02 TATA Gurson

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1Copyrig ht Tata Motors Ltd.

CRASH SIMULATIONS AT TATA MOTORS

VPG-CRASH

3 Dec 2012



2

CAE Capabilities – Passenger Car

Ful l F rontal Offset Frontal Seat Belt Anchorage Pedestri an leg forms

Side door in trusion Roof crush Side pole crash Pedestrian head forms

Side impact Rear impact Occupant Restrain ts



3

CAE Capabilities – Commercial Vehicles

Full CAE capability for Bus Rollover simulation (ECE R66)

Under Run Protection Device Strength Commercial Vehicle Cabin Strength (ECE R29)



4

Offset Frontal Test of Chassis Front End

CHASSIS FRONT END TEST

Test speed = 47 kmph



1Copyright Tata Motors Ltd.

Damage Modeling




Contents

1. Important Material Property Aspects for Crash Simulation

2. Current Material Modeling Process

3. Need of Damage Modeling

4. Gurson Model


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Yield locus

Hardening characteristics

Material damage due instability and Damage modeling(Damage state of stress/strain dependent material weakening and reduction in ductility)

Material Anisotropy

Strain Rate effects

Important Material Property Aspects for Crash Simulations



Current Material Modeling Process

Test to Model Process:



1. Standard Coupons prepared for Uniaxial Tension test to get Force- Deflection data.

2. Force-Deflection curve data is converted to Engineering Stress-Strain curve as follows.

3. Engineering Stress-Strain Curves is then converted to True Stress-Strain curve as follows

Current Material Modeling Process-contd.



Current Material Modeling Process-contd.

4. True Stress-Strain curve is converted to Effective Stress-Strain curve by removing the elastic strains as follows.

5. Resulting hardening curve relates the yield stress as a function of effective plastic strain.



Limitations of Current Material Modeling Process

Modeling of Elasto-Viscoplastic material Behavior

1. Stress State not constant at fracture location

For purely Elastic deformations , stresses are uniquely defined by final configuration of the

material regardless of how this final state is reached. For Plastic deformations , because of

presence of irreversible elements , plastic analysis need to follow path along which final

configuration is reached.

2. Total Elongation from tension test is based on complete measurement length.

Flow stress is derived from uniaxial tension test. Deformation is localized in diffused necking or

localized necking beyond uniform elongation (Refer fig.). Cross section reduction at fracture is

first qualitative measure for ductility of the material. Hence this value cannot be used for

fracture model.

3. Result of Test data at the Onset of Necking cannot be directly used.

Slope of Engineering Stress-Strain curve is zero a the onset of necking. Slope of True Stress-

Strain curve is greater than zero at the onset of necking. For simulation data beyond necking ,

iterative approach is the only way to match the Force-Deflection curve.



Sample1 – Uniaxial Tension Test without Damage included

t=0 ms t=40 ms

Comparison of Force vs Displacement curve between Test and Simulation

Sample2 – Uniaxial Tension Test with Damage included

t=0 ms t=35 mst=40 ms

Need of Damage Modeling



Need of Damage Modeling-contd.

In tensile testing , uniform extension ceases while when tensile load reaches material specific maximum. At this point sample

begins to neck. The state of stress changes gradually from simple uniaxial to complicated condition of triaxial stress.

Because of onset of necking destroys the uniaxial state of stress it is impossible to determine uniaxial true stress strain

relation by standard tensile test once necking has started.

Process Chain of Sheet Metal Manufacturing

Forming – a. Transferring local sheet thickness after forming to improve geometric description

b. Distribution of local pre-strain as a scalar quantity transferred from one simulation to another.



Strong dependence of failure strains on actual loading conditions is observed in high strength steels. Hence local plastic

strain values are not sufficient to define local-predamage of part since loading history data not available.

Strain Rates under crash and forming loading are of different nature making criterion like maximum plastic strain to failure

suitable for very special load cases.

To avoid this problem , is the use of damage models for both sides of the process chain.

Need of Damage Modeling-contd.

Mapping Forming Results in Crash Simulations



Damage / Fracture is defined as relative loss of ductility.

