หน้าปก - MITweb.mit.edu/nuwong/Public/Armor/F-17_Report_final_sim… · Web viewTel: 0-2564-6500 ext 4700, Fax: 0-2564-6403, E-mail: [email protected] Abstract. This

1

หนาปกรายงานการวจย พฒนาและวศวกรรม ฉบบสมบรณ

รหสโครงการ……………..……

ชอโครงการ ………………………………………………………………………

(ภาษาไทย)

ชอโครงการ ………………………………………………………………………

(ภาษาองกฤษ)

คณะผวจย1. ………………………………………………….2. …………………………………………………3. …………………………………………………

หนวยงานทสงกด

…………………………………………………………………………………………………………

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สนบสนนทนวจยโดยศนยเทคโนโลยโลหะและวสดแหงชาต

สำานกงานพฒนาวทยาศาสตรและเทคโนโลยแหงชาตประจำาปงบประมาณ…………………

แบบรายงานฉบบสมบรณโครงการวจย พฒนาและวศวกรรมเสนอ ศนยเทคโนโลยโลหะและวสดแหงชาต

สำานกงานพฒนาวทยาศาสตรและเทคโนโลยแหงชาต………………………………………………………………………

…โครงการยอยท 4

เรมแรกโครงการไดมการศกษาและคนควาขอมลทางวชาการทเกยวของกบการตอบสนองของวสดเมอมการปะทะดวยวสดแขงทเคลอนทมาดวยความเรวสง โดยจะแบงฐานขอมลตามลกษณะของวสดทศกษา เพอใหสอดคลองกบวสดทใชในเกราะกนกระสน โดยแตละวสดไดมการศกษาและคนควาถงขอแตกตางในการเสยรปอนเนองมาจากแรงกระทำาจากภายนอก เพอเปนแนวทางในการพฒนาสมการเนองจากโครงสราง ทใชในการจำาลองการเสยรปของวสดนนๆ (ตามเอกสารแนบทายท 1)

ตอมา โครงการไดทำาการศกษาและรวบรวมผลงานวจยทเกยวของ เพอใชเปนแนวทางในการพฒนาแบบจำาลองการเสยหายของวสดประเภทโลหะและเซรามกส ภายใตสภาวะสถต โดยพยายามเลอกหาสมการเนองจากโครงสราง เงอนไขขอบเขต และเกณฑการลมเหลวของวสดทเหมาะสม ตลอดจนคาพารามเตอรทเกยวของกบความนาเชอถอของแบบจำาลองทพฒนาขน ตอมาไดขยายกรอบแบบจำาลองไปยงสภาวะแบบพลวต ซงไดพบวาการประมาณคาความสมพนธเนองจากโครงสรางทขนกบอตราการรบภาระของวสดทใชในโครงการนน คอนขางลำาบากเพราะไมสามารถหาคณสมบตเชงกลของวสดทคาอตราความเครยดสงๆ ได จงจำาเปนตองอางองจากบทความทางวชาการของผอน

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ทใชวสดชนดใกลเคยงกน ซงไดมการพฒนาแบบจำาลองทสามารถใหผลการจำาลองทใกลเคยงกบผลทรายงานในบทความทางวชาการทศกษา ซงเปนการแสดงใหเหนถงความถกตอง และความนาเชอถอของแบบการจำาลองทพฒนาขน อกทงไดมการเปรยบเทยบเชงคณภาพกบผลการทดสอบยงจรงภายในโครงการเปนทนาพอใจ เชน ในการยงกระสนชนดเดยวกนทความเรวตนเทากนบนแผนเซรามกสทมความหนาตางกน แผนทหนากวาจะรบแรงกระแทกไดมากกวาแผนบาง โดยพนททไดรบความเสยหายจะกวางกวาดวย (ตามเอกสารแนบท 2)

เนองจากการพฒนาแบบจำาลองการกระแทกของวสดประเภทคอมพอสทดวยกระสน ประสบอปสรรคในดานขอจำากดเชงเทคนคของโปรแกรมทใช (ABAQUS) และบทความเชงวชาการทเกยวของทใช ABAQUS มไมมาก ทางคณะผวจยจงเปลยนมาศกษาการใชงานโปรแกรม LS-DYNA ซงไดผลเปนทนาพอใจในการพฒนาแบบจำาลองเพอทำาซำาผลทรายงานในบทความเชงวชาการทเกยวของ (Gu and Xu, Composites B 35 (2004), 291) ดงรายละเอยดขางลาง อยางไรกตามปญหาทพบขณะนคอการหาคาคณสมบตทถกตอง เพอใสในแบบจำาลองทสรางขน เพอเปรยบเทยบกบผลการทดลองจรงในโครงการ

โมเดลของ Gu and Xu (2004) แบบจำาลองทสรางขน

รายละเอยดของโมเดล

F-MT-RDE-17 Rev.1

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1.แผนเปาหมาย-ในการทดลองจรงของ Gu and Xu (2004) ใชวสดแบบ

Twaron® /epoxy composites -ขนาดของแผนเปาหมาย คอ 45 100 หนา 5 มลลเมตร วาง

เอยงทำามม 30 กบแนวดง- Solid element 8 node hexahedral 25000

elements-ตรงดานบนและลางของแผนเปาหมาย-โปรแกรมสามารถทำานายความเสยหายจากการแตกราวของ Matrix โดยคำานวณจากความเสยหายแรงดงของ fiber และ ความเสยหายแรงอดของคอมพอสต- การคำานวณหาคณสมบตของ คอมพอสตใชวธการแบบ microstructure โดย fiber กำาหนดใหวสดเปนแบบ transversely isotropic และ matrix กำาหนดใหวสดเปนแบบ isotropic คำานวณไดคณสมบตของวสดตามตาราง (Material Type22 Composite Damage Model on Ls-DYNA)

2.กระสน -เสนผานศนยกลาง 7.87 มลเมตร ยาว 26.8 มลเมตร - Rigid element 4 node tetrahedral 617 elements - คณสมบตกำาหนดใหเปนเหลก ความหนาแนน 8625.864 kg/m3, คา E เทากบ

F-MT-RDE-17 Rev.1

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210 GPa , = 0.3, มวล 7.95 g -เคลอนทเฉพาะแนวแกน Z ดวยความเรว 300- 650 เมตรตอวนาท ไมมการหมนรอบแกนใดๆ

ผลลพธ ผลการจำาลองปรากฏวากระสนทะลผานไดทความเรวตางๆ แมจะตางจากการจำาลองของ Gu and Xu (2004) อยบาง แตกใกลเคยงกบผลการทดลองจรง ทงลกษณะความเสยหายกมลกษณะเดยวกบผลการทดลองจรงเปรยบเทยบไดจากกราฟดงน

Residual Velocity & Strike Velocity

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700

Strike Velocity

Resi

dual

Vel

ocity

FEM result(GU)

Experimental result

FEM result(My model)

ในการคำานวณไมคำานงถงแรงเสยดทานระหวาง กระสนกบแผนเปาหมาย เพราะมคานอยมากเมอเทยบกบพลงงานจลนทแผนเปาหมายดดซบไดในขณะทกระสนกำาลงเจาะทะลแผนเปาหมาย

กราฟผลการจำาลองเปรยบเทยบความเรวของกระสนขณะทะลผานแผนคอมพอสตขางลาง จะเหนไดวาความเรวตกคางมความใกลเคยงกนพอสมควร ท 372 m/s กบ 372.06 m/s แตถาเทยบทเวลาเทากน ความเรวมคาตางกนพอสมควรอาจเปนเพราะวาเรมตนทกระสนยงไมไดเรมสมผสกบแผนเปาหมาย และลกษณะของกราฟกยงแตกตางF-MT-RDE-17 Rev.1

6

กนพอสมควรทงเมอกระสนทะลผานออกไปแลวยงมคาความเรวเพมขนนดหนอย

ผลการจำาลองของ Gu and Xu (2004)

ผลการจำาลองของแบบจำาลองทสรางขน

ผลการจำาลองทตางกนสามารถตรวจสอบไดเพมเตมจากกราฟขางลาง ซงเปรยบเทยบความเรงของกระสนขณะทะลผานแผนคอมพอสต โดยกราฟของ Gu and Xu (2004) มลกษณะแปลกๆ เพราะในชวงเวลาทกระสนทะลผานแผนคอมพอสตไปแลวความเรวคงท ความเรงจงไมนาจะเพมขน สวนทไดจากแบบจำาลองทสรางขนนาจะมความเปนไปไดมากกวาเพราะความเรงแมในชวงแรกจะลดลงจากการกระแทกพนผวแลวความเรงกเพมขนจนถงจดๆหนงแลวกลดลงอกตามความเรวของกระสนทลดลงจนกระสนทะลผานคอมพอสตไป ความเรงกมคาเปนศนยทความเรวมคาคงท

F-MT-RDE-17 Rev.1

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ผลการจำาลองของ Gu and Xu (2004) ผลการจำาลองของแบบจำาลองทสรางขน

รปขางลางแสดงผลการจำาลองขณะกระสนทะลผานแผนเปาหมายเมอเทยบกบผลการจำาลองของ Gu and Xu (2004) ซงมลกษณะใกลเคยงกนทเวลาตางๆ แตแบบจำาลองทสรางขนแสดงใหเหนถงลกษณะความเสยหายทเปนรอยแตกตามยาวของแผนเปาหมาย

ผลการจำาลองของ Gu and Xu (2004)

F-MT-RDE-17 Rev.1

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t=0 s t=14 s t=30 s

t=40 s t=60 s t=90 s

ผลการจำาลองของแบบจำาลองทสรางขน

จากการเปรยบเทยบผลของแบบจำาลองทสรางขนกบผลของ Gu and Xu (2004) พบวามความใกลเคยงกนในระดบหนง ความแตกตางของคาทเกดขนอาจมสาเหตมาจากปจจยตางๆ เชน element ของกระสนทใชในโมเดลมความแตกตางกน จำานวน element ของแผนคอมพอสตมความแตกตางกน รวมทงคาบางอยางของ Gu and Xu (2004) ไมมความชดเจนและผลทไดบางอยาง ยงมคาทไมนาจะเปนไปได แตอยางไรกตามผลโดยรวมถาเปรยบเทยบกบการทดลองของ Gu and Xu (2004) ยงมคาใกลเคยงกนพอสมควรทนาจะนำาไปทำาการวเคราะหใชสำาหรบโมเดลคอมพอสตแบบ Kevlar/epoxy ได ซงมคณสมบตของวสดทใกลเคยงกน

ตอมาทางคณะไดแบงงานออกเปน 2 สวน สวนแรกคอการปรบปรงแบบจำาลองทไดสรางขนและไดมการเปรยบเทยบกบบทความ

F-MT-RDE-17 Rev.1

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เชงวชาการทเกยวของ (Gu and Xu, Composites B 35 (2004), 291) โดยมการศกษา (Parametric Study) เพอใหบอกไดถงคณสมบตของแผนคอมพอสททสำาคญตอประสทธภาพในการรบแรง ตลอดจนขนาดของผลกระทบเมอคาคณสมบตบางตวเปลยนไป ในสวนทสองคอการพยายามหาคาคณสมบตจากแผนคอมพอสทชนงานจรง เพอนำาไปใชในแบบจำาลองทสรางขน

ในสวนของแบบจำาลองทสรางขนในชวงทรายงานความกาวหนาครงทผานมา ถงแมวาผลการจำาลองทไดจะใกลเคยงกบบทความเชงวชาการทเกยวของ (Gu and Xu, 2004) แตคณสมบตของแผนคอมพอสทและลกษณะการทกระสนเขาปะทะมความแตกตางจากแผนชนงานจรงทใชในโครงการและการทดสอบยงจรง ในงานของ (Gu and Xu, 2004) นนแผนคอมพอสทเปนแบบ uni-directional ซงมคา Young’s modulus สงสดในแกนเดยว ดงทแสดงในตารางขางลาง เปรยบเสมอนแผนคอมพอสททเกดจากการเรยงกนเปนแนวเดยว ซงตางจากแผนคอมพอสททเกดจากการถกทอแบบ woven ซงจะใหคา Young’s modulus สงสดในสองแกน (bi-directional) ในแนวระนาบ ดงนนจงจำาเปนตองมการปรบแบบจำาลองทสรางขนใหเปนแบบ bi-directional อกทงตองมการปรบแบบจำาลองเดมทกระสนเขาปะทะทมม 30 องศาไปเปนกระสนเขาปะทะในแนวตงฉาก

ตารางคณสมบตระหวางแบบจำาลองเดม และแบบจำาลองใหม

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property แบบจำาลองเดม (uni)

แบบจำาลองใหม (bi)

E1 longitudinal Young’s modulus, GPa

20.44 20.44

E2 transverse Young’s modulus, GPa

8.9 20.44

E3 normal Young’s modulus, GPa

8.9 8.9

21 Poisson’s ratio 21 0.31 0.4931 Poisson’s ratio 31 0.31 0.3132 Poisson’s ratio 32 0.49 0.31G12 shear modulus 12,

GPa3.03 6.84

G23 shear modulus 23, GPa

1.64 1.64

G31 shear modulus 31, GPa

1.64 1.64

Eb bulk modulus of failed material, GPa

20.44 20.44

S1 longitudinal tensile strength, GPa

1.145 1.145

S2 transverse tensile strength, GPa

1.145 1.145

C2 transverse compressive strength,

GPa

0.65 0.65

S12 in-plane shear strength, GPa

0.39 0.39

nonlinear parameters of shear stress

0 0

mass density, g/cm3 1.23 1.23

ผลการกระจายของคลนความเคนของแบบจำาลองเดมเมอเทยบกบแบบจำาลองใหมไดถกแสดงไวตามรปขางลาง จะเหนไดอยางชดเจนวาการกำาหนดลกษณะการทอคอมพอสทแบบเรยงแนวเดยว (uni-

