Size effect in microcompression of epoxy micropillars

S. Wang • Y. Yang • L. M. Zhou • Y.-W. Mai

Received: 28 February 2012 / Accepted: 18 April 2012 / Published online: 4 May 2012

� Springer Science+Business Media, LLC 2012

Abstract Understanding the size effect on the mechani-

cal properties of polymers is of great importance for a

robust design of today’s polymer-based micro-devices. In

this article, we propose the microcompression approach

based on the focused ion beam milling technique to probe

the possible size effect on the mechanical behavior of

epoxy micropillars. By systematically reducing their size

from the micrometer to submicron scale, these micropillars

display a constant elastic modulus in their inner cores while

exhibit an increasing yield and fracture strengths with

decreasing diameters. Such a size effect is attributed to the

intrinsic material heterogeneity at the submicron scale and

the presence of a nano-scale stiff surface layer wrapping

around the micropillars. This study provides a theoretical

framework for the microcompression analysis of polymer-

based micropillars, paving the way for future study of a

variety of polymer-based advanced material systems by

microcompression.

Introduction

Since the 1990s, polymers have been increasingly used as

functional or structural materials in micro-electro-

mechanical systems (MEMS) [1, 2]. As an alternative to

the conventional MEMS materials, such as silicon and

metals, polymers possess their advantages of higher

mechanical robustness, lower fabrication costs, a greater

versatility in microfabrication, and more chemical, struc-

tural, and biological functionalities [1, 2]. Because of this,

today’s micro-devices, such as displays [3], photo voltaic

devices [4], memory, and transistors [5], are strongly

migrating towards polymers. While the ultimate goal is to

achieve the full integration of the polymer-based MEMS

with those in like material systems one day, knowledge of

the mechanical properties of polymers at the small size

scale is one of the prerequisites that must be acquired.

As compared with silicon and metals, which have

received extensive research efforts during the past decades

for understanding their size-dependent mechanical behav-

iors [6–16], the investigation of polymers is comparably less

regarding their mechanical behavior at different length

scales [17, 18]. One of the commonly used tools for the size

effect study in polymers is nanoindentation [13]. Although

polymers possess rate-dependent plasticity and have the

tendency to pile up under indentation, which defies the direct

use of the standard indentation method [13], research efforts

have been made for extending the realm of applicability of

the standard indentation method to include polymers

[19–21]. By indenting polymers at different depths, their

hardness for different indent sizes can be extracted. As a

result, it was found that the hardness of polymers seemed to

obey a similar size effect trend as other materials, such as

metals [12], i.e., the smaller the indent size, the harder the

material becomes, which was then attributed to the strain

gradient effect that gave rise to a higher density of molecular

kinks at a shallower indent in polymers [17]. It was even

argued that such a strain gradient effect should be ubiquitous

among different material systems [14].

On the other hand, a recently emerging research interest

is to study the mechanical properties of materials under the

S. Wang � Y. Yang (&) � L. M. Zhou � Y.-W. Mai

The Department of Mechanical Engineering,

The Hong Kong Polytechnic University, Hung Hom,

Kowloon, Hong Kong, China

e-mail: mmyyang@polyu.edu.hk

Y.-W. Mai

School of Aerospace, Mechanical and Mechatronic Engineering

J07, University of Sydney, Sydney, NSW, Australia

123

J Mater Sci (2012) 47:6047–6055

DOI 10.1007/s10853-012-6513-0

conditions free of an overall strain gradient [7], which

represents the scenarios in which materials should exhibit

the lowest mechanical strengths than otherwise, and is

apparently more closely relevant to the design of MEMS

devices. Based on the prior study, it is known that the size

effect still persists even without the presence of strain

gradient in metals and silicon [7, 8]. Such important find-

ings imply that, apart from the stiffness and strength, the

external dimension of materials should also be considered

as one of the key parameters in the design of the MEMS

devices made of those materials. However, similar studies

for polymers are still rare up to date.