Ductility is measure of failure strain relative to yield or peak strain. Fracture is sudden change in configuration but the damage

is cumulative process.

Type of Fracture :

a. Brittle Fracture - Fracture of interatomic bounds without noticeable plastic

deformation. This fracture occurs when the local strain energy becomes

larger than the energy necessary to pull the atom layers apart.

Mainly occurs in high strength metals with poor ductility and toughness.

Surface of brittle fracture is characterized by it’s flat appearance and also

it is perpendicular to the applied load.

b. Ductile Fracture - Fracture caused by instability which is a result of very

high plastic deformations occurring in surroundings of crystalline defects.

Deformation in ductile fracture can be small and large depending on the

density of the defects.

What is Damage / Fracture




Gurson Model Most popular model currently used for model damage failure.

Micromechanical Model. Microscopic approach to fracture.

Able to predict , both homogenous and localized dilatational deformation phases caused by presence of voids.

Derived based on the assumption that deformation mode of matrix material surrounding a void is homogenous.

Hence able to predict material softening behaviour due to nucleation and growth of voids. This is extended to predict the shift of

a homogenous deformation mode to a localized mode by void coalescence.

Gurson yield function is as follows

where , f = void volume fraction which is average measure of void matrix aggregate

q1, q2 = Constants

σm = mean normal stress

σeq = conventional von-mises equivalent stress

σM = flow stress of matrix material

f* = void volume fraction

where f c = critical void fraction

f f = void volume fraction at fracture




Gurson Model – contd.

LS-DYNA Card for MAT_120 Gurson Model – Important data required for the model is listed as below

Q1 = Gurson flow function parameter

Q2 = Gurson flow function parameter

FC = Critical void volume fraction where void begins

to aggregate

F0 = Initial void volume fraction (where void

nucleation starts)

FN = Void Volume fraction of nucleating particles

EN = Mean Nucleation strain

EPS1 to EPS8 = Effective plastic strain values





ES1 to ES8 = Corresponding yield stress values

L1 to L4 = Element length values

FF1 to FF4 = Corresponding void volume fraction

LCFF = Load curve defining failure void fraction vs

Element length

LCF0 = Load curve defining initial void fraction vs

Element length

LCFC = Load curve defining critical void fraction vs

Element length

LCFN = Load curve defining void volume fraction of

nucleating particles vs Element length





Limitations of Gurson Model:

1. Large no. of Input Parameters

In order to use Gurson material for predicting damage, input parameters of the model have to fitted to existing

test data. Due to numerous input parameters which are actually coupled by complex functions of flow rule and

damage evolution creating input data card is difficult and time consuming.

2. No shear consideration in the model.

The growth rate of voids is zero due to constant pressure. If the total volume fraction to be nucleated is less

than void volume fraction at fracture, the material is predicted not to fail. Hydrostatic pressure remains constant

in simple shear and there is no macroscopic dilatation

3. Gurson model is not able to describe failure under conditions of mean stress near zero or negative. In some

applications of deep drawing, there are remarkable magnitudes of shear and compressive shear deformation

which causes pre-damage which is not considered in Gurson model.

4. Due to symmetry of the yield function w.r.t zero or mean stress , Gurson model doesn't predict increase in

strength w.r.t hydrostatic pressure.



Parametric Identification of DamageParameters of LS-DYNA Gurson

Material Model

Karthik Chittepu

Ganesh Gadekar, Kedar Joshi

2nd Optimization & Stochastic Days 2012, Dec 3-4, Pune, India



2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune

Acknowledgement

Project has been carried out as a collaboration

CADFEM India

Karthik Chittepu

Tata Motors

Ganesh Gadekar

Kedar Joshi



Crash Application

Importance of crashsimulation?

- Safety

Why simulating?- Compression of developmentcycles

- Cost reduction

Why optiSLang?- Unknown sensitivities

- Many parameters




Why Gurson Material Model?

