Upadrasta RamamurtyDepartment of Materials EngineeringIndian Institute of ScienceBangalore-560012, India

Structural materials of the futurethe case of bulk metallic glasses

76th annual meeting of the Indian Academy of Sciences

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You can also drop them without worrying about breaking them… tough

can cast, forge, roll, extrude, bend, cut, stamp, and twist them….. malleable!

Metals are easy to work with….

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The boon for metals is also their bane!

πτ

2modulusshear

max ≈

Alloy design for strengthening…… reaching the limit!

Several GPaPDF Crea

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What are the alternatives?Ceramics are difficult to shape and brittle

How about glasses?

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Glasses……can also be shaped

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…they are strong tooStrength of freshly drawn glass ~ 15 to 20 GPa

A 20 ton truck can be pulled by a 4-6 mm dia wire

Skywalk, Grand Canyon

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…but, glasses are brittle,hence extremely sensitive to defects

“we never test the strength of glass: all we test is the weakness of its surface” J. T. Littleton (1941)

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Metallic glasses or amorphous alloys• Under normal conditions,

metals crystallize upon cooling from liquid to solid state

• Crystallization can be prevented by applying high cooling rates (~ million K/s)

• Metastable amorphous phase known as metallic glass can be obtained

• Only thin ribbons or wires (10 –100 µm) can be produced using rapid solidification techniques

what if we make glasses out of metals?

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ØIn 1990, Inoue found new classes of metallic glasses that can be made in bulk

Ø The bulk metallic glasses are composed of three or more metals in the alloy meltØCooling rates of the new alloys are from 100 Ks-1 to 1 Ks-1ØThe possible thickness of the metallic glass

increased from micrometers to centimetersØJohnson & Peker (1992) discovered that Be-containing Zr-based alloys form BMGs

Bulk Metallic Glasses (BMGs)

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Taken from Greer & Ma, MRS Bulletin

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Tg

TxT

m

rg = (T

g/T

m) ~0.71

-10

-5

0

5

10

15

20

100 200 300 400 500 600

Temperature, T (C)

Supercooled LiquidRegime

Scan Rate = 20°C/min

Reduced glass transition temperature Trg = Tg/Tm ~

0.71Supercooled liquid region

(TX) = TX Tg ~ 75K

Hea

t Flo

w

(mW

)

Pd40Ni10Cu30P20

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Structure PerformanceRelationships

Microstructure

Performance• Stiffness• Inelastic

deformation• Ultimate failure• Reliability • Life timeAllows for tailoring of the microstructure to

obtain desired behavior

Processing

“Seeing is Believing”

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Scales in Crystalline Metals

1 μm

Dislocation width

Dislocation substructure (0.1 μm)

Slip systems

1 nm 0.1 μm 1 μm

Dislocation substructure

Stacking fault width

AB

AA

BA

Microstructure

Fracture Process Zone

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Structure of a Glass

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Toughness

Stiffness Strength

Fundamental Mechanical Properties

Metallic Glasses

Quasi-static loading, room temperature

No intrinsic length scale

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Fracture in metallic glasses

What are the connections between nano- and micro-mechanisms and toughness?

Metallic glasses are schizophrenic in the fracture

sense

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Stress based (RKR) fracture criterion Models failure by brittle micro-cracking

(Ritchie et. al, 1973 and MTS theory of mixed mode fracture)

Failure occurs when σθθ exceeds a critical value σc over a critical distance rc from the notch tip

Strain based fracture criterionModels failure by brittle micro-crackingFailure occurs when lnεp1 exceeds critical value εc over a critical distance rc from the notch tip

Suitable for brittle materials

Suitable for ductile materials

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BMG Kc (MPa√m )

Elastic Modulus

(GPa)

Poisson’s ratio

Hardness(GPa)

VitreloyZr41.2Ti13.8Cu12.5Ni10Be22.5

30-68 96 0.36 5.9

Amorphous steel Fe48Cr15Mo14Er2C15

B6

3.8 ± 0.3 187 0.28-0.32 17.8±0.73

What controls the toughness of BMGs?PDF Crea

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FE analysis of a stationary crack in BMGsP