F-MT-RDE-17 Rev.1

11

directional) ซงใหคา Young’s modulus สงสดในแนวเดยวบนระนาบ ทำาใหคลนความเคนกระจายตวไดเรวกวาในทศทางทมคา Young’s modulus สงกวา เนองจากความเรวของคลนความเคนแปรผนตามรากทสองของอตราสวนระหวาง Young’s modulus กบความหนาแนน โดยในแบบจำาลองทงสองมการยดแผนคอมพอสทไวเฉพาะดานบนและดานลาง

0 s 14 s 30 s 43 s 60 s 88 s(ก)

15 s 30 s 45 s 60 s 75 s 90 s(ข)

การกระจายตวของคลนความเคนในคอมพอสทประเภท (ก) uni-directional และ (ข) bi-directional เมอโดนกระสนเขาปะทะดวย

ความเรวตน 390 m/s

เมอพจารณาถงความเรวตกทายของกระสนทผานแผนคอมพอสท ดงรปทแสดงไวขางลาง จะเหนไดวาแผนคอมพอสทแบบ bi-directional สามารถรบแรงปะทะของกระสนไดมากกวาคอมพอสทแบบ uni-directional เนองจากความเรวตกทายของแผนคอมพอสทแบบ bi-directional มคานอยกวา ซงสอดคลองกบกราฟแสดงพลงงานท

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แสดงใหเหนวาแผนคอมพอสทแบบ bi-directional รบพลงงานไดมากกวาแผนคอมพอสทแบบ uni-directional และหากเปลยนความเรวตนของกระสนในชวง 300-650 m/s เพอเปรยบเทยบประสทธภาพของแผนคอมพอสททงสองแบบ พบวาในชวงความเรวของกระสนตำา แผนคอมพอสทแบบ bi-directional สามารถรบแรงไดมากกวา เนองจากความเรวตกทายนอยกวา แตความแตกตางนจะนอยลงเมอความเรวตนสงขน

time (s)

bulle

t vel

ocity

(m/s

)

325

350

375

400

unidirectionalbidirectional

time (s)0 25 50 75 100 125 150ab

sorb

ed e

nerg

y in

the

targ

et (J

)

0

5

10

15

20

25

strike velocity (m/s)300 400 500 600 700

resi

dual

vel

ocity

(m/s

)

200

300

400

500

600 unidirectionalbidirectional

(ซาย) กราฟแสดงความเรวตกทายของกระสนททะลผานแผนคอมพอสทและพลงงานทแผนรบไวสำาหรบการจดเรยงตวแบบ uni- และ bi-directional สำาหรบกระสนทความเรวตน 390 m/s (ขวา) ความเรวตกทายของกระสนท

เขาปะทะดวยความเรวตนตางๆ สำาหรบแผนคอมพอสททงสองแบบ

อยางไรกตาม ในลกษณะของการทดสอบยงจรงนนจะใชแผนรปสเหลยมจตรสในการทดสอบ ดงนนจงไดมการปรบแบบจำาลองใหมขนาดใหญขนโดยขยายความกวางของแบบจำาลองเดมใหเทากบความยาว 100x100 mm2 โดยการกระจายของคลนความเคนจะมลกษณะ

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เปนวงกลมขยายออกไปทกทศทางจนถงขอบแผนคอมพอสท ดงทแสดงไวในรปขางลาง

15 s 30 s 45 s

60 s 75 s 90 sการกระจายตวของคลนความเคนในคอมพอสทแบบ bi-directional

เมอโดนกระสนเขาปะทะดวยความเรวตน 390 m/s

ในสวนของการพยายามหาคาคณสมบตทแทจรงของแผนคอมพอสททใชทดสอบในโครงการ ไดมการดำาเนนการขอความอนเคราะหใชเครองมอทดสอบทภาควศวกรรมเครองกล จฬาลงกรณมหาวทยาลย โดยวางแผนทำาการทดสอบเพอหาคา Young’s modulus ของแผนคอมพอสท ตามมาตรฐาน ASTM D3039 และ D3518 ซงใชแผนคอมพอสทรปสเหลยมผนผา (Uniform cross-section) และทำาการยดจบดงรปทแสดงขางลาง การทดลองนมความลาชาเนองจากการสงซอ strain gage จากตางประเทศผานตวแทนจำาหนายในประเทศไทย มความลาชา โดยขณะนไดทำาการทดลองไปแลวสวนหนง ปญหาทเกดไดแก การจบยดชนงานไมแนนพอ หากแนนไปจะทำาใหเกด

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การแยกชน (delamination) ของแผนคอมพอสท ในบางครงชนงานทดสอบเกดการเสยหายภายดานปลาย ทำาให strain gage ไมสามารถวดคาได หรอไมกเกดการแยกชน (delamination) และสลปในทสด ในเบองตนนไดผลคาความเคนและความเครยดจากการดงแบบ tensile test ดงรปขางลาง คาคณสมบตทได (Young modulus) มความใกลเคยงกบคาใน literature แตควรจะทำาหลายชนงานกวาน เพอทำาการหาคาเฉลยเชงสถตทเหมาะสม เพอใชปอนเขาแบบจำาลองทสรางขน

0102030405060708090

100

0 0.01 0.02 0.03Strain

Stre

ss (M

Pa)

From Strain gage

From Extensometer

(บนซาย) รปการทดลองหาคา Tensile Young’s modulus ของชนงานคอมพอสท ซงจะให (บนขวา) คาความเคนและความเครยดจากซอฟแวร และนำา

มา (ลาง) ประมวลผลเพอหาคาเฉลยทางสถต

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แบบจำาลองทสรางขนซงสามารถเปรยบเทยบกบงานทเกยวของของ Gu and Xu (2004) นน จำาเปนตองมการดดแปลงเพอใหเหมาะสมกบชนงานทใชทดสอบในโครงการ โดยไดมการทำาการทดลองเพอหาคาคณสมบตทแทจรงของชนงานในโครงการควบคกนไป

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ผลลพธจากงานวจย (Output) ทเกดขน (ดเอกสารแนบประกอบ)1. ฐานขอมลทเกยวของการการจำาลองแบบความเสยหาย 2. T. Vanichayangkuranont, K. Maneeratana and N.

Chollacoop, “Simulation of Stress Wave Propagation from Dynamic Loads,” 19th Conference of Mechanical Engineering Network of Thailand (ME-NETT19), October 19-21, 2005, Phuket, Thailand

3. T. Vanichayangkuranont, N. Chollacoop and K. Maneeratana, “Numerical Simulation of Ballistic Impact on Ceramic Armor,” 4th Thailand Materials Science and Technology Conference (MSAT IV), March 31 – April 1, 2006, Pathumthani, Thailand

4. T. Vanichayangkuranont, K. Maneeratana and N. Chollacoop, “Numerical Simulations of Level 3A Ballistic Impact on Ceramic/Steel Armor,” 20th Conference of Mechanical Engineering Network of Thailand (ME-NETT20), October 18-20, 2006, Nakhon Ratchasima, Thailand

5. T. Vanichayangkuranont, N. Chollacoop and K. Maneeratana, “Numerical Simulations of Ballistic Impact of ss109 on Alumina/Steel Armor,” NSTDA Conference 2007, March 28-30, 2007, Pathumthani, Thailand

6. P. Kumrungsie, K. Maneeratana and N. Chollacoop, “Simulation of Ballistic Impact on Polymer Composite Armor,” NSTDA Conference 2007, March 28-30, 2007, Pathumthani, Thailand

7. P. Kumrungsie, K. Maneeratana and N. Chollacoop, “Effects of Fiber Orientation on Ballistic Impact upon Polymer Composite Plate,” 21st Conference of Mechanical Engineering Network of Thailand (ME-NETT21), October 17-19, 2007, Chonburi, Thailand

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18Summary of Literature Survey on Ballistic Modeling

2001 B.A. Roeder and C.T. Sun

Dynamic penetration of alumina/aluminum laminates: experiments and modeling

Int. J. Impact Eng, 25, 169-185

Goals: Investigate the effect of structural layering and thermal residual stresses on impact resistance of Al/Al2O3 via experiment and modeling using ABAQUS/Explicit.

Results: Thick layer laminates allow less penetration than thin layer laminates. Thermal residual stress by high temperature curing is minor

Details:

Tested at velocity between 100 and 300 m/s. Layering effect is done by fixing the volume fraction of Al and Al2O3 but varying

the number of layers. Projectile is 14 mm in diameter with hemispherical head and 28.1 mm long (mass

= 31 g). Simulation was run for 100 s with automatic time step of 0.1-10 ns. Steel not allowed to fail. Al has ductile tensile failure by limiting pressure stress

to hydrostatic cutoff stress, leaving deviatoric stress component unaffected. Alumina has brittle tensile failure by setting deviatoric stress component to zero and pressure stress is required to be compressive.

Since alumina directly below projectile tip is crushed and reformed in the experiment, the model assumes that a small number of alumina elements directly below projectile are not allowed to fail in tension greatly improve stability of the solution.

Weakness in model: can’t model radial cracking, no adhesive layer, crude model for alumina compressive behavior.

Use developed model in parametric study:o Penetration dominated by yielding of Alo Fairly insensitive to change in compressive strength of alumina

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1999 G. Ben-Dor, A. Dubinsky and T. Elperin

On the order of plates providing the maximum ballistic limit velocity of a layered armor


Goals: To determine the order of plates in the armor that provides maximum ballistic limit velocity.

Results: Claim that the ratio of distortion pressure to density of plate is the key parameter to determine the order of the layer (must be placed in the order of increasing this parameter regardless of their thickness)

Details: very math with no experimental data/numerical simulation

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1999 T. Borvik, M. Langseth, O.S. Hopperstand and K.A. Malo

Ballistic penetration of steel plates


Goals: Study impact behavior of Weldox 460 E steel plate by blunt-nosed cylindrical projectile

Results: Good agreement between simulation and experiment, overestimating ballistic limit by 10%

Details:

Use compressed gas gun to do high-precision test with digital high-speed camera Coupled constitutive model of viscoplasticity and ductile damage implemented in

non-linear FE code LS-DYNA Blunt-nosed cylindrical projectile has mass (mp) = 197 g, diameter (dp) = 20 mm,

length (lp) = 80mm. Weldox 460 E steel plate target has thickness (hp) = 12 mm, clamped at diameter

of 500 mm Experimental ballistic limit curve fitted to a model by Lambert (with a = 0.76, p =

2.36)

But if p = 2, a = 0.85 (model of Recht and Ipson gives p = 2 and Assume isotropic material and von Mises plasticity, engineering model proposed

by Johnson and Cook gives

Johnson-Cook modified to include damage factor

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2001 T. Borvik, O.S. Hopperstand, T. Berstad and M. Langseth

A computational model of viscoplasticity and ductile damage for impact and penetration

Eur. J. Mech A/Solids, 20, 685-712

Goals: Detail of computational model

Results: Good agreement between simulation and experiment

Details:

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2001 T. Borvik, O.S. Hopperstand, T. Berstad and K.A. Malo

Numerical simulation of plugging failure in ballistic penetration

Int. J. of Solids and Struct, 38, 6241-6264

Goals: Compare simulation results of different level of material model sophistication

Results:

Element size is a vital parameter All levels of model show good agreement at v >> ballistic limit but error increases

when v ballistic limit Strain rate, temperature and stress state are also important Not yet include adaptive meshing, which will be necessary for ductile hole

enlargement by conical projectile

Details:

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2002 T. Borvik, M. Langseth, O.S. Hopperstand and K.A. Malo

T. Borvik, O.S. Hopperstand, T. Berstad and M. Langseth

Perforation of 12mm thick steel plates by 20 mm diameter projectiles with flat, hemispherical and conical noses Part I: Experimental studyPart II: Numerical simulations

Int. J. Impact Eng, 27, 19-35, 37-64

Goals: Study the effect of projectile tip geometry on ballistic behavior of steel target.

Results: Blunt causes failure by plugging (dominated by shear banding) while hemispherical and conical cause failure by pushing material in front of projectile aside.

Details:

In simulation, need adaptive meshing for conical projectiles

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2003 W. L. Cheng, S. Langlie, S. Itoh

High velocity impact of thick composites


Goals: Model for ballistic impact onto thick composites (punching, fiber breaking, delamination) using orthotropic constitutive behavior with stress-based failure criteria (DYNA2D)

Results:

Details:

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2001 H.D. Espinosa, H-C Lu, P.D. Zavattieri and S. Dwivedi

A 3-D finite deformation anisotropic visco-plasticity model for fiber composites

J. of Composite Materials vol 35, p. 369-410

Goals: 3D anisotropic visco-plasticity integraded into in-house FE code FEAP98 for GRP composites

Results:

Details:

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2001 V.P.W. Shim, C.T. Lim and K.J. Foo

Dynamic mechanical properties of fabric armor

Int. J. Impact. Eng., vol 25, p. 1-15

Goals: Calibrate material model for Twaron fabric by experimental split Hopkinson bar with three-element linear viscoelastic model (2 springs and 1 dashpot)

Results: Show good agreement with experiment

Details: -viscoelastic, strain-rate dependent constitutive relation-can use simple spring-dashpot system to capture dynamic response reasonably well (k1, k2 and k2 are assigned values of 110.6 GPa, 2.724 GPa and 4.8 MPas) with strain-rate-based failure criteria

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This constitutive relation was implemented in C.T. Lim, V.P.W. Shim, Y.H. Ng, International Journal of Impact Engineering 28 (2003) 13-31 using DYNA3D (Mat Type 19)

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2003 C.T. Lim, V.P.W. Shim and Y.H. Ng

Finite-element modeling of the ballistic impact of fabric armor

Int. J. Impact. Eng., vol 28, p. 13-31

Goals: Model ballistic response of Twaron fabric by a spherical ball

Results:

Details:

using DYNA3D (Mat Type 19) with time step scaling factor satisfying

to simulate a ball hitting a fabric sheet with high velocity

The following results show good agreement.