Increasing requirement on crash safety of automotive components

Also increasing demand of light weight and life cycle cost efficient

components

Accurate prediction and numerical simulation of fracture and material

failure




Methodology

LSDYNA Pre Processing

LSDYNA Post processing

CAD Model

LSDYNA Gurson Material Model

LSDYNA (Batch-Run)

optiSLang

Mesh

Effective Plastic Strain &Effective Stress

Post processing in optiSLang

Damage Parameter (EN,FC, FF0, F0, SN, and FN)

Boundary Conditions

Plasticity Area

Failure Strain

optiSLang

Uniaxial Tensile test

Input Parameters

Output Parameters

N ew

P ar am e t er s

e t




Uniaxial Tensile Test & Simulation Model

Tensile test is carried with one end

fixed and constant rate of motionon the other end

Force and displacement aremeasured

Engineering stress-strain curves isplotted based on themeasurements

FE model is developed based ontest specifications

Stress-strain curveFE Model

Uniaxial TensileTest




Calibration of Effective Plastic strain and stress

• Besides Young’s Modulus and Poisson’s ratio, the input of a

uniaxial true stress-strain function is required• Usually determined by the ASTM method

• At material specific max. stress, necking of sample begins

• Stress changes gradually from the simple uniaxial tension to acomplicated condition of biaxial stress

• After necking, weighted averagemethod is used.

Where w = is the weight constant




Gurson Material Model

In metals and metallic alloys ductile fracture is linked to the

micromechanical process of micro-voids growth to coalescence Gurson Model adopts this void growth and nucleation approach

Under plastic deformation, the material strain hardens, and voids

nucleate and grow, and subsequently lead fracture

Ductile fracture process which consist of void

nucleation, growth and coalescence

This behaviour is governed by the damage parameters.




Damage Parameters

5

In this parametric identification process the following damage

parameters in the Gurson model has to be identified :

– FC: which is the critical void volume fraction,

where voids begin to aggregate.

– EN: which is the mean nucleation

– FF: which is the failure void volume fraction

– F0: which is the initial void ratio

– SN: which is standard deviation of EN

– FN: which is void fraction of nucleation

particles

– FF0: which is failure void fraction




Post Processing

• After the simulation the force and displacement are estimated.

•

Based on these value Stress-strain plot is plotted.• For the parametric identification following parameters are calculated from thestress-strain curve

– Area Under Plastic Region

– Maximum stress

– Failure Strain




Basic Criteria

1. Difference of area underplastic region between Testand Simulation Target: 0

2. Difference of maximum

stress between Test andSimulationTarget: 0

3. Difference of failure strainbetween Test and

SimulationTarget: 0




Sensitivity Analysis

Sensitivity analysis is used to scan thedesign space by varying designoptimization parameters within upper andlower bounds

Global Sensitivity of responses withrespect to design variables variation

Identification of important input

parameters and possible reduction ofthe design space dimension foroptimization

Understanding and verification of theoptimization problem

Choosing a start design for optimization Proof of numerical robustness

Preparation of the optimization problemand reduction of the problem dimension

Latin HypercubeSampling




Sensitivity Analysis

• EN, FN, SN and FF0 have major influence on maximumstress value of the curve

• EN, FF0 and FN have major influence on the failure strainand area under plasticity region.

• All design parameters are considered for optimization




Optimization - Evolutionary Algorithm

Evolutionary algorithm is used. Its ametaheuristic algorithm. Thisalgorithm is selected due to the lowcomputation time of each design inthis project

Evolutionary algorithm usuallyfeatures

- Robust

- Can handle any complexity

- Takes time to converge




Optimization - Evolutionary Algorithm

Objective HistoryBest Design Data

Output Data of Best Design

Damage parameters of the optimized Gurson material are shown in figureabove (Best Design Data)




Summary

In Crash simulation, numerical simulation of fracture andmaterial failure is important

Gurson Material model can define the material failure usingthe void growth and nucleation approach

Identification of the damage parameters of the GursonMaterial model through tests in expensive

Material identification task is completed automated usingoptiSLang

Sensitivity analysis is carried out to find out most influentialdesign parameters and also start design for optimization

All design parameters are considered for optimization

Evolutionary algorithm is used due to low simulation timefor each design

More research has to be done to understand the Gursonmodel behavior




Thank You

02 TATA Gurson

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