuous
me allic ma ix and a me iculously selec ed ein o cemen ,
which is delibe a ely chosen based on i s speci ic p ope -
ies and he desi ed ea u es o he composi e ma e ial [3, 5,
6]. I is known ha he shape o ein o cemen ( ibe s and
pa icles) a ec s he s uc u e and p ope ies o composi e
ma e ials [7].
A endy b anch o MMC p epa a ion ep esen s he
me hods o powde me allu gy (PM), such as ho ex usion
and ho p essing [8]. Besides hem, spa k plasma sin e ing
(SPS) is a p omising me hod in his espec i small pa s
should be p epa ed. Compa ed o o he PM me hods, SPS
allows he p ese a ion o ine mic os uc u e [9, 10] due o
he sho - e m na u e o he p ocess, which ypically com-
bines only a ew minu es o sin e ing and consolida ion in o
a single ope a ion s ep [8, 11]. A wide ange o ma e ials
can be p oduced by he SPS echnique [12, 13], o exam-
ple, high-en opy alloys [9], composi es wi h ex emely high
s eng h [14], and in e me allics [15].
Recen ly, co e–shell powde s ha e become a popula
ma e ial used o MMC p oduc ion [16–20]. A combina ion
o he SPS echnique wi h he usage o co e–shell powde s
enables he p oduc ion o me as able me al ma ix compos-
i es (m-MMCs) hanks o he sin e ing o he shell su aces
and supp ession o he di usion p ocesses be ween he co e
and shell [21]. Recen ly, we s udied he s uc u e and plas ic
* Angelina S akošo á
s akoso[email p o ec ed]
1 Ins i u e o Physics, Czech Academy o Sciences, Na
Slo ance 2, 18200P ague, CzechRepublic
2 Uni e si y o Chemis y andTechnology, Technická 5,
16628P ague, CzechRepublic
3 SAFINA a.s, Vídeňská 104, 25250Ves ec, CzechRepublic
1572 The In e na ional Jou nal o Ad anced Manu ac u ing Technology (2025) 139:1571–1580
de o ma ion o Ag–Cu m-MMCs p epa ed om Cu@Ag
co e–shell powde s, whe e he co e and shell ma e ials show
e y simila mechanical p ope ies [21, 22]. On he o he
hand, i could be a e y in e es ing opic o combine wo
ma e ials wi h diame ically di e en p ope ies o p oduce
MMCs. One o such ma e ials could be MMCs, which a e
used in elec onics as elec ical con ac s and a e a combina-
ion o wo immiscible me als, such as sil e and ungs en
[23]. Such composi es, which can also ha e an ibac e ial
po en ial, ha e usually been o med by sphe ical pa icu-
la es in a so ma ix and a e usually p oduced by ho p ess-
ing Ag and W powde s [23, 24]. Only a ew a emp s ha e
been pe o med o p oduce mic o-sized MMCs om Ag@
(W/WO3) co e–shell powde s [16, 25–27] and s udy hei
mechanical and elec ic p ope ies [28–30]. Un o una ely,
he p esen knowledge on Ag-based MMCs is sca ce. The e-
o e, hei p oduc ion and examina ion o he mic os uc u e
and o he beha io s, such as he mechanical p ope ies o
Ag-W MMCs, a e in iguing and impo an opics.
In he p esen wo k, we desc ibe he mic os uc u e and
mechanical beha io o a model MMC combining a e y
so Ag ma ix (densi y = 10.5 g cm−3, ha dness = 300–700
MPa; bulk esis i i y = 1.63 µΩ cm [31]) ein o ced wi h
high-s eng h W pa icula es (densi y = 19.3 g cm−3; ha d-
ness = 1200–4000 MPa; bulk esis i i y = 5.44 µΩ cm [31])
p epa ed om W@Ag co e–shell powde using he SPS
echnique. Compa ed o he abo emen ioned Ag–Cu sys-
em, Ag–W MMC epo ed he e exhibi s en i ely di e en
comp ession beha io , no only in e ms o mechanical p op-
e ies bu also due o i s comple e immiscibili y.