In this article, we propose the microcompression

method, which was pioneered originally for the study of

single-crystal metals [7], for the size effect study of poly-

mers. This method combines the nanoindentation and

focused ion beam (FIB) micro-fabrication techniques to

probe the possible size effect in a uniaxially loaded

material. The variety of issues, such as the finite substrate

compliance, micropillar tapering, and ion-milling effect,

arising from the use of ion beam milling, will be discussed

pertaining to the microcompression of polymers. Through

this study, it can be demonstrated that the microcompres-

sion method can be extended from hard materials, such as

metals and silicon, to soft materials, such as polymers for

mechanical characterization at the micrometer scale.

Materials and experiments

As a model material, an as-received epoxy resin system

including Araldite-F (diglycidyl ether of bisphenol A,

DGEBA) and Piperidine was used for this study (for the

details of material preparation, please see Ref. [22]). Fol-

lowing the sequential ion-milling approach [15, 23], a

series of epoxy micropillars were carved out on the

mechanically polished surface of the bulk epoxy sample

using the FIB technique on a Quanta 200 3D FIB/SEM

Dual-BeamTM

System (FEI Company, Hillsboro, OR,

USA). Prior to the ion-beam treatment, the epoxy sample

was coated with an Au/Pd thin film with a thickness of a

few nanometers to enhance electric conductivity. Under the

current voltage of 30 keV, the Ga? ion beams of a current

density of 3 nA were first used to create an annular crater

with a 20-lm outer diameter at the depth close to that of

the micropillar to be fabricated. As the precursor, the crater

had an inner diameter a few micrometers larger than the

desired pillar’s diameter. Subsequently, the ion beams with

incrementally decreasing densities were used for shaping

the micropillar. At the final step of trimming, the ion beam

with the current density down to a few tens of pA were

utilized to remove the severely damaged materials because

of the previous use of the high-density ions. Note that a

similar process has also been commonly employed to

prepare FIB-milled polymer thin foils for transmission

electron microscopy (TEM) [24]. In spite of these laborious

experimental efforts, the FIB-milled micropillars were still

tapered, with an average taper angle of *2�, because of the

ion-beam divergence. As shown in Fig. 1, it can be seen

that the typical geometry of the FIB-milled epoxy micro-

pillar is similar to those of FIB-milled metallic and ceramic

micropillars, as archived in the literature [8, 15, 23].

To study the possible size effect in polymers, the FIB-

milled micropillars had diameters and aspect ratios rang-

ing, respectively, from *0.7 to *5 lm and *3:1 and

*4:1. The microcompression experiments were then car-

ried out at a load-controlled mode on the TriboscopeTM

Nanoindentation System (Hysitron, Minneapolis, MN,

USA), which was equipped with a 10-lm flat-end conical

diamond indenter. For simplicity, the nominal stress rate

adopted in the microcompression experiments was fixed at

*35 MPa/s.

Results and discussion

Experimental load–displacement curves

From the microcompression experiments, it was found that

the epoxy micropillars underwent a reversed trend of size-

induced ductile-to-brittle transition in contrast to amor-

phous-metal micropillars [25], i.e., the smaller epoxy

micropillars exhibited brittle-like fracture while the larger

ones deformed seemingly in a plastic way. As shown in

Fig. 2a, the load–displacement curve from the 4-lm epoxy

micropillar smoothly transitions from elastic to plastic

deformation and then levels off at a somewhat constant

load as the plastic flow continues. Considering the tapering

effect and the lateral expansion of the micropillar, the

constant load is implicative of a strain softening behavior,

which can be attributed to the stable crack growth in the

micropillar, as can be seen from the ex situ scanning

electron microscopy (SEM) images (Fig. 2b). In sharp

contrast, the micropillar with the diameter of about *1 lm

exhibits the brittle-like fracture. As shown in Fig. 2c, a

sudden load drop occurs at limited plastic deformation.

Note that the brittle-like fracture was caused by shear

failure (Fig. 2d), which is, however, often regarded as the

manifestation of the plastic flows in quasi-brittle materials

at the macroscopic scale, such as ice [26].

Before proceeding, it is worthwhile to mention that

pronounced surface wrinkling was also observed in those

‘plastically’ deformed epoxy micropillars (Fig. 3). These

surface wrinkles were developed around the cracks

exposed on the micropillar’s surface, exhibiting a well-

defined periodic structure along the crack length and

6048 J Mater Sci (2012) 47:6047–6055

123

diminishing with distance away from the surface cracks.

