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CAE Capabilities – Passenger Car
Full Frontal Offset Frontal Seat Belt Anchorage Pedestrian leg forms
Side door intrusion Roof crush Side pole crash Pedestrian head forms
Side impact Rear impact Occupant Restraints
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)
2 Copyright Tata Motors Ltd.
Contents
1. Important Material Property Aspects for Crash Simulation
2. Current Material Modeling Process
3. Need of Damage Modeling
4. Gurson Model
3 Copyright Tata Motors Ltd.
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
5 Copyright Tata Motors Ltd.
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.
6 Copyright Tata Motors Ltd.
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.
7 Copyright Tata Motors Ltd.
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.
8 Copyright Tata Motors Ltd.
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 ms t=40 ms
Need of Damage Modeling
9 Copyright Tata Motors Ltd.
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.
10 Copyright Tata Motors Ltd.
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
11 Copyright Tata Motors Ltd.
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
12 Copyright Tata Motors Ltd.
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 fc = critical void fraction
ff = void volume fraction at fracture
13 Copyright Tata Motors Ltd.
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
14 Copyright Tata Motors Ltd.
Gurson Model – contd.
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
15 Copyright Tata Motors Ltd.
Gurson Model – contd.
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 Damage Parameters 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 crash simulation?
- Safety
Why simulating? - Compression of development cycles
- Cost reduction
Why optiSLang? - Unknown sensitivities
- Many parameters
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
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
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
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
New
Para
mete
r set
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
Uniaxial Tensile Test & Simulation Model
Tensile test is carried with one end fixed and constant rate of motion on the other end
Force and displacement are measured
Engineering stress-strain curves is plotted based on the measurements
FE model is developed based on test specifications
Stress-strain curve FE Model
Uniaxial Tensile Test
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
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 a complicated condition of biaxial stress
• After necking, weighted average method is used.
Where w = is the weight constant
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
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.
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
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
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
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 the stress-strain curve
– Area Under Plastic Region
– Maximum stress
– Failure Strain
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
Basic Criteria
1. Difference of area under plastic region between Test and Simulation Target: 0
2. Difference of maximum stress between Test and Simulation Target: 0
3. Difference of failure strain between Test and Simulation Target: 0
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
Sensitivity Analysis
Sensitivity analysis is used to scan the design space by varying design optimization parameters within upper and lower bounds
Global Sensitivity of responses with respect to design variables variation
Identification of important input parameters and possible reduction of the design space dimension for optimization
Understanding and verification of the optimization problem
Choosing a start design for optimization
Proof of numerical robustness
Preparation of the optimization problem and reduction of the problem dimension
Latin Hypercube Sampling
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
Sensitivity Analysis
• EN, FN, SN and FF0 have major influence on maximum stress value of the curve
• EN, FF0 and FN have major influence on the failure strain and area under plasticity region.
• All design parameters are considered for optimization
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
Optimization - Evolutionary Algorithm
Evolutionary algorithm is used. Its a metaheuristic algorithm. This algorithm is selected due to the low computation time of each design in this project
Evolutionary algorithm usually features
- Robust
- Can handle any complexity
- Takes time to converge
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
Optimization - Evolutionary Algorithm
Objective History Best Design Data Output Data of Best Design
Damage parameters of the optimized Gurson material are shown in figure above (Best Design Data)
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
Summary
In Crash simulation, numerical simulation of fracture and material failure is important
Gurson Material model can define the material failure using the void growth and nucleation approach
Identification of the damage parameters of the Gurson Material model through tests in expensive
Material identification task is completed automated using optiSLang
Sensitivity analysis is carried out to find out most influential design parameters and also start design for optimization
All design parameters are considered for optimization
Evolutionary algorithm is used due to low simulation time for each design
More research has to be done to understand the Gurson model behavior
2nd Optimization & Stochastic Days 2012: Dec 3-4, Pune
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