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F-MT-RDE-17 Rev.1

47The 19th Conference of Mechanical Engineering Network of Thailand

19-21 October 2005, Phuket, Thailand

Simulations of Stress Wave Propagation from Dynamic Loads

Tarin Vanichayangkuranont1, Kuntinee Maneeratana1 and Nuwong Chollacoop2

1 Department of Mechanical Engineering, Chulalongkorn University, Bangkok 103302 National Metal and Materials Technology Center (MTEC), Pathumthani 12120

Email [email protected], [email protected] and [email protected]

AbstractStress waves in solid bodies from dynamic

loads are simulated by the ABAQUS finite element package. The considered body geometries are 1D & 2D bars and thick & thin walls. The 2D plane strain condition is assumed. Material properties are elastic and bi-linear elastic plastic with non-linear geometry stipulation. The 1D elastic results are compared with available analytical solutions while the additional effects of geometries and materials are monitored, described and clarified. It is shown that the wave propagations should not be neglected, particularly under very high dynamic loadings. The simulations show that a reasonably fine mesh is required in conjunction with the time increment of an appropriate Courant number Co – fraction of the smallest element that the stress wave travels in one time step. The Co values of up to 0.5 are acceptable but 0.1 is recommended to ensure the grid and time independency solutions.

Keywords: stress wave propagation, Courant number, dynamic loadings, ABAQUS, finite element method

1. IntroductionThe National Metal and Materials

Technology Center (MTEC) has initiated a project to develop the light weight hard armour for the Royal Thai Military Armoury [], aiming to improve materials and design, produce and test hard armour prototypes. In the process, materials and design prototypes must be assessed by standard firing tests (Fig. ) which are time consuming and expensive.

Figure 1 Standard firing tests.

As hard armours comprise of layers of ceramic, steel and polymer plates, the design involves the parameter specification on ceramic tile shape/sizes, thicknesses and arrangements of material layers. The design by trials and errors would require a lot of firing tests on prototypes. Thus, the numerical simulation is proposed as the alternative method of analysing ballistic loads on the armours, obtaining design specifications as well as reducing the number of firing tests. The advantages of the method include the cost and time reduction in the design process with the suggested guidelines, particularly parameter adjustments for the optimised configuration.

These simulations must contain many complex models, including the impact of deformable bullets on the armour, large deformation of materials with various degrees of strain-rate sensitivities, stress waves and material failure modes from bullet penetration. It is the modelling of stress wave that is the focus of this paper.

In dynamic impact problems, there are shock waves travelling through the solid medium in very much the same way as in fluids, but at a much higher velocity. For instance, when a ship is subjected to a underwater explosion, the detonation produces a shock wave moving from the source at the speed of around 1500 m/s []. However, when the shock reaches the ship and the energy is transferred to the hull, the elastic wave speed in the steel approaches 5000 m/s, resulting in a much faster shock front and more complicate wave reflection and superposition.

F-MT-RDE-17 Rev.1


mailto:[email protected]

48This discrepancy of wave speeds may be the reason that the solid waves are often ignored [] as the stress in the solid reaches quasi-static conditions due to wave interference with respect to the time increments of fluid shocks.

Nonetheless, the shock wave propagation and superposition in solids may be neglected at one’s own perils. The high explosive squash head (HESH) effect or the high explosive plastic (HEP) method of attacking armour [] is a prime example of stress wave utilisation in military applications. The detonation of high explosive in contact with the armour plate produces the shock wave travelling through the armour. The superposition of the stress wave at the rear surface of the plate can detach a large scrab at a high velocity of up to 130 m/s. That is, the complete penetration or perforation is not necessary to cause damage as the scrab acts as a projectile on the other side of the plate.

Another example is the use of high performance polymeric fibres – characterised by low density and high strength which help increasing the wave speed – in lightweight armours. High wave speeds in the fibres are greatly desirable as they facilitate a fast and efficient absorption of the impact energy through the enlarged deformed regions [], [].

In this study, the conditions for numerical modelling of wave propagations in solids are studied in details, particularly the time increment and grid independency requirements. The ABAQUS finite element package is used to model elastic and bi-linear elastic plastic stress waves in simple geometries – 1D & 2D bars and thick & thin walls. Numerical predictions are then compared with available analytical solutions.

2. ABAQUS Finite Element PackageRelevant parts of the package are

mentioned [].

2.1 ABAQUS/Explicit PackageThe ABAQUS/Explicit is used instead of

the normal ABAQUS/Standard as the Explicit package is more suitable for the analyses in which high speed, non-linear, transient response dominates the solutions.

2.2 Material Constitutive ModelsThe elastic and bi-linear elastic plastic

isotropic material models are used. In the elastic region, the stress and strain relationship are related by 2 material properties: Young's modulus E and the Poisson's ratio ,

,

where is the Kronecker’s delta.

In the plastic region, the simple metal plasticity model with isotropic hardening is employed. The strain rate is decomposed into the elastic el and plastic pl components. For the yield surface, the von Mises equivalent stress with the associated flow rule are used with the deviatoric stress and strain such that,

, ()

where is the equivalent plastic strain rate.In addition, the geometrically non-linear

analysis with large displacements, the NLGEOM option, is used. Elements are formulated in the current configuration using current nodal positions. Strains are calculated as the integral of the rate of deformation and used together with the Cauchy stress.

Values of properties for illustration purposes are as follows: density

, , or 0.3, yield stress , and 0 at

MPa.

2.3 ElementsThe plane strain, 4-node bi-linear CPE4R

elements with reduced integration and hourglass control are used. The reduced integration uses a lower-integration for the element stiffness. The advantages of the reduced integration elements include the strain and stress calculations at the Barlow points which provide optimal accuracy, the reduction in CPU time and storage requirements from the reduced number of integration points as well as acceptable performances for approximately incompressible material behaviours. The main disadvantage is the element rank-deficient from the zero-energy modes with excessive deformations. This problem can be reduced with the hourglass control procedure which adds a small artificial stiffness.

3. Elastic Wave PropagationsIn this section, the elastic wave theory is

outlined and the stress wave propagations in simple geometries from uniform load pulses are simulated.

When an elastic solid is subjected to a stress pulse, the elastic stress wave propagates through the body at the sonic speed c [],

. ()

In wave simulations, the finite different concept is used to determine the relationship between the sizes of time increment and grids []. The stability consideration limits the maximum size of the time increment by the Courant number Co,

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where is the smallest element size. In other words, the distance travelled by the fastest wave in the body should be smaller than the smallest typical element size in the mesh during one time step so that the wave passage through the elements can be detected.

3.1 1D Elastic BarWhen, a long elastic bar is subjected to

a pressure pulse with maximum amplitude at one end, the longitudinal elastic stress wave propagates through the bar at the sonic speed c. When the wave reaches the bottom end of the bar, it reflects and travels backwards. In the simulations, the 1D mesh is obtained through constraining top and bottom sides of the bar as shown in Figure 2a.

a) 1D barσ p

5 m

0 .2 mx

b) 2D bar σ p

5 m

0 .2 mx

y

c) thick wallσ p

1 m

0 .2 mx

1 m

y

0 .1 m

d) thin wall4 m

0 .2 my

F p

x

0 .0 4 m

Figure 2 Problem descriptions.

First, the zero-, plane strain problems, with the analytical wave speed of 4935 m/s, are considered. The elements mesh is used for the simulations with different time steps 0.5, 1, 5 and 10 s, or equivalent to Co of 0.049, 0.099, 0.49 and 0.99, respectively.

Figure 3 shows the comparison between the analytical and numerical axial stresses from the modelling with at various time instants. The numerical results display the classic overshoots and subsequently damping around the analytical values or the oscillatory response of stress at the shock fronts due to the inertia from sudden loading and unloading. The propagation of stress wave may be traced from the graph of maximum axial stress (Figure 4), from which the time of pulse reflection and superposition can be observed and compared with the analytical value of 1.01 ms.

Then, the size of time increment is considered. The results from simulations with

and are essentially the same,

i.e. the time step independency is obtained. However, when , amplitude of the oscillating stress decreases slightly (Figure 5). Hence, the time increment of is recommended but the use of time step size up to

is acceptable as the differences in stress amplitudes are quite small.

It is noted that when the time step size is still within the limit of Co = 1, the combination of sharp shock from the near-square stress pulse and associated sudden deformation destabilise the simulations, yielding the total numerical broken-down. For this problem, the limit is found to occurs at or at Co = 0.97.

x, m0 1 2 3 4 5

xx / p

-2.0

-1.5

-1.0

-0.5

0.0

0.1 ms 0.4 ms 0.7 ms 1.2 ms

wave direction

exact solutionsnumerical predictions

Figure 3 Elastic stress pulses from the 1D bar with 400 plane strain elements, & t = 1

s (Co ≈ 0.1).

t, ms0.0 0.2 0.4 0.6 0.8 1.0 1.2

max

(xx

) /

p

-60

-40

-20

0start of wave reflection

and superposition

0v 0.3v

Figure 4 Maximum stress amplitudes from the 400-plane strain element model with, & t

= 1 s.

x, m0 1 2 3 4 5

xx

-a

/p

-0.2

0.0

0.2

0.4

0.4 ms 1.2 ms

t = 1 st = 5 s

Figure 5 Stress difference comparisons from the model with 400 plane strain elements, &

t = 5 and 1 s.

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x, m0 1 2 3 4 5

xx / p

-2.0

-1.5

-1.0

-0.5

0.0

0.1 ms 0.4 ms 0.7 ms 1.2 msexact solutionsnumerical predictions

Figure 6 Elastic stress pulses from the 1D bar with 100 plane strain elements, & Co ≈

0.0025.

A coarse zero-, plane strain grid of elements is modelled with 0.5, 0.1,

and 0.05 s, or roughly Co of 0.025, 0.0049 and 0.0025, respectively. It is found from the numerical predictions that if the mesh is too coarse, some solution features may not be captured, particularly the shock fronts, even when Co is very low (Figure 6).

Then, simulations are repeated with a non-zero material. The 0.3 value of Poisson’s ratio boosts the analytical wave speed up by 16% to 5726 m/s. The overall results are very similar to the zero modelling but with a higher wave speed such that the stress wave arrives at the end of the bar at the time t = 0.87 ms as shown in Figure 4. It is also found that if the stress load is replaced by boundary velocity, the resulting stresses from zero and non-zero materials are different with axial stress in the non-zero material are higher by some 15%.

3.2 2D Elastic BarThe problem is set up in the same

conditions as the 1D bar with the exception of the top constraints (Figure 2b). Even though the stress wave propagation is still dominated by the axial components, the Poisson effect causes lateral expansions and contractions under a propagating pulse and generates the secondary transverse waves travelling in the bar [].

The zero-, plane strain bar is first considered in the numerical simulations for the effect of Poisson’s ratio. As expected, the numerical predictions are the same as those obtained from the 1D bar.

4 ms

7 ms

12 msFigure 7 Stress Mises contours (MPa) at various time t of the 2D bar with 400 elements,

& t = 1 s.

4 ms

7 ms

12 ms

Figure 8 Exaggerated (4000) Poisson deformation at various t of the 2D plane strain bar, & t = 1 s.Then, the non zero- problem is

investigated, employing the recommended modelling parameters in the previous section. The stress wave propagations in mainly axial directions but with some trailing lateral reflections (Figure 7) as well as the lateral deformations (Figure 8) may be observed. Figure9 respectively shows the axial, lateral and von Mises elastic stress pulses along the bar at various time instants. Even though the early axial stress stays close to , the values roughly increase by 15% at t = 0.3 ms due to the boundary expansion of bar as whole pulses appears and becoming stabilised. In addition, the sharp axial pulse is lost and no longer closely emulates the applied near-square stress pulse. The yy pulse dissipates very quickly as the bar is thin in that direction as well as the fact that the free end is more flexible.

x, m0 1 2 3 4 5

Mis

es / p

0.0

0.5

1.0

1.5

2.0

0.1

ms

0.3

ms

0.7

ms

1.1

ms

0.9

ms

0.5

ms

xx / p

-2.0

-1.5

-1.0

-0.5

0.0

0.5

zz / p

-0.4

0.0

yy/

p

-0.2

0.0

0.2

Figure 9 Elastic stresses from the 2D bar with 400 plane strain elements, & t = 1 s

(Co ≈ 0.11).

3.3 Elastic Thick WallWhen an infinite medium is subject to a

F-MT-RDE-17 Rev.1

51pointed near-square force pulse, the wave front propagates outwards from the disturbance source with gradually decreased amplitude as the energy is dispersed into larger regions. However, if the body is finite (Figure 2c), several types of elastic waves are generated, principally the compression, shear and Rayleigh (surface) waves [].

A non zero- grid of elements is modelled with 0.5 s, or Co = 0.29. The stress contours are shown in Figure 10 while the stresses at y = 0 are plotted in Figure 11. It is clear from Figure 10 that the stress propagates from the source. The stresses in areas directly in front of the short applied pressure move directly forwards while the stresses at the end of the applied source spread in the semi-circle fashion. The stress amplitude decreases as the stress wave dissipates the impact energy into wider areas.

