1. ANISH ROY
VAHID NEKOUIE
GAYAN ABEYGUNAWARDANE-ARACHCHIGE
VADIM SILBERSCHMIDT
1
Mechanics of Advanced
Materials Research Group

2. What is a Bulk Metallic Glass?
2
• amorphous material: atoms “frozen” in non-crystalline form
• first formed in 1957 by Duwez by rapid quenching
 gold-silicon alloy
 only very thin, small samples could be produced (order or micrometers)
• first believed atoms were randomly packed together densely like hard spheres
in a liquid
 solvent atoms randomly arranged with solute atoms fitting into open cavities
• now believe short-range, even medium-range order exists in materials
Sheng et al. (2006), Nature

3. What is a Bulk Metallic Glass?
3
BMG
Compared to metals in general, BMGs
have high strength, f and low
stiffness, E
Unusually high Elastic Strain, f/E
From: Material selection in mechanical design, MF Ashby (1999)
Very high Elastic stored energy

4. Applications
4
Digital light processor, hinges
made of Ti-Al metallic glass with
no fatigue failure after 1012 cycles.
Micro components in
MEMS devices
LENGTH SCALES

5. Introduction & Motivation
 Deformation mechanisms of metallic glass are unique
 plastic shear flow in the micro scale, but brittle fracture in macro scale
 At ambient temperatures/high stress: flow localization in shear bands (SB)
 At high temperatures/low stress: homogeneous viscous flow
Research Objectives
 Experiments: study SB initiation and evolution under loads. Characterise SBs
mechanically.
 Modelling: Develop a continuum model of SB initiation and propagation,
which can then be used to study component deformations across length
scales
5

6. What is a Shear band?
 Localised thin bands (~ 10 - 20 nm).
 Cohesion is maintained across the planes.
 Propagation is inhomogeneous
 Propagation depends on loading conditions, sample imperfection.
 Origin of SB is controversial: structural change? Temperature rise? Localised melting?
6
Source – nature materials

7. BMG alloy and experiments
BMG alloy manufactured at IFW/Dresden
Zr48Cu36Al8Ag8
Samples: 70 mm × 10 mm × 2 mm ; 40 mm × 30 mm × 1.5 mm
7
Characterisation (is it actually amorphous?)
X-ray diffraction (XRD)
No obvious presence of
crystalline phases

8. Experiment : 3 point bending
E
(GPa)
ν σy
(MPa)
95.4 0.345 930
3mm
TensionCompression
100 µm
Vein like structures on the surface

9. Experiment : 3 point bending
E
(GPa)
ν σy
(MPa)
95.4 0.345 930
400 µm
10 µm
Shear Bands are evident

10. Nano-indentation studies
10
• Fracture surface is noticeably weaker than the bulk material
• There is a large variation of the mechanical properties on the fractured surface
Objective: To assess if there is any difference in the mechanical characteristics of the
fracture surface in comparison to the bulk material
 Vickers indentation
 Total load 100 mN
 Loading rate 2 mN/s

11. Fractured surface analysis
11
Indentation Load = 500 mN

12. Wedge indentation studies
Why wedge?
Observing shear bands in Nano/Microindentation is difficult
o Shear bands initial in the material volume
o Bonded interface method is not ideal
With a Wedge we have a 2D plane-strain scenario
 Observe shear bands terminating on the surface as they initiation and evolve.
 Relatively easy to setup
 Easy to model
12

13. 1. Sample cut and polished
2. Loaded into a custom rig
Wedge indentation: Experimental steps
13
Zygo Talisurf
Ra = 2 to 3 nm
BMG Spring

14. Wedge indentation: details
Incremental loading: 1 KN to 3 KN
Deformation mode: Compression
Displacement rate: 0.5 mm/min
Indenter: HSS
14
60 µm
1kN
22 m
400 µm
50 m

15. Wedge indentation: Results (SEM)
60 µm
1kN
22 m
1-2kN
60 µm
50 m
1-2-3kN
60 µm
85m
400 µm 400 µm 400 µm
85 m 130m
50 m

16. Wedge indentation: Load-Displacement Curve
Single load, different locations
Incremental load, same location
~ 50µm
~22 µm
Area under the curve will give us work done for plastic deformation

17. Shear Bands: XRD results
17
XRD results are inconclusive since crystalline phases < 5% is hard to detect

18. Shear Band analysis/ TEM + SAED
18
Virgin Sample Shear Band
Crystalline material
FIB
milling
TEM/SAED sample
Shear Bands are fully
amorphous

