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Customer Training Material
Appendix 6B
Viscoplasticity with
ANANDs Model
Structural Nonlinearities
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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
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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
.
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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
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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
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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).
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Customer Training Material... ANAND Model
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,,
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Customer Training Material... ANAND Model
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
&
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reempera ua so u e=
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Customer Training Material... ANAND Model
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
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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
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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).
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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
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event that adjustment to time step range or
convergence criteria is necessary
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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
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