Note that a similar phenomenon of surface wrinkling was

also observed by Moon and co-workers when they

bombarded the surface of a polydimethylsiloxane (PDMS)

sheet using the Ga? ion beams with different ion fluence

[27]. As a result of the ion-induced residual strain and

Fig. 1 The scanning electron microscopy (SEM) image of the micropillars fabricated through focused ion beams on the polished surface of the

epoxy sample coated with Au thin films

Fig. 2 a The load–

displacement curve of the epoxy

micropillar with the top

diameter of *4.1 lm, b the

micrograph of the cracked

4.1-lm micropillar, c the load–

displacement curve of the epoxy

micropillar with the top

diameter of *0.7 lm and d the

micrograph of the fractured

0.7-lm micropillar

J Mater Sci (2012) 47:6047–6055 6049

123

surface stiffening, surface wrinkling develops in the PDMS

sheet to minimize elastic energy storage [27].

Micromechanical properties of epoxy micropillars

Elastic modulus

Unlike in regular compression tests, the extraction of the

mechanical properties of the epoxy micropillars from the

microcompression tests is nontrivial. Aside from the

above-mentioned surface stiffening effect, the micropillar

tapering and base rounding together with the compliance of

their base material defy the measurement of the pillars’

Young’s moduli. However, according to Yang et al. [15],

the combined effects from the imperfect sample geometries

and base compliance can be accounted for with the fol-

lowing formula:

E ¼ WH

D0

; b;q

D0

� �1þ p 1� mð ÞD0

8H

� �

� 4H

pD0 D0 þ 2H tan bð ÞdP

dh; ð1Þ

where H is the height of the micropillar, D0 is the top

diameter of the micropillar, b is the taper angle, q is the

radius of curvature at the base of the micropillar, m is the

Poisson’s ratio (*0.35 for the epoxy resins), W is a

dimensionless function as derived from the finite-element

(FE) simulations in Ref. [15], and dP/dh is the slope of the

loading curve in the elastic regime (Fig. 1a, c). Note that

the elastic behavior of a micropillar was implicitly assumed

to be rate independent when deriving Eq. (1), which works

quite well for metallic glasses and most metals. However,

elasticity in polymers is known to be rate dependent;

therefore, the elastic moduli of the micropillars so obtained

from Eq. (1) might be rate dependent as well. To minimize

such a rate effect, the stress rate was fixed at *35 MPa s-1

in our microcompression experiments.

Using Eq. (1), the Young’s moduli of the micropillars

can be extracted from the experimental data. As shown in

Fig. 4, they exhibit an apparent ‘size effect’ with their

magnitudes increasing with decreasing D0. However, as the

pillar’s top diameter increases beyond *3 lm, the

extracted Young’s moduli levels off to an average value of

*4 GPa, which is comparable to the average Young’s

Fig. 3 The micrographs of the

surface wrinkles observed on

the plastically deformed epoxy

micropillar with surface cracks

Fig. 4 The variation of the

obtained modulus of the

micropillars with their top

diameters. (Note that the shadedarea denotes the range of the

Young’s modulus of the epoxy

obtained from standard

nanoindentation tests and the

inset to the right of the plot is

the schematic of the composite

structure of the FIB-milled

epoxy micropillar, consisting of

an epoxy core and a FIB-

induced stiff skin)

6050 J Mater Sci (2012) 47:6047–6055

123

modulus (3.9 ± 0.1 GPa [m ? SD]) as measured from the

standard nanoindentation tests with a holding load (see

Appendix A), implying that the rate effect is negligibly

small in both microcompression and nanoindentation

experiments under these experimental conditions. In con-

trast, the 1-lm micropillar shows a Young’s modulus of

*8 GPa, which doubles that of the bulk epoxy. The

apparent size effect on the elastic modulus can be attrib-

uted to the ion-induced surface stiffening [27]. In view of

this, the epoxy micropillar can be envisaged as a composite

of an epoxy ‘core’ wrapped around by a FIB-induced stiff

skin (the inset of Fig. 4).

