lecture 6 material modelling€¢there are 3 material models in the non-linear elastic family: –...

© 2015 ANSYS, Inc. February 12, 2015 0 Release 15.0

15.0 Release

Lecture 6 Material Modelling

Workbench LS-DYNA

(ACT Extension) Training


Summary of material data

In general, materials have a complex response to dynamic loading and ANSYS Workbench LS-DYNA materials offer many features including:

– Strain rate dependent plasticity models with strain failure criterion

– Temperature dependent and temperature sensitive plasticity models

– Equations of state

– Failure

Engineering Data offers a selection of models from which you can choose based on the material(s) present in your simulation


Available Material Models

These materials are created from one or more of 9 GUI categories for convenience:

– Physical Properties

– Linear Elastic

– Hyperelastic

– Plasticity

– Thermal

– Equation of State

– Failure

– Forming Plasticity

– Foams


…Available Material Models


Linear Elastic Materials

• There are three different material models in the linear elastic family:

– Isotropic : Material properties are the same in all directions

– Orthotropic : Properties have 3 mutually orthogonal planes of symmetry

– Anisotropic : Properties independent of position at a point within material

• Linear elastic materials do not undergo plastic deformations and are fully defined by

the generalized Hooke’s law:

jijIc


Isotropic :

– Most engineering metals (e.g., steel) are isotropic

Orthotropic : – Orthotropic materials are defined with 9 independent constants – Transversely Isotropic (a special case of orthotropy) materials are defined with five

independent constants

– Orthotropic materials are defined with respect to a specified coordinate system ID, which is defined from Design Modeler

Anisotropic :

– Anisotropic materials defined with 21 independent constants

– Local coordinate system and data table can be used

... Linear Elastic Materials


• There are 3 material models in the non-linear elastic family: – Blatz-Ko : Compressible foam-type materials (e.g., polyurethane rubbers)

– Mooney-Rivlin, Yeoh, Polynomial : Incompressible rubber materials

• Non-linear elastic materials can undergo large recoverable elastic deformations. All hyperelastic material (Blatz-Ko and Mooney-Rivlin) strain is reversible, but the viscous portion of viscoelastic material strain is non-recoverable. The elastic strain portion is recoverable.

• Blatz-Ko Hyperelastic : – Blatz-Ko materials are only for rubber materials under compression

– Poisson’s ratio (NUXY) is automatically set to 0.463 by ANSYS LS-DYNA, so only DENS and GXY are required

– Material response is defined through the strain energy density function, W

Nonlinear Elastic Materials

. 32 invariants strain the areandwhere

52

23

3

2 II

IGxyW


... Nonlinear Elastic Materials

Mooney-Rivlin Hyperelastic : – Used to define the material response of incompressible rubbers

– Nearly identical to the ANSYS implicit 2-parameter model

– DENS, NUXY, and constants C10 and C01 are required for input

– To ensure incompressible behavior, NUXY must be between 0.49 and 0.50

Material response defined through the strain energy density function, W: where 1 , 2 , and 3 are the strain invariants and K is the bulk modulus.

23201110 15.3C3CW


Plasticity

• Plasticity models comprise the majority of the nonlinear inelastic materials available in ANSYS Workbench LS-DYNA. The selection of a specific plasticity model depends on the type of material being analyzed, the application, and the availability of material constants.

• The plasticity models can be separated into 4 main categories:

– Category 1: Strain rate independent plasticity for isotropic materials

– Category 2: Strain rate dependent plasticity for isotropic materials

– Category 3: Strain rate dependent plasticity for anisotropic materials

– Category 4: Temperature sensitive plasticity

• It is very important to select the correct category for the material being analyzed. It is less important to select the specific model within a category, which is usually controlled by the material data available.


... Plasticity

• The accuracy of most highly nonlinear finite element analyses hinges upon the quality of the material constants used. For best results, obtain constants from material suppliers or pay to have the material specially analyzed.

