# links between scales ¢â‚¬â€œ multiscale material modeling...

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Homarus Americanus

0.55 Gyr age

The cuticle is one of the

oldest natural materials

for structural and armor

applications, already

present in the fossil

records of crab, lobster

or shrimp about 550Myr

ago, and thus, among

the most successful

animals living on the

earth

http://www.fossilmuseum.net/Fossil_Sites/Lebanese-Lagerstatt/Scyllaridae/Scyllaridaeb.htm

Nikolov, S, Petrov, M, Lymperakis, L, Friak, M, Sachs, C, Fabritius, H-O, Raabe, D and Neugebauer, J.: "Revealing the

Design Principles of High-Performance Biological Composites using Ab initio and Multiscale Simulations: The Example of

Lobster Cuticle" Advanced Materials,21 (2009), 1-8

Fracture mechanics problem is a complex multiscale phenomenon

M.J. Buehler, H. Gao, 2005

Links between scales – Multiscale Material Modeling

Multiscale approach to fracture in steels

”1D”

Continuum

Micro

Atomistic

•Brittle fracture

•Hydrogen induced fracture

Structure

• Ductile tearing

• Cleavage fracture

Multiscale Materials Modeling

1nm 1µm 100µm 10mm 10m

New interatomic

potentials for steel

Grains

Primary particles Atoms

Precipitates

Dislocations

Plastic flow Continuum laws

Load

Geometry

Stacking fault

energy Crystal plasticity Mechanics

modeling

Constraint

Scale

Modelling

techniques

Experimental

techniques

1-105 m 0.01-1 m 10-6-10-3 m 10-8-10-7 m 10-10-10-9 m

Structure/

material

Continuum

mechanics Crystal

plasticity Quasi-

continuum

Molecular

dynamics

Large-scale

testing Small-scale

testing

Nano

indentation Micor-pillars/

Focused ion beam

Top-down

approach

Bottom-up

approach ”Hand-

shake”

region

”Dislocations

”

”Atoms”

E Østby and C Thaulow

Cybersteel 2020

Multiscale modeling of ductile fracture

Hao S, B. Moran, W. K. Liu and G.B. Olson 2004

RVE

εij

P. Klein and H. Gao, 1998 (and following years)

calculate

T=0, no entropy

one atom with six neighbors

3 bonds

6 neighbors

only the two first terms

for small deformations

harmonic pot

spring constant

Atomistic FE

Atomistic FE

Need an additional term to account for temperature:

the entropy due to the vibrations

volume of unit cell

Elasticity as function of temperature

E Tadmor, R Miller, W Curtin et al

http://www.qcmethod.com/

The code can be downloaded

http://www.qcmethod.com/

Limited to 0 degree

14 leading multiscale methods

http://www.qcmethod.com/

You can download two code packages on this page:

•Multibench Test Suite version 1.0 (May 2009)

•Quasicontinuum Method Distribution version 1.3 (May

2007)

http://www.qcmethod.com/

Dynamic effects

BA region treated atomistically

BC region modeled as a continuum, FE

BI interface region, further subdivided in handshake region (H) and padding (fyll)

region (P)

Multiscale Materials Modeling of Fracture

• Compared different

crystallographic

orientations

• Modified boundary layer

(MBL) with different T –

stresses

• Anisotropic vs. isotropic

MBL

• Simulations with mixed

mode loading (mode I

and II, mode I and III)

Work done at the Department for Engineering Design and Materials, NTNU

Inga Ringdalen Vatne, PhD Arctic Materials

Multiscale Material Modeling of Fracture in bcc-Fe

10 nm

0.14 mm

400 nm

Coarse FE mesh

Finer FE mesh

Atomistic modeling

I R Vatne, E Østby and C Thaulow, “Multiscale Material

Modeling of Fracture in Fe using Modified Boundary

Layer(MBL)” Presented at ECF18, Dresden, Germany,

Sept 2010.

QuasiContinuum model

Multiscale modeling of fracture in bcc-Fe

• Using the Quasicontinuum

method.