To extract the true Young’s modulus of the epoxy core,

the simple rule of mixture can be employed. Assuming a

uniform thickness of the stiff skin, the Young’s modulus,

Em, of the epoxy core can be derived as:

Em ¼E � 4Ef

tfD0� tf

D0

� �2� �

1� 2tfD0

� �2; ð2Þ

where Ef and tf denote the Young’s modulus and thickness

of the stiff skin, respectively. Based on the elastic wrin-

kling theory [27], it can be shown that both Ef and tf can be

estimated from the surface wrinkles (Fig. 3) and the

average modulus of the bulk epoxy measured from nano-

indentation (E = 3.9 GPa), which gives Ef = 30 ±

10 GPa and tf = 31 ± 7 nm (Appendix B). Here, it is

worth mentioning that the interface in a real material must

be diffusive rather than sharp in its profile; therefore, the

thickness estimated by using Eq. (2) corresponds to an

effective interface producing the same mechanical effect as

a real one. Despite this mathematic simplification, the order

of magnitude of the estimated tf and Ef is consistent with

the available experimental results reported in the literature

[24, 27]. Note that not all micropillars displayed the

wrinkle patterns after deformation; however, we did not

find any conspicuous size effect on the thickness of the stiff

layer based on the available experimental results and the

corresponding calculations. This is consistent with the

notion that, when the density of the ions is low, the damage

they can cause is only limited to a material surface. Given

the ion density we used for final trimming being extremely

low, which produced a stiff layer only about 30-nm thick in

the micropillars of 2–3 lm in diameter, we believe that a

size effect on the layer thickness is unlikely when the same

ion beams were used to trim the micropillars of 1 lm in

diameter. In such a case, we basically assume that the layer

thickness is size independent in this study. Substituting the

related parameters into Eq. (2), Em can be then extracted.

As shown in Fig. 4, after ruling out the effect of the ion-

induced surface stiffening, there is no discernable size

effect on the Young’s modulus of the epoxy core Em,

which shows a constant value of 3.9 ± 0.5 GPa consistent

with the previous nanoindentation results (3.9 ± 0.1 GPa).

Mechanical strength

To extract the yield strengths of these micropillars, the

yielding load, Py, is taken as the one corresponding to the

departure of the load–displacement curve from the elastic

response (Fig. 1a, c). To be consistent with the micro-

compression literature [7–9, 23, 28], the yielding strengths

of the micropillars were computed using ry ¼ 4Py=pD20

without considering the effect of pillar tapering.1 However,

in view of the surface stiffening, this only gives the mea-

surements of the ‘composite’ yield strengths of the

micropillars. With the skin’s Young’s modulus known to be

*30 GPa, the yield strength of the epoxy core can be then

estimated by subtracting the skin stress from ry, which is

ry ¼ 4 Py � Pf

� =p D0 � 2tfð Þ2. Here, Pf denotes the pos-

sible maximum stress that can be attained in the stiff skin at

the yielding point, which roughly equals EfAfhy/H, where Af

denotes the cross sectional area of the stiff skin and hy the

displacement of the micropillar at the yielding point.

Figure 5a presents the yield strengths of the micropillars

as a function of the pillar’s top diameters. Evidently, even

after excluding the skin effect, there is still a significant

size effect on the measured yield strengths. As shown in

Fig. 5a, the pillars’ yield strengths experience a drastic

change for the diameters less than *1 lm, exhibiting the

trend of ‘the smaller, the harder’ as usually witnessed from

the other types of micropillars [7–9]. Consistent with the

trend of the ‘composite’ Young’s moduli, the measured

yield strengths also level off at a value of *100 MPa with

the increasing pillar sizes. Note that the constant yield

strength of *100 MPa is comparable with those of bulk

epoxy samples measured under similar loading condition

[29]. Figure 5b displays the nominal fracture strengths of

the micropillars, which were measured from the maximum

loads attained before fracture, as a function of the pillar’s

top diameters. As compared with the case of the yield

strengths, the pillars’ fracture strengths exhibit the size

effect at the top diameter of around *2 lm and gradually

level off to around *200 MPa with the increasing pillars’

diameters. Note that the difference between the yield and

fracture strengths in the size effect regime cannot be totally

attributed to the post-yielding lateral expansion of these

micropillars, as the post-yielding deformation involved is

quite limited. Accompanying the change in the fracture

strengths, the fracture modes of the micropillars also

1 The tapering effect on the measured yielding strength of micropil-

lars has been studied in Ref [16]. With a taper angle of less than *3�,

the error incurred with the use of the traditional formula is expected to

be less than 10 %.

