Bijish Babu, Division of Material Mechanics

Material Modelling and Physically Based Models

Bijish Babu Division of Material Mechanics

Bijish Babu, Division of Material Mechanics

Process: Forming

Process: Metal Deposition Process: Welding

Process: Heat Treatment

Manufacturing chain

Process: Milling

Bijish Babu, Division of Material Mechanics

Microstructural Mechanism Map

Typical isothermal forming

Arbitrary path

Bijish Babu, Division of Material Mechanics

Stress-strain behaviour of SS 304 stainless steel at 650ºC

LEDS Low Energy Dislocation Substructures

Dislocation density

Bijish Babu, Division of Material Mechanics

Material Model

Physically based Constitutive Model

Stress-Strain Data Phase, Texture, Morphology

Grains, Sub-cells, Precipitates

Dislocations, Vacancies

Bijish Babu, Division of Material Mechanics

Dislocation Dynamics

Annihilation

Creation

Recovery

Hardening

mobile Dislocation

Density Immobile

Dislocation Density

Courtesy: Ashby & Frost!

Bijish Babu, Division of Material Mechanics

Physics of Deformation

Strain hardening

Recovery & Recrystallization

Dislocations Vacancies Grains, Subcells

Strain Energy

Courtesy: Ashby & Frost!

Bijish Babu, Division of Material Mechanics

Flow Stress

!

" y = m#Gb $i +" th 1% kT&Fb3 ln

˙ ' ref˙ ' p

(

) *

+

, -

(

) * *

+

, - -

1q(

)

* *

+

,

- -

1p

Long Range Short Range

Bijish Babu, Division of Material Mechanics

Evolution Equations

( )223

2 eqieqv

vv

pi

pi kT

GbccDc

bm

!!"!"! # $$%$&

= !!!

Immobilisation Glide Climb

Vacancy Creation Jogs Self Diffusion Temperature

!

˙ c vex = "

m#Gb2

Qvf

$i + %c j

4b2

&

' (

)

* + ,0

b˙ - .Dvm

1/2

0

1 2

3

4 5 cv . cv

eq( ) + cveq Qvf

T 2

0

1 2

3

4 5 6T

Bijish Babu, Division of Material Mechanics

Parameter optimisation

Bijish Babu, Division of Material Mechanics

GMoP – In-house optimisation tool

Bijish Babu, Division of Material Mechanics

316L-Low Strain Rates

Bijish Babu, Division of Material Mechanics

316L-Low High Rates

Bijish Babu, Division of Material Mechanics

!-" Phase Transformation Ti-6Al-4V

Bijish Babu, Division of Material Mechanics

Diffusion in Ti-6Al-4V

Bijish Babu, Division of Material Mechanics

Parameters for Ti-6Al-4V

Bijish Babu, Division of Material Mechanics

Ti-6Al-4V (20-300°C)

Bijish Babu, Division of Material Mechanics

Ti-6Al-4V (400-700°C)

Bijish Babu, Division of Material Mechanics

Ti-6Al-4V (800-1100°C)

Bijish Babu, Division of Material Mechanics

Stress Relaxation in Ti-6Al-4V

Bijish Babu, Division of Material Mechanics

•  Connects Macro to Nano Scales •  Parameters are accessible from conventional mechanical

tests •  Easy to implement in a standard FE code •  Has already been used for forming, welding, MD and

heat treatment simulations

Summary