ANSYS AUTODYN- Chapter 9: Material Models
Transcript of ANSYS AUTODYN- Chapter 9: Material Models
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Chapter 9
Material Models
ANSYS AUTODYN
Material Models
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Training ManualMaterial Models in Explicit Dynamics (ANSYS)
Failure Model
Strength Model
Equation of State
AUTODYN
Material Models
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Training ManualAUTODYN Material Models• An AUTODYN material model consists of 3 components
– Equation of State (EOS)
– Strength Model
– Failure ModelEOS Strength Failure
Models Also Available in Explicit Dynamics (ANSYS)
Material Models
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Training ManualAUTODYN Additional Material Models
• Ideal Gas Equation of State
• Two Phase Equation of State
• SESAME Tables
• Cumulative Damage Model
• Beam Resistance Model
• Fragment Analyzer
• Rigid Materials (specification is different in AUTODYN)
• Orthotropic Materials
– Orthotropic Solids
– Composite Shells
• High Explosives (HE)
– Detonation – Expansion of detonation
products (gases)– After-burn– Ignition and Growth
• Slow-burning Explosives
• User Material Models
Material Models
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• Energy dependant EOS
γ = ideal gas constant, Gammaρ = density,
e = specific internal energy
• Adiabatic Constant, C– Enter non-zero value to calculate adiabatic
response
P/ργ = C• Pressure shift
– Lets you subtract atmospheric pressure
( ) e1P +ρ−γ=
Ideal Gas Equation of State
Material Models
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• Used to model the expansion and vaporization of superheated liquids– e.g. a reactor coolant
• Used together with a compression EOS
• A Gruneisen EOS is used for the single phase region– Saturation curve is the reference curve
• The saturation curve for the material is defined in user subroutine EXTAB– The saturation curve for water is provided with AUTODYN
Two Phase Equation of State
Specific Volume
Single phaseLiquid region
Two phaseLiquid and Vapour region
Single phaseVapour region
Pressure
Material Models
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Training ManualSesame Library• The Sesame library is not an EOS but a table
format for storing state data
– Contains data for over 200 materials including metals, minerals, polymers and mixtures
– Most of the tables have data for very wide ranges of density and internal energy, but were developed for particular applications where a particular range was required
– Use with caution
• The Sesame Library is US export-controlled
– Not included in standard distribution
– Library can be obtained from ANSYS if required permissions are provided
– Can also be obtained directly from LANL
Material Models
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• Allows progressive degradation of the strength of a material•
• Early model developed to represent brittle materials under crushing
– Predates the Johnson-Holmquist Model
• First developed using User Subroutines
– Good example of the effective combination of multiple user subroutines
Cumulative Damage Failure Model
Material Models
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• Strength data for the beam-resistance model is defined using four 10 point piecewise linear curves
– Axial Force vs. Axial Strain along axis 11– Moment vs. Curvature about axis 11– Moment vs. Curvature about axis 22– Moment vs. Curvature about axis 33
• Load-deflection data from experiments on reinforced concrete beams fed directly into beam resistance model to obtain realistic structural response
• There is no inter-dependence between the four piecewise curves defining the axial, torsional and bending response of the elements
Beam Resistance Model
Material Models
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Courtesy of AWE (A), UK
Beam Resistance Model
• Example: 1/3 Scale Pullover Tests
– Experiment
• Failure Load: 86kN ± 4KN
– Simulation
• Failure Load: 83kN ± 5KN
Material Models
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Courtesy Sandia National Lab.