FE MESH for Boundary Layer (SSY) analysis

Crack line

R = 4000 b0

Elastic KI, KII based displ. field

b0

Near tip region

SSY conditions

u (KI,KII) PDF Crea

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Material constitutive modelAnand-Su model for metallic glasses

– based on Mohr-Coulomb yield criterion– involves discrete shearing accompanied by dilatation– dilatation induced strain softening– captures inhomogeneous deformation of BMGs well

Anand and Su (JMPS, 2005)

1tanφ µ−= 1tanφ µ−=4 2π φθ = +

Ø

Plastic dilatancy function (β)Ø Cohesion functionPDF Crea

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Simulation of shear bands around the notch root

Simulation using statistical distribution of initial cohesion in the finite elements

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Stress based (RKR) fracture criterion Models failure by brittle micro-cracking

(Ritchie et. al, 1973 and MTS theory of mixed mode fracture)

Failure occurs when σθθ exceeds a critical value σc over a critical distance rc from the notch tip

Strain based fracture criterionModels failure by brittle micro-crackingFailure occurs when lnεp1 exceeds critical value εc over a critical distance rc from the notch tip

Suitable for brittle materials

Suitable for ductile materials

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23(All dimensions are in mm)

Mixed-mode fracture experiments

Pure mode I tests: Symmetric four-point bend specimen

ØMaterial: Vitreloy 1 ( )

ØWire-cut EDM machined 46 mm x 5 mm x 3 mm (thickness)

Ø Notch diameter : 60 μm

Ø d controls mode mixityHSS Loading pins

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notch

Near tip mesh

Finite element analyses• Typical finite element mesh

ØTwo analyses: a. Linear elastic b. Elastic-plastic ØConstitutive model: Anand and Su model implemented through UMAT in ABAQUS/StandardØMaterial properties for Vitreloy 1: E = 97 GPa; ν=0.36; c0=890 MPa; μ=0.06; b=120 MPaØDetermine: a. Elastic mode mixity parameter Me b. Plastic mode mixity parameter Mp

c. Calibrate of J against P for each specimen using both the above analyses d. Find critical energy release rate Jc e. Simulate near-tip shear band patterns

§ No. of elements = 14394§ 64 elements around the notch root§ Frictionless contact§ Downward displacement prescribed for nodes on arcs abc and def§ Nodes on arc ghi and jkl are fixed

1

0

( , 0)2lim tan( , 0)

p

rr

rMr

θ θ

θ

σ θπ σ θ

−

→

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25

• Notch deformation• Shear banding• Stable crack growth

inside a dominant shear band

• Final failure

In-situ observations

100 μm

Video

Speed: 16x

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ExperimentSimulation

Mixed Mode Fracture

Tandaiya et al., JMPS 2009.

Me = -0.089 (~ pure mode II)PDF Crea

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ExperimentSimulation

P = 14.1 kN

Mixed Mode Fracture

Mp= 0.484 (mixed mode)PDF Crea

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Crack trajectories

AS4PB-1 AS4PB-2

AS4PB-4 S4PB-1

Incipient crack growth occurs inside a dominant shear band for all the specimens

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Variation of fracture toughness with mode mixity

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ØTwo types of morphologies

1.Smooth and shallow features involving highly smeared vein patterns within 45-60 µm from the notch front

2. Rough and deep features involving coarse dimple patterns superposed on ridges and valleys beyond 60 µm from the notch front

Fracture mechanism is ductile involving growth of shear crack inside a dominant shear band

Process zone size ≈ 60 μm

Ø Similar observations apply for other specimens also60 μm

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in closing……

• Large scope for conducting exciting research on amorphous alloys, which are of interest from both technological as well as scientific stand points of view.

• Key is to identify relevant length scales that control deformation and fracture.

• Design alloys that have high strength and high toughness!!PDF Crea

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