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