Title
Weixin Li and KT Ramesh
Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, MD, 21218
How We Fit Technical Approach
Key Accomplishments/Path Forward
Key Goals
Major Results
Contribution to MEDE Legacy
Materials-by-Design Process
Transitions to ARL, within
CMRG and to other CMRGs
Mechanism-based Approach
UNCLASSIFIED
UNCLASSIFIED
Incorporating plasticity into the Ceramics Integrative Model
Integrative model
❑ The objectives of this task are to
• integrate models developed within each mechanism supertask for
the dynamic behavior of ceramics,
• provide guidance to each supertask on approaches that are more
easily integrated, and
• provide guidance to the CMRG on materials design for a canonical
application.
❑ The basic deformation mechanisms involved in the integrative model
are lattice plasticity & amorphization, fracture & fragmentation and
granular flow.
❑Microcrack informed damage model
A micromechanics-based damage
model is used to describe the effect of
microcracking.
𝑙
ϕ
2s
𝜎1𝑒
𝜎2𝑒
𝜎1𝑒
σ2
σ1 • Wing crack initiation and growth
• Initial flaw distribution:
𝑔 𝑠 =𝜁𝑠min
𝜁𝑠−(𝜁+1)
1 − Τ𝑠min 𝑠max𝜁
• Crack growth dynamics
ሶ𝑙 =𝐶𝑟𝛼𝑐
𝐾𝐼 − 𝐾𝐼𝐶𝐾𝐼 − 0.5𝐾𝐼𝐶
𝛾𝑐
𝐷𝑚 = 𝜂
𝑖=1
𝑁
𝑠𝑖 + 𝑙𝑖3
• Damage variable
❑Granular flow model
𝑓(𝝉) = 𝝉′: 𝝉′ − 𝑌 + 𝐴tr(𝝉)
3− 𝐵
Granular flow is currently modeled with
Drucker-Prager plasticity. A more
elaborate breakage model from
granular flow supertask will be soon
available.
• Yield function:
❑ Continuum viscoplasticity model
• Mises yield criterion:
• Perzyna-type viscoplasticity:
In addition to amorphization model for
B4C (Zeng and Ramesh 2019), a
constitutive description of the lattice
plasticity mechanism is incorporated
into the integrative model. The
continuum viscoplasticity model is used
to describe the metal-like plastic flow.
𝑓(𝝉) = 𝝉′: 𝝉′ −2
3𝑌0 + 𝑘(𝛼)
ሶ𝜆 =1
𝜂Φ 𝑓 ; Φ 𝑓 =
𝑓
𝑌0
𝑛
1000 2000 3000 40002000
4000
6000
8000
10000
12000
Mean stress (MPa)
Devia
toric s
trength
(M
Pa)
Brannon et al. 2007
Wang and Ramesh 2004: quasi-static
Wang and Ramesh 2004: dynamic
Simulation: quasi-static
Simulation: dynamic
10-5
10-3
10-1
101
103
105
0
2000
4000
6000
8000
10000
12000
Strain rate (s-1)
Str
ength
(M
Pa)
Sarva and Nemat-Nasser 2001
Wang and Ramesh 2004
Simulation
❑ Calibration of the damage model against strength measurements for SiC
❑ Simulation of plate impact experiments on silicon carbide (SiC)
0
0.5
1
1.5
2
2.5
3
0 0.5 1 1.5 2
Part
icle
vel
oci
ty (
km/s
)
Time (μs)
Experiment
SimulationN6
N1 N2
N3
N7
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Part
icle
vel
oci
ty (
km/s
)
Time (μs)
Experiment
Simulation
N11
N12
N13
N15
N10
❑ Enhanced the model capacity by incorporating lattice plasticity
into the integrative model in addition to amorphization,
microcracking, equation of state, and granular flow;
❑ Implemented the model as a user-defined subroutine in ABAQUS;
❑ Calibrated the damage and viscoplasticity model parameters for
SiC and simulated plate impact experiments in Vogler et al. 2006;
❑ Interaction between different mechanisms will be explored and
more extensive model validation will be conducted.
❑ The integrative model incorporates the modeling outputs from (i)
the quasi-plasticity supertask, (ii) the fracture and fragmentation
supertask and (iii) the granular flow supertask;
❑ The model has been implemented in ABAQUS as UMAT and
VUMAT. It can be extended to other codes used within ARL;
❑ Drucker-Prager model is incorporated to describe granular flow.
A more elaborate model based on breakage mechanics will be
soon available;
❑ The material parameters will be refined using the experimental
data from each mechanism, and then validated using canonical
experiments.
❑ The model integrates the major mechanisms identified during
the dynamic impact events into a single material model, and can
simulate the response of ceramics in application scale;
❑ It allows quantitative assessment of the relative importance of
different mechanisms under complex loading conditions;
❑ Using microstructural inputs, it allows us to address materials-
by-design through an objective function supplemented by a
canonical model.
• Strain rate dependency of SiC-N strength was explored by Sarva and Nemat-
Nasser 2001 and Wang and Ramesh 2004 through kolsky bar tests;
• Pressure dependency was explored by Brannon et al. 2007 through quasi-
static triaxial tests and by Wang and Ramesh through confined kolsky bar tests;
• Rate and pressure dependency can be captured by the damage model.
• Viscoplasticity model parameters were calibrated against the shock-
release experiments by Vogler et al. 2006;
• Comparison with the shock-reshock experiments validated the model.
Inelastic mechanisms
Fracture & Fragmentation
Granular Flow
Equation of State (EOS)
Integrative model
Identified mechanisms
Material design