J Mater Sci (2012) 47:6047–6055 6051

123

transition from splitting fracture in the larger micropillars

to shear failure in the smaller ones, as shown by the insets

of Fig. 5b.

Possible origin of size effect

Unlike crystalline materials, there is no intrinsic structural

length scale in the pure epoxy that could influence its yield

strength at the micrometer scale; however, as pointed out in

Ref. [30], yielding in glassy polymers entails the stress-

induced percolation of weak bonds in the three-dimen-

sional network composed of cross-linked and randomly

oriented molecular chains. Based on our understanding, it

is reasonable to propose that the witnessed variation of the

yield strengths be related to the diminishing number of

available weak bonds in the epoxy micropillars. In other

words, even though the molecular structure of the epoxy

would look alike in topology at the submicron and mac-

roscopic scales, the availability of the weak bonds might be

different. In such a case, the multi-parameter Weibull

theory can be applied to investigate the size effect on the

yield strengths of the epoxy micropillars, from which the

probability of yielding in the micropillar can be written as

[16]:

P ry;D0

� ¼ 1� exp �Dn

0

ry

R

� �m� �; ð3Þ

where R is the reference yield strength, m is the Weibull

modulus, and n is the dimensionality constant. Based on

Eq. (3), the scaling relation for the size effect ry / D�n

m

0 can

be deduced. From the inset of Fig. 5a, it can be clearly seen

that n/m = 0.89 for the epoxy micropillars. On the other

hand, the Weibull modulus, m, can be determined using the

following equation [16]:

x ¼C 1þ 2

m

� � C2 1þ 1

m

� �0:5C 1þ 1

m

� ; ð4Þ

where x denotes the ratio of the standard deviation to the

mean value of the measured yield strengths. Based on the

measurements of the size-affected yield strengths (the inset

of Fig. 5a), the Weibull modulus m can be obtained as

around *3 from Eq. (4), which then gives the dimen-

sionality constant n * 2.7. Physically, this behavior

implies that the yielding behavior of the micropillar is a

consequence of volume deformation which may be related

to the molecular-scale percolation rather than a surface

effect which is caused by the mechanical mismatch

between the indenter and micropillar.

Different from the yielding of the epoxy micropillars,

which involves inelastic deformation throughout the

micropillar’s volume, the onset of their fracture entails

crack nucleation in the presence of the stiff surface skin,

which constraints the subsequent propagation of the cracks.

In the large micropillars, the cracks propagated in the

tensile direction, which resulted in the pillar splitting along

the lateral direction (Fig. 2b). It is noteworthy that these

tensile cracks propagated in a stable manner, which might

be caused by the limited elastic energy release from the

micropillar and is responsible for the extensive plastic flow,

as can be witnessed from Fig. 2a. By contrast, in the small

micropillars, the cracks propagated along an inclined plane

and in an unstable manner, leading to the brittle-like shear

failure (Fig. 2d).

The size effect on the fracture of the micropillars can be

understood in the context of fracture of quasi-brittle

materials [26, 31]. For those kinds of materials, their

fracture modes under compressive loadings are strongly

dependent on the biaxial stress state, R, which is defined as

Fig. 5 a The variation of the yield strength of the FIB-milled epoxy

micropillar with the pillar’s diameter (the inset: the power-law fitting

of the size effect on the yield strengths); and b the variation of the

fracture strength of the FIB-milled epoxy micropillar with the pillar’s

diameter with the insets showing the size-induced fracture mode

transition (scale bars in the insets = 1 lm)