0.08

ms

0.14

ms

0.2

ms

xx xy Mises

Figure 10 Stress contours (MPa) in the elastic thick wall with & t = 0.5 s (Co ≈

0.29).

xx / p

-0.3

-0.2

-0.1

0.0

x, m0.0 0.2 0.4 0.6 0.8 1.0

Mis

es / p

0.0

0.1

0.2

0.3

0.04

ms

0.08

ms

0.16

ms

0.20

ms

0.12

ms

xy/

p

-0.010

-0.005

0.000

0.005

Figure 11 Stresses in the elastic thick wall with 10,000 plane strain elements, & t = 0.5

s (Co ≈ 0.29).

3.4 Elastic Thin WallWhen a plate is subject to a transverse

load (Figure 2d), as in the ballistic impact, an extremely complicate propagation, reflection and superposition of different wave types occurs, even within an elastic solid. In practice [], the stresses are often simplified into the transverse wave with the velocity of , which is a function of shear modulus and ,

. ()The problem is modelled with non-zero-,

plane strain mesh with elements and the time step 0.5 s or Co = 0.14. The stresses in Figure 12 show that the wave moves in the transverse direction by repeated reflecting with the boundaries of the wall. The von Mises graphs show the motion of wave fronts is just slightly slower than the approximated transverse wave speed = 3061 m/s,

F-MT-RDE-17 Rev.1

52

xx / p

-0.2

-0.1

0.0

0.1

y, m0.0 0.5 1.0 1.5 2.0

Mis

es / p

0.0

0.1

0.2

0.3 0.1 ms 0.2 ms 0.5 ms0.3 ms

xy / p

-0.1

0.0

0.1

yy/

p

-0.1

0.0

0.1

0.4 ms

0.1

ms

0.2

ms

0.5

ms

0.3

ms

0.4

ms

loca

tion

oftra

nsve

rse

wav

e fr

ont

Figure 12 Stresses in the elastic thin wall with 2,000 plane strain elements, & t = 0.5

s (Co ≈ 0.14).

4. Elastic Plastic Wave PropagationsSimulations are repeated with elastic-

plastic solids.

4.1 1D Elastic Plastic BarWhen the magnitude of the load

pulse on 1D bar in section 3.1 exceeds the yield strength of the materials, the solid becomes elastic plastic and exhibit the characteristics accordingly (Figure 13). When the load is increased, the values of von Mises stress raises very slowly after it reaches the yield stress, showing as a rather flat cut-off in the graph due to the low values of plastic modulus. Even without the Poisson effect, the incompressible plastic deformation induces stresses in other directions and there is a secondary plastic-induced stress trails behind the main stress pulse.

4.2 2D Elastic Plastic BarThe elastic plastic simulation (Figure

14) show similar characteristics as the elastic modeling, the introduction of stresses in other directions. As the plastic deformation limits the increase of von Mises stress, other stress components are relatively higher and the truncation of von Mises stress after the yielding

is observed.

xx / p

-0.8

-0.4

0.0

x, m0 1 2 3 4 5

Mis

es / p

0.0

0.2

0.4

0.6

0.1 ms

0.4 ms 0.7 ms1.2 ms

zz / p

-0.6

-0.4

-0.2

0.0

Figure 13 Elastic plastic stress pulses from 1D bar with 400 plane strain elements, & t =

1 s.

xx / p

-1.0

-0.5

0.0

x, m0 1 2 3 4 5

Mis

es / p

0.0

0.5

0.1 ms 0.3 ms 0.7 ms 1.1 ms0.9 ms0.5 ms

zz / p

-0.6

-0.4

-0.2

0.0

0.2

yy/

p

-0.2

0.0

0.2

0.4

Figure 14 Elastic plastic stresses from 2D bar with 400 plane strain elements, & t = 1

s.

4.3 Elastic Plastic Thick WallAs before, the plastic deformations

inhibit the sharp cut-off of von Mises stress with

F-MT-RDE-17 Rev.1

53increasing load (Figure 15). It can be seen that the plastic deformations occurs near the loads and as the wave propagates into wider regions, the stress amplitude may be reduced until only elastic deformation occurs. However, as the wave reaches the other surface, the amplitude is increased from wave superposition and plasticity may again takes place.

xx / p

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

x, m0.0 0.2 0.4 0.6 0.8 1.0

Mis

es / p

0.0

0.1

0.2

0.04

ms

0.08

ms

0.16

ms

0.20

ms

0.12

ms

xy/

p

-0.01

0.00

0.01

Figure 15 Stresses in the elastic plastic thick wall with & t = 0.5 s (Co ≈ 0.29).

4.4 Elastic Plastic Thin WallThe stresses in the load directions are

very high near the source, introducing the plasticity in that area (Figure 16). As the load is dispersed sideway, the stress amplitude reduces such that the deformation becomes wholly elastic. Yet, the localised plasticity introduces higher values of transverse stresses and the shape of stress pulses is comparatively flatten.

5. ConclusionElastic and elastic plastic stress wave

propagations from near-square stress pulses are simulated. In all, 4 simple geometries are considered. It is clear that, apart from extremely simple problems, the stress wave propagations are very complex. The numerical method is required for the analyses with special cares on the Courant number Co selection. Even though the state of stress reaches quasi-static conditions very quickly in the order of milli-seconds, the superposition of waves at free surfaces can pose problems as the stress amplitude doubles and can cause localised failures. In armour applications, the ejection of broken pieces may prove dangerous [] and hence, the stress waves should be taken into considerations in the armour

design, both as the mean of improving energy dissipation as well as the possible source of fracture.

AcknowledgmentsThis research is supported by the National

Metal and Materials Technology Center (MTEC), contract no. MT-B-48-CER-07-188-I. Special thanks are due to Dr. K. Sujirote, Dr. D. Atong, Dr. K. Prapakorn, Dr. A. Manonukul, Assc. Prof. Dr. T. Amornsakchai, Asst. Prof. Dr. S. Rimdusit and Maj. Gen. Dr. W. Phlawadana.

xx / p

-0.3

-0.2

-0.1

0.0

0.1

y, m0.0 0.5 1.0 1.5 2.0

Mis

es / p

0.0

0.1

0.2

0.1 ms 0.2 ms 0.5 ms0.3 ms

xy / p

0.0

0.1

yy/

p

-0.1

0.0

0.1

0.4 ms

Figure 16 Stresses in the elastic plastic thin wall & t = 0.5 s (Co ≈ 0.14).

References[] K. Prapakorn, K. Maneeratana, K. Sujirote,

D. Atong, T. Amornsakchai, N. Chollacoop, S. Rimdusit, and A. Manonukul, “Development of light weight hard armor for the Royal Thai Military Armory”, NSTDA Annual Conference 2005, Bangkok, 28-30 March 2005, code P030 (in Thai).

[] P. Siribodhi, W. Wongdontri and P. Twinprawat, “Damage assessment of naval surface vessels resulted from underwater explosions”, ME-NETT 17 Conference, Pracheanburi, Thailand, 15-17 October 2003, code AM002 (in Thai).

[] K.J.W. Goad and D.H.J. Halsey, Ammunition (Including Grenades & Mines), Brassey’s Battlefield Weapons

F-MT-RDE-17 Rev.1

54Systems & Technology Volume III, Brassey, UK, 1982, pp. 116-118.

[] S.S. Morye, P.J. Hine, R.A. Duckett, D.J. Carr and I.M. Ward, “Modelling of the energy absorption by polymer composites upon ballistic impact”, Composites Science and Technology, Vol. 60, 2000, pp. 2631-2642.

[] M.J.N.Jacbos and J.L.J. van Dingenen, “Ballistic protection mechanisms in

personal armour”, Journal of Material Science, Vol. 36, 2001, pp. 3137-3142.

[] ABAQUS Inc., ABAQUS 6.3.1 Documentation, Rhode Islands, USA, 2003.

[] K.F. Graff, Wave Motion in Elastic Solids, Oxford, Clarendon Press, 1975.

[] K.-J. Bathe, Finite Element Procedures, Prentice-Hall, New Jersey, 1996, pp. 814-822.

F-MT-RDE-17 Rev.1

55

Numerical Simulation of Ballistic Impact on Ceramic Armor

Tarin Vanichayangkuranont1, Nuwong Chollacoop2 and Kuntinee Maneeratana1 1 Department of Mechanical Engineering, Chulalongkorn University, Bangkok 10330

Phone 0-2218-6639, Fax. 0-2252-2889, E-Mail: [email protected] and [email protected] National Metal and Materials Technology Center (MTEC), Pathumthani 12120

Phone 0-2564-6500 ext 4700, Fax. 0-2564-6403, E-Mail: [email protected]

Abstract

A preliminary investigation of ballistic

impact on ceramic armor was carried out by

recourse to numerical simulation using finite

element method. Following our earlier study []

on the effect of stress wave propagation from

dynamic loads, the current computational model

was developed with built-in brittle failure

criteria, aiming to correlate with experimental

ballistic testing. It was found that the rate that the

ceramic armor absorbed the bullet kinetic energy

raised as the armor thickness increased.

Keywords: Ballistic impact, finite element

method, ceramic armor

1. Introduction

The National Metal and Materials

Technology Center (MTEC) had initiated a

collaborative research project to develop the

light-weight hard armor for the Royal Thai

Military Armory []. The project aims to build

import-comparable armor prototypes made from

various materials available and/or assembled

domestically in order to reduce the quantity of

armor imported annually.

As hard armors typically comprise of layers

of ceramic, metal and polymer, there are many

design parameters involved in the construction of

prototypes. Even if all materials are selected,

geometrical factors such as size, thickness and

arrangement are critical to the performance. The

design by trials and errors would require a lot of

firing tests on prototypes, which are both time-

consuming and expensive (Fig. 1). The numerical

simulation provides an alternative approach for

analyzing ballistic impact, helps guiding the design process and reducing the number of the firing tests required to achieve the optimal configuration.

Fig. 1 Standard firing tests [].

The present study aims to develop computational model that can qualitatively describe ballistic impact of fast moving bullet onto ceramic armor during the firing tests []. The effects of ceramic thickness are discussed in terms of deformation area and energy absorption.

2. Computational Model

F-MT-RDE-17 Rev.1





56All finite element calculations are

performed using ABAQUS/Explicit [] due

to the nature of high speed, non-linear transient

responses in the solutions. An axisymmetric model is used for simulations of a round-shape bullet penetrating a layer of ceramic material, as shown in Fig. 2.

The modeled bullet emulates the caliber 0.22 long rifle cartridge with the 40 grains lead round nose (LRN) bullet. However, the diameter of the modeled bullet body is slightly reduced to match those of head and heel. The bullet geometry composes of a half-hemisphere with radius wh and the cylindrical body of arbitrary length hb. Both parameters are set to wh = 2.794 mm and hb = 7.21 mm in this study such that the model corresponds to commercial bullets in terms of diameter and mass.

The ceramic layer has the thicknesses hc of 3 and 6 mm, corresponding to the tested ceramic tile. In order to eliminate edge effects, the ceramic layer has a much larger radius wc of 60 mm was used for both cases.

Due to the anticipated severe deformation at contact, the fine mesh (0.1×0.1 mm2) is used at the ceramic region directly beneath the bullet tip while coarser mesh (0.1×0.5 mm2) is used further away to reduce computational expense, as shown in Fig. 2.

The fully restrained boundary condition is applied to the right edge of the ceramic layer while the left side of

the model follows axisymmetric boundary condition. The bullet is given a downward initial speed of 437 m/s, the actual average bullet speed obtained from the firing test.

Fig. 2 The bullet/ceramic configuration and meshes

The bullet is modeled as an elastic material with Young’s modulus and Poisson’s ratio of 204 GPa and 0.33, respectively, approximating the hardened tool steel. The modified density is used to obtain the bullet mass of 3.2814 g used in the actual firing test. The effect of deforming bullet will be studied in the future.

The ceramic armor is modeled as an alumina layer with Young’s modulus of 303 GPa, Poisson’s ratio of 0.21 and density of 3,720 kg/m3. Brittle failure criterion is invoked to simulate failure in the layer. Crack initiates when cracking stress reaches flexural strength, assumed here as 300 MPa []. Then, the material strength deteriorates linearly to zero at the critical cracking strain of 1% []. When this local cracking strain at a material point is reached, the material point fails and all the stress components are set to zero. When all of the material points in an element fail, the element

F-MT-RDE-17 Rev.1

57is removed from the mesh. For the shear behavior, the shear modulus is reduced to 1% of the undamaged value when the critical cracking strain [] is reached.

3. Results and DiscussionsThe bullet is allowed to penetrate

the ceramic layer completely. Fig. 3a shows Mises stress contour plot for the 3-mm-thick layer at initial, half-way and full penetration whereas Fig. 3b shows the results for the 6-mm-thick armor. The blue-to-red stress levels range from 0 to 300 MPa (flexural strength) in an equal incremental order. The red color denotes that areas in which the Mises stress exceeds the flexural strength. In addition, these contours clearly show ripples of interfering stress waves traveling away from the impact [1].

The larger region experiencing high Mises stress in the thicker sample in Fig. 3 agrees with the larger damaged areas in the actual firing tests of thicker ceramic tiles []. Furthermore, this observation is confirmed in the energy breakdown plots in Fig. 4, showing the total energy (TE), kinetic energy (KE) and internal energy (IE) of the system (sys), bullet (bul) and ceramic armor (cer). The initially large kinetic energy (KEbul) from the bullet is largely transmitted through the kinetic energy of the ceramic layer (i.e. flying fractured pieces) and some via internal energy (IEsys) of the remaining ceramic layer. A reduction in the total energy (TEsys) of the whole system due to mass

erosion (element removal after critical cracking strain) is also observed as pointed out in [].