• Some of the plasticity models require the addition of an Equation of State (EOS). These equations will be discussed in detail after all of the plasticity models are presented.

• Some models span several categories, but are listed only once.


Rate Independent Isotropic Plasticity

• Category 1: Strain rate independent plasticity for isotropic materials

– 1a: Classical Bilinear Kinematic Hardening

– 1b: Classical Bilinear Isotropic Hardening

• These models are most typically used in processes where the overall forming duration is relatively long (e.g., sheet metal stamping), and apply to most engineering metals (steel, aluminum, cast iron, etc.).

• Both models use two slopes, the elastic modulus (EX) and the tangent modulus (ETAN), to represent the stress-strain behavior. The required input parameters for these 2 models are identical:

– Density, Young Modulus, and Poisson’s Coefficient

– Yield Stress and Tangent Modulus


... Rate Independent Isotropic Plasticity

• The hardening assumption is the only difference between the BKIN and BISO models.

– Kinematic Hardening assumes secondary yield to occur at 2y

– Isotropic Hardening assumes secondary yield to occur at 2max


Rate Dependent Isotropic Plasticity

• Category 2: Strain rate dependent plasticity for isotropic materials

– 2a: Plastic Kinematic: Cowper-Symonds model with failure strain

– 2b: Power Law: Cowper-Symonds with strength and hardening coeffs.

– 2c: Piecewise Linear: Cowper-Symonds with multilinear curve & failure strain

– 2d: Rate Sensitive: Ramburgh-Osgood model for superplastic forming

• Model 2a can be used for general metal and plastic forming analyses of isotropic materials

• Model 2a utilizes the Cowper-Symonds model, which scales the yield stress based on the strain rate factor :

P

1

C1

– where C and P are the Cowper-Symonds strain rate parameters.


... Rate Dependent Isotropic Plasticity

Plastic Kinematic :

• Bilinear hardening plasticity (y and ETAN)

• Hardening parameter between 0 (kinematic) and 1 (isotropic)

• The yield function is given by:

where 0 is the initial yield stress,

peff is the effective plastic strain,

Ep is the plastic hardening modulus which is given by:

effo

1

εEC

1 pP

P

y

tan

tan

PEE

EEE



Power Law : • Plastic behavior with bilinear isotropic hardening

• Power law hardening defined with strength coefficient k and hardening

coefficient n

• The yield function is given by:

npe

P

y

eff

1

εkC

1

where e is the elastic strain.

• As with the Plastic Kinematic model, strain rate effects are accounted for by the Cowper-Symonds strain rate parameters, C and P.



Piecewise Linear :

• Model is very efficient in solution and is most commonly used in crash simulations

• Similar to the TB, MISO model in ANSYS implicit

• Stress-strain behavior defined with load curve of effective true stress versus effective plastic true strain. Up to ten different curves can be entered to represent different strain rates.

• Yield surface can be scaled for strain rate dependence by the Cowper-Symonds model



nm

yk

Rate Sensitive :

This specialized model is used specifically for superplastic forming.

• Ramburgh-Osgood constitutive relationship for the yield stress:

where

k is the material coefficient,

m is the hardening coefficient,

n is the strain rate parameter,

and is the strain rate.


Rate Dependent Anisotropic Plasticity

• Category 3: Strain rate dependent plasticity for anisotropic materials

– 3a: Transversely Anisotropic: Hills yield criterion with strain rate dependence

– 3b: 3 Parameter Barlat: Orthotropic model for aluminum sheet metal forming

– 3c: Barlat Anisotropic: Anisotropic model for 3-D continuum forming

– 3d: Transversely Anisotropic Forming Limit Diagram Hardening

• Model 3a is for modeling high strain rate forming processes of general anisotropic materials

• Models 3b and 3c were developed at ALCOA for specialized aluminum processes

• Model 3d is used specifically for sheet metal forming


... Rate Dependent Anisotropic Plasticity

Transversely Anisotropic :

• Most commonly used for sheet metal forming of anisotropic materials

• Optional load curve parameter can be defined for the relationship between the effective yield stress and the effective plastic strain