• Atomistic description at the crack

tip. (adaptive)

• Continuum mechanical description

in the rest (Cauchy Born)

• Using modified boundary layer

analysis with different T-stress

and mode I and II. Isotropic and

anisotropic.

• Investigated three different

crystallographic orientations.

Method and model

• Quasicontinuum method – adaptive

atomistic where high accuracy is

needed, FE with Cauchy Born

elsewhere.

• Square model, 1500 x 1500 Å

• 0 K, static simulations, 2D

• EAM potential by Mendelev et. al.

Orientation Crack plane/

Crack front

1 (010)[101]

2 (110][001]

3 (011)[011]

4 (010)[001]

Crack

FE domain

Atomistic

domain

Mendelev, M.I et. al. Development of new interatomic potentials appropriate for crystalline and liquid iron Phil. Mag. 2003

Miller, R.E et al. The Quasicontinuum method: Overview, applications and current directions J. comp. mat. Des. 2002

Crack tip mechanisms

Orientation 2

Crack growth on {011} plane (which

have lowest surface energy for

potential). Creation of fcc area at crack

tip with Nisishima-Wassermann

orientation relationship.

Orientation 1

Crack growth on {001} plane. Creation of

fcc area at crack tip with Bain orientation

relationship.

Details of mechanisms at crack tip with pure mode I loading. Visualized in Ovito with common neighbor analysis (cna). Blue – bcc, green – fcc, red – twinning, white – other

Stukowski, A. OVITO – the Open Visualization Tool Mod.and Simul. In Mater. Sci. and Engineering, 2010

Crack tip mechanisms

Orientation 3

Emission of edge dislocation with

½[111] Burgers vector on the {112}

plane

Stukowski, A. OVITO – the Open Visualization Tool Mod.and Simul. In Mater. Sci. and Engineering, 2010

Orientation 4

Crack propagation on a {011} plane and

creation of fcc area with a Nisishima-

Wassermann orientation relationship like

orientation 2.

Details of mechanisms at crack tip with pure mode I loading. Visualized in Ovito with common neighbor analysis (cna). Blue – bcc, green – fcc, red – twinning, white – other

Mixed mode simulations (mode I and II)

w = 1w = 0.4w = 0.2w = 0

O ri e n ta

ti o n 1

O ri e n ta

ti o n 3

Stress intensity factors given by w through: KI=K*(1-w), KII=K*w

Mixed mode simulations (mode I and III)

Stress intensity factors given by w through: KI=K*(1-w), KIII=K*w

O ri e n ta

ti o n 1

O ri e n ta

ti o n 4

w = 0.5w = 0.3

w = 1w = 0.6w = 0.2

Concurrent Multiscale Methods

Challenges with multiscale methods:

• Timestep • Limited by atomistic vibrations also in continuum domain

• Temperature • How to account for kinetic energy • What to do with waves

• Interface • How to enforce compability and equilbrium across interface • Can cause spurious forces

CYBER STEEL 2020

USA

STAHL AB INITIO

GERMANY

DEVELOPMENT OF NANOTECHNOLOGY BASED STEELS

Stahl ab initio - Germany

Quantum mechanics-guided design of new Fe based materials: Fe-Mn-C

Multiscale material modelling of ductile fracture in steel

Particle-matrix

interface debonding

Void nucleation and growth

Shear localization

Fracture

1

3

4

2

21

3

4

Atomic scale

Hao S, B. Moran, W. K. Liu and G.B. Olson 2004

Microstructure of high strength and high toughness steel

Macro scale

Micro scale

Sub-micro scale

primary particles (~mm) – yield strength

secondary particles

(~0.1mm) – ductility

Fracture surface

• Deformation of microstructure at each scale is important in the

fracture process

•Need a general multi-scale continuum theory for materials that

accounts for microstructure deformation and interactions

Heterogeneous material

Interfacial strength between inclusions influence the strength and ductility

Classical MD

• Main point: calculate atomic interaction