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99-3435

Damage Initialization for Modeling of Dynamic Shear Banding

Michael B. Prime, ESA-EARick L. Martineau, DX-5Carl R. Necker, Jr., MST-6

ASME Mechanics and Materials Conference June 27-30, 1999,Blacksburg, Virginia USA

ASME 1999ASME 1999

Modeling of Dynamic Shear Banding

Michael B. Prime1, R. L. Martineau2, & C. R. Necker, Jr3.

1 Engineering Sciences & Applications Division2 Dynamic Experimentation Division

3 Materials Science & Technology DivisionMaterials Science & Technology Division

Los Alamos National LaboratoryLos Alamos, New Mexico, USA

• Introduction

• Experiments

A l i• Analysis

Engineering Analysis

Los Alamos National LaboratoryEngineering Sciences & Applications

ASME 1999Introduction

ASME 1999

• Adiabatic shear banding– Adiabatic: high rate = no heat transfer

– Plastic work: dT

1

Plastic work:

– If thermal softening > strain hardening

localization ----> shear banding

pp

dC

T

0



ASME 1999Introduction

ASME 1999

• Shear Banding in Dynamically ExpandingShear Banding in Dynamically Expanding Shells

– Flux compression generators

– Explosive Forming

– Explosive Containment vessels

– Explosive Bonding

• Desire to Predict Timing & EvolutionFinite element modeling (explicit)– Finite element modeling (explicit)



ASME 1999Cylinder Experiments

ASME 1999

• Explosively-loaded, end-detonated

• Copper: grainsize: 40m (large cylinders), ~100m (small)

• 2 tests: 4" (100mm) ID, 16" (400mm) long, PBX-9501 (energetic HE) filled, 0.1" & 0.2" (2.5 & 5mm) wall

• 2 tests: 2" (50mm) OD, 8" (200mm) long, ~ 0.25" (6mm) annulus of nitromethane, 0.3 ” & 0.36 ” (7.6 &



9.2 mm) wall, inner copper cylinder

ASME 1999ASME 1999



ASME 1999Experiments - Diagnostics

ASME 1999

• Diagnostics:g– Fast framing camera (used 3-5 s frame time)

– Visar/Fabry-Perot interferometry

• Uses:– Validate finite element model with disps, velocities

– Observe shear banding formation on surface, final fracture



ASME 1999Experiments - Recovered Fragments

ASME 1999

Failed shear band

Shear band

30 mm

• Cross-Section of soft-catch fragment, smaller cylinders only

• Many Shear bands evident

• Data– Shear band spacing

– fragment thickness gives upper bound on final failure



failure

ASME 1999Experiments - Recovered Fragments

ASME 1999

• Same test, 20% thicker cylinder

• Void plane

• Less developed shear bandsLess developed shear bands

• lower strain at failure



ASME 1999Modeling Approach

ASME 1999

• Axisymmetric FEM• Axisymmetric FEM model

– ABAQUS Explicit + VUMAT

– Adiabatic Heatingg

– HE burn, JWL EOS

– Matches data

– Wrong plane for shear bands



ASME 1999Plane Strain Model

ASME 1999

• Pressure load instead of HE elements– carefully extracted from axisymmetric contact forces

• Refined mesh to capture shear banding• Refined mesh to capture shear banding



ASME 1999

Quantifying Model ResultsASME 1999

•Track final fragment thicknesses•Plateaus quickly•Unambiguous•No fragments for energetic shots

•tmin/tmax = 0.9•Compare with optical record of perturbation appearance



perturbation appearance

ASME 1999Model Predictions - Johnson-Cook

ASME 1999

4

4.5

experiment

JC

Big cylinders

necking too late

2.5

3

3.5

r/r0

at

neck

JC necking too late

2

thin thick

0.17

0.18

Small Cylinders

0 11

0.12

0.13

0.14

0.15

0.16

ag

me

nt t

hic

kne

ss

(in

ch)

i t

fragments too thin (=necking too late)

0.08

0.09

0.1

0.11

3 4

fra experiment

J-C

FEM with Johnson-Cook constitutive law predicts shear banding too late in time



ASME 1999MTS constitutive model

ASME 1999

• Physically realistic • Mechanical Threshold Stress is internal state variable

(as compared to just strain strain rate temperature)(as compared to just strain, strain rate, temperature)

• Evolution controlled by thermally activated interaction of dislocations with obstacles