(a) 3

-mm

-thick

cer

amic

arm

or

0.4 μs

4.8 μs

7.9 μs

(b) 6

-mm

-thick

cer

amic

arm

or 0.6 μs

6.9 μs

15.6 μs

Fig. 3. The Mises contour plots of (a) 3mm and (b) 6mm thick layers at

initial, half-way and through penetrations.

4. ConclusionIn this study, a preliminary

investigation of ballistic impact was conducted via finite element method. The developed computational model was consistent with the experimental results from the firing test. Further refinement of the current model is warranted for quantitative predictability.

F-MT-RDE-17 Rev.1

58

Acknowledgments

This research is supported by MTEC,

contract no. MT-B-48-CER-07-188-I with

special thanks for Dr. K. Sujirote, Dr. D. Atong,

Dr. K. Prapakorn, Dr. A. Manonukul, Assc. Prof.

Dr. T. Amornsakchai, Asst. Prof. Dr. S. Rimdusit

and Maj. Gen. Dr. W. Phlawadana.

time t, s0 5 10 15

TE, K

E (J

)

0

50

100

150

200

250

IE (J

)

0

5

10

15

TE, K

E (J

)

0

50

100

150

200

250

IE (J

)

0

5

10

15

TEKEIE

TE, K

E (J

)

0

50

100

150

200

250

IE (J

)

0

5

10

15

sys

bul

cer

time t, s0 5 10 15 20 25 30

TE, K

E (J

)

0

50

100

150

200

250

IE (J

)

0

5

10

15

TE, K

E (J

)

0

50

100

150

200

250

IE (J

)

0

5

10

15

TEKEIE

TE, K

E (J

)

0

50

100

150

200

250IE

(J)

0

5

10

15

sys

bul

cer

(a) 3-mm-thick armor (b) 6-mm-thick armor

Fig. 4 Breakdown of energy in components.

References

[] Vanichayangkuranont, T., Maneeratana, K.

and Chollacoop, N., Simulations of stress wave

propagation from dynamic loads, ME-NETT 19

Proceedings, Phuket, 19-21 October 2005.

[] MTEC, MT-B-48-CER-07-188-I Report,

Research-in-progress Report (6 months), 2005.

[] Habbitt, Karlsson and Sorensen Inc.,

ABAQUS version 6.3 Theory Manual,

Pawtucket, 2003.

[] Medvedovski, E., Alumina ceramics for

ballistic protection, American Ceramic Society

Bulletin, 81(3): 27-32, 2002.

[] Fawaz, Z., Zheng, W. and Behdinan, K.,

Numerical simulation of normal and oblique

ballistic impact on ceramic composite armours,

Composite Structures, 63(3-4): 387-395, 2004.

F-MT-RDE-17 Rev.1

59

F-MT-RDE-17 Rev.1

60The 20th Conference of Mechanical Engineering Network of Thailand

18-20 October 2006, Nakhon Ratchasima, Thailand

Numerical Simulations of Level 3A Ballistic Impact on Ceramic/Steel Armor

Tarin Vanichayangkuranont1, Kuntinee Maneeratana1 and Nuwong Chollacoop2

1 Department of Mechanical Engineering, Chulalongkorn University, Bangkok 10330, ThailandTel: 0-2218-6639, Fax: 0-2252-2889, *E-mail: [email protected] and [email protected]

2 National Metal and Materials Technology Center (MTEC), Pathumthani 12120, ThailandTel: 0-2564-6500 ext 4700, Fax: 0-2564-6403, E-mail: [email protected]

F-MT-RDE-17 Rev.1


AbstractThis article concerns with the ABAQUS simulation

of 9-mm-bullet impacts with initial velocities between 419 – 431 m/s on ceramic/steel armor plates, which complies with the level 3A of the National Institute of Justice (NIJ) standard. In most studies, the impactators are very hard compared to the armor. In reality, the bullets are quite soft and frequently disintegrate upon impacts, making them particularly difficult to model. This preliminary study aims to confirm that the relative strength of the bullet and armor is a major aspect in the ballistic simulations. Without trying to accurately capture the bullet rupture, pragmatic numerical models may be obtained by using hard bullets and armor plates with heightened strengths. That is, the bullet is elastic while the strength of ceramic armor, whose function is to shatter the bullet, is raised by increasing the tensile strength. It can be argued that rough simulations of impacts may be obtained and numerical results of 4 simulations, in which the tensile strength of ceramics are heightened, qualitatively agree with the experimental observations.Keywords: Ballistic impact, ceramic, steel, ABAQUS

1. IntroductionThe National Metal and Materials Technology

Center (MTEC) has initiated a project to develop the light weight hard armor, aiming to improve materials, design and produce hard armor prototypes with local materials []. As hard armors comprise of layers of ceramic, steel and polymer plates, the design involves the parameter specification on ceramic tile shape/sizes, thicknesses and arrangements of material layers. Thus, the numerical simulation is used to analyze ballistic impacts on the armors in order to obtain rough guidelines, particularly parameter adjustments for the prototype configuration.

So far, the investigated aspects of ABAQUS finite element simulation were the effects of stress wave propagation from dynamic loads, involving elastic and elastic plastic armor plate [] as well as the impact of elastic bullet on an alumina plate which fails by brittle failure criterion [].

During ballistic impacts between a bullet and armor, the bullet tries to punch through the plate and may disintegrate in the process. This phenomenon involves many complex mechanisms, e.g. large deformation, crack and fracture, of both bullet and armor. Thus, it is extremely difficult to emulate these mechanisms in the simulation and may be beyond a normal package capability. Even though modeling of plastically deformed impactators on relatively low strength armors, like composites plates, are achievable in previous studies, impactators on ceramics, which are much harder, are usually assumed to be rigid or elastic in the simulations [], []. In reality, the bullet materials are quite soft, resulting in very large deformation and shattering of bullets upon impacts. Moreover, it is necessary to specify the contact surfaces of the objects coming into contact. The material failure and subsequent removal of both bullet and armor violates and invalidates this contact

specification, preventing very meaningful results. That is, the impact simulation of relatively soft impactators on such targets causes substantial problems.

This study aims to show that the relative strength of the bullets and armors is a major aspect in the ballistic simulations. Without trying to accurately capture the rupture mechanism of soft bullets, pragmatic numerical models may be obtained by using hard bullets and armor plates whose resistance to fracture is artificially raised. That is, the bullet is elastic and does not fail while the armor plates can. As the particular armor prototype under consideration consists of only alumina and steel layers, only the fracture resistance of the ceramics, which is used to break down the bullet material integrity, are heightened while the property of steel remains unchanged. In addition, as it is unable to obtain accurate material properties at such high strain rates due to the budget and procedure limitation, the results are not expected to be accurate but may be able to point out certain characteristics of the problems. In short, this approach may be quite imprecise, but if it produces some reasonable results that can be analyzed to extract some useful overview tendency or used as a basis for further model refinements, it is definitely better than none at all.

2. Case StudiesThe experiments on alumina ceramics and steel

plates are used as the case studies []. They were conducted at the certification firing range (Figure 17) in an arsenal on 25-26 August 2005. A single 9-mm-bullet was fired upon each specimen. The impact falls under the 3A threat-level of the NIJ standard [], which is also adopted into an equivalent code for the Royal Thai Military.

In all, 4 armor specimens, each made up of an alumina plate in the front and a steel back layer, are tested. The alumina plates are constructed from hexagonal ceramic tiles which are glued together and wrapped up by a dynema cloth before assembling with the back steel plate. The thicknesses of these ceramic tiles are 4 mm, 6 mm, 8 mm and 8 mm respectively for the 4 test cases while all steel plates are always 1.5 mm thick. The velocity of the bullets V0, measured by the sensors after the bullets leave from the barrel (Figure 17, left), ranges from 419 – 431 m/s as summarized in Table 1.

Figure 17. Standard firing tests

The images of the plate damages after impact are shown in Table 2 while the main result, the ability of the plate to withstand impacts and prevent clean penetration, is summarized in Table 1 under the experiment column. Each specimen showed some localized damages on a single tile while the back steel plates show large bulge which causes petal damages in the single test case that the back steel plate is penetrated.

Table 1. Case studies and main results

case V0 (m/s) specimens (thickness in mm) exp. num.I 431 ceramics (4) + steel (1.5) plates II 419 ceramics (6) + steel (1.5) plates III 426 ceramics (8) + steel (1.5) plates IV 422 ceramics (8) + steel (1.5) plates

The bullet penetrates through the plates. The bullet does not penetrate through the plates.

3. Numerical SimulationsAll finite element simulations are performed using

ABAQUS/Explicit [] due to the high speed, non-linear transient responses in the solutions. An axisymmetric model is used for simulations of a round-shape bullet penetrating layers of ceramics and steel plates, as shown in Figure 18.

A real 9-mm Full Metal Jacketed Round Nose (FMJ RN) bullet is made of an outer copper alloy jacket covering a softer lead core and has the nominal mass of 8.0 g. In the modeling, the bullet is assumed to be one solid cylinder with a round nose with the 4.5-mm radius and has total length of 10 mm such that the model corresponds to commercial bullets in terms of diameter and mass. Meanwhile, the armor plates, which are assumed to be homogeneous in each layer, have the 30-mm diameters.

Table 2. Plate damages after impacts

case ceramic metal side

I

fron

tba

ck

II

fron

tba

ck

III

fron

tba

ck

IV

fron

tba

ck

Due to the anticipated severe deformation at contact, a fine mesh is used at the ceramic region directly beneath the bullet tip while a coarser mesh is used further away to reduce computational expense (Figure 18). The bullets are modeled with 46 axisymmetric elements while 1350 elements are used for the steel plates. The ceramic plates use up 5712, 6750 and 9000 elements for the 4, 6 mm and 8-mm-thick specimens, respectively. The time step size δt = 3.2 ns.

Figure 18. The bullet and central section of armor meshes

The fully restrained boundary condition is applied to the outer edge of the armor plates while the center (left side) of the plate follows axisymmetric boundary condition. In addition, the interaction between the bullet and ceramic plate are defined by the surface-to-surface contact model. Using the kinematic contact method, the bullet nose is assigned to be the master surface while the armor plate is the slave node region.

The elastic bullet is modeled after the gliding copper [] with the Young’s modulus E of 115 GPa and the Poisson’s ratio ν of 0.307. However, the density ρ is changed to ensure that the modeled bullet has the mass of 8.0 g.

The ceramic layer of the armor is made of alumina [] which has ρ = 3900 kg/m3, E = 350 GPa and ν = 0.22. The material is assumed to be elastic-perfectly plastic with the compressive yield stress σyc of 2400 MPa. The tensile strength σts of the ceramics is artificially raised from 360 MPa to 600 MPa.The Johnson-Cook model is used for the steel plate as it is well suited to model metals that are subjected to high strain rate loadings []. The yield stress at non zero strain rate depends on the strain hardening, strain rate hardening and temperature softening such that

, ()

where is the equivalent plastic strain, is the reference strain rate. The parameters A, B, C, n and m are material parameters measured at or below the transition temperature . The is the nondimensional temperature which is equal to 1 when the current temperature is greater than the melting temperature , 0 when , and linearly proportional in-between. The Johnson-Cook shear failure is based on the damage parameter , ()

where is an increment of the equivalent plastic strain and is the strain at failure., ()

where p is the pressure or mean stress, q is the Mises stress, d1 – d5 are failure parameters. Failure occurs when the value of exceeds 1.The parameters values of the steel are adjusted

from [] and [9] such that ρ = 7870 kg/m3, E = 200 GPa and ν = 0.33. The yield stress and strain hardening parameters are A = 532 MPa, B = 229 MPa and n = 0.3024. It is noted that the values of A and B are reduced as the normal graded steels, with weaker properties, are used in the experiments. The strain rate hardening constants are C = 0.0114 and . The temperature softening parameters are specific heat capacity Cp = 452 J/kgK, inelastic heat fraction α = 0.9, coefficient of thermal expansion , m = 1, = 283 K and = 1793 K. The fracture strain constants d1 = 0.0705, d2 = 1.732, d3 = 0.54, d4 = 0.015 and d5 = 0.

4. Results and DiscussionsThe qualitative results from the simulations are

summarized in Table 1 which shows that the bullet can cleanly penetrate the armor in the first case study with the 4-mm-thick ceramic plate but cannot in the other three, conforming to the experimental results. The ability of the bullet to penetrate the armors or, in a reverse viewpoint, the ability of the plates to resist damages can be judged from the depths of bullet penetration as displayed in Figure 19 which shows the displacements in the z directions (Figure 18) of the bullet tips. It is clear that the bullet in case study I penetrates through the armor while other bullets are repelled backwards.

time t, ms0.00 .05 .10 .15 .20 .25

disp

lace

men

t of b

ulle

t tip

, mm

-15

-10

-5

0

5

case I

case II

case IV

case III

Figure 19. The depths of bullet penetration.

Figure 20 shows the contours of von Mises stress on deformed meshes, in which failed elements are deleted, of all test cases at various time instants t during

the impact. They exhibits high stresses during the first period after the initial impact at the center of the ceramic plates. The stress values decrease afterwards as elements in the high stress regions fail and are deleted from the grids. Damages at back sides of the ceramics, producing many broken pieces, are more extensive than the front sides which receive the direct impact. These damages clearly affect the metal plates which are layered after the

ceramics, causing large deformations in the form of bulging. In addition, the deformation in case study I, which shows the bullet penetration, displayed the petal damage characteristics. Both damage characteristics of steel plates concur with the photos from experiments in Table 2.

case I case II case III case IVFigure 20. The deformation and von Mises stress at time instant t = 0.01, 0.03, 0.05, 0.07 and 0.09 ms.

