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A parallel macro/micro elastoplasticity model for aluminum deformation and comparison with experiments

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Abstract

A finite-element-based macro/micro crystal plasticity model is presented for large deformation of metals. The model development is based on the updated Lagrangian approach for large plastic deformation, coupled with a micromechanical description of multisurface plastic flows associated with individual single crystals. The macroscopic Lagrangian description of deformation processes uses either the hypoelastoplasticity formulation, with the incremental objective stress-time integration scheme, or the hyperelastoplasticity formulation, with the total formulation based on multiplicative decomposition. The macroscopic stress is linked to the microstructural behavior of crystals by tracking the motion of each active dislocation in slip systems underlining the plastic deformation. The microscopic treatment entails a multisurface-type stress-update algorithm, which ensures the plastic deformation defined by each slip system to be on the local yield surface. During each increment, the number of slip systems active during deformation is determined by either the single-value decomposition (SVD) technique or the diagonal-shift method. Simulations using these types of microscale models can be computationally intensive, especially when a large number of crystals are applied. For these cases, a parallel computing algorithm can be particularly efficient, and numerical tests show that, for these cases, which often are used in simulations for more realistic deformation processes, the computational time approaches asymptotically the theoretical limit of the parallel processing. The parallel macro/micro model is checked with various benchmark deformation and micromechanical testing problems reported in literature. Numerical simulations are carried out and results are compared with measurements of individual crystallite orientations made intermittently during the deformation of a low-angle bicrystal and a two-dimensional columnar-grained, multicrystal aluminum sample in channel-die compression. Texture development in a copper sample being flat-rolled under commercial operating conditions is also predicted using the micro/macro model and is compared with the measured data. For all these cases, the macro/micro model predictions are in reasonably good agreement with experimental measurements.

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Abbreviations

B :

finite element matrix

b :

body force

Ĉ :

right Cauchy-Green Tensor

C :

constitutive matrix

D ij :

ij component of strain rate tensor

D αβ :

α, β the component of matrix D

F :

deformation gradient tensor

g :

slip resistance

h,h αβ :

hardening moduli, αβ component of element of hardening matrix

H :

plastic modulus

H 1 :

finite element matrix

I :

identity tensor

J :

Jacobian

K :

stiffness matrix

L :

velocity gradient tensor

l :

constitutive 4th order tensor

l v :

Lie derivative

n :

normal

\(\hat P\) :

co-variant tensor field

P :

stress power

\(\hat Q\) :

contra-variant tensor field

q :

cross hardening parameter

R :

Reaction force

S ij , S α :

ij component of first Piola-Kirchhoff stress tensor, αth slip direction

S 0, S s :

initial and saturated slip deformation resistance

\(\hat S\) :

second Piola-Kirchhoff stress tensor

U :

Nodal displacement vector

v :

velocity

t :

time

ie255-6a :

traction

x, X :

x-coordinate of current and initial configurations

σ :

Cauchy stress tensor

\(\bar \sigma \) :

effective tensor

τ :

Kirchhoff stress tensor

τ s :

resolved shear stess

λ:

plastic parameter

\(\dot \gamma \) :

flow rate

ρ:

density

Ω:

domain of integration

∂Ω:

boundary of the domain of integration

i, j, k:

i, j, k components

Ln:

linear

NLn:

nonlinear

r:

reference

s :

Schmidt

∇J :

Jaumann rate

\(\dot A\) :

Time derivative of variable A

α, β :

α, βth slip system

e :

elastic

c :

uniform stress

p :

plastic

T:

transpose

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Author notes

  1. R. Prasannavenkatesan (Graduate Student, Engineer)

    Present address: the School of Mechanical and Materials Engineering, Washington State University, 99164, Pullman, WA

Authors and Affiliations

  1. GE India John F. Welch Technology Centre, Bangalore, India

    R. Prasannavenkatesan (Graduate Student, Engineer)

  2. the School of Mechanical and Materials Engineering, Washington State University, 99164, Pullman, WA

    B. Q. Li (Professor) & D. P. Field (Assistant Professor)

  3. the Alcoa Technical Center, 15996, Alcoa Center, PA

    H. Weiland (Technical Specialist)

Authors
  1. R. Prasannavenkatesan
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  2. B. Q. Li
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  3. D. P. Field
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  4. H. Weiland
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Correspondence to B. Q. Li.

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Prasannavenkatesan, R., Li, B.Q., Field, D.P. et al. A parallel macro/micro elastoplasticity model for aluminum deformation and comparison with experiments. Metall Mater Trans A 36, 241–256 (2005). https://doi.org/10.1007/s11661-005-0156-6

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  • DOI: https://doi.org/10.1007/s11661-005-0156-6

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