ANSYS AUTODYN- Chapter 9: Material Models

Chapter 9 Material Models

ANSYS AUTODYN

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February 27, 2009 Inventory #002665

Material Models

Material Models in Explicit Dynamics (ANSYS)

Training Manual

AUTODYN Equation of State Strength Model Failure Model

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February 27, 2009 Inventory #002665

Material Models

AUTODYN Material Models

Training Manual

• An AUTODYN material model consists of 3 components – Equation of State (EOS) – Strength Model – Failure Model

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Models Also Available in Explicit Dynamics (ANSYS)

EOS

Strength

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Failure

February 27, 2009 Inventory #002665

Material Models

AUTODYN Additional Material Models

Training Manual

• Orthotropic Materials

• Ideal Gas Equation of State

– Orthotropic Solids

• Two Phase Equation of State

– Composite Shells

• SESAME Tables

• High Explosives (HE)

• Cumulative Damage Model

– Detonation – Expansion of detonation products (gases) – After-burn – Ignition and Growth

• Beam Resistance Model • Fragment Analyzer • Rigid Materials (specification is different in AUTODYN)

• Slow-burning Explosives • User Material Models

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February 27, 2009 Inventory #002665

Material Models

Ideal Gas Equation of State

Training Manual

• Energy dependant EOS

P = (γ −1)ρe + γ = ideal gas constant, Gamma ρ = 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 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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February 27, 2009 Inventory #002665

Material Models

Two Phase Equation of State

Training Manual

• 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 Pressure

Single phase Vapour region

Single phase Liquid region Two phase Liquid and Vapour region Specific Volume ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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February 27, 2009 Inventory #002665

Material Models

Sesame Library

Training Manual

• 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 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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Material Models

Cumulative Damage Failure Model

Training Manual

• 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

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February 27, 2009 Inventory #002665

Material Models

Beam Resistance Model

Training Manual

• Strength data for the beam-resistance model is defined using four 10 point piecewise linear curves – – – –

Axial Force Moment Moment Moment

vs. vs. vs. vs.

Axial Strain along axis 11 Curvature about axis 11 Curvature about axis 22 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 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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February 27, 2009 Inventory #002665

Material Models

Beam Resistance Model

Training Manual

• Example: 1/3 Scale Pullover Tests – Experiment • Failure Load: 86kN ± 4KN

– Simulation • Failure Load: 83kN ± 5KN

Courtesy of AWE (A), UK ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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February 27, 2009 Inventory #002665

Material Models

Fragment Analyzer

Training Manual

• View and Tabulate the fragments formed during an analysis • Example: Out-of-barrel Bullet Deflagration

Courtesy Sandia National Lab.

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February 27, 2009 Inventory #002665

Material Models

Rigid Materials

Training Manual

• 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 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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February 27, 2009 Inventory #002665

Material Models

Rigid Materials

Training Manual

• Example: 3D Oblique Impact

Deformable Projectile

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Rigid Projectile

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Material Models

Rigid Materials

Training Manual

• Example: Sheet Metal Forming – Rigid Punch and Die – Unstructured Shell (Quad dominant) Work Piece

Punch Work Piece

Die ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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Material Models

Orthotropic Materials

Training Manual

• 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 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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February 27, 2009 Inventory #002665

Material Models

Orthotropic Materials

Training Manual

• Use Orthotropic EOS, Yield and Softening models to obtain fully response Orthotropic EOS Orthotropic Yield Orthotropic Softening

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February 27, 2009 Inventory #002665

Material Models

Orthotropic Materials

Training Manual

• Orthotropic materials are represented using solid continuum elements

OR

Laminated Composite

2

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Represented by a continuum with equivalent orthotropic material properties - individual layers not represented explicitly

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Material Models

Orthotropic Materials

Training Manual

• Orthotropic Linear-elastic Response – Linear Equation of State implicitly assumed for the volumetric response

C

=

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S = C-1 =

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Material Models

Orthotropic Materials

Training Manual

• Orthotropic elastic response coupled with a nonlinear equation of state – Polynomial – Shock – Porous

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Material Models

Orthotropic Materials

Training Manual

• Orthotropic Plasticity – Uses Generalized quadratic plasticity surface 2 2 2 f (σ ij ) = a11σ 11 + a22σ 22 + a33σ 33 + 2a12σ 11σ 22 + 2 2a23σ 22σ 33 + 2a13σ 11σ 33 + 2a44σ 23 + 2 2 2a55σ 31 + 2a66σ 12 =k

– 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

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February 27, 2009 Inventory #002665

Material Models

Orthotropic Materials

Training Manual

• 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

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February 27, 2009 Inventory #002665

Material Models

Orthotropic Materials

Training Manual

• OrthotropicFailure : Damage Model – The failure initiation criteria (surfaces) for this model are

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February 27, 2009 Inventory #002665