2 Expe imen al
2.1 S a ing ma e ial
The W@Ag co e–shell powde wi h a olume a io o W
and Ag 50:50 was manu ac u ed in SAFINA a.s. The p o-
duc ion o he powde consis s o wo s eps: i) gas a omiza-
ion o W powde and ii) dosage o AgNO3 in an alkaline
solu ion o ob aining pu e Ag o p ecipi a ion o Ag on W
pa icula es. The powde pa icle dis ibu ion was measu ed
by lase di ac ion on he Mal e n Panaly ical Mas e size
3000 machine (Mal e n, Uni ed Kingdom).
2.2 P oduc ion o Ag–W MMC
The co e–shell powde was compac ed by SPS echnology
using FCT Sys eme HP-D 10 de ice (Rauens ein, Ge many)
o p oduce a ounded sample wi h a diame e o 20 mm and a
heigh o 6mm. Fo each sample, 30 g o powde was used. The
pa ame e s o he compac ion p ocess we e iden ical o hose
desc ibed in de ail o he p oduc ion o Cu–Ag m-MMCs in
he wo k [21], i.e., i) a o ce o 25 kN (co esponds o a p essu e
o 80 MPa), ii) a hea ing a e o 100 °C min−1, iii) a compac-
ion empe a u e o 700 °C, i ) a dwell ime o 5min, and ) a
cooling segmen — u ning o he hea ing o achie e he maxi-
mal cooling a e o he de ice. The ime dependencies o he
eco ded heigh educ ion, s ep empe a u e, cu en low, and
applied o ce du ing he p ocess a e shown in Fig.1.
2.3 MMC cha ac e iza ion
A mo phology o he de aul W@Ag co e–shell powde , as
well as i s mic os uc u e and he mic os uc u e o he Ag–W
MMC, we e cha ac e ized using scanning elec on mic oscopy
(SEM, Tescan Mi a, Czech Republic) equipped by ene gy-dis-
pe si e X- ay spec oscopy (EDS, Ox o d Ins umen s X-Max
20, Uni ed Kingdom). The de ailed mic os uc u al cha ac e i-
za ion o he as-p oduced Ag–W MMC was pe o med on a
50 × 80 µm a ea wi h a s ep size o 0.1 µm using SEM (FEI
Quan a 3D FEG, The mo Fishe , Czech Republic), including
elec on backsca e di ac ion (EBSD, Ga an, The Uni ed
S a es o Ame ica). The ob ained EBSD da a we e p ocessed
using TSL OIM8 so wa e ( . 8.0). All he mic os uc u es
we e obse ed on he g ound and polished su aces.
2.4 De o ma ion es s
Tensile and comp ession es s we e pe o med o in es iga e
he mechanical p ope ies o he ob ained Ag–W MMC. In
bo h cases, he Ins on 5882 machine (Ins on, The Uni ed
S a es o Ame ica) wi h a de o ma ion a e o 10–3 s−1 a
ambien empe a u e was used. Tensile es s we e pe o med
on samples wi h a “dog-bone” shape wi h dimensions o
7.0-mm leng h, 2.0-mm wid h, and 0.55-mm hickness.
Cuboid samples wi h a 6.0-mm heigh and a squa e base o
4 × 4mm we e used o comp ession es s. Samples o en-
sile and comp ession es s we e p epa ed by elec o-e osi e
Fig. 1 Reco ded heigh educ ion (blue), applied o ce (black), cu -
en low (g ay), and sample empe a u e ( ed) du ing he SPS p ocess
1573The In e na ional Jou nal o Ad anced Manu ac u ing Technology (2025) 139:1571–1580
cu ing om he samples p oduced by SPS. Tensile/com-
p ession ue s ess– ue s ain cu es a e au oma ically
de e mined by Bluehill so wa e, which is used by he
Ins on 5882 machine. The c oss-sec ions o he de o med
ma e ials we e obse ed using SEM Tescan Mi a.
3 Resul s anddiscussion
3.1 Cha ac e iza ion o  hes a ing ma e ial
The dis ibu ion o pa icle size in he W@Ag co e–shell
powde is shown in Fig.2. The pa icle sizes exhibi a ypical
Gaussian dis ibu ion wi h dimensions anging om 20 o 80
µm wi h a median alue o 37.1 µm, which is app oxima ely 10
µm la ge han he size o Cu@Ag co e–shell desc ibed in [21].
