Post on 20-Apr-2022
Multiscale crystal plasticity modeling
Dr. Veera Sundararaghavan1
1Department of Aerospace Engineering University of Michigan
Center for PRedic.ve Integrated Structural Materials Science
Materials modeling
Aerospace composite finite element models
Modeling of carbon fiber degradation
Microstructural fatigue crack growth models
Crystal plasticity
Process modeling using microstructure descriptors
Atomistic modeling of composite matrix material (epoxy)
Multiscale structural simulations laboratory, Prof Veera Sundararaghavan
3 Multiscale Structural Simulations Laboratory May 24, 2017
Real Space DFT PRISMS-‐RSDFT
Fourier Space DFT (e.g. VASP)
Atomic scale cons.tu.ve laws
Sta.s.cal Mechanics CASM
Phase Diagrams CASM/CALPHAD
Disloca.on Dynamics LLNL-‐ParaDIS
Phase Field Crystal PRISMS-‐PFC*
Phase Field PRISMS-‐PF
Crystal Plas.city PRISMS-‐Plas1city
Con.nuum Plas.city PRISMS-‐Plas1city
EXPERIMENTS(nuclea.on kine.cs, etc.)
EXPERIMENTS (slip, twinning, crack, etc.)
Mechano-‐Chemistry PRISMS-‐MC*
PRISMS Center Integrated Framework Enabling accelerated predic.ve materials science
4
Center for PRedictive Integrated Structural Materials Science
Crystal plas.city finite element
Single crystal constitutive model at element level
Equilibrium (and compatibility) across grains are enforced via Finite Element Method (FEM)
EBSD serial sec.oning
CPFE simula.ons
5 Multiscale Structural Simulations Laboratory May 24, 2017
• Code highlights: – Parallel 3D crystal plas.city models
implemented over Ellip.c PDE base class – Support for reading external microstructures
post-‐processing capabili.es (pole figures, orienta.on distribu.on func.ons, etc)
– Demonstrates parallel performance and scaling on large-‐scale problems running on hundreds of processors.
– Training at the PRISMS Workshop following this conference
ODF ε=0 ODF ε=-‐0.25
PRISMS CPFE
Pole Figures -‐MTex Visualiza.on -‐ Paraview
Virtual Microstructure -‐ Neper
PRISMS Center: Mg-‐RE alloys
6
Goal: To model microstructural deforma.on using CPFE and validate using grain level strain data from SEM-‐DIC
Valida.on experiments: in-‐situ strain mapping
7 Center for PRedic.ve Integrated Structural Materials Science
Quan1ta1ve local analysis of the rela1onships between microstructure and deforma1on/damage • Approach: in-‐SEM digital image correla1on (SEM-‐DIC)
• Full-‐field maps of deforma.on at different length scales (see Fig.) • Slip ac.vity, twinning, strain localiza.on have been quan.ta.vely resolved during
loading
EBSD orienta.on data is mapped in PRISMS-‐CPFE, following which deforma.on fields from SEM-‐DIC and CPFE can be compared.
As received (80x80 µm) Peak aged (1000x1000 µm)
8 Multiscale Structural Simulations Laboratory May 24, 2017
Upcoming NSF work: Modeling localiza7on using peridynamics Strain maps courtesy of the Daly lab (Alan Githens; co-‐advised by John Allison and Sam Daly).
T5 temper-‐2.91% Strain
T5 temper-‐2.91% Strain
L M
A
B
C
E
F G
H
I
K
J D
L M
A
B
C
E
F G
H
I
K
J D
9 Multiscale Structural Simulations Laboratory May 24, 2017
Strain maps courtesy of the Daly lab (Alan Githens; co-‐advised by John Allison and Sam Daly).
T5 temper-‐2.91% Strain
T5 temper-‐2.91% Strain
A
B C
A
B C
∑↑▒𝛾↓𝑏𝑎𝑠𝑎𝑙 /∑↑▒𝛾
10 Multiscale Structural Simulations Laboratory May 24, 2017
Strain maps courtesy of the Daly lab (Alan Githens; co-‐advised by John Allison and Sam Daly).
T5 temper-‐2.91% Strain
T5 temper-‐ compression 4.2% Strain
LIFT-‐UTRC project: Mul.scale Modeling of Al-‐Li alloys
Crystal plas.city • ODF • FEM
Volume frac.ons of crystals in orienta.on space is tracked
Most efficient microstructure representa.on
Conservation principle
Solve for evolution of the ODF with deformation
Based on the Taylor hypothesis
EVOLUTION EQUATION FOR THE ODF (Eulerian)
Mul.scale modeling
Mul.scale anima.on
Multiscale Structural Simulations Laboratory
MULTISCALE INVERSE PROBLEMS
Objective: Design the initial preform such that the die cavity is fully filled and the yield strength is uniform over the external surface (shown in Figure below). Material: FCC Cu
Uniform yield strength desired on this surface
Fill cavity
Multi-objective
optimization
• Increase Volumetric yield
• Decrease property variation
+
Multiscale Structural Simulations Laboratory
MULTI-SCALE DESIGN FOR OPTIMUM STRENGTH: UNOPTIMIZED
70
80
90
100
110
120
130 Large
Underfill
variation in yield strength
Yiel
d st
reng
th (
MPa
)
Multiscale Structural Simulations Laboratory
70
80
90
100
110
120
130 Underfill
Yiel
d st
reng
th (
MPa
)
Optimal yield strength
Optimal fill
MULTI-SCALE DESIGN FOR OPTIMUM STRENGTH: OPTIMIZED