In the explicit runs, the amount of artificial strain energy, AE, that are generated by the programs in order to prevent unduly high deformation and distortion of elements has to be considered. This artificial energy should be low compared to the total internal energy, IE, of the system for reliable results ]. In these simulations, the ratio of artificial energy over internal energy never exceeds 5% () which is considered satisfactory.

The energy of the systems, namely the internal energy (IE), the kinetic energy (KE) and total energy (TE), during impacts are plotted in Figures 6 for the case studies I to IV, respectively.

time t, ms0.00 .05 .10 .15 .20 .25

AE/

IE, %

0.0

1.0

2.0

3.0

case Icase II

case IVcase III

Figure 21. Ratio of AE over IE during the runs

inte

rnal

ene

rgy

IE, J

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steelarmor

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tern

al e

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, J

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kine

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bullet

armor ceramics

steel armor

ceramics

bulletsteel

Case IV

Figure 22. Energy plots of the case studies I to IV

From the kinetic energy graphs, the KE of bullets decreases rapidly for the first 0.02 ms, signifying that the bullet velocities are greatly reduced during the initial impacts. The bullet KE of the case I remains high as the bullet penetrates through the armor while bullet KE of other cases drops to near zero values.

From strain and total energy plots, it can be seen that the armors can effectively absorb the impact energy of the bullets. If the bullets do not penetrates, as in cases II to IV, the armors can respectively absorb 98.5, 97.4 and 97.8% of the bullet energy. Meanwhile, only 74.0% of the impact energy is absorbed in the case I in which the bullet penetrates through.

When the energy absorption between the ceramic and steel plates are compared, most of the energy that the armor absorbs are stored in the ceramics, accounting for 73.3, 86.5, 92.0 and 90.8% of the total energy that the armor absorbed from the bullet impacts from cases I to IV respectively. This leaves only 26.8, 13.5, 8.1 and 9.3% of the total strain energy in the steel plates.

5. ConclusionsThe simulations use the impact model of

9-mm bullets upon ceramic and steel plates. The results show that ceramic absorbs most of the impact energy from the bullets, accounting for more than 80% of the total energy. The most severe damages to the armor occur at the back sides of the ceramic plates due to the superposition of reflecting stress waves. The Johnson-Cook material model can effectively simulates the damages characteristics of the steel plates. The pragmatic model, employing heightened tensile strengths of ceramics with elastic bullets, enables the results to qualitatively agree with the experimental observations.



References[] MTEC, 2005. MT-B-48-CER-07-188-I

Report, 1-year progress report, National Metal and Materials Technology Center, Thailand.

[] Vanichayangkuranont, T., Maneeratana, K., and Chollacoop, N., 2005. Simulations of stress wave propagation from dynamic loads, Proceedings of the 19th Conference of Mechanical Engineering Network of Thailand (ME-NETT19), Phuket, Thailand, October 19-21, CST022.

[] Vanichayangkuranont, T., Chollacoop, N., and Maneeratana, K., 2006. Numerical simulation of ballistic impact on ceramic armor, Proceedings of the 4th Thailand Materials Science and Technology Conference (MSAT IV), Pathumthani, Thailand, March 30 - April 1, A02.

[] Roeder, B. A., and Sun, C. T., 2001. Dynamic penetration of alumina/aluminum laminates: Experiments and modeling. International Journal of Impact Engineering, Vol. 25, No. 2, pp. 169-185.

[] NIJ, 2001. NIJ Standard–0101.04, Revision A: Ballistic Resistance of Personal Body Armor, National Institute of Justice, U.S. Department of Justice.

[] Habbitt, Karlsson and Sorensen Inc., 2003. ABAQUS version 6.3 Theory Manual, Pawtucket.

[] Automation Creations, Inc., 1996-2006. MatWeb: Material Property Data. http://www.matweb.com (accessed on may 2005).

[] Borvik, T., Hopperstad, O. S., Berstad, T., and Langseth, M., 2001. Numerical simulation of plugging failure in ballistic penetration. International Journal of Solids and Structures, Vol. 38, pp. 6241-6264.

[9] Park, M., Yoo, J., Teak Chung, D., An optimization of a multi-layered plate under ballistic impact. International Journal of Solids and Structures 42 (2005), pp. 123-137.

Numerical Simulations of Ballistic Impact of ss109 on Alumina/Steel Armor

Tarin Vanichayangkuranont1, Nuwong Chollacoop2 and Kuntinee Maneeratana1

1 Department of Mechanical Engineering, Chulalongkorn University, Bangkok 10330 Tel: 0-2218-6639, Fax: 0-2252-2889, *E-mail: [email protected],

[email protected] National Metal and Materials Technology Center (MTEC), Pathumthani 12120

Tel: 0-2564-6500 ext 4700, Fax: 0-2564-6403, E-mail: [email protected]

ABSTRACT – This article concerns with the ABAQUS simulation of ss109 bullet impacts with initial velocities about 936 m/s on alumina/steel armor plates, which is rated between the level 3A and 4 of the National Institute of Justice (NIJ) standard. The current model setup was extended from the prior investigation [1] of the 9-mm bullet impact with the initial velocity of about 420 m/s (level 3A of NIJ standard), with the implementation of frictional effect between impacting bullet and armor plate. Despite the seemingly simple computational model, the simulation result showed qualitatively good agreement with the experimental observations of the armor testing.KEY WORDS – Ballistic impact, ss109, alumina, steel, ABAQUS

บทคดยอ – บทความนไดทำาการศกษาเกยวกบการจำาลองการปะทะแบบขปนะ โดยใช ABAQUS จำาลองการยงกระสนแบบ ss109 ดวยความเรวตนประมาณ 963 เมตรตอวนาทไปยงแผนเกราะอลมนา/เหลก ซงจดวาเปนการทดสอบความแขงแรงของเกราะอยในระดบระหวาง 3A และ 4 ตามมาตรฐานของกระทรวงยตธรรม ประเทศสหรฐอเมรกา (NIJ) ซงทางกระทรวงกลาโหมของไทยไดใชเปนแนวทางอางอง โมเดลทใชไดทำาการพฒนาเพมเตมมาจากงานวจยกอนหนาน [1] ทใชกระสนขนาด 9 มลลเมตร และมความเรวตนประมาณ 420 เมตรตอวนาท (ระดบ 3A มาตรฐาน NIJ) ทงนเนองจากความเรงทเพมขนเปนสองเทาสำาหรบกระสนแบบ ss109 แบบจำาลองทศกษาในงานวจยนจงจำาเปนตองมการเพมผลกระทบของแรงเสยดทานระหวางลกกระสนกบแผนเกราะ ซงผลจากการจำาลองนใหผลในเชงคณภาพตรงกบผลการทดสอบยงจรงบนเกราะทศกษานคำาสำาคญ – การกระแทกทางขปน, ss109, อลมนา, เหลก, ABAQUS


Technology Center (MTEC) has initiated a project to develop the light weight hard armor, aiming to improve materials, design and produce hard armor prototypes with local materials [2]. As hard armors comprise of layers of alumina, steel and polymer composite plates, the design involves the parameter specification on alumina tile shape/sizes, thicknesses and arrangements of material layers. Thus, the numerical simulation is used to analyze ballistic impacts on the armors in order to obtain rough guidelines, particularly parameter adjustments for the prototype configuration.

The prior studies on various aspects of

ABAQUS finite element simulation were the effects of stress wave propagation from dynamic loads, involving elastic and elastic plastic armor plate [3], the impact of elastic bullet on an alumina plate failed by brittle failure criterion [4], and the preliminary development of the computational model for NIJ level 3A ballistic testing [1].This study aims to extend the previously developed computational model for the greater damage ballistic testing with the sharper bullet (ss109) and faster speed of 936


m/s. At this high impacting velocity (almost 3x speed of sound in the air), the effect of frictional interaction is significant. Such implementation enables the qualitative prediction of the experimental results. 2. Experimental Observations

The shooting experiments on alumina/steel plates are used for comparison with the simulation [2]. They were conducted at the certification firing range (Fig. 1) in an arsenal on 25-26 August 2005. A single ss109 bullet was fired upon each specimen. The impact was classified between the 3A and 4 threat-level of the NIJ standard [5], which is also adopted into an equivalent code for the Royal Thai Military.

Among many cases, two armor specimens, each made up of a layer of alumina on top of a steel back layer, were chosen for numerical study. The alumina layers were constructed from hexagonal ceramic tiles of 8cm2

area, which were bonded together with epoxy and wrapped up by a dynema cloth (shown white in Table 1) before being bonded to the back steel plate with the same epoxy. The thickness of the ceramic tile was 8mm for both samples with the steel plate of 1.5mm thick. The velocity of the bullets V0, measured by the sensors after the bullets left from the barrel (Fig. 1, left), were 924 and 936m/s for sample I and II, labeled respectively. Post firing test revealed that the bullet hit sample I (925m/s) at the edge of the alumina tile while it hit sample II at the center of the alumina tile.

Figure 1. Standard firing tests

The images of the plate damages after impact are shown in Table 1. Both specimens showed some localized damages on a single tile while the back steel plates showed full penetration by petal damage in sample I and large bulge on sample II, due to the differences in

the locations of the alumina tiles impact. The edges of the alumina tiles were weaker due to the epoxy bond.

Table 1. Plate damages after impacts

case ceramic metal side

I

fron

tba

ck

II

fron

tba

ck

3. Numerical SimulationsAll finite element simulations in the present

study were performed using ABAQUS/Explicit solver [6] due to the high speed, non-linear transient responses expected in the solutions. An axisymmetric model was chosen for simulations of a spear-shape bullet penetrating layers of alumina and steel plates, as shown in Fig 2.

A real ss109 Full Metal Jacketed (FMJ) bullet is made of an outer copper alloy jacket covering a softer lead core and has the nominal mass of 3.95-5.18 g. In the modeling, the bullet was assumed to be a single piece (homogenized) with a sharp tip and a total length of 18 mm, estimating the commercial bullets in terms of diameter and mass. Meanwhile, the armor plates were assumed to be homogeneous in each layer spanning the total length of 30 mm in diameter to minimize the effect from the far field condition. Complication from the finite alumina tiles were not yet taken into account for the present investigation. Due to the anticipated severe deformation at contact, a finer mesh was used at the region directly beneath the bullet tip for both alumina and steel layers while a coarser mesh

was used in the region further away to reduce computational expense, as shown in Fig. 2. All regions were modeled with axisymmetric 4-node elements with enhanced hour-glass control. There were 95, 9000 and 1800 elements for the bullet, alumina and steel sections, respectively.

Figure 2. Mesh design for the bullet and central layers of alumina and steel (red indicates steel).

The fully restrained boundary condition was applied to the outer edge (right side) of the armor plates while the center (left side) of the plate assumed axisymmetric boundary condition. In addition, the interaction between the bullet and alumina layer were governed by the surface-to-surface contact model with friction coefficient of 0.3. Using the kinematic contact method, the bullet nose was assigned to be the master surface while the armor plate was the slave node region. The impact was simulated by assigning the initial downward velocity to the bullet. To ensure numerical accuracy and stable computation, the time step size is automatically calculated against the smallest element size in each increment for stable stress wave propagation throughout the computation.

The elastic bullet was modeled after the gliding copper [7] with the Young’s modulus E of 115 GPa and the Poisson’s ratio ν of 0.307. However, the density ρ was modified to approximate the commercial ss109 bullet mass. The alumina layer was modeled with elastic-perfectly plastic constitutive relation having ρ = 3,900 kg/m3, E = 350 GPa, ν = 0.22, the compressive yield stress σyc = 2400 MPa [8] and the tensile strength σts = 600 MPa [1]. During the impact, the elements were removed when any component of the stress exceeded 600 MPa in tension.

The Johnson-Cook model was used for the steel plate as it has been well suited to model metals that are subjected to high strain rate loadings [9]. The yield stress at non zero strain rate depends on the strain hardening, strain rate hardening and temperature softening such that

, ()

where is the equivalent plastic strain, is the reference strain rate. The parameters A, B, C, n and m are material parameters measured at or below the transition temperature . The is the nondimensional temperature which is equal to 1 when the current temperature is greater than the melting temperature , 0 when

, and linearly proportional in-between. The Johnson-Cook shear failure is based on the damage parameter

, ()

where is an increment of the equivalent plastic strain and is the strain at failure.

, ()

where p is the pressure or mean stress, q is the Mises stress, d1 – d5 are failure parameters. Failure occurs when the value of exceeds a unity.

The parameters values of the steel were adjusted from [9] and [10] such that ρ = 7,870 kg/m3, E = 200 GPa and ν = 0.33. The yield stress and strain hardening parameters were A = 532 MPa, B = 229 MPa and n = 0.3024. It is noted that the values of A and B were reduced from [9] as the normal graded steels, with weaker properties, were used in the experiments. The strain rate hardening constants were C = 0.0114 and . The temperature softening parameters were specific heat capacity Cp = 452 J/kgK, inelastic heat fraction α = 0.9, coefficient of thermal expansion , m = 1,

= 283 K and = 1793 K. The fracture strain constants d1 = 0.0705, d2 = 1.732, d3 = 0.54, d4 = 0.015 and d5 = 0.

4. Results and DiscussionsThe contour plots of von Mises stress on the

deformed mesh at various times after initial impact are shown in Fig. 3. Failed elements predicted from the constitutive relations of each layers were deleted from the simulation results for visualization purpose. They exhibits high stresses during the first period after the initial impact at the center of the ceramic plates. The stress values decrease afterwards as elements in the high stress regions fail and are deleted from the grids. Damages at the back sides of the alumina layer, producing many broken pieces, are more extensive than the front sides that receive the direct impact. These damages clearly

affect the metal plates in the next layer, causing large deformations in the form of bulging and subsequent the petal damage characteristics. Both damage characteristics of steel plates concur with the photos from experiments in Table 1.