The mo phology o he W@Ag co e–shell powde is
cha ac e ized by a sphe ical/ ounded shape wi h he su ace
looking like he o ange peel ex u e (Fig.3). The e can also
be seen oids on he su ace o some pa icles (Fig.3a, yel-
low a ows). The p esence o hese de ec s (as well as he
su ace oughness desc ibed in he s udy [21]) can a ec he
mic os uc u e o he composi e p oduced by he SPS p o-
cess. I he oid is oo deep and eaches he W co e, islands
o sin e ed W can be obse ed wi hin he mic os uc u e o
he p oduced composi e.
The mic os uc u e and he chemical composi ion o
he W@Ag co e–shell powde c oss-sec ion a e shown
in Fig.4. Un o una ely, a heigh di e ence be ween he
ha d W co e and he e y duc ile Ag shell occu ed du -
ing he me allog aphic p epa a ion o he sample due o a
di e en esponse o Ag and W o he g inding and sub-
sequen polishing. In addi ion, wide hollow po es a e is-
ible be ween he wo componen ma e ials, an example o
which is ma ked by a ed a ow in Fig.4. The o igin o his
de ec is unclea ; i could occu ei he du ing he me allo-
g aphic p epa a ion o he manu ac u ing me hod du ing he
Ag deposi ion on o he W co e. In his case, i could esul
om he 25% di e ence in la ice pa ame e s o cc Ag (a =
0.4086 nm [32, 33]) and bcc W (a = 0.3155 nm [34, 35]).
Fig. 2 Size dis ibu ion and cumula i e cu e o he W@Ag co e–
shell powde
Fig. 3 SEM mic og aphs o he W@Ag co e–shell powde mo phology wi h di e en magni ica ions. Yellow a ows in (a) ma k he oids in he
shell o he pa icles
1574 The In e na ional Jou nal o Ad anced Manu ac u ing Technology (2025) 139:1571–1580
3.2 Cha ac e iza ion o  heAg–W MMC
The mic os uc u e o he Ag–W MMC is shown in Fig.5.
I is seen ha he SPS p ocess made i possible o p oduce
he MMC cha ac e ized by Ag ma ix and W pa icula es.
Howe e , a lo o W clus e s a e obse ed he e. As was men-
ioned abo e, i can be a esul o a de ec i e su ace o he
co e–shell powde pa icles (Fig.3a, yellow a ows), which
makes i possible o join he W co e oge he du ing he SPS
p ocess. Figu e5 also shows a high numbe o oids in he
MMC mic os uc u e. I is appa en ha he shape and size o
he oids co espond o he size and shape o W pa icula es.
These oids occu ed because o d opping ou o he W pa -
icula es du ing he g inding and polishing o he ma e ial.
The d opping ou o he W pa icula es is a consequence o
he ac ha he W and Ag do no show any solubili y acco d-
ing o he phase diag am [36]. A weak bonding be ween Ag
and W was also obse ed in [16], whe e he W–Ag com-
posi es we e p epa ed wi h di e en Ag con en s. As a
esul , i was impossible o cha ac e ize he po osi y o he
Ag–W MMC. We migh expec ha he ue po osi y o he
Fig. 4 SEM mic og aph and EDS elemen s dis ibu ion maps o W and Ag a he c oss-sec ion o he W@Ag co e–shell powde . A ed a ow
shows he a ea o bad adhesion be ween he shell and co e
Fig. 5 SEM mic og aph o he Ag–W MMC p oduced by SPS, di e en magni ica ions
1575The In e na ional Jou nal o Ad anced Manu ac u ing Technology (2025) 139:1571–1580
compac ed MMC will be on he same le el as ha de e -
mined o Ag–Cu MMCs, i.e., o he o de o 10−2–10−1%.
Figu e6 depic s he EBSD esul s o he Ag–W MMC p o-
duced by he SPS echnique. In e se pole igu e (IPF) maps
show a dual s uc u e o he MMC—la ge W pa icula es con-
sis ing o a ew g ains while being embedded in he Ag ma ix
wi h nanosized g ains. The g ain size analysis o bo h W and
Ag (Fig.7) documen s ha W g ains ha e sizes in a ange om
a ew mic ome e s up o almos 30 µm. Con e sely, he majo -
i y o Ag g ain sizes ange be ween 500 nm and 1µm. The
di e ence in g ain sizes o he wo componen s o he MMC
esul s om he p oduc ion way o he co e–shell powde —
a omiza ion o W pa icles and deposi ion o he Ag shell.