• The yield function is defined by:

2

122211

2

22

2

11y1R

1R22

1R

R2

p

33

p

22εR

ε

• The anisotropic hardening parameter, R, is defined by the ratio of the in-plane plastic strain rate to the out-of-plane plastic strain rate:



3-Parameter Barlat :

• Developed for aluminum sheet metal forming under plane stress

• For the linear hardening rule, input y and ETAN

• For the exponential hardening rule, input n and m

• Recommended Barlat exponents:

– m=6 for BCC metals and m=8 for FCC metals

• Orthotropic Lankford coefficients used for length to thickness ratios

• Orthotropic material coordinate system



Barlat Anisotropic :

• Model useful for metal forming processes of 3-D continuum materials, especially aluminum

• Mostly used for solid materials (i.e., not sheet materials)

• 6 anisotropic parameters determined from experiments: a,b,c,f,g,h

• Recommended Barlat exponents: – m=6 for BCC metals and m=8 for FCC metals

• The yield strength is given by: y=k(o+ p)n

where o and p are initial yield and plastic strains



Transversely Anisotropic FLD :

• Model used for simulating sheet forming processes with transversely isotropic metals

• Available only for shell elements

• Yield behavior can be defined using y and ETAN or a load curve of the effective stress versus plastic strain

• Forming Limit Diagram can also be input using load curves to compute maximum strain ratio


Temperature Sensitive Plasticity

• Category 5: There is one plasticity model in ANSYS WORKBENCH LS-DYNA that account for temperature effects. this model also requires an additional Equation of State (EOS) to be defined with them:

– 5a: Johnson-Cook: High strain rate and temperature dependent problems


Johnson-Cook :

Johnson-Cook model used primarily for high strain rate processes such as machining where there are large temperature increases

Model originally developed for ballistics

DENS, EX, and NUXY required for input

The yield stress is defined by:

A, B, C, m, and n are experimentally determined constants and p is the effective plastic strain

The effective plastic strain rate is also required and is given by:

... Temperature Sensitive Plasticity

m_n

py T1lnC1BA

roommelt

room

TT

T-TT :is etemperatur homologous the and

o

p


• For temperature calculations, the specific heat, melt temperature, and room temperature are required

• A failure strain can be incorporated into the model by the implementation of the failure constants D1-D5 as described by:

where

• After the Johnson-Cook parameters are entered, the equation of state constants must be entered for either the linear polynomial or Gruneisen models (discussed later)

... Temperature Sensitive Plasticity

TD1lnD1expDD 54

D

21

f 3

stress. effective to pressure the of ratio effσ

Ρσ


Equations of State (EOS)

• There are 2 different EOS types in ANSYS WORKBENCH LS-DYNA:

– Linear Polynomial : EOS which is linear in internal energy

– Gruneisen : EOS which defines pressure volume relationship in 2 ways

Linear Polynomial :

• EOS which is linear in internal energy

• The pressure is defined in terms of and the linear coefficients Ci:

P = C0 + C1 + C2

2 + C3

3 + (C4 + C5

+C6

2) E

where = /0 – 1 and and 0 are the current and initial densities

Gruneisen :

• Pressure volume relationship is dependent on whether material is compressed or expanded. The Gruneisen EOS with cubic shock velocity-particle velocity defines pressure in terms of and the Gruneisen coefficients C, a, S1, S2, S3, and 0 for compressed materials as:

Ea

SSS

aC

p o

o

o

2

3

3

2

21

22

1111

2211


Foam Materials

• There is 1 foam model available in ANSYS Workbench LS-DYNA:

– Low Density Foam: highly compressible (e.g., padded seat cushions)

• The selection of a specific model depends on the type of material being analyzed

• All of the foam models in ANSYS LS-DYNA are primarily used in automotive impact applications


Low Density Foam :

– Used primarily for seat cushions in automobiles

– Both DENS and EX are required

– Stress-strain behavior input using a load curve ID (LCID)

– In compression, model assumes hysteretic behavior with possible energy dissipation

– In tension, model behaves linearly until tension cut-off stress is attained

– NUXY approximately set to zero

– When hysteretic unloading is used, the reloading will follow the unloading curve if the decay constant, = 0.