The velocity (V2) and depth (U2) of the bullet tip are also shown in Fig. 4. Note that the negative value of U2 implies the bullet penetrating into the armor layers. The velocity V2 of the bullet is reduced from the initial value of 936 m/s to almost zero at t = 0.2 ms, implying that the bullet has come to a complete stop. Further confirmation on the bullet arresting event is shown by the upcoming energy plots in Fig. 7.

The 180 sweep of the axisymmetric deformed plot at t = 0.2 ms with the steel plate profile at various time are shown in Fig. 5 for comparison with the experimental observation in Table 1. The bulge area with diameter of 50 mm predicted by the simulation in Fig. 5 is in a good agreement with the value of 50-55 mm observed in the post-firing samples in Table 1.

Figure 3. The deformation and von Mises stress at time instant t = 5, 10, 15, 35, 95 and 200 s after the impact.

0

200

400

600

800

1000

1200

0 0.05 0.1 0.15 0.2-30

-25

-20

-15

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0

Figure 4. The velocity and depth of bullet penetrating into the armor plate.

5 s

10 s

max240022002000180016001400120010008006004002000

Mises (MPa)max240022002000180016001400120010008006004002000

Mises (MPa)

15 s

35 s

200 s

95 s

95 s

Figure 5. The deformed plot at t = 0.2 ms for bulge area measurement (top) with the steel layer profile at various time (bottom)

In the explicit runs, the amount of artificial strain energy, AE, which are generated by the programs in order to prevent unduly high deformation and distortion of elements, has to be considered. This artificial energy should be low compared to the total internal energy, IE, of the system for reliable results [6]. Figure 6 shows that the ratio of artificial energy over internal energy (AE/IE) for the present simulation never exceeds of 5%, the recommended value from ABAQUS [6]

The energy of the systems, namely the internal strain energy (IE), the kinetic energy (KE) and total energy (TE), during impacts are plotted in Fig. 7, along with the frictional work from the interaction between penetrating bullet and armor plate.

0%

1%

2%

3%

4%

5%

0 0.05 0.1 0.15 0.2

Figure 6. The ratio of the artificial strain energy to the internal energy (AE/IE) during the simulation run.

Figure 7. The energy distribution plots for all parts (top: IE = Internal Strain Energy, middle: KE = Kinetic Energy, and bottom: TE = Total Energy, Fric = Frictional work)

From the kinetic energy graphs in Fig. 7, the KE of bullet decreases rapidly for the first 0.015 ms, which corresponds to the duration where the bullet is being stopped in the alumina layer, as shown in Fig. 3. This is consistent with the much larger energy absorption in the alumina layer, as shown by the IE plot. Between t = 0.015-0.05 ms, the KE decreases further but with a slower

IE

0100200300400500600700800900

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)

CeraSteelArmorBullet

KE

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Steel Displacement

-5

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00 10 20 30x (mm)

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(mm

)

0 us5 us10 us15 us20 us25 us30 us35 us35 us200 us

rate till it almost vanishes about 0.075 ms, corresponding to when the bullet is completely stopped by the steel layer shown in Fig. 3. Note that the shape of the bullet KE plot is consistent with the bullet velocity in Fig. 4.

From strain and total energy plots, it can be seen that the armor plate can effectively dissipate the impact energy of the bullet into the internal strain energy in each layer and the frictional work due to the contacting interactions. Note that the friction during the bullet impact is significant, which is about half the internal strain energy absorbed in the participating armor layers.

5. ConclusionsThe computational model from the

previous studies [1, 3-4] was extended and modified to simulate the ballistic impact of ss109 bullet traveling with the speed of over 900 m/s upon the armor plate, consisting of alumina and steel layers. The results show that alumina layer absorbs about two-thirds of the impact energy from the bullets with the remaining one-thirds dissipating into frictional work from the contacting interaction. The most severe damages to the armor occur at the back side of the alumina layer due to the superposition of reflecting stress waves [1]. The Johnson-Cook material model can effectively simulates the damages characteristics of the steel layer, with the bulge area qualitatively consistent with the experimental observation.



References[1] T. Vanichayangkuranont, K. Maneeratana

and N. Chollacoop, “Numerical Simulations of Level 3A Ballistic Impact on Ceramic/Steel Armor”, Proceedings of the

20th Conference of Mechanical Engineering Network of Thailand (ME-NETT20), Nakhon Ratchasima, Thailand, October 18-20, 2006.

[2] MTEC, 2005. MT-B-48-CER-07-188-I Report, 1-year progress report, National Metal and Materials Technology Center, Thailand.

[3] T. Vanichayangkuranont, K. Maneeratana and N. Chollacoop, “Simulations of stress wave propagation from dynamic loads”, Proceedings of the 19th Conference of Mechanical Engineering Network of Thailand (ME-NETT19), Phuket, Thailand, October 19-21, 2005.

[4] T. Vanichayangkuranont, N. Chollacoop and K. Maneeratana, “Numerical simulation of ballistic impact on ceramic armor”, Proceedings of the 4th Thailand Materials Science and Technology Conference (MSAT IV), Pathumthani, Thailand, March 30 - April 1, 2006.

[5] NIJ, 2001. NIJ Standard–0101.04, Revision A: Ballistic Resistance of Personal Body Armor, National Institute of Justice, U.S. Department of Justice.

[6] Habbitt, Karlsson and Sorensen Inc., 2003. ABAQUS version 6.3 Theory Manual, Pawtucket.

[7] Automation Creations, Inc., 1996-2006. MatWeb: Material Property Data. http://www.matweb.com.

[8] B.A. Roeder and C.T. Sun, “Dynamic penetration of alumina/aluminum laminates: Experiments and modeling”, International Journal of Impact Engineering, Vol. 25, No. 2, 2001. pp. 169-185.

[9] T. Borvik, O.S. Hopperstad, T. Berstad and M. Langseth, “Numerical simulation of plugging failure in ballistic penetration”, International Journal of Solids and Structures, Vol. 38, 2001. pp. 6241-6264.

[10]M. Park, J. Yoo and D Teak Chung, “An optimization of a multi-layered plate under ballistic impact”, International Journal of Solids and Structures, Vol. 42, 2005. pp. 123-137.

Simulation of Ballistic Impact on Polymer Composite Armor

Prayut Kumrungsie 1, Kuntinee Maneeratana 1 and Nuwong Chollacoop 2

1 Department of Mechanical Engineering, Chulalongkorn University, Bangkok 10330Tel. 0-2218-6639, Fax. 0-2252-2889, E-mail: [email protected],

[email protected] National Metal and Materials Technology Center (MTEC), Pathumthani 12120

Tel. 0-2564-6500 ext 4700, Fax. 0-2564-6403, E-mail: [email protected] ABSTRACT – This article concerns with the numerical computation of rigid bullet impacts at 30° angle on 5-mm-thick polymer composite plates, which closely follows a study by Gu & Xu [1]. The LS-DYNA finite element package is used to simulate the impacts. The armor plates are modeled with the composite damage (type-22) material model with Twaron®/epoxy composite properties. The bullet strike velocities vary between 300 and 650 m/s. After the projectiles perforate the armor plates, the residual velocities between 250 and 630 m/s are predicted. The resulting simulated residual velocities show good agreements with the previous numerical study and experimental measurements [1].KEY WORDS – Ballistic impact, polymer composites, LS-DYNA

บทคดยอ บทความนไดทำาการศกษาแบบจำาลองของกระสนปะทะในแนว – 30 องศา ลงบนแผนพอลเมอร คอมพอสต ทความหนา 5 มม. โดยอางองแนวทางจากงานของ Gu & Xu [1] ซงใชโปรแกรมไฟไนเอลเมนต LS-DYNA โดยกำาหนดวสดแผนเกราะทใชเปนแบบ Material type 22 ในการจำาลองแผนคอมพอสต Twaron®/epoxy และกำาหนดใหกระสนเปนวสดแบบแขงแกรงโดยมความเรวตนระหวาง 300 ถง 650 m/s หลงจากทกระสนทะลผานแผนเกราะคอมพอสต ความเรวของกระสนลดลงเหลอประมาณ 250 ถง 630 m/s ผลจากแบบจำาลองทสรางขนนสอดคลองอยางดกบผลการจำาลองและการทดลองยงจรงใน [1] คำาสำาคญ -- การปะทะแบบขปนะ, แผนเกราะคอมพอสต, โปรแกรม LS-DYNA


Technology Center (MTEC) has initiated a project to develop the light weight hard armor, aiming to improve materials, design and produce hard armor prototypes with local materials. The numerical simulation is used to analyze ballistic impacts on armors in order to obtain rough guidelines, particularly parameter adjustments for the prototype configuration. Previous studies for this project involved the ABAQUS simulation of impacts on alumina/steel plates [2].

As a hard armor comprises of layers of alumina, steel and polymer composite plates, the composite armors must also be computationally

studied. With new composites developed for the project [3], their properties have yet to be reliably obtained. Thus, it was decided to proceed on building a computational model which can be compared and verified with previous literature [1] such that a template model can be obtained for further investigations with newly developed composites.

During the feasibility study, it was found that the ABAQUS finite element package was not very well suited to the task due to the limitation on the anisotropic material modeling of composite armor plates. Thus, available, licensed software was studied and the LS-DYNA


[4], which is very popular for dynamic simulations, is chosen instead.

The literature [1] that are used to compare and verify the proposed model was published in 2003, involving LS-DYNA simulation of rigid bullet strikes on deformable composite plates at the velocities of 250-630 m/s and 30° impact angle (figure 1). The residual velocities as the projectiles punched through the plate are thus predicted and compared with experiments.

2. Material CharacterizationThe composite is modeled as the

transversely isotropic, employing the LS-DYNA material type 22 (composite damage model), which is based on Chang-Chang criterion [5] and contains three failure criteria. The stress-strain relationship is as follows:

where 1 and 2 are normal strain parallel to and perpendicular to fiber direction, respectively, 12

is in-plane shear strain; 1, 2 and 12 are stresses corresponding to1, 2 and 12, respectively. The moduli E1, E2 and G12 are stiffness constants in the similar order. The 1

and 2 are Poisson’s ratio in 1 and 2 directions, respectively, while is nonlinear parameter of shear stress.

These fibers are considered to be transversely isotropic, and thus five independent constants are needed to describe their properties. The matrix is considered to be isotropic with three independent material constants. All independent parameters of the composite can be calculated using the microstructure approach. Some parameters, such as G23 and 23 that can not be calculated from the microstructure approach due to the incompatibility in 3D composite physical meaning, can be obtained from the assumption of transverse material of unidirectional laminar. From the elastic constant parameters and critical strength of laminar, the LS-DYNA algorithm predicts damage from matrix cracking followed by fiber tensile failure and composite compressive failure, if any.Failure of a composite occurs when the combined stresses reach a critical value, which may result from fiber fracture, matrix cracking or compressive failure in accordance with the following rules:(a) Fiber fracture (Ffiber 1): When a fiber is fractured, the mechanical properties E1, E2, G12, 1 and 2 are all set to zero.

(b) Matrix cracking (Fmatrix 1): When matrixes fail, E2, G12, 1 and 2 are all set to zero.

(c) Compressive failure (Fcomp 1): When compressive failures occur, E2, 1 and 2 are set to zero.

A fiber matrix shearing term augments each damage mode such that:

where S1, S2, S12 and C2 are longitudinal tensile strength, transverse tensile strength, in-plane shear strength and transverse compressive strength, respectively.

3. ModelThe model composed of three parts,

namely the bullet, target armor plate and their interaction.

3.1 Bullet The 7.95-g conically cylindrical

projectile has the maximum diameter of 7.87 mm and is 26.8 mm long. The bullet is modeled with material type 20 (rigid material), assuming no deformation of the projectile after ballistic impact. The bullet domain is divided into 164 8-node hexahedron elements in [1] while 1552 4-node tetrahedral elements are used in the proposed model in order to better capture the curved body of conically cylindrical bullet as shows in figure 1.

3.2 Target The target plate of 45×100 mm2 area

and 5 mm thick is fixed at the top and bottom. The material type 22 (composite damage model) is used with following Twaron®/epoxy properties, density = 1.25 g/cm3, Young’s moduli E1 = 20.4 GPa and E2 = E3 = 8.9 GPa, shear moduli G12 = G13 = 1.64 GPa and G23 = 3.03 GPa, bulk modulus Eb = 20.4 GPa, Poisson’s ratios 12

= 13 = 0.31 and 23 = 0.49, shear strength S12 = 0.39 GPa, longitudinal tensile strength S1 = 1.145 GPa, transverse tensile strength S2 = 0.13 GPa, transverse compressive strength C2 = 0.65 GPa and nonlinear parameters of shear stress = 0. The plate is modeled with 8-node 37,728 hexahedron elements in [1] while the new model

uses 40,000 elements in inclined plate as shown in figure 1.

Figure 1. The proposed finite element model.

3.3 Bullet-Target InteractionAs in [1], the friction between the

projectile and composite is small compared to the kinetic energy absorption of the perforation. However, the exact value of friction coefficient is not specifically specified in [1]. In this study, the coefficient value is reduced to around 0.1 in order to better match the experimental residual velocities.In addition, the previous study [1] did not specify the interaction between bodies. However, the new model specifies the automatic surface-to-surface contact.