6052 J Mater Sci (2012) 47:6047–6055

123

the ratio of the applied longitudinal to lateral stress. For

R = 0 which corresponds to the case of uniaxial loading,

the cracks in those materials would propagate in the tensile

direction; however, they will gradually change to an

inclined direction if a constraining stress is imposed from

the lateral direction, which corresponds to a positive R

ratio. For the epoxy micropillars, which can be viewed as a

quasi-brittle material, the ion-induced surface stiffening

naturally leads to a geometric constraint on loading on the

inner epoxy core. From linear elasticity, the associated R

ratio can be simply derived as 2tfEfm= D0 � 2tfð ÞEm. Based

on such a derivation and the obtained material properties,

the R ratio can be found ranging from *0.001 for the 5-lm

micropillar to *0.005 for the 1-lm micropillar. In Ref.

[26], it was found out that even the low confinement with

R = 0.005 could trigger the deformation mode transition in

ice. Therefore, it is reasonable to propose here that the

increasing R ratio should be responsible for the elevation in

the fracture strengths of the epoxy micropillars and also

their fracture mode transition. Because the fracture of the

small micropillars entails the breakage of the stiff surface

skin, the seeming brittleness as seen in Fig. 2c suggests the

brittle nature of the nano-scale surface skin induced by the

ion-beam milling.

Concluding remarks

In summary, the microcompression experiment is per-

formed and carefully investigated in this article on the FIB-

milled epoxy micropillars. Based on the experimental

results, salient conclusions can be drawn from this study,

which are listed as follows:

(1) In sharp contrast to the cases of metals and ceramics,

the Ga? ion machining of the bulk epoxy results in a

non-negligible stiff surface skin with a Young’s

modulus of *30 GPa and a thickness of *30 nm.

(2) The presence of the stiff surface skin leads to a size

effect on the ‘composite’ elastic modulus of the

micropillar; however, the elastic modulus of the inner

epoxy core is size independent.

(3) There is a strong size effect on the yield strengths of

the epoxy micropillars at the submicron scale even

though the surface stiffening effect is excluded, which

can be attributed to the Weibull statistics. However, at

the micrometer scale, the yield strengths of the

micropillars exhibit the trend of size independence

and are comparable with those of the bulk samples.

(4) The fracture of the ion-milled epoxy micropillars is

strongly related to the presence of the stiff surface

skin. Under microcompression, the latter acts as a

geometrical constraint that triggers the fracture mode

transition from axial splitting at the micrometer scale

to shear failure at the submicron scale. Owing to the

brittleness of the surface skin, shear failure appears

brittle on the load–displacement response.

From the above conclusions, it can be seen that great

caution should be taken when interpreting the results from

the microcompression of FIB-milled polymeric micropil-

lars owing to the confounding effects from the ion-beam

milling. In particular, our finding shows that the surface

effect plays an important role in the microcompression of

the epoxy micropillars. It is expected that such an effect

may still persist even in the polymeric micropillars fabri-

cated by other means because of the exposure of the

polymers to light and air for some time before the exper-

iments or to a process that occurs during fabrication. In

such a sense, our study provides a useful experimental and

analytical framework to quantify such a surface effect and,

therefore, paves the way for the future use of microcom-

pression in the study of a variety of polymer-based

advanced material systems, such as nano-composites,

polymer thin films, and polymer-based microstructures.

Acknowledgements S.W. and Y.Y. acknowledge the financial

support provided by the Hong Kong Polytechnic University for newly

recruited academic staff. Y.Y. is thankful to Prof. Y.L. of University

of Sidney for the invaluable discussions.

Appendix A

The standard nanoindentation method based on the Oliver

and Pharr’s approach was used to measure the Young’s

modulus, E, of the bulk epoxy sample [13]. To exclude the

creep effect, a holding section was included into the load

function as seen from the inset of Fig. A1a. For consistency

of experimental data, only those load–displacement curves

following a mater curve in the loading portion were

selected for the analysis. Furthermore, to attain a time-

independent property, the duration of the holding section

was varied such that the time dependence of the modulus

could be monitored. The results showed that, once the

holding time reached more than *2 s, there was no sys-

tematic change in the distribution of the measured modu-

lus, as shown in Fig. A1a. Based on our experimental

results, the extracted Young’s modulus displays a normal

distribution with a mean value of 3.9 Pa and a standard

deviation of 0.1 GPa for the bulk epoxy sample (note that

the Poisson’s ratio of the epoxy was assumed as *0.35 in

the data analysis).