19. Nano-indentation studies on a Shear Band
 Vickers indentation
 Total load 100 mN
 Loading rate 2 mN/s
19

20. Nano-indentation studies on a Shear Band
20

21. MODELLING OF WEDGE INDENTATION
/Finite Element Modelling
21

22. Microscale modelling – Bulk material
 Drucker – Prager : hydrostatic stress component is considered.
 Captures the rise of shear strength with the increase of hydrostatic pressure
increase. – Major cause for adoption.
𝐹 = 𝐽2 − 𝜃𝐼1 − 𝑘
J2 – second deviatoric stress invariant 𝜃 – constant for a given material
I1 – first stress invariant 𝑘 – hardening and softening function
ABAQUS 6.12 is used to model
Linear Drucker - Prager criterion is used:
𝒇 = 𝒕 − 𝒑𝒕𝒂𝒏𝜷 − 𝒅 Here: 𝜷 = 𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏 𝒂𝒏𝒈𝒍𝒆 and 𝒅 = 𝒄𝒐𝒉𝒆𝒔𝒊𝒐𝒏 𝒑𝒂𝒓𝒂𝒎𝒆𝒕𝒆𝒓
To calculate, 𝒕 and 𝒅: 𝑡 =
1
2
q 1 +
1
𝑘
− 1 −
1
𝑘
𝑟
𝑞
3
and 𝑑 = 1 −
1
3
𝑡𝑎𝑛𝛽 𝜎𝑐
𝑞 = 𝑣𝑜𝑛 𝑚𝑖𝑠𝑒𝑠 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑎𝑛𝑡 𝑠𝑡𝑟𝑒𝑠𝑠, 𝑘 = 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝑖𝑛 𝑡𝑟𝑖𝑎𝑥𝑖𝑎𝑙 𝑠𝑡𝑎𝑡𝑒
𝑟 = 𝑡ℎ𝑖𝑟𝑑 𝑖𝑛𝑣𝑎𝑟𝑖𝑎𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑒𝑣𝑖𝑎𝑡𝑜𝑟𝑖𝑐 𝑠𝑡𝑟𝑒𝑠𝑠
22

23. Microscale modelling – Shear band
 Cohesive Zone Elements with traction separation law.
 Shear band thickness lies in the ~nm scale. This fact prompt to employ
traction separation laws.
23
Linear elastic behaviour
𝜀 𝑛 =
𝛿 𝑛
𝑇0
, 𝜀 𝑠 =
𝛿 𝑠
𝑇0
, 𝜀𝑡 =
𝛿 𝑡
𝑇0
Traction – Separation response
Damage initiation criterion
𝜀 𝑛
𝜀 𝑛
0
2
+
𝜀 𝑠
𝜀 𝑠
𝑜
2
+
𝜀𝑡
𝜀𝑡
𝑜
2
= 1
Nominator calculated by the solver,
Denominator is user input dependent.
Linear damage evolution
𝐷 =
𝛿 𝑚
𝑓
𝛿 𝑚
𝑚𝑎𝑥−𝛿 𝑚
0
𝛿 𝑚
𝑚𝑎𝑥 𝛿 𝑚
𝑓
−𝛿 𝑚
0
𝛿 𝑚
𝑓
− effective displacement at complete failure,
𝛿 𝑚
0
− effective displacement at damage initiation
𝛿 𝑚
𝑓
− effective traction at damage initiation,
𝛿 𝑚
𝑚𝑎𝑥
− maximum value of the effective displacement

24. 24
• Wedge Indenter Radius: 43 μm
• FE Model Dimension: (2000 × 2000 ) µm
• Displacement Given to Indenter: 4 µm to 10 µm
• Element type:
Bulk Specimen and indenter – CPE4R
Shear bands – COH2D4
• Wedge Indenter: Deformable Body
FE model
2D Plain Strain
BC: bottom rigid

25. 25
FE model – Material Properties
Drucker-Prager parameters
Hardening
Angle of
friction(β)
Flow stress
ratio
Dilation angle (ψ)
0.01° 1 0.02°
Shear damage parameters
Yield stress (MPa) Plastic strain
Fracture
strain
Shear stress
ratio
Strain rate ( s-1 )
930 0
0.05 1 0.016
• Material Properties for bulk metallic glass –
E (GPa) ν
95.4 0.345
• Material Properties for deformable indenter (HSS)–
E (GPa) ν
231 0.30
• Material properties for CZE were chosen by sensitivity analysis.

26. 26
FE model: Results
Damage initiation and propagation through the shear band

27. Outlook & Future Work
 SB and Fracture surface are weaker than bulk material
 SB are amorphous … rules out melting
 Cohesive Zone Elements can be used to determined the
propagation along the shear band.
 A gradient plasticity based approach is currently being developed
to capture the nucleation and the effect of the local shear bands.
27

28. 28
• Wedge Indenter Radius: 21 μm
• FE Model Dimension: (2000 × 2000 ) µm
• Element type:
Bulk Specimen and indenter – CPE4R
Shear bands – COH2D4
• Wedge Indenter: Deformable Body
FE model
2D Plain Strain
BC: bottom rigid