– If is nonzero, the original loading is governed by 1- e-t A viscous coefficient (0.05-0.5) can be used to model damping effects.

– Bulk viscosity can be activated by setting the flag to 1

– A shape unloading factor is used for hysteretic unloading. Values less than one reduce energy dissipation.

– A hysteretic unloading (HU) factor between 0 and 1 is input. If HU=1, there is no energy dissipation.

... Foam Materials


Discrete Element Properties

• Discrete elements require spring or damper properties

– Springs need a stiffness constant or force versus deflection curve

– Dampers need a damping constant or force vs. deflection rate curve

– Rotational properties may be used instead of translational ones

• Discrete spring properties:

– Linear Elastic Spring

– Linear Elastic Discrete Beam

• Discrete damper property:

– Linear Viscosity Damper


…Discrete Element Properties

Linear Elastic Spring

This provides a translational or rotational elastic spring located between two nodes. Only one degree of freedom is connected

Linear Elastic Discrete Beam

This material model is defined for simulating the effects of a linear elastic beam by using six springs each acting about one of the six local degrees-of-freedom. The two nodes defining a beam may be coincident to give a zero length beam, or offset to give a finite length beam. The distance between the nodes of a beam should not affect the behavior of this model. A triad is used to orient the beam for the directional springs. Translational/rotational stiffness and viscous damping effects are considered for a local Cartesian system. Applications for this element include the modeling of joint stiffness.


Cable Element Properties

• Elements in compression (slack cable) carry no load

• The density (DENS) and elastic modulus (EX) need to be defined

• The cable stiffness is defined as:

K = (E) (Area0) / (L0 – Offset)


LS-DYNA has the capability to have elements fail.

• By default, failed elements are removed from subsequent calculations

• This is often called element erosion

• Stress and stiffness is set to zero in these elements

• Some material models allow the material to remain in the solution with zero shear stiffness. In some of these models, the failed material will maintain hydrostatic stiffness (the material acts like a fluid or powder).

Failure occurs in one of two ways:

• Material allowable exceeded

• The time step drops below a minimum time step

– Must add the following to the LS-DYNA input file:

• Set ERODE=1 on *CONTROL_TIMESTEP and define DTMIN on *CONTROL_TERMINATION

Failure


Material failure options are also included in some material models

• Example: Modified Cowper-Symonds Piecewise Linear Plasticity

Failure modeling is very challenging

• Failure criteria should be calibrated to test data.

• Failure stress could be affected by element size

Failure


Plastic Strain Failure

• Models ductile failure

• Failure occurs if the Effective Plastic Strain in the material exceeds the Maximum Equivalent Plastic Strain

– Material fails instantaneously

• This failure model must be used in conjunction with a plasticity model

Failure


Johnson Cook Failure

• Used to model ductile failure of materials experiencing large pressures, strain rates and temperatures.

• Consists of three independent terms that define the dynamic fracture strain (εf) as a function of pressure, strain rate and temperature:

• Can only be applied to solid bodies.

Failure


General Material Guidelines

1. Not all material models are available for every element type.

2. Some models require specifying an Equation of State to complete the material definition.

3. For each material model, not all constants and options are required input. For example, a strain rate dependent plasticity material with Cowper-Symonds constants can be used as a rate independent model by setting these to constants to zero. This might be done to access an allowable failure strain

4. Make sure to use consistent units when defining your material properties. Incorrect units will not only effect the material response, but will also effect the contact stiffness. An error in units can even prevent a model from running.

5. Don’t underestimate the importance of accurate material data. Spend the extra time and money to obtain accurate data.

lecture 6 material modelling€¢there are 3 material models in the non-linear elastic family: –...

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