As complement to the histogram of the measured

modulus, Fig. A1a and b shows its variation with the

indentation contact depth, which seemingly reveals a sur-

face effect, that is, the measured modulus appears slightly

J Mater Sci (2012) 47:6047–6055 6053

123

higher near the surface than in the bulk. Similar findings

were reported by Briscoe and co-workers from nanoin-

dentation of the surfaces of a variety of polymers [32].

Likewise, the measured indentation hardness, H, also

exhibits a size effect, as shown in Fig A1c, which may be

attributed to a confounding effect of surface stiffening and

strain gradient. To assess the possible influence of material

pileup, which may cause an overestimation of *10 % in

the above measurements [15, 21, 25], the parameter of

S2/P is plotted in Fig A1d, where S and P denote the

stiffness and maximum indentation load, respectively,

which can be extracted from an indentation load–displace-

ment curve [13]. As S2/P scales with E2/H and is inde-

pendent of the contact area, the slightly ascending tread of

S2/P in the near-surface region indicates a physically stiff-

ened surface even though H could be regarded as a constant.

Appendix B

According to Ref. [27], the critical strain associated with

the buckling of a uniform stiff elastic skin attached to a

compliant elastic matrix, ec, is approximately:

ec � 0:52Em

Ef

� �23

; ðA1Þ

where Em and Ef are the Young’s modulus of the matrix

and stiff skin, respectively. Furthermore, as shown in

Fig. A2, the wavelength of the wrinkles, k, of the stiff skin

as normalized by its thickness tf can be approximated as

[27]:

ktf

� 4Ef

Em

� �13

: ðA2Þ

In microcompression, the epoxy core and the stiff skin

are simultaneously compressed to the same amount of

deformation. If the epoxy core has already yielded while

the stiff skin is still within the elasticity regime, residual

elastic deformation will remain even after full unloading.

In such a case, surface wrinkling will take place as to

minimize the overall elastic energy storage if the associated

plastic strain in the epoxy core reaches the critical value.

Fig. A1 a The normal

distribution of the Young’s

modulus of the bulk epoxy

sample measured from

nanoindentation (the insetshows the experimental load–

displacement curves in

nanoindentation); and the

variation of the measured

b Young’s modulus, c hardness

and d squared stiffness to load

parameter (S2/P) with the

indentation contact depth

Fig. A2 The schematics of the a undeformed and b wrinkled surface

skin attached to the bulk epoxy resin

6054 J Mater Sci (2012) 47:6047–6055

123

Note that almost all surface wrinkles were observed around

the surface cracks in the plastically deformed micropillars

(Fig. 3). This is because, as the constraint in the hoop

direction is released on the two inner faces of the surface

cracks, the stress state there in the stiff skin and its adjacent

epoxy resin is closer to that for elastic wrinkling as

predicted by Eqs. (A1) and (A2).

To estimate tf and Ef, the plastically deformed epoxy

micropillars were carefully examined using high-resolution

scanning electron microscopy. The wavelengths k were

recorded with the corresponding plastic deformation in the

micropillar and, then used together with the Young’s

modulus of the bulk epoxy, as measured from nanoinden-

tation (Em * 3.9 GPa), to solve for tf and Ef from

Eqs. (A1) and (A2). Based on our experimental data,

k * 250 nm and ec * 0.12, which then leads to

tf * 30 nm and Ef * 30 GPa. As compared with amor-

phous-metal micropillars, such as Zr-based metallic glass

whose FIB damage layer was measured to be a few

nanometers in thickness [28], the epoxy micropillars pos-

sess a much thicker stiffened FIB damage layer, which may

result from chain scission and formation of new cross-links

in the polymeric materials because of ion irradiation [33].