EDS elemen dis ibu ion maps (Fig.6) show some ine
pa icles o W in he Ag ma ix. I is appa en ha hei dis i-
bu ion, size, and shape a e comple ely coinciden al. Figu e5b
shows he same ype o pu e elemen al pa icles o W in he
Ag ma ix. The e o e, hei occu ence can be a ibu ed o
he me allog aphic sample p epa a ion when he ha d bu
b i le W is b oken and s u ed in o a e y so and duc ile Ag.
3.3 Mechanical es ing
To in es iga e he mechanical p ope ies o he Ag–W
MMC p oduced by SPS echnique, ensile and comp es-
sion es s we e aimed o be pe o med. Reg e ably, i was
impossible o ob ain any easonable esul om ensile es s.
Samples o a “dog-bone” shape end o b eak apa du -
ing hei inse ion in o he de ice clamp. Fo illus a ion,
Fig. 6 IPF and EDS maps o he Ag–W MMC ob ained om EBSD analysis
Fig. 7 The plo s o he g ain sizes in he Ag–W m-MMC: (a) W and
(b) Ag

1576 The In e na ional Jou nal o Ad anced Manu ac u ing Technology (2025) 139:1571–1580
he ac u e su ace o such a damaged sample is shown in
Fig.8. The ac u e su ace shows nonde o med W pa icu-
la es. Mo eo e , when sepa a ed om he Ag ma ix, hese
pa icula es le he dimples wi h co esponding shapes and
sizes ha a e almos 100% smoo h. I indica es ha he e
was he weakes cohesion be ween he ma ix and ein o ce-
men pa icula es.
This inding can be ela ed o he pulling ou o he W
pa icula es du ing g inding and polishing (Fig.5). Figu e8
also shows ha he a ea a ound he sphe ical pa icula es
exhibi s a ac u e, cha ac e ized by dimples, con i ming a
duc ile beha io o he Ag ma ix. In ac , his ac u e uns
along he weakes pa h o he ma ix among close pa icula es
whe e he lowes o ce is necessa y o sepa a e he ma e ial.
The EDS elemen dis ibu ion maps (Fig.8) p o e he p es-
ence o nonde o med W pa icula es in he duc ile Ag ma ix.
Simila beha io o composi e ma e ial ailu e by a decohe-
sion along he in e ace be ween he ha d pa icula es (Z O2/
SiO2) and he so ma ix (Al) was desc ibed in he s udy
[7]. In addi ion, he au ho s o [37] desc ibed h ee ypes o
pa icula e de ec s a he ac u e su ace o 6082Al ma ix
composi e ein o ced wi h Mo pa icula es: (i) ac u ed pa -
icula es, (ii) pull-ou pa icula es, and (iii) pull-ou pa icu-
la es pi s. In he p esen s udy, he ac u ed pa icula es we e
no obse ed; howe e , he (ii) and (iii) ypes a e shown in
Fig.8 and ma ked by blue and ed a ows, espec i ely.
The dependence o he ue s ess– ue s ain in comp es-
sion o Ag–W MMC, oge he wi h hose o pu e Ag as well as
o ecen ly s udied Ag–Cu MMC [21], is shown in Fig.9. As
expec ed, he alue o he comp ession yield s ess (CYS) o
Ag–W MMC is much highe han he CYS o pu e Ag. On he
o he hand, i is nea ly he same as ha o Ag–Cu MMC, con-
aining much so e ein o cing pa icula es. Acco ding o he
ecen wo k [21], he CYS o Ag–Cu MMC (153 ± 10 MPa) is
highe by 467% han ha o he pu e Ag ma ix (27 ± 6 MPa).