• View and Tabulate the fragments formed during an analysis• Example: Out-of-barrel Bullet Deflagration
Fragment Analyzer
Material Models
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• Select “EOS Rigid” in the standard material input
• Fill any Unstructured Part with a rigid material
– Not available for Structured Parts
• Elements filled with a Rigid material will act as a single rigid body with mass / inertia
• Mass / inertia is defined by
– Material density and volume of filled elements
– Explicitly in the material definition
• You can use more that one Rigid material to define multiple rigid bodies
Rigid Materials
Material Models
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Deformable Projectile Rigid Projectile
• Example: 3D Oblique Impact
Rigid Materials
Material Models
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• Example: Sheet Metal Forming– Rigid Punch and Die
– Unstructured Shell (Quad dominant) Work Piece
Punch
Work Piece
Die
Rigid Materials
Material Models
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• AUTODYN has extensive capabilities for modeling orthotropic materials under a wide range of loading conditions
– Orthotropic linear-elastic response (structural loading)• Orthotropic elastic stiffness matrix
– Linear volumetric response
– Orthotropic elastic response coupled with a non-linear equation of state (transient shock loading)
• Modified orthotropic elastic stiffness matrix– Non-linear volumetric response
– Orthotropic plasticity• Generalized quadratic plasticity surface
– Orthotropic failure• Damage model
• Brittle Failure
Orthotropic Materials
Material Models
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Orthotropic EOS
Orthotropic Softening
Orthotropic Yield
Orthotropic Materials• Use Orthotropic EOS, Yield and Softening models to obtain fully response
Material Models
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12
3
Represented by a continuum with equivalent orthotropic material
properties - individual layers not represented explicitly
Laminated Composite
• Orthotropic materials are represented using solid continuum elements
Orthotropic Materials
OR
Material Models
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S = C-1 =C =
Orthotropic Materials
• Orthotropic Linear-elastic Response
– Linear Equation of State implicitly assumed for the volumetric response
Material Models
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Training ManualOrthotropic Materials• Orthotropic elastic response coupled with a non-
linear equation of state
– Polynomial– Shock– Porous
Material Models
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– Shape of the surface defined by coefficients, aij
– Hardening defined by the parameter, k
– General form reduces to
• Hills orthotropic yield function
• Von-mises yield function
kaa
aaa
aaaaf ij
=+
+++
++++=
21266
23155
22344331113332223
22111223333
22222
21111
22222
2)(
σσ
σσσσσ
σσσσσσ
Orthotropic Materials
• Orthotropic Plasticity
– Uses Generalized quadratic plasticity surface
Material Models
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• Orthotropic Failure : Brittle Failure
– Three orthotropic brittle failure initiation models are available
• Material Stress
• Material Strain
• Material Stress / Strain
– These allow different tensile and shear failure stresses and/or strains to be specified for each of the principal material directions
Orthotropic Materials
Material Models
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• OrthotropicFailure : Damage Model
– The failure initiation criteria (surfaces) for this model are
Material Models
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Training ManualOrthotropic Materials• OrthotropicFailure : Damage Model
– Once failure is initiated, a damage tensor is computed and used to soften the failure surfaces
Material Models
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• Static Tensile Test results for KEVLAR®-epoxy
Orthotropic Materials
Material Models
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• Example: Impact of a fragment onto a GFRP target
Orthotropic Materials
Material Models
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• Layered Composite Shells– Intended for thin composite structures
under structural (rather than shock) type loading
– Layered composite shells are defined during the “Fill” of the shell part
• Select the Composite button
• Lay-up’s are applied to the mesh along with the normal initial conditions
– Any number of lay-up’s can be defined, stored and selected
• Each layer can be an isotropic or orthotropic material
– For orthotropic materials, you must specify the 11 direction
• Each layer is assigned a thickness
• Each layer can be viewed independently
Orthotropic Materials
Material Models
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• Layered Composite Shells– Material models
• Models compatible with standard shells can be applied to individual layers of composite shell elements
• Orthotropic material models can also be used– Material directions need to be define
