Multiscale Integrated Model-Guided Process Design:

To quantify the effects of Inclusions on the Properties of Steel Sheet

1

Akash Gupta, Sharad Goyal, A. K. Singh

TRDDC-TCS Innovation Labs, TCS Ltd., Pune, India

Tajendra Mehta

IIT Kanpur, Kanpur, India

N. Anand Balu

IIT Bhubaneswar, Odisha, India

K. A. Padmanabhan

SEST, University of Hyderabad, Hyderabad, India

1st International Workshop on Software Solutions for Integrated Computational Materials Engineering

Rolduc Abbey / Aachen

Motivation for our TCS-ICME Program

TCS General

Reduce Lead Time for New Materials Development

Reduce Dependence on Expensive Experimentation

Enhanced Interaction Between Design and Materials Engineering

Reduce Dependence on Tacit Knowledge of Experts

ICME Platform Requirements

Facilitate integrated design of products and materials

Integration of models and simulation tools across multiple length scales and levels

of granularity

Capture knowledge of materials, products and manufacturing processes

Capture data on material compositions, properties, microstructure, etc

From experiments, simulations

Support a standard ontology

Interoperability, information exchange

Enable data mining and learning

Learn models from experimental data to fill gaps in theory

Extensible architecture

Add new products, design processes, etc without touching implementation

TCS-PREMAP

4

ACKNOWLEDGEMENTS

Prof. Farrokh Mistree

Prof. Janet Allen

Prof. Jitesh Panchal

Prof. Surya Kalidindi

Gautham, Sreedhar, Smita and Ratnamala and their team members

Ravindra, Niranjan, Prabhash, Ravikiran, Dhanashree, Rishabh,

Sourabh, Madhusudan and Suryanaman

Dr. Pradip and Mr. K Ananth Krishanan

Motivation

Motivation

Requirements in automobiles

• Improving fuel efficiency, Recyclability, Higher safety norms, Low Cost

– Advanced high strength steels need to be developed

Scale up of a new grade from the Lab to the Industry

• Non uniformity of properties

– Steel industry has to carry out a number of plant trials

– Time required ~20 years

• Several unit operations

5

Can the huge time and trial requirements be

reduced while producing new AHSS grades?

Objective

To develop a Multiscale Integrated modeling framework to facilitate the

attainment of suitable final gauge properties in respect to inclusions.

• Performance and properties of steel sheets are dependent on various

factors: Microstructure, Macrostructure, Segregation, Inclusions, etc.

CFD and Thermodynamics model

Multiscale model

Thermal-Solidification model

Motivation

cooling

Solid State Processing

Liquid Metal Processing Solidification

Conceptual design of ICME framework for inclusion problem

Inclusions

Inclusions

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Ref: H. Jacobi, F. Rakoski, 1995 Ref : L. Zhang, B.G. Thomas, 2003.

Ref : L. Zhang, B.G. Thomas, 2003.

Ref: T.J. Baker, J.A. Charles,1971.

Ref: N. Wolanska et al, 2007

Ref: Hai-liang Yu et al, 2009

Methodology

Ladle and Tundish model

• CFD and thermodynamics based models

• Initial inclusion distribution at caster entry is obtained

Caster model

• FEM based thermal-solidification model

• Inclusion distribution in cast slab is obtained using CET predictions

Micro-mechanical model

• FEM based micro-model to simulate local behaviour of material close to inclusions

• Modified constitutive equation obtained for steel as a function of inclusion fraction

Hot rolling model

• FEM based thermo-mechanical model

• To study the effect of inclusions on hot rolling process.

Initial Inclusion distribution coming to caster

CFD and thermodynamics models of ladle and tundish are used to

obtain initial inclusion distribution at mold entry in caster

9

Model1 : Continuous caster model

2-D Slice based thermal-solidification model of continuous caster is

developed using FEM.

Columnar to Equiaxed Transition (CET) in the continuous casting slab

is predicted using this model.

Inclusion distribution in the cross-section of cast slab is obtained using

predicted CET

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Conduction based Model for CET

Assumptions

• Enhanced thermal conductivity in mushy and liquid region

• Axial heat transfer ignored

The governing equation:

Scheil equation

fl = [T - TP

TL - Tp]

1/(pk-1) (5)

Hunt’s Model: the structure is equiaxed when

GL < 0.617 N1/3

o[1 -

T3

N

T3

c

] Tc

and, the structure is fully columnar when

GL > 0.617 (100No)1/3

[1 -

T3

N

T3

c

] Tc

where,

Tc = (VCo/A)1/2

t

f

C

L

y

T

x

T

C

k

t

T s

pp

2

2

2

2

)(%18)(%2)(%2)(%5)(%5.1)(%4

)(%25)(%30)(%5)(%8)(%881537

TiVMoCuCrNi

SPMnSiCTL

5.0

max

5.0

max

/ ,zz

/ ,z z

Uzqqfor

Uzqz

zqfor

mouldc

c

c

mouldc

44

wsurfswsurfss TTTThq

44

wsurfss TTq

CET in cast slab and final inclusion distribution

12

Chill zone solidifies very fast and captures some of the inclusions.

The solidification front pushes the larger size inclusion which are

captured in Equiaxed zone but the smaller size inclusions are captured

in Columnar zone.