The yield s ess,
𝜎C
, o a comp essed composi e can be
w i en as ollows [21, 38–41]:
(1)
𝜎C=𝜎m+ (Δ𝜎D,Δ𝜎LT ,Δ𝜎GB,Δ𝜎O ,Δ𝜎SS,…)
whe e
𝜎m
is he CYS o he ma ix,
Δ𝜎D
is he s ess o
he disloca ions,
Δ𝜎TM
is a he mal misma ch,
Δ𝜎GND
is
he geome ical necessi y,
Δ𝜎LT
is he con ibu ion o he
load ans e ,
Δ𝜎GB
is he con ibu ion o g ain bounda y
(Hall–Pe ch) s eng hening,
Δ𝜎O
is he con ibu ion o he
pa icle (O owan) s eng hening, and
Δ𝜎SS
is he s ess con-
ibu ion om he solid solu ion. The unc ion in Eq. (1) is
complex [42, 43]; howe e , i can also be conside ed as a
simple sum o he componen s [38, 39, 44]. In he Ag–W
MMCs, we can exclude he con ibu ion o
Δ𝜎SS
as Ag and
W a e immiscible.
The con ibu ion
Δ𝜎D
may be w i en as [45]:
wi h he cons an A, he shea modulus G, he Bu ge s
ec o b, and he summa y disloca ion densi y
𝜌dis
. Accep -
ing A = 0.55 [45], GAg = 24.3 GPa [46] and |b(Ag)|= 0.290
(2)
Δ
𝜎
D
=AG
�
𝐛
�√
𝜌
dis
Fig. 8 SEM mic og aph and
EDS maps o he Ag–W
m-MMC ac u e su ace a e
he “ ensile” es . Blue a ows
depic he W pa icula es, and
ed a ows ma k he holes a e
d opped W pa icula es
Fig. 9 Comp ession ue s ess– ue s ain cu es o he Ag–W
MMC. Fo compa ison, he comp ession cu es o pu e Ag and Ag–
Cu (45:55) MMC [21] a e also shown
1577The In e na ional Jou nal o Ad anced Manu ac u ing Technology (2025) 139:1571–1580
nm [47], and supposing he disloca ion densi y in Ag o be
8 × 1013 m–2, i.e., simila o ha measu ed in he Ag–Cu
MMC [22], he mean con ibu ion o disloca ions in he
ma ix o he s ess is
Δ𝜎D
= 35 MPa.
The o m o he e m
Δ𝜎LT
can be gi en as ollows [48]:
whe e
𝜅
is he aspec a io o he ein o cemen s,
𝜎y
is he
yield s ess o he pa icula e, and is he olume ac ion
o he ein o cemen phase. To es ima e i s con ibu ion, we
can use he alues o
𝜅
= 1,
= 0.50, and
𝜎y
= 56 MPa [21].
Then,
Δ𝜎LT
= 14 MPa.
The con ibu ion o he g ain bounda ies (Hall–Pe ch
con ibu ion) in polyc ys alline ma e ials wi h he g ain
size
dg
causes an inc ease in he s ess [49]:
wi h
KGB
being cons an . Fo Ag, we can use he alues o
dg
= 0.75 μm and
KGB
= 2.51 MPa mm1/2 [49]. Supposing
ha he ac i e a ea o Ag is 50% in he MMC, which is
composed o 50% o bo h Ag and W, we ob ain he alue o
Δ𝜎GB
= 45 MPa.
Then, he e ec o he O owan s eng hening mus no
be conside ed he e. The la ge non-de o mable pa icu-
la es se e in he MMC as la ge objec ions educing he
ac i e a ea. This e ec was conside ed in he Hall–Pe ch
s eng hening abo e.
Supposing a simple addi ion o indi idual con ibu ions,
he summa y inc ease o
𝜎m
in he composi e is hen o
abou 94 MPa. This es ima ed alue is close o he di e ence
be ween he measu ed alues o CYS o he Ag–W MMC
(135 MPa) and o he Ag ma ix (35 MPa) [21], i.e. 100 MPa.
The ac ha he alues o CYS o Ag–W and Ag–Cu
MMCs a e e y simila (Fig.9) esul s om he ac ha
plas ic de o ma ion s a s when he disloca ions become
mobile in he Ag ma ix and ha he modi ica ions o he
alues o CYS in bo h cases a e domina ed by he beha io
o he Ag ma ix.