• Tsai-Wu, Hoffman and Tsai-Hill failure criteria can be applied– Including both compressive and tensile failure strengths– Bulk failure only
– Material Directions• 11 and 22 always in plane of shell
• 33 always through thickness
• Material Axes Options– I-J-K (recommended)
• Default 11 : direction of increasing K lines• Set θ to rotate 11 about centre of element• 22 always perpendicular to 11 in plane of element
– X-Y-Z
Orthotropic Materials
Material Models
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• Example: Bird Strike on Aircraft Wing (Composite Shell used for wing)
Orthotropic Materials
Material Models
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• Detonation process
– Burn on time
• Initiation points / planes
– Burn on compression
• Not recommended
– Insufficient physics
– Use ignition and growth model instead
• Expansion of detonation products (gases)
– JWL Equation of State (Jones, Wilkins, Lee)
High Explosives
Material Models
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Detonation Fronts
Initiation Node
Cell
T1
T2
S1
S2
T1 = S1 / DT2 = S2 / D
• Burn on Time– Detonation is initiated at a node or plane
(user defined)
– Detonation front propagates at the Detonation Velocity, D
– Cell begins to burn at time T1
– Burning is complete at time T2
– Chemical energy is released linearly from T1to T2
• Burn fraction increases from 0.0 to 1.0 over this time
– Element Variable alpha–
= -T1, T<T1
= Burn fraction, T>T1
High Explosives – Detonation Process
Material Models
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• Burn on Time
– Direct Path detonation
• Detonation paths are computed by calculating a straight line from the detonation node to each cell center (not necessarily through explosive regions)
– Indirect Path detonation
• Detonation paths are computed by finding either a direct path through explosive regions or by following straight line segments connecting centres of cells containing explosives
High Explosives – Detonation Process
Good use of direct path detonation
Bad use of direct path detonation
Material Models
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Training ManualHigh Explosives – Detonation Process• Burn On Time
– Indirect path with multiple initiation points
• Detonation in the shadow zone is calculated accurately only if point #2 is defined
Material Models
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Direct Path
Indirect Path 1 det. point
Indirect Path 2 det. points
Indirect Path 3 det. points
High Explosives – Detonation Paths
Material Models
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• JWL EOS
– Used to model the rapid expansion of high explosive detonation products (gases)
– The JWL EOS is empirical and the data required is derived from fitting numerical experiments to physical experiments
– Data for a wide range of high explosives is available
– The pressure for the expanding gas is given by
– where A, B, R1, R2, ω are empirically derived constants and ρ = density, ρ0 = reference density, η = ρ / ρ0, e = specific internal energy
eeR
1BeR
1AP21 R
2
R
1
ωρ+⎟⎟⎠
⎞⎜⎜⎝
⎛ ωη−+⎟⎟
⎠
⎞⎜⎜⎝
⎛ ωη−= η
−η
−
log p
High Explosives – Expansion of Detonation Products
log v
Material Models
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Training ManualHigh Explosives – Expansion of Detonation Products
• JWL EOS
– Input parameters include
• EOS parameters
• Detonation Velocity
• Chemical Energy / unit volume
– Data for most High Explosives are included in the standard material library distributed with AUTODYN
– Burn on compression fraction and Pre-burn bulk modulus
• Not recommended, leave zero
– Auto-convert to Ideal Gas
• Recommended for accuracy
Material Models
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nm Padtd )1( λλ
−=
whereQ = additional specific energy,a = energy release constant,m = energy release exponent,n = pressure exponent
High Explosives – Expansion of Detonation Products
VQEe
VRBe
VRAP VRVR )()1()1( 21
21
λωωω ++−+−= −−
• JWL EOS – Miller Extension
– Non-ideal explosives, containing Aluminum (Al) or Ammonium Perchlorate (AP) can release substantial amount of energy from burning Al and AP particles after detonation
– Miller extension models this energy release
Material Models
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Training ManualHigh Explosives – Expansion of Detonation Products
• JWL EOS - Energy release extension
– Thermobaric explosives produce more explosive energy than conventional explosives
• Typically achieved by inclusion of Aluminum
• Undergoes combustion with atmospheric oxygen after detonation (after-burning)
– Additional Energy option in JWL EOS lets you model this time-dependent energy release
• Energy deposition over specific time interval
Material Models
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0
2000
4000
6000
8000
10000
12000
14000
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Time (ms)
Pres
sure
(KPa
) TNT + additional Energy
TNT
0
100
200
300
400
500
600
700
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Time (ms)