Spatial inclusion distribution in cast slab

Following criteria based on CET was used to distribute inclusions in slice:

2 % of all inclusion goes to chill zone

Inclusions less than 10 micron remain in columnar zone

Rest of the inclusions greater than 10 micron are pushed in equiaxed zone

Volume fraction of inclusion in each element of mesh is computed and will

be used in hot rolling model

13

Model 2: Micro mechanical model

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Contour plot of von Mises stress in the micro-

model. Inclusion is at the centre of the matrix

with void formation at interface during plane

strain compression test.

2-D finite element based micro-mechanical model is developed

100X100 micron - micro model unit cell

Elasto-plastic inclusion of up to 30 micron radius

Elasto-plastic steel matrix

Inclusion-Matrix interface

Cohesive zone model and coulomb friction are used to model inclusion/steel interface

behaviour.

Ref : L. Zhang, BG Thomas, National

Steelmaking Symposium, 2003. Ref : C. Luo - Evolution of voids close to an

inclusion in hot deformation of metals, 2001.

Performance and quality of final steel sheet is strongly influenced by properties

(hard or soft), morphology and size of inclusions.

Inclusions with sharp edges like rhombus, square and trapezium shapes give

rise to stress concentrations and higher values of stresses compared with the

spherical shape.

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Effect of inclusion shape and elastic modulus on the maximum stress

Results

Validation: Comparison between present simulation fig (a,b) and Yang

[2009] fig (c,d)

(a) (b)

P Q

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To establish multiscale linkages, plane strain compression tests are simulated

using micro-model assuming different temperatures, strain rates and inclusion

sizes as being present in steel matrix for the case of spherical hard inclusion.

Updated constitutive equation is obtained for the steel matrix which can be used

for macro-model with flow stress as a function of inclusion volume fraction (Vi).

Updated constitutive equation obtained for the steel matrix with flow stress as a

function of inclusion volume fraction (Vi), is implemented in ANSYS for the

macro model of hot rolling.

Results

CQVTf i ,%,,, ,

Mif V 88.2

1

1000

273133.0

23.06 276.05000

exp1037.3

T

MT

M – flow stress in steel matrix

f – flow stress in the unit cell with inclusion

Vi – Inclusion volume fraction

T Temperature

Ref: Gupta A, et. al (2013). NUMIFORM 2013, AIP Conf Proc.

Stress decreases with an increase in the inclusion volume fraction (in compression

tests and single inclusion at the center), i.e. the load bearing capacity of material

decreases due to the formation of voids.

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Variation of flow stress with inclusion volume fraction present in steel at ε =

0.01, έ = 0.01 s-1. Plots are shown for three temperatures of 1200, 1300 and

1400 °C. Typical inclusion radii assumed are 1-30 micron.

Stress-Strain plots from compression test simulations of different inclusion volume

fraction cases. Plots are shown for three volume fraction of 0, 1 and 3 %.

Effect of Hard Inclusion on Flow Stress

Multiscale Model for hot rolling

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Macro model of hot

rolling (m)

Micro model (µm)

Inclusion Steel matrix

Model 3: Hot rolling macro model

2-D model of hot rolling is developed using FEM

Coupled thermal-structural element used

Roll-rigid, Strip- viscoplastic

Roll is assumed as a perfect Target contact without assigning any Thermal

Properties.

Model is validated for single pass

19 Ref: M.P.Phaniraj,et.al,2004

Geometrical Modeling- Combined Thermal and Structural

specifications- Meshing with a common element.

Apply B.C’s , I.C’s and both Thermal and Structural Loadings

Solving Thermal and Structural Equations

Solution Converged

End of Step

NO

LOAD STEP= n+1

Heat due to Plastic work and friction

END

Solution Methodology of macro model of rolling

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Hot rolling results – Temperature contour

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Temperature at center and surface of strip at various thickness

reduction changes.

By increasing the strip thickness the min. temperature of the surface

decreases and max. temperature of strip center increases.

Surface temperature is minimum

Hot rolling results – Effective stress contour

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Due to lower speed, Temperature loss occurs more at the exit region

and minimum temperature point at exit region is more dominant than

max. strain at the entry region and thus max. effective stress occurs at

the minimum temperature region(exit region).

Maximum stress occurs at surface at roll contact

Hot rolling with updated constitutive equation

Updated constitutive equation is used for steel developed using micro-

model analysis and based on inclusion volume fraction in elements of

slice calculated using CET, different element is assigned different

material property.

Load bearing capacity of material decreases due to higher inclusion

volume fraction (because of void formation) hence maximum stress

occurs at element 2 instead of surface element 1 as in last slide

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Mif V 88.2

1

M – flow stress in steel matrix

f – flow stress in the unit cell with inclusion

Vi – Inclusion volume fraction

Effect of inclusions on hot rolling

Stress-strain plots comparing the elements with and

without inclusions and with varying inclusion volume

fractions

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0 0.01 0.01 0.02 0.02 0.03 0.03

0

10000000

20000000

30000000

40000000

50000000

60000000

70000000

80000000

Elem4

Elem4(7%)

Elem3

Elem3(11%)

Elem2

Elem2(16%)

Summary

Using ICME methodology a multiscale integrated modelling framework is

presented to show the influence of inclusions in rolling operation which

allows

the evaluation of effect of inclusions on the properties of steel sheets, and

prediction of upper size limit of inclusions that can be tolerated

Continuous caster model, Micro-mechanical model and Hot rolling model

are developed and individually validated

A methodology is proposed to obtain inclusion distribution in cast product

using CET and to show the effect of inclusion on the stress of a formed

sheet. Similar method can be used for inclusions of various other

shapes, sizes and properties.

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Thank you

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