ˆ)(

ˆ)(

TSTS ia 00

),(),(

TSTSi

is shear modulus = f(T)a is athermal, rate independent term (interaction of dislocations with long-range barriers like g b ’s)dislocations with long range barriers, like g.b. s)

constant ,ln1),(

11

30

0

i

pq

i

ii

i

igb

kTTS

intrinsic barriers (e.g. Peierls stress), non-evolving intrinsic barriers (e.g. Peierls stress), non evolving

tanh

,ˆˆ

tanh

1,ˆ

0

TT

d

d s

strain-evolving

• Dislocation accumulation (strain hardening)• Dislocation annihilation (recovery)

R t iti it



• Rate sensitivity

ASME 1999MTS model

ASME 1999

• 4 tests with our Copper– 2 low rate, Troom tensile

– 2 high rate Hopkinson bar, Troom & 200 Cg p ,

300

350

400

MTS fit excellent

• Use well-studied

100

150

200

250

2800/s,298K

2600/s,473K

0.1/s,298K

0 001/ 298K

str

es

s (

MP

a)

Use well studied Copper parameters, slight changes only for our material

• Well calibrated for

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0

50 0.001/s,298K

strain

400

Well calibrated for higher strains

Johnson Cook fit

150

200

250

300

350

2800/s,298K

2600/ 473K

res

s (

MP

a)

Johnson-Cook fit poor

• Does not capture physical behavior

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0

50

100

2600/s,473K

0.1/s,298K

0.001/s,298K

str

strain



ASME 1999MTS model

ASME 1999

4

4.5

experiment

JC

Big cylinders

2.5

3

3.5

r/r0

at

neck

JC

MTS necking too late

0.18

2

thin thick

S ll C li d

0.14

0.15

0.16

0.17

kne

ss

(in

ch)

Small Cylinders

fragments only slightly too thin

0.09

0.1

0.11

0.12

0.13

fra

gm

en

t th

ick

experiment

J-C

MTS

0.08

3 4

Better - but not quite



Better but not quite

ASME 1999Modeling Approach

ASME 1999

Homogeneous Models Don’t Work• Shear bands come later than observed

I iti l A hInitial Approach• Void growth model (Gurson)

• Predictions good if use random spatial variation in initial void volume fraction

• Voids not observed experimentally

Mechanisms (Meyers; Curran, Seaman, & Shockey)

• Second phase particles & carbides form voids

Di l ti il & l t i b d i• Dislocation pileup & release at grain boundaries

• Grain size inhomogeneity

• Textural localization

ALL HAVE GRAIN SIZE LENGTH SCALE

MTS athermal stress• Long range (i.e., grain size) interactions

• depends on grain size (Gourdin & Lassilla 1991)

Initialize with a variation on grain size scale

MPain m,in ,278.0

21 d

da



ASME 1999Initializing Random Damage

ASME 1999

ge

RANDOM NUMBERS BY ELEMENT= Element Integration Point

Elementsize

PositionIn

itial

Dam

a gRefined Mesh

size

Elementsize

Grainsize

.

Grainsize

Element sizeElement size

Element size



Grainsize

ASME 1999Initialized Athermal Stress

ASME 1999

+1.17e+07+1.25e+07+1.33e+07+1.42e+07+1.50e+07

(Ave. Crit.: 75%)

SDV56

+5.00e+06+5.83e+06+6.67e+06+7.50e+06+8.33e+06+9.17e+06+1.00e+07+1.08e+07

• Randomly initialized a

• Element size = 90 m• Element size = 90 m

• 5MPa to 15MPa



ASME 1999Predicted fragment sizes

ASME 1999

4

4.5

experiment

JC

2.5

3

3.5

r/r0

at

neck

MTS

perturbed

0 17

0.18

2

thin thick“perturbed” = random spatial variation in

0.13

0.14

0.15

0.16

0.17

t th

ickn

es

s (

inch

)

variation in strength

0.08

0.09

0.1

0.11

0.12

3 4

fra

gm

en

t

experiment

J-C

MTS

perturbed

• Conclusion: perturbations important, probably grain-sized

• Very speculative: much more work

3 4



Very speculative: much more work needed

ASME 1999Framing Camera Pictures

ASME 1999g



ASME 1999Plane Strain Model

ASME 1999

• Beginning of shear localization



• Equivalent plastic strain rate plotted here

ASME 1999

Experiments - Recovered FragmentsASME 1999

Failed shear bandShear band

• Cross-Section of soft-catch fragment, smaller cylinders only30 mm

• Many Shear bands evident

• Data: Shear band spacing, fragment thickness gives upper



bound on final failure

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