Bao Wierzbicki

Fracture Prediction of Navy SteelsFracture Prediction of Navy SteelsA System ApproachA System Approach

Tomasz WierzbickiPresentation at the NNR Review Meeting, St. Louis, June 2nd, 2004

Impact & Crashworthiness Lab, MITImpact & Crashworthiness Lab, MIT

MIT team members: Professor Frank McClintockDr. Yingbin BaoMr. Young-Woong LeeMr. Xiaoqing TengMr. Yuanli Bai


Damaged Area as a Measure of Ships SurvivabilityDamaged Area as a Measure of Ships Survivability

USDHUSDH

x

y

L0

0.0 0.1 0.2 0.3 0.4 0.50.0

0.1

0.2

0.3

0.4

0.5

Water rushes into the hole

Adpative (ηcb = 0.0002)

USDH (ηcb = 0.0761)

ηcb : Normalized cracked area of bottom plate

ξ0 = 0.5; V = 1.14; τ = 0.55; Bottom face plate; 1/4 model

Nor

mal

ized

dis

tanc

e ζ

= y

/ L0

Normalized distance ξ = x / L0

MIT Simulation


Fracture at Six Different LevelsFracture at Six Different Levels

5. Bay

4. Stiffeners & Panels

1. Microvoids

3. Specimens & Weldment

2. Unit Cube with defects

6. Ship

VirginiaTech/MIT

MIT

Michigan/MIT

5. Bay

4. Stiffeners & Panels

1. Microvoids

3. Specimens & Weldment

2. Unit Cube with defects

6. Ship

VirginiaTech/MIT

MIT

Michigan/MIT

MURI project : Development of blast resistance adaptive ship structures (Harvard University and MIT)Level 3 & 4

NNR project : Fracture prediction of navy steels (MIT through ATI )Level 2 & 3

NNR Project : Design of ships for survivability (jointly between Virginia Tech., UMich and, MIT )Level 1, 2, 5, & 6

ONR Project : DURIP instrumentation grant (awarded to MIT)Level 3


Deliverables under NNR Funding Deliverables under NNR Funding through ATI ( 7/03through ATI ( 7/03--6/04)6/04)

Five technical reports (out of which, three have been submitted to major international journals)

Installation of three new pieces of equipment in the Impact and Crashworthiness Lab for fracture testing (3-D optical strain measuring device, Instron 9250NH DynatupDrop Tower, Zeiss microscope for fracture surface examination)

Completion of the design of 50 kN biaxial testing machine (joint project with Instron)

Design and manufacture of a universal specimen for fracture testing under combined loading

Study of physical aspects of ductile fracture (Report #112, 120)Study of numerical aspects of ductile fracture (Report # 114,

127)


Deliverables under NNR Funding through ATI ( 7/03-6/04) (cont.)

Presentations and discussions of the industrial approach to fracture at :•Sandia National Labs Albuquerque and Livermore •Stanford Research Institute •Applied Research Associates •Weidlinger Associates•Earnst Mach Institute in Freiburg, Germany•BMW R&D Center in Munich, Germany•EuroPAM Conference in Mainz, Germany•AmeriPAM Conference in Warren, MI•ABAQUS User Meeting in Cambridge, MA

Two new US citizen graduate students admitted


Publications of the MIT Team Completed for NNR Funding through ATI ( 7/03-6/04)

Necking, Fracture Initiation, and Crack Propagation in Flat Tensile Specimen, Y.W. Lee, T. Wierzbicki and Y. Bao, February, 2004, Impact andCrashworthiness Lab., Report #114 (to be submitted to Mechanics of Materials)

Bridgman Revisited: On the History Effects on Ductile Fracture, T. Wierzbicki and Y. Bao, January, 2004, Impact and Crashworthiness Lab., Report #112 (Submitted to Journal of the Mechanics and Physics of Solids)

Evaluation of the Wilkins (and other) Fracture Model, Y. Bao, Y.W. Lee and T. Wierzbicki, May 2004 Impact and Crashworthiness Lab., Report #120 (Submitted to Engineering Fracture Mechanics)

A Comparative Study of Shell Element Deletion and Element Split, H. Alsos, June, 2004, Impact and Crashworthiness Lab., Report #127 (MS Thesis)

Prediction of High Velocity Impact Fracture of Large Structural Systems, T. Wierzbicki, March, 2004, Impact and Crashworthiness Lab., Report #118 (Summary Report)


Equipment Recently Purchased under DURIPEquipment Recently Purchased under DURIPInstrumentation Grant to ICLInstrumentation Grant to ICL