In con as o pu e Ag and Ag–Cu MMC exhibi ing a
simila cou se o he ue s ess– ue s ain cu e, i s cou se
o Ag–W MMC is quan i a i ely di e en du ing comp es-
sion (Fig.9). This is caused by he ac ha W pa icula es
do no de o m plas ically, hus limi ing plas ic de o ma ion
o a mo e limi ed olume han i is in he case o bo h pu e
Ag and Ag–Cu MMC. In he la e one, plas ic de o ma ion
also occu s in he pa icula es, which s ongly con ibu es
o an inc ease o he s eng hening and supp esses he ac-
u e o he ma e ial. In his espec , he W pa icula es ep-
esen an objec ion o he plas ic de o ma ion o he MMC.
Supposing he alue o Young’s modulus o W o be 370
(3)
Δ
𝜎LT =
1
2
𝜎y𝜅
,
(4)
Δ
𝜎GB =
K
GB
√
d
g
,
GPa [50], he elas ic de o ma ion a 210 MPa, whe e he
plas ic de o ma ion o he MMC is 15.4% (Fig.9), is abou
0.068% only. This causes la ge in e nal s ess a he Ag/W
in e ace, which esul s e en ually in ac u ing he MMC.
Addi ionally, a a he la cou se o he de o ma ion cu e
can be ela ed o a ela i ely la ge size o he ein o cing
pa icula es [51].
To cha ac e ize he plas ici y du ing he comp ession,
we can e alua e he wo k ha dening a e as he change o
ue s ess, σ, wi h ue s ain, ε, unde cons an de o ma-
ion a e,
𝜀
[52],
and he wo k ha dening exponen n [52],
The dependences o bo h pa ame e s on he ue s ain
a e shown in Fig.10. Due o he la dependence o σ s.
ε discussed abo e, he wo k ha dening a e is quickly
dec easing o ze o a he ul ima e comp ession s ess
(UCS) and eaching nega i e alues du ing he ac u -
ing o he sample along he Ag/W in e aces as well as in
he Ag ma ix (Fig.10a). I con as s wi h he beha io o
pu e Ag and Ag–Cu MMC cha ac e ized by a con inuous
inc ease o he s ess wi h he s ain (Fig.9). This di -
e ence esul s om he ac ha W pa icula es do no
de o m plas ically while he Cu ones in Ag–Cu MMCs
do, and in addi ion, Cu pa icula es in he co espond-
ing MMC as well as pu e Ag-con ained la ge g ains [21]
which s eng hen simila ly as documen ed in Fig.10a.
The wo k ha dening exponen na a es abou he mecha-
nism o plas ic de o ma ion. The alues o n = 0.15–0.18
ound o he Ag–W MMC (Fig.10b) indica e ha he
de o ma ion is ealized by he slip and climb o disloca ions
in ine-g ained Ag. A simila mechanism o de o ma ion
was epo ed o ine-g ained Ti [53]. A simila alue o n =
0.21 was also measu ed a he ea ly s age o he de o ma-
ion o Ag–Cu MMC, e e ing o he s a ing o he dis-
loca ion mo ion in he ine-g ained Ag ma ix. Howe e ,
wi h inc easing s ess, de o ma ion also occu s in coa se-
g ained Cu pa icula es, which is e lec ed in an inc eased
alue o n (n = 0.31). As an inc ease o n is a ibu ed o
de o ma ion winning in Ti [53], we may deduce ha win-
ning is also ope a ing in he Cu pa icula es. In he case o
Ag possessing a g ain size o 0.5 mm, winning can easily
occu al eady a he ea ly s age o de o ma ion and lead o
he subsequen inc ease o n alue om 0.28 o 0.53. In
Ag–W MMC, winning was supp essed due o small g ain
size and non-de o mabili y o W pa icles; hus, an insig-
ni ican inc ease o n was obse ed.
(5)
Θ=(𝜕𝜎
𝜕𝜀 )𝜀
,
(6)
n
=(
𝜕ln 𝜎
𝜕ln 𝜀
)
𝜀
1578 The In e na ional Jou nal o Ad anced Manu ac u ing Technology (2025) 139:1571–1580
The mic os uc u e o he ac u e su aces o Ag–W
MMC a e comp ession de o ma ion is shown in Fig.11.