Material Models

Orthotropic Materials

Training Manual

• OrthotropicFailure : Damage Model – Once failure is initiated, a damage tensor is computed and used to soften the failure surfaces

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February 27, 2009 Inventory #002665

Material Models

Orthotropic Materials

Training Manual

• Static Tensile Test results for KEVLAR®-epoxy

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February 27, 2009 Inventory #002665

Material Models

Orthotropic Materials

Training Manual

• Example: Impact of a fragment onto a GFRP target

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February 27, 2009 Inventory #002665

Material Models

Orthotropic Materials

Training Manual

• 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 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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February 27, 2009 Inventory #002665

Material Models

Orthotropic Materials

Training Manual

• 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 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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February 27, 2009 Inventory #002665

Material Models

Orthotropic Materials

Training Manual

• Example: Bird Strike on Aircraft Wing (Composite Shell used for wing)

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February 27, 2009 Inventory #002665

Material Models

High Explosives

Training Manual

• 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)

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February 27, 2009 Inventory #002665

Material Models

High Explosives – Detonation Process

Training Manual

• Burn on Time – Detonation is initiated at a node or plane (user defined) – Detonation front propagates at the Detonation Velocity, D

Detonation Fronts T1

– Cell begins to burn at time T1

T2 Cell

– Burning is complete at time T2 – Chemical energy is released linearly from T1 to T2 • Burn fraction increases from 0.0 to 1.0 over this time

S1 S2 Initiation Node

– Element Variable alpha –

T1 = S1 / D

= -T1, TT1 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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February 27, 2009 Inventory #002665

Material Models

High Explosives – Detonation Process

Training Manual

• 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 Good use of direct path detonation

Bad use of direct path detonation ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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Material Models

High Explosives – Detonation Process

Training Manual

• Burn On Time – Indirect path with multiple initiation points • Detonation in the shadow zone is calculated accurately only if point #2 is defined

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February 27, 2009 Inventory #002665

Material Models

High Explosives – Detonation Paths

Training Manual

Direct Path

Indirect Path 1 det. point

Indirect Path 2 det. points

Indirect Path 3 det. points

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Material Models

High Explosives – Expansion of Detonation Products

Training Manual

• 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

log p

– Data for a wide range of high explosives is available – The pressure for the expanding gas is given by

⎛ ωη ⎞ ⎟⎟e P = A ⎜⎜1 − R1 ⎠ ⎝

−

R1 η

⎛ ωη ⎞ ⎟⎟e + B⎜⎜1 − ⎝ R2 ⎠

−

R2 η

log v

+ ωρ e

– where A, B, R1, R2, ω are empirically derived constants and ρ = density, ρ0 = reference density, η = ρ / ρ0, e = specific internal energy ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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Material Models

High Explosives – Expansion of Detonation Products

Training Manual

• 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 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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Material Models

High Explosives – Expansion of Detonation Products

Training Manual

• 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

P = A(1 −

ω R1V

)e−R1V + B(1 −

ω R2V

)e−R2V +

ω( E + λQ) V

dλ = a(1 − λ )m Pn dt where Q= a = m= n = ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

additional specific energy, energy release constant, energy release exponent, pressure exponent 9-36

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Material Models

High Explosives – Expansion of Detonation Products

Training Manual

• 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

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Material Models

High Explosives – Expansion of Detonation Products

Training Manual

• 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

14000

700

12000

600

10000

500

TNT + additional Energy TNT

Impulse (Pa S)

Pressure (KPa)

– Longer pulse duration and increased impulse

8000 6000 4000

400 300 200

TNT + additional energy TNT

2000

100

0

0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Time (ms) ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Time (ms)

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Material Models

High Explosives

Training Manual

• 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

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Material Models

High Explosives

Training Manual

• Lee-Tarver Ignition & Growth Model – Example: Sympathetic Detonation

0.5 km/s ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

0.7 km/s 9-40

1.0 km/s February 27, 2009 Inventory #002665

Material Models

Slow-burning Explosives

Training Manual

• Powder Burning Model – Simulates combustion of materials where dominant physical characteristic is deflagration (incendiary devices, munitions)

Numerical Cell of Volume V

– 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

Solid Particles

Gas

– 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 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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Material Models

Slow-burning Explosives

Training Manual

• Powder Burn Model Model – Example: Sabot and projectile inside gun chamber

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Material Models

Material Libraries

Training Manual

• 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

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Material Models

What Material Models to use?

Training Manual

• 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 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.

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Material Models

User Subroutines for Material Modeling •

Training Manual

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

MDEOS_USER_1

Equation of state

MDSTR_USER_1

Strength (Yield and/or Shear) Model

MDFAI_USER_1

Failure criteria

MDERO_USER_1

Erosion criteria

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February 27, 2009 Inventory #002665

Material Models Training Manual

• 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

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Material Models

Global and Material Erosion

Training Manual

• 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 a mechanism 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

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