Mechanical-Nonlin 13.0 App6B Viscoplasticity

8/12/2019 Mechanical-Nonlin 13.0 App6B Viscoplasticity

1/13

Customer Training Material

Appendix 6B

Viscoplasticity with

ANANDs Model

Structural Nonlinearities

A6B-1ANSYS, Inc. Proprietary

2010 ANSYS, Inc. All rights reserved.Release 13.0

December 2010


2/13

ANSYS Mechanical Viscoplasticity with ANANDs Model

Customer Training MaterialChapter Overview

This appendix presents an optional lecture on the ANAND

material model.

ANAND is an advanced rate dependent metal plasticity model

useful for modeling highly nonlinear rate dependent metal plasticity.

The following topics will be covered:

A. Background on ViscoplasticityB. The ANAND Model

C. Defining the material input

. E. Reviewing viscoplastic results



December 2010


3/13


Customer Training MaterialA. Background on Viscoplasticity

In contrast to rate-independent plasticity discussed earlier, rate-

dependent plasticity is dependent on the strain rate or time.

, .

Usually, for engineering purposes, creep is used to describe the

evolution of strain under a constant load. Creep deformation usually is

important when the temperature is about 30-60% of the materials melting

temperature. Also, the time period tends to be much longer; the creep

and plastic strains are decoupled.

Viscoplasticity option involves high-strain rate (i.e., impact, hot metal

forming) loading situations. The inelastic strains are not decoupled as

.



December 2010


4/13


Customer Training Material... Background on Viscoplasticity

Comparison of Creep Models and ANAND Viscoplasticity Model

CREEP ANAND

Isotropic IsotropicYield Surface No explicitly defined yield surface No explicitly defined yield surface. However,

includes evolution equation.

Combination

with rate-

independentlasticit

Possible to combine with plasticity, which is

decoupled with creep strains

No additional rate-independent plasticity

allowed. Inelastic strains are coupled

BISO, MISO, and BKIN None

Strain Rates Suitable for small strain rates Suitable for small and large strain rates

Time scale Long periods, creep and plasticity have

different t ime scales

Short/medium periods

Temperature

Effects

Temperature effects included as part of

equation (or material constants can be

temperature-dependent)

Anand's equation considers temperature effects

directly. No need to input temperature-

dependent material constants



December 2010


5/13


Customer Training MaterialB. ANAND Model

The rate-dependent plasticity option proposed by Anand has the

following characteristics:

used (i.e., no Bauschinger effect), unlike rate-independent models.

Plastic flow is assumed to occur at all non-zero stress values, although,

a ow s resses, e p as c ow may e neg g e.

Anands model uses an internal scalar variable called the deformation

resistance (denoted by s) to represent the isotropic resistance to the

inelastic flow of the material. This is output as NL,PSV (plastic state

variable).

of the melting temperature.

Output of inelastic strains is plastic strain



December 2010


6/13


Customer Training Material... ANAND Model

Anands model was originally developed for high-temperature metal

forming processes such as rolling and deep drawing.

Anand, L., Constitutive Equations for Hot-Working of Metals,

International Journal of Plasticity, Vol. 1, pp. 213-231 (1985).

Brown, S. B., Kim, K. H., and Anand, L., An Internal Variable Constitutive

Model for Hot Working of Metals, International Journal of Plasticity, Vol.

5, pp. 95-130 (1989).

However, some companies have also used this constitutive model forother a lications such as anal ses of solder oints in electronics

packaging.

Darveaux, R., Solder Joint Fatigue Life Model, Proceedings of TMS

Annual Meeting, pp. 213-218 (1997).

Darveaux, R., Effect of Simulation Methodology on Solder Joint CrackGrowth Correlations, Proceedings of 50th Electronic Components &

Technology Conference, pp. 1048-1058 (2000).



December 2010


7/13



Anands model for viscoplasticity:

The flow equation can be written as:

1

m

RT

Q

insAe sinh

=

&

,

with Generalized Garofalo (hyperbolic sine) creep equation:

C

The main difference between the hyperbolic sine creep equation and Anands

( )[ ] 321 sinh CT

cr CeC

=&

model is the evolution equation [the deformation resistance (s)], explainednext

QCCCAC ==== 4321 ,

1,,



December 2010


8/13



The evolution equations (strain hardening/softening) are:

( )n

Q

in

a

o BBhs =

&

&&

RTin eA

sss

B

== 1 **

&

resistancendeformatio

stressCauchyeffective

=

=

=

s

in

resistancendeformatioofderivativetime

resistancendeformatioofvaluesaturation*

=

=

s

s

&



December 2010

reempera ua so u e=


9/13



Additional terms are defined as material constants:

Mat'l Parameter Description Units

Constant

1 so initial value of deformationresistance

stress(e.g., psi, MPa)

2 Q/R activation energy divided by

universal gas constant

energy/volume

(e.g., kJ/mole)

pre-exponen a ac or me

(e.g., 1/second)

4 mutiplier of stress dimensionless

5 m strain rate sensitivity of

stress

dimensionless

6 hardenin /softenin stress

constant (e.g., psi, MPa)

7 coefficient for saturation

value of deformation

resistance

stress

(e.g., psi, MPa)

8 n strain rate sensitivity of dimensionless

s

saturat on va ue

(deformation resistance)

9 a strain rate sensitivity of

hardening or softening

dimensionless,

a>1.0



December 2010

.


10/13


Customer Training MaterialC. Defining Material Input

As with other material models, ANANDs model can be inserting from

the Plasticity Folder of the Engineering Data Toolbox

No temperature-dependent constants are allowed since temperature

e ec s are nc u e n nan s equa on.

s



December 2010


11/13


Customer Training Material... Defining Material Input

Determination of the material parameters for Anands model is

performed by curve-fitting a series of isothermal stress-strain tensile

tests at different temperatures and strain rates.

A detailed discussion of the transformation of experimental data tomaterial constants can be found in the following references:

Anand, L., Constitutive Equations for Hot-Working of Metals,

International Journal of Plasticity, Vol. 1, pp. 213-231 (1985).

Model for Hot Working of Metals, International Journal of Plasticity, Vol.

5, pp. 95-130 (1989).



December 2010


12/13


Customer Training MaterialD. Analysis Settings for Viscoplasticity

The Analysis Settings will be similar for

most nonlinear problems

viscoplasticity problem, the solution can bestatic or transient. This would exclude or

nc u e ner a e ec s.

Ensure that the plastic strain increments

are small enough to capture the path

dependent response.

Large Deflection = ON is recommend

For large models with long run times andpotential convergence trouble, consider

setting up a Restart Control strategy in the



December 2010

event that adjustment to time step range or

convergence criteria is necessary


13/13


Customer Training MaterialE. Reviewing Viscoplastic Results

Results such as plastic strain and strain energy can be reviewed with

same procedure as used with metal plasticity.

-

plastic strain



December 2010

Mechanical-Nonlin 13.0 App6B Viscoplasticity

Documents

Transcript of Mechanical-Nonlin 13.0 App6B Viscoplasticity