SUPPLEMENTARY MATERIALS
Shear Avalanches in Metallic Glasses under Nanoindentation:
Deformation Units and Rate Dependent Strain Burst Cut-off
X.L. Bian1, G. Wang1,*, K.C. Chan2, J.L. Ren3, Y.L. Gao1, Q.J. Zhai1
1
Laboratory for Microstructures, Shanghai University, Shanghai 200444, China
2
Department of Industrial and System Engineering, the Hongkong Polytechnic
University, Kowloon, Hongkong
3
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001,
China
*Corresponding author: g.wang@shu.edu.cn
Contents
I. Experimental procedures………………………………………………………….2
II. Fig. S1 Load-displacement (P-h) of three metallic glasses………..……………3
III. Fig. S2 Determination of the instrument noise……………………...………....4
IV. Fig. S3 Strain burst size distributions as a function of indentation depth at
four loading rates…………………………………………………………………….5
1
I. Experimental procedures
Ingots of the Co-based, Fe-based, Zr-based and Ce-based metallic glasses were
prepared by arc melting a mixture of pure metal elements, followed by suction casting
in a Cu-mould to form rod-like metallic glasses. For the Mg65Cu25Gd10 metallic glass,
a Cu-Gd mixture was firstly pre-alloyed by arc melting the mixture of pure metal
elements in an argon atmosphere, and then the mixture of pure Mg element and
Cu-Gd pre-alloy was induction melted, and injected into the copper mould to form the
rod-like samples. Structural analyses were ascertained using X-ray diffraction (XRD).
Prior to indentation experiments, each metallic glass sample was mechanically
polished to a mirror finish.
Instrumented nanoindentation experiments were performed using a MTS Nano
Indenter XP (Oak Ridge, TN) with a Berkovich diamond tip. Fused silica was used as
a standard sample for the initial calibration. Before indentation, the tip was brought
into contact with the specimens’ surface at a depth of 2 µm to obtain the maximum
loads, and then indentations were conducted under a load-control mode to the
maximum loads at different loading rates of 0.2, 0.6, 1, 2 to 3 mN/s. The peak load
was held constant for 5 s to eliminate instrument noise. Before fully unloading, a load
holding segment was undertaken at about 10% of the peak load for 77 s (as indicated
by the red arrows in Fig. 1 and Fig. S1), serving as a thermal drift calibration. Testing
at each loading rate was repeated 10 times to generate enough statistical information,
and at the same time to exclude the occasional case.
2
0.2 mN/s
2 mN/s
(a)
1 mN/s
(b)
360
350
340
330
320
310
300
1100 1150 1200 1250 1300
400
300
200
400
Load (mN)
500
Load (mN)
0.6 mN/s
3 mN/s
300
200
100
100
0
(c)
0.2 mN/s
0.6 mN/s
1 mN/s
2 mN/s
3 mN/s
300
600
900 1200
Displacement (nm)
0
1500
500
1000 1500 2000
Displacement (nm)
250
Load (mN)
200
0.2 mN/s
0.6 mN/s
1 mN/s
2 mN/s
3 mN/s
150
100
50
0
500
1000 1500 2000
Displacement (nm)
2500
Fig. S1 Load-displacement (P-h) curves during nanoindentation at various loading
rates for three metallic glasses. The start points of the curves are offset for clearly
viewing. (a) Fe41Co7Cr15Mo14C15B6Y2, (c) Zr41.25Ti13.75Ni10Cu12.5Be22.5, and (c)
Ce68Al10Cu20Co2.
3
2500
(a)
Displacement (nm)
1997.1
1996.4
1995.7
1995.0
1994.3
Experimental data
Fitting line
1993.6
(b)
231 232 233 234 235 236 237 238 239
T (s)
hraw-hfit (nm)
1.0
0.5
0.0
-0.5
h = 2 nm
-1.0
231 232 233 234 235 236 237 238 239
T (s)
Fig. S2 Determination of instrument noise. (a) Fitting curve of displacement plotted
against time for the holding segment on Mg65Cu25Gd10 at a loading rate of 1 mN/s.
The scattered points are experimentally measured from the holding segment. The red
solid line is fitted by a linear function. (b) The difference between the raw
displacement data and the fitted curve versus time. The maximum h value (marked
by the red arrows) is equal to 2 nm, indicative of the background noise is 2 nm.
4
(b) 0.10
(a) 0.24
h/h
0.16
0.2 mN/s
0.12
0.08
Co-based
Fe-based
Zr-based
Mg-based
Ce-based
h/h
0.20
0.06
1 mN/s
0.04
0.08
0.04
0.02
0.00
0.00
0
800 1200 1600 2000
h (nm)
0.08
400
800 1200 1600 2000
h (nm)
(d)
0.06
2 mN/s
h/h
0
0.04
0.08
Co-based
Fe-based
Zr-based
Mg-based
Ce-based
0.06
h/h
(c)
400
Co-based
Fe-based
Zr-based
Mg-based
Ce-based
0.04
0.02
0.02
0.00
0.00
0
400
800 1200
h (nm)
1600
2000
3 mN/s
0
400
800 1200
h (nm)
Co-based
Fe-based
Zr-based
Mg-based
Ce-based
1600
2000
Fig. S3 Strain burst size distributions as a function of indentation depth for the five
metallic glasses at different loading rates. One can see that the strain burst sizes at all
loading rates exhibit random fluctuations, although the size distributions of the five
metallic glasses seem to have a declining trend as the indentation depth increases.
Additionally, the maximum strain burst size increases with loading rate decrease.
5