Zeiss microscope

Instron 9250NH Dynatup Drop

Tower

3-D optical strain

measuring device


Custom Made 50 Custom Made 50 kNkN Biaxial Testing RigBiaxial Testing Rig


New Types of Specimens for Biaxial TestingNew Types of Specimens for Biaxial Testing

2nd generation 3rd generation


Testing to FractureTesting to Fracture

Steel specimen under tension

Al 2024 in combined shear/compression


Fracture vs. No FractureFracture vs. No Fracture

Round specimens subjected to hydrostatic pressure and tension


Experimentally Determined Fracture LocusExperimentally Determined Fracture Locus

12 34 5

6 7 8

9 10 11

Bao-Wierzbicki fracture locus


Calibration of BW ModelCalibration of BW ModelEvaluation of Calibration Constant Evaluation of Calibration Constant DDc c (high stress triaxiality)(high stress triaxiality)

Stre

ss tr

iaxi

ality

σm / σ

Equivalent strain ε

diffuse necking localized necking fracture initiation Critical

damage parameter


Comparison of Seven Fracture Envelopes

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

FFLD

Johnson-Cook T-criterion

FLD: Storen/Rice

εf = const.

FLD: Hill

Wilkins

(1/3, b)

(0, a)

0.8

0.4

Maximum shear stress τmax = const.

Bao-Wierzbicki

Al2024-T351; a = 0.205; b = 0.54; n = 0.15

σm/σ

εf


Comparison of Seven Fracture Envelopes

FFLD

T-criterion

Johnson-Cook

FLD: Hill

εf = const.

τmax = const.

Bao-Wierzbicki

FLD: Storen and Rice

0.5

0.5-0.5

Al2024-T351; a = 0.205; b = 0.54; n = 0.15

Wilkins

α = dε2 / dε1

α = -2compression

0.0

α = -1 shear

α = -0.5 uni-axial tension

α = 0 plane strain

α = 1 equi-biaxial tension

ε2

ε1


Application of BaoApplication of Bao--Wierzbicki Fracture LocusWierzbicki Fracture Locus

Bao-Wierzbicki’s Constant fracture strain

An aluminum beam impacted by a round-nosed mass at V0 =300 m/s

Johnson-Cook’s • Large differences among three fracture loci;

• BW’s fracture criterion gives realistic results.

Eroded elements


Double Hulls under Localized Impulsive Loading

outer hull

inner hull

initial

deformed

adaptive core


Crack Formation and Propagation(Adaptive Sandwich Core Strucutre)

Initial FE mesh (1/2 model)Initial FE mesh (1/2 model)Onset of fracture(top face plate) Stress triaxialityStress triaxiality

Equivalent strainEquivalent strainFinal FE mesh (1/2 model)Final FE mesh (1/2 model)

Dimensionless loading area ξ0 = 0.5Dimensionless applied impulse V = 1.14

τ = 0.0

τ = 0.5

τ = 0.05

τ = 0.05


USDHUSDH NavtrussNavtruss

Y-webY-web AdaptiveAdaptive

Fracture Patterns of Inner Hull with Four Different Core Arrangements



Comparison of Damaged Area

USDH Navtruss Y-web Adaptive0.00

0.05

0.10

0.15

η0 = 0.25; V = 1.14

Nor

mal

ized

cra

ck a

rea η cb

Type of Core Structures


Effect of Intensity of Applied Impulse (USDH)

USDH: V = 0.93USDH: V = 0.93

Dimensionless loading area ξ0 = 0.5

USDH: V = 1.14USDH: V = 1.14 USDH: V = 1.8USDH: V = 1.8

Outer hull (top), Inner hull (bottom)


Damaged Area with Varying Intensity of Applied Impulse (USDH)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

V = 1.14 (ηcb = 0.0761)

V = 1.05 (ηcb = 0.0196)

ξ0 = 0.5; USDH (Bottom face plate)

Nor

mal

ized

dis

tanc

e ζ

= y

/ L0

Normalized distance ξ = x / L0

V = 1.7 (ηcb = 0.2178)

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40ξ0 = 0.5; USDH (Bottom face plate)

Nor

mal

ized

cra

ck a

rea η cb

Normalized impulse V


Distribution of Stress Triaxiality

Stress triaxialityStress triaxiality


τ = 0.5

AdaptiveAdaptive

USDHUSDH


Future Work

lling

Fracture calibration of two or three types of Navy steel

Cooperation with the Bath Iron Shipyard and NSWC to acquire suitable material samples

Validation on the component level

Implementation into commercial FE codes in cooperation with the developers of LS-DYNA, ABAQUS and, PAM-CRASH

Application to several types of weapon threats.

Transfer of new technology to the Navy labs and Shipyards

Bao Wierzbicki

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