I is appa en ha he W pa icula es emain unchanged
(in e ms o size and shape) a e comp ession es s, which
con i ms ha W was de o med elas ically only. The abo e-
men ioned concen a ion o he s ess a he Ag/W in e -
aces esul s in he occu ence o c acking he e. Then, he
ac u e con inues in a duc ile manne h ough he joining
Ag ma ix. The e a e wo ypes o mo phology o he ac-
u e: he dimple cha ac e o simple ac u e and he shea in
he Ag ma ix caused by he ha d pa icula es mo ing du ing
comp ession (Fig.11). Ne e heless, he de o mabili y o
he Ag–W MMC, exhibi ing mo e han 15%, is ela i ely
e y good.
Fig. 10 Cha ac e is ics o plas ic de o ma ion o Ag–W MMC. (a) wo k ha dening a e; (b) wo k ha dening exponen . The dependences o pu e
Ag and o Ag–Cu MMC a e shown o compa ison
Fig. 11 SEM mic og aphs o he ac u e su ace o he Ag–W MMC a e comp ession es s a di e en magni ica ions
1579The In e na ional Jou nal o Ad anced Manu ac u ing Technology (2025) 139:1571–1580
4 Conclusions
In his s udy, an Ag–W MMC was success ully ab ica ed
using SPS om W@Ag co e–shell powde . As a esul , a
dual s uc u e cha ac e ized by an Ag ma ix wi h g ain
size anging om 500 nm o 1μm ein o ced by W pa -
icula es wi h g ain size o up o 30 μm was p oduced. The
inc ease in CYS o he MMC compa ed o ha o pu e
Ag by app oxima ely 467% is a ibu ed o he s eng h-
ening e ec s o disloca ion (by 35 MPa), load ans e
(by 14 MPa), g ain bounda ies (Hall–Pe ch, by 45 MPa),
bu also o he s eng hening o he mal misma ch and
geome ical necessi y, as e alua ed quan i a i ely. A low
and nea ly cons an alue o he wo k ha dening exponen
(n = 0.15–0.18) implies ha plas ic de o ma ion occu s
in he Ag–W MMC ia disloca ion mo ion in he ma ix,
while he pa icula es do no de o m du ing comp ession.
The in e ace be ween he ma ix and ein o cemen pa -
icula es, howe e , was iden i ied as he weakes link in
he MMC s uc u e. I sugges s ha u he esea ch is
needed, as di e en condi ions o he SPS p ocess o
using o he me hods o PM, o imp o e he s eng h o
his in e ace.
Au ho con ibu ion All au ho s made signi ican con ibu ions o
he s udy concep ion and design. Ma e ial p epa a ion, da a collec-
ion, and analysis we e pe o med by Angelina S akošo á, D ahomí
D o ský, Filip P ůša, O solya Molná o á, S anisla Hab , Jakub S o-
boda, and I ona Sedlářo á. The i s d a o he manusc ip was w i -
en by Angelina S akošo á, D ahomí D o ský, and Pa el Lejček,
and all au ho s commen ed on p e ious e sions o he manusc ip .
Funding was secu ed by Pa el Lejček. All au ho s ead and app o ed
he inal manusc ip .
Funding Open access publishing suppo ed by he ins i u ions
pa icipa ing in he CzechELib T ans o ma i e Ag eemen . This
wo k was inancially suppo ed by he Czech Science Founda ion
unde he g an No. 23-05139S. AS acknowledges he g an o he
Czech Academy o Sciences unde g an No. L100102403. FP and
DV acknowledge inancial suppo om he p ojec “Mechani-
cal Enginee ing o Biological and Bio-inspi ed Sys ems,” unded
as p ojec No. CZ.02.01.01/00/22_008/0004634 by P og amme
Johannes Amos Commenius, call Excellen Resea ch. We acknowl-
edge CzechNanoLab Resea ch In as uc u e suppo ed by MEYS
CR (LM2023051).
G an o á Agen u a České Republiky, 23-05139S, Pa el
Lejček;Akademie Věd České Republiky,L100102403,Angelina
S akošo á;P og amme Johannes Amos Commenius,call Excel-
len Resea ch, CZ.02.01.01/00/22_008/0004634; Minis e s o
Škols í,Mládeže a Tělo ýcho y,LM2023051.
Da a a ailabili y The da a used in his manusc ip a e a ailable in
he Zenodo eposi o y a he ollowing link:h ps:// doi. o g/ 10. 5281/
zenodo. 14775 989.
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