VAHID NEKOUIE

GAYAN ABEYGUNAWARDANE-ARACHCHIGE

ANISH ROY

VADIM SILBERSCHMIDT

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Mechanics of Advanced Materials Research Group

What is a Bulk Metallic Glass?

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• 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

What is a Bulk Metallic Glass?

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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

Applications

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Digital light processor, hinges made of Ti-Al metallic glass with no fatigue failure after 1012 cycles.

Micro components in MEMS devices

LENGTH SCALES

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 lengthscales

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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?

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Source – nature materials

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

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Characterisation (is it actually amorphous?)

X-ray diffraction (XRD)

No obvious presence of

crystalline phases

Experiment : 3 point bending

E (GPa)

ν σy

(MPa)

95.4 0.345 930

3mm

TensionCompression

100 µm

Vein like structures on the surface

Experiment : 3 point bending

E (GPa)

ν σy

(MPa)

95.4 0.345 930

400 µm

10 µm

Shear Bands are evident

Nano-indentation studies

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• 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

Fractured surface analysis

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Indentation Load = 500 mN

Wedge indentation studies

Why wedge?

Observing shear bands in Nano/Microindentation is difficulto 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

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1. Sample cut and polished

2. Loaded into a custom rig

Wedge indentation: Experimental steps

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Zygo Talisurf

Ra = 2 to 3 nm

BMG Spring

Wedge indentation: details

Incremental loading: 1 KN to 3 KN

Deformation mode: Compression

Displacement rate: 0.5 mm/min

Indenter: HSS

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60 µm

1kN

22 m

400 µm

50 m

Wedge indentation: Results (SEM)

60 µm

1kN

22 m

1-2kN

60 µm

50 m

1-2-3kN

60 µm

85m

400 µm 400 µm 400 µm

85 m 130m50 m

Wedge indentation: Load-Displacement CurveSingle load, different locations

Incremental load, same location

~ 50µm

~22 µm

Area under the curve will give us work done for plastic deformation

Shear Bands: XRD results

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XRD results are inconclusive since crystalline phases < 5% is hard to detect

Shear Band analysis/ TEM + SAED

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Virgin Sample Shear Band

Crystalline material

FIB milling

TEM/SAED sample

Shear Bands are fully amorphous

Nano-indentation studies on a Shear Band

Vickers indentation

Total load 100 mN

Loading rate 2 mN/s

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Nano-indentation studies on a Shear Band

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MODELLING OF WEDGE INDENTATION

/Finite Element Modelling

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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 − 𝑘J2 – 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

2q 1 +

1

𝑘− 1 −

1

𝑘

𝑟

𝑞

3and 𝑑 = 1 −

1

3𝑡𝑎𝑛𝛽 𝜎𝑐

𝑞 = 𝑣𝑜𝑛 𝑚𝑖𝑠𝑒𝑠 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑎𝑛𝑡 𝑠𝑡𝑟𝑒𝑠𝑠, 𝑘 = 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑠𝑠 𝑖𝑛 𝑡𝑟𝑖𝑎𝑥𝑖𝑎𝑙 𝑠𝑡𝑎𝑡𝑒

𝑟 = 𝑡ℎ𝑖𝑟𝑑 𝑖𝑛𝑣𝑎𝑟𝑖𝑎𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑒𝑣𝑖𝑎𝑡𝑜𝑟𝑖𝑐 𝑠𝑡𝑟𝑒𝑠𝑠

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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.

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Linear elastic behaviour

휀𝑛 =𝛿𝑛

𝑇0, 휀𝑠 =

𝛿𝑠

𝑇0, 휀𝑡 =

𝛿𝑡

𝑇0

Traction – Separation response

Damage initiation criterion

휀𝑛

휀𝑛0

2

+휀𝑠휀𝑠𝑜

2

+휀𝑡휀𝑡𝑜

2

= 1

Nominator calculated by the solver,

Denominator is user input dependent.

Linear damage evolution

𝐷 =𝛿𝑚𝑓

𝛿𝑚𝑚𝑎𝑥−𝛿𝑚

0

𝛿𝑚𝑚𝑎𝑥 𝛿𝑚

𝑓−𝛿𝑚

0

𝛿𝑚𝑓− effective displacement at complete failure,

𝛿𝑚0 − effective displacement at damage initiation

𝛿𝑚𝑓− effective traction at damage initiation,

𝛿𝑚𝑚𝑎𝑥 −maximum value of the effective displacement

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• Wedge Indenter Radius: 20 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

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FE model – Material Properties

Drucker-Prager parameters

HardeningAngle of

friction(β)

Flow stress

ratio

Dilation angle (ψ)

0.01° 1 0.02°

Shear damage parametersYield 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.

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FE model: ResultsDamage initiation and propagation through the shear band

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.

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• 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