Enterprise for Multi-scale Research of Materials

An Integrative Model for the Dynamic Behavior of Ceramics

How We Fit Technical Approach

Key Accomplishments

Key Goals

Major Results

Impact

Materials-by-Design Process

Transitions to ARL, within

CMRG and to other CMRGs

Mechanism-based Approach

UNCLASSIFIED

UNCLASSIFIED

Qinglei Zeng1, A.L. Tonge2, Lori Graham-Brady1, Mark Robbins1, Ryan C. Hurley1, Jerry LaSalvia2, K.T. Ramesh1

1Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, MD, 212182Army Research Laboratory, Weapons and Materials Research Directorate, Aberdeen Proving Ground, MD 21005

❑Multiple mechanisms are integrated in a multiplicative formulation:

❑ The basic deformation mechanisms involved in the integrative model

are lattice plasticity & amorphization, fracture & fragmentation and

granular flow.

Integrative model

Lattice Plasticity

and Amorphization

Fracture and

Fragmentation

Granular Flow

Identified mechanisms

Material design

❑ 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.

𝑭 = 𝑭𝑒𝑑 ∙ 𝑭𝑔 ∙ 𝑭𝑎𝑭𝑒𝑑: due to elasticity and cracks

𝑭𝑔: due to granular flow

𝑭𝑎: due to amorphization

❑ Amorphization model

❑ Crack-induced damage model

❑Granular flow model

Onset of

amorphization bands

Sliding along

amorphization bands

• Initiation:Amorphization is incorporated by

describing the initiation and evolution

of amorphization bands.ො𝜎(𝑖) = 𝛼2 𝜎𝑠

(𝑖) 2 + 𝜎𝑛(𝑖) 2 ≥ 𝑃𝐴

• Sliding along bands:

ሶ𝛾𝑛(𝑖) = −𝜂𝑐 ሶ𝜉(𝑖)

ሶ𝛾𝑏𝑎𝑛𝑑(𝑖)

=𝜎𝑠

(𝑖) − 𝜏𝑐(𝑖)

𝜇𝑏𝑎𝑛𝑑, if 𝜎𝑠

(𝑖) > 𝜏𝑐(𝑖)

A micromechanics-based damage

model is used to describe the effect of

microcracks.

Macroscale Mesoscale Microscale

𝐷𝑚 =1

𝑉

𝑖=1

𝑁

𝑠𝑖 + 𝑙𝑖3

• Microcrack-induced damage:

• Initial flaw distribution:

• Crack growth law:

𝑔 𝑠 =𝜁𝑠min

𝜁𝑠−(𝜁+1)

1 − Τ𝑠min 𝑠max𝜁

ሶ𝑙 =𝐶𝑟𝛼𝑐

𝐾𝐼 − 𝐾𝐼𝐶𝐾𝐼 − 0.5𝐾𝐼𝐶

𝛾𝑐

𝑓(𝝉) = 𝝉′: 𝝉′ − 𝑌 + 𝐴tr(𝝉)

3− 𝐵

Granular flow is currently modeled

with Drucker-Prager plasticity, and we

will soon switch to a more elaborate

breakage model from granular flow

supertask.

• Yield function:

(Vogler et al., 2004)

❑ Simulation of plate impact experiments on boron carbide (BC)

❑ Simulation of sphere-on-cylinder impact (LaSalvia et al., 2007)

Plate impact experiments on BC are

modeled and the simulated particle velocity

profiles are compared with experiments.

• Sphere-on-cylinder impact is

modeled with a range of impact

velocities, and the damages

induced by micro-cracking and

amorphization are shown on

the right.

❑ Incorporated lattice plasticity and amorphization, microcracking-

based damage and granular flow in the integrative model based

on Tonge-Ramesh model;

❑ Implemented the model as a user-defined subroutine in ABAQUS;

❑ Calibrated material parameters for BC and simulated plate impact

experiments in Vogler et al. 2004;

❑ Simulated sphere-on-cylinder impact and compared them to

LaSalvia’s experiments.

❑ The integrative model incorporates the modeling outputs from (i)

the amorphization 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;

❑ Currently granular flow is described by Drucker-Prager model

for simplicity. A more elaborate granular flow model is being

incorporated into the integrative model by Dr. M. Cil (JHU);

❑ The material parameters will be refined using the experimental

data from each mechanism, and then validated using canonical

experiments.

❑ The model integrates three major mechanisms into a single

material model, which can capture 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.

Integrative model

• For impact velocities below

400 m/s, micro-cracking and

granular flow are dominated

mechanisms.

Damage induced by micro-cracking

Damage induced by amorphization