References

1. Liu C (2007) Adv Mater 19:3783

2. Wilson SA, Jourdain RPJ, Zhang Q, Dorey RA, Bowen CR,

Willander M, Wahab QU, Willander M, Al-hilli SM, Nur O,

Quandt E, Johansson C, Pagounis E, Kohl M, Matovic J, Samel

B, van der Wijngaart W, Jager EWH, Djinovic CDZ, Wegener M,

Moldovan C, Iosub R, Abad E, Wendlandt M, Rusu C, Persson K

(2007) Mater Sci Eng R 56:1

3. Forrest SR (2004) Nature 428:911

4. Park SH, Roy A, Beaupre S, Cho S, Coates N, Moon JS, Moses

D, Leclerc M, Lee K, Heeger AJ (2009) Nat Photonics 3:297

5. Briseno AL, Mannsfeld SCB, Ling MM, Liu S, Tseng RJ, Reese

C, Robert ME, Yang Y, Wudl F, Bao Z (2006) Nature 444:913

6. Stolken JS, Evans AG (1998) Acta Mater 46:5109

7. Uchic MD, Dimiduk DM, Florando JN, Nix WD (2004) Science

305:986

8. Ostlund F, Rzepiejewska-Malyska K, Leifer K, Hale LM, Tang

YY, Ballarini R, Gerberich WW, Michler J (2009) Adv Funct

Mater 19:2439

9. Uchic MD, Shade PA, Dimiduk DM (2009) Annu Rev Mater Res

39:361

10. Fleck NA, Muller GM, Ashby MF, Hutchinson JW (1994) Acta

Metall Mater 42:475

11. Fleck NA, Hutchinson JW (1997) Adv Appl Mech 33:295

12. Gao H, Nix WD (1998) J Mech Phys Solids 46:411

13. Oliver WC, Pharr GM (1992) J Mater Res 7:1564

14. Lam DCC, Chong ACM (2001) Mater Sci Eng A 318:313

15. Yang Y, Ye JC, Lu J, Liu FX, Liaw PK (2009) Acta Mater

57:1613

16. Ye JC, Lu J, Yang Y, Liaw PK (2010) Intermetallics 18:385

17. Chong ACM, Lam DCC (1999) J Mater Res 14:4103

18. Tan EPS, Lim CT (2006) Comp Sci Tech 66:1102

19. Feng G, Ngan AHW (2002) J Mater Res 17:660

20. Stone DS, Jakes JE, Puthoff J, Elmustafa AA (2010) J Mater Res

25:611

21. Choi Y, Lee H-S, Kwon D (2004) J Mater Res 19:3307

22. Wang G-T, Liu H-Y, Saintier N, Mai Y-W (2009) Eng Fail Anal

16:2635

23. Greer JR, Oliver WC, Nix WD (2005) Acta Mater 53:1821

24. White H, Pu Y, Rafailovich M, Sokolov J, King AH, Giannuzzi

LA, Urbanik-Shannon C, Kempshall BW, Eisenberg A, Schwarz

SA, Strzhemechny YM (2001) Polymer 42:1613

25. Ye JC, Lu J, Yang Y, Liaw PK (2009) Acta Mater 57:6037

26. Wachter LM, Renshaw CE, Schulson EM (2009) Acta Mater

57:345

27. Moon MW, Lee SH, Sun JY, Oh KH, Vaziri A, Hutchinson JW

(2007) Proc Nat Acad Sci USA 104:1130

28. Lai YH, Lee CJ, Cheng YT, Chou HS, Chen HM, Du XH, Chang

CI, Huang JC, Jian SR, Jang JSC, Nieh TG (2008) Scripta Mater

58:890

29. Mayr AE, Cook WD, Edward GH (1998) Polymer 39:3719

30. Stachurski ZH (1997) Prog Polym Sci 22:407

31. Bazant ZP, Planas J (1998) Fracture and size effect in concrete

and other quasibrittle materials. CRC, Boca Raton

32. Briscoe BJ, Fiori L, Peillo E (1998) J Phys D Appl Phys 31:2395

33. Sasuga T, Kawanishi S, Nishi M, Seguchi T, Kohno I (1991)

Radiat Phys Chem 37:135

J Mater Sci (2012) 47:6047–6055 6055

123