Impu
lse
(Pa
S)
TNT + additional energy
TNT
High Explosives – Expansion of Detonation Products
• JWL EOS - Energy release extension
– Effect of adding 2.15MJ/kg between 0.12 and 0.55 msec. to a spherical charge of 10kg TNT
– Longer pulse duration and increased impulse
Material Models
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• Lee-Tarver Ignition & Growth Model
– Equation of State used for High Explosive (HE) initiation studies
– Assumes ignition starts at local hot spots and grows outward from these sites
– Consists of three basic parts:
• An equation of state for the inert explosive (a choice between a Shock form or a JWL form)
• JWL equation of state for the reacted detonation products
• Reaction rate equation to describe, ignition, growth and completion of burning
High Explosives
Material Models
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0.5 km/s 0.7 km/s 1.0 km/s
High Explosives• Lee-Tarver Ignition & Growth Model
– Example: Sympathetic Detonation
Material Models
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• Powder Burning Model– Simulates combustion of materials where
dominant physical characteristic is deflagration (incendiary devices, munitions)
– Two phase model
• Gas and solid present in a cell at the same time
• Solid Phase: Linear/Compaction EOS
• Gas Phase: JWL/Exponential
– Burn velocity, c, dependant on gas pressure, Pg
– Burn rate dependent on gas pressure , Pg and burn fraction, F
– Formulation: A Atwood, EK Friis and JF Moxnes, A Mathematical Model for Combustion of Energetic Powder Materials, 34th International Annual Conference of ICT, June 24-27, 2003, Karlsruhe Federal Republic of Germany
Slow-burning Explosives
GasSolid Particles
Numerical Cell of Volume V
Material Models
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Training ManualSlow-burning Explosives• Powder Burn Model Model
– Example: Sabot and projectile inside gun chamber
Material Models
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• A collection of published material models and data is supplied with AUTODYN
• Accessed through ‘Material’, ‘Load’
• Materials can be sorted by Name, EOS, Strength or failure model
• All materials have an EOS defined, most a strength model and only a few have a failure model defined
• You can add to or modify data in the supplied library or create new libraries
• Data is converted into current units when it is retrieved
Material Libraries
Material Models
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Training ManualWhat Material Models to use?• How do we choose a set of material modelling options for a particular
material ?
– In terms of material itself, it is relatively easy to identify the basic category that a material lies in
• Liquid or Solid?• Isotropic or Anisotropic/Orthotropic ?• Inert or Reactive?• Porous or Not ?• Ductile or Brittle ?• Pressure Dependant Strength (cohesive) or not ?
– The actual set of models used however are highly dependant on the application and the available material data
– Start with simple models and progress, as required, to more complex models
• Lets you understand how parameters influence response and which parameters are critical for good results
Material Models
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Erosion criteriaMDERO_USER_1
Failure criteriaMDFAI_USER_1
Strength (Yield and/or Shear) ModelMDSTR_USER_1
Equation of stateMDEOS_USER_1
• Modularized Material Modeling Routines let you:
– Build an input GUI
– Check the consistency of input parameters
– Map input parameters to solver parameters
– Write the solver equations
• Written in Fortran 90
User Subroutines for Material Modeling
Material Models
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• Example Layout : Strength Model– Module STR_USER_1
• Declare scalar and array variables used in the model here
– INIT_STR_USER_1• Define input parameters and create a menu to
read them in
– SET_STR_USER_1• Copy input parameters to solver scalar/array
variables
– CHECK_STR_USER_1• Check that input parameters are valid
– SOLVE_STR_USER_1• Strength model solver
Material Models
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Training ManualGlobal and Material Erosion• Erosion is a numerical mechanism for the
automatic removal (deletion) of elements during a simulation.
– Removes very distorted elements before they become inverted (degenerate).
– Ensures time step remains reasonably large.– Ensures solutions can continue to the End Time. – Can be used to allow simulation of material fracture, cutting
and penetration
• In Explicit Dynamics (ANSYS), an erosion model can be specified globally
– Covered in the Explicit Dynamics training course
• In AUTODYN, an Erosion model can be specified for each material
– Erosion is not a physical effect (or material property). It is amechanism to combat mesh distortion
• There are five options available to initiate erosion of elements in AUTODYN
– Geometric Strain– Plastic Strain– Timestep– Failure– User Erosion
• Program user subroutine EXEROD