4. ResultsWhen the simulated results are

compared with simulated and experimental solutions from [1], they very well agreed especially for the fact that the damage zone occurs mainly around the perforation holes. The penetration process of lamina target and projectile is shown in figure 2 for various time snapshots. When the bullet hit the target, the stress is mainly dissipated along the fiber longitudinally to the top and bottom due to the higher stress wave velocity from the higher material strength in that direction (figure 3). The stress waves warp the plate and induce damages at the high stress locations at the plate corners The bullet horizontal velocity decreases with time due to the resistance of the armor plate during the impact. After full perforation, the bullet velocity becomes constant at the residual velocity (figure 4). When the bullet acceleration (figure 5) is studied, the acceleration magnitude decreases initially but increases for some period afterwards due to the material resistance before the far side of the plate surface is punctured (figure 2). There is another acceleration change as the bullet completely exits the plate and the elastic section of the plate recoils back. The acceleration is then reduced to zero with the constant residual velocity. When the predicted numerical residual velocities at various strike velocities are obtained, it is found that they are

similar to the experimental and numerical results from [1] (figure 6).

Figure 2. Simulated perforations from the impact of bullet at 390 m/s at time instants 0, 14, 30, 40, 60 and 90 s.

Figure 3. Simulated stresses from the impact of bullet at 390 m/s at time instants 0, 14, 30, 40, 60 and 90 s.

Figure 4. Bullet velocities during the perforation with the strike velocity of 390m/s.

Figure 5. Bullet acceleration during the perforation with the strike velocity of 390m/s.

Figure 6. Comparison of residual velocities from different strike velocities.

With this proposed model, the ballistic limit of the Twaron/epoxy plate can be numerically predicted. Figure 7 shows the maximum strike velocity of the bullet that the armor can withstand without a complete perforation.

Figure 7. Ballistic limit of Twaron/epoxy plate that is obtained from the proposed model.

In addition, the angle of the armor plate relative to the bullet trajectory can be changed for further analyses. For instance, figure 8 shows the residual velocities when the plate is further inclined from 0°, 30° and 45°, representing the situation of the perpendicular impact, the proposed model and a more inclined plate. The results are consistent with previous study, which found that the perforation from the perpendicular impact is most severe with highest residual velocities [6]. The stress distributions, and hence damages, to the plates after complete perforation are also shown in figure 9.

Figure 8. Relative residual velocities in the 0° and 45° inclined plates compared to the proposed model at 30° inclination with the bullet strike velocity of 390m/s.

Figure 9. Composite damages after bullet perforation at the strike velocity of 390m/s through the vertical (left), 30° incline (center) and 45° incline (right) plates.

5. ConclusionThe work closely follows the simulation by Gu & Xu [1] in order to construct and validate a finite element model for the ballistic impacts upon the polymer plates at 30° inclination. With good

agreements with the previous experimental and numerical results, important performance and geometrical parameters, such as the ballistic limit and effects of plate inclination, can be numerically predicted and studied. The future work will focus on systematic studies of effects of mechanical parameters on the armor performances during and after perforation.

AcknowledgementsThis research is supported by MTEC, contract no. MT-B-48-CER-07-188-I.

References[1] B. Gu and J. Xu, “Finite element calculation of 4-step 3-dimensional braided composite under ballistic perforation”. Composites Part B: Engineering. Vol 35, No. 4, 2004, pp. 291-297. [2] T. Vanichayangkuranont, K. Maneeratana, and N. Chollacoop, “Numerical simulations of level 3A ballistic impact on ceramic/steel armor”, Proceedings of ME-NETT 20. Nakhon Ratchasima, 18-20 October 2006, CST048, 6 pages.[3] T. Amonsukchai and S. Rimdusit, Development of Polyethylene Fiber, Composites from Benzoxazine-Based Alloys and Polyethylene or Kevlar Fiber and Polymer Composites/Metal or Ceramic for Armory, MTEC report, 2004.[4] Livermore Software Technology Corporation, LS-DYNA Theoretical Manual: Version 970, 2005.[5] F. K. Chang and K. Y. Chang, “Progressive damage model for laminated composite containing stress concentration”. Journal of Composite, Vol. 21, 1987, pp. 834-55. [6] Z. Fawaz et al, “Numerical simulation of normal and oblique ballistic impact on ceramics composite armours”. Composite Structures, Vol. 63, 2004, pp. 387-395.

The 21st Conference of Mechanical Engineering Network of Thailand17-19 October 2007, Chonburi, Thailand

Effects of Fiber Orientation on Ballistic Impact upon Polymer Composite Plate

Prayut Kumrungsie1, Kuntinee Maneeratana1 and Nuwong Chollacoop2

1 Department of Mechanical Engineering, Chulalongkorn University, Bangkok 10330Tel. 0-2218-6639, Fax. 0-2252-2889, E-mail:[email protected], [email protected]

2 National Metal and Materials Technology Center (MTEC), Pathumthani 12120Tel. 0-2564-6500 ext 4700, Fax. 0-2564-6403, E-mail: [email protected]

Abstract This article concerns with the simulation of

ballistic impact on polymer composite with in-plane bidirectional fiber direction instead of unidirectional as in our previous work [1], which was inspired by Gu & Xu [2]. The models consist of bullet impact on 5-mm-thick polymer composite plates with different side lengths and boundary conditions. The LS-DYNA FEM package is used to simulate the impact result. The bullet is rigid while the composite armor plate is modeled by the type-22 composite damage material with Twaron®/epoxy composite properties. The simulation reveals that the stress waves progress outwards from the point of impact in both fiber directions to the target edges unlike the domination of wave movement along the single fiber direction in the unidirectional plate. The residual bullet velocities on bidirectional plates are lower than those on the unidirectional plates. The fixed edge condition acts as an artificial boundary stiffener when the plate is not sufficiently large such that the reflected stress waves and zero boundary displacement interfere with the perforation mechanisms.Keywords: Ballistic impact, polymer composite, LS-DYNA


Technology Center (MTEC) has initiated a project to develop the locally-made, light weight hard armor. The numerical simulation is used to analyze ballistic impacts on armors in order to obtain rough guidelines, particularly parameter adjustments for the prototype configuration.

Even though new composites have been developed for the project [3], their properties have yet to be reliably obtained. Thus, it was decided to proceed to formulate computational simulation which can be compared and verified with previous literature [2] such that a template

model can be obtained for further investigations with newly developed composites.

During the preliminary study, it was found that the ABAQUS finite element package is not best suited for the task due to the anisotropic and dynamic material behaviors of composite armor plates. Thus, an alternative commercial finite element code LS-DYNA [4], which has been popular for dynamic problems, is chosen instead.

Our previous work [1] was well-calibrated with the experimental and numerical results from Gu & Xu [2]. However, the model was based on the unidirectional fiber composite whereas the real composites under development [3] are made up of bidirectional or woven fibers. Thus, this work aims to extend the previous model to the bidirectional fiber composite with some variations of plate size and boundary conditions.

2. Material CharacterizationThe composite is modeled as the transversely isotropic,

employing the LS-DYNA material type 22 (composite damage model), which is based on Chang-Chang criterion [5] with the stress-strain relationship as follows:

(1)

where 1 and 2 are respectively normal strains parallel and perpendicular to fiber direction; 12 is the in-plane shear strain; 1, 2 and 12 are stresses which correspond to 1, 2

and 12, respectively. The moduli E1, E2 and G12 are stiffness constants in the same order. The 1 and 2 are Poisson’s ratio in 1 and 2 in-plane directions, respectively, while is the nonlinear parameter of shear stress.

These fibers are approximated to be transversely isotropic, and thus five independent elastic constants are needed to fully describe their elastic properties. The matrix is considered to be isotropic with three independent elastic material constants. All independent parameters of the composite can be calculated using the microstructure approach. Some parameters, such as G23 and 23 that can not be calculated from the microstructure approach due to the physical meaning incompatibility in 3D composites, can be obtained from the assumption of transverse material in the unidirectional lamina. From the elastic constant parameters and critical strength of lamina, the LS-DYNA algorithm


predicts damage from matrix cracking followed by fiber tensile failure and composite compressive failure, if any.

Failure of a composite occurs when the combined stresses reach a critical value, which may result from fiber fracture, matrix cracking or compressive failure in accordance with the following rules.(a) Fiber fracture (Ffiber 1): When a fiber is

fractured, the mechanical properties E1, E2, G12, 1 and 2 are all set to zero.

(2)

(b) Matrix cracking (Fmatrix 1): When matrixes fail, E2, G12, 1 and 2 are all set to zero.

(3)

(c) Compressive failure (Fcomp 1): When compressive failures occur, E2, 1 and 2 are set to zero.

(4)

A fiber matrix shearing term augments each damage mode such that:

(5)

where S1, S2, S12 and C2 are longitudinal tensile strength, transverse tensile strength, in-plane shear strength and transverse compressive strength, respectively.

3. Simulation of Uni and Bidirectional Fiber Direction

The 7.95-g conically cylindrical projectile has the diameter and length of 7.87 and 26.8 mm, respectively. The bullet is modeled by 618 4-node tetrahedral elements with LS-DYNA type 20 rigid material.

The 45-mm×100-mm, 5-mm-thick target plate is fixed at the top and bottom and modeled with 25,000 8-node hexahedron elements (Figure23). The material type 22 composite damage model is chosen to model the bidirectional Twaron®/epoxy plate in which the property is changed from unidirectional, equivalent to only the same alignment of fiber layers [1], to bidirectional, in which the adjacent fiber layers are aligned perpendicular to one another (Table3). It is noted that the directions 1 and 2 represent in-plane direction while 3 represents the out-of-plane orientation.

Table 3 Unidirectional [1] and bidirectional properties

property uni biE1 longitudinal Young’s modulus, GPa 20.44 20.44E2 transverse Young’s modulus, GPa 8.9 20.44E3 normal Young’s modulus, GPa 8.9 8.921 Poisson’s ratio 21 0.31 0.4931 Poisson’s ratio 31 0.31 0.3132 Poisson’s ratio 32 0.49 0.31G12 shear modulus 12, GPa 1.64 6.84G23 shear modulus 23, GPa 3.03 1.64G31 shear modulus 31, GPa 1.64 1.64Eb bulk modulus of failed material, GPa 20.4 20.4S1 longitudinal tensile strength, GPa 1.145 1.145S2 transverse tensile strength, GPa 1.13 1.145C2 transverse compressive strength, GPa 0.65 0.65S12 in-plane shear strength, GPa 0.39 0.39 nonlinear parameters of shear stress 0 0 mass density, g/cm3 1.23 1.23

model initial step

Figure 23 The computational model setup

When the bullet hit the target with unidirectional fiber orientation, the stress is mainly dissipated along the fiber longitudinally to the top and bottom due to the higher stress wave velocity from the higher material strength in that direction (Figure 24) as in [1].

For the bidirectional fiber plate, the stress contours (Figure 25) shows that the stresses waves are initiated from the point of impact in both in-plane directions and expand towards target edges (e.g. t = 15 and 30 s) because of the bidirectional properties of the composite. Later, the stress wave starts to elongated lengthwise (e.g. t = 60 and 75 s) due to the fixed boundary condition, followed by the wave reflection at the clamp (e.g. t = 90 s).

The bullet horizontal velocity decreases with time due to the resistance of the armor plate during impact (Figure 26). After full perforation, the bullet velocity is leveled off at the residual velocity. As expected, the bidirectional target yields a lower residual velocity by absorbing more energy. The bidirectional plate also shows less deformation around the impact locality.

When the side views of the impact are visually inspected (Figure 24 and Figure 25), the side edges, which are not constraint, are noticeably deformed and curved from the bullet impacts for both uni and bidirectional fiber plates. In addition, the energy history of the plate (Figure 27) shows sporadically changes in internal and kinetic energy components while the sum of both energy remains relatively

1

2

constant after the bullet starts to punch through the plate. This characteristic may be due to the stress wave propagation and the boundary conditions and is, thus, further investigated in the next section.

4. Effects of Fixed Boundary Condition The 45-mm×100-mm, 5-mm-thick target

plate, as in the previous section, is fixed at all edges in the simulations with the same material properties.

Figure 28 and Figure 29 show the Mises stress contours during the perforation of the unidirectional and bidirectional fiber plates, respectively. While the stress contour characteristics, which are found in the previous cases, are still observed, the side edges are subjected to high stress due to the fixed boundary condition. With magnified visual inspection, less gross deformation of the plates are observed in both uni and bidirectional fiber plates when all edges are constrained with fixed boundary instead of leaving the side edges free to bend, reminiscing a stiffening effects on the plates.

0 s 15 s 30 s 45 s 60 s 75 s 90 s

Figure 24 Mises stress contours and perforation at various time instants t from 390 m/s bullet impact on a unidirectional fiber plate with fixed top and bottom edges, resulting in 359 m/s residual velocity. The color blue

represents no stress while red is for 1.0 GPa.

0 s 15 s 30 s 45 s 60 s 75 s 90 s

Figure 25 Mises stress contours and perforation at various time instants t from 390 m/s bullet impact on a bidirectional fiber plate with fixed top and bottom edges, resulting in 344 m/s residual velocity. The color blue represents no stress

while red is for 1.0 GPa.

time (s)0 25 50 75 100 125 150

bulle

t vel

ocity

(m/s

)

325

350

375

400


Figure 26 Bullet velocities during the perforation from 390 m/s bullet impact on the plates with fixed top and

bottom edges

time (s)0 25 50 75 100 125 150

ener

gy (J

)

0

5

10

15

20 IE+KE

IE

KE

Figure 27 Internal energy (IE) and kinetics energy (KE) of the bidirectional fiber plates with fixed top and bottom edges during the perforation from 390 m/s bullet impact

0 s 15 s 30 s 45 s 60 s 75 s 90 s

Figure 28 Mises stress contours and perforation at various time instants t from 390 m/s bullet impact on a unidirectional fiber plate with fixed edges, resulting in 349 m/s residual velocity. The color blue represents no stress

while red is for 1.0 GPa.

0 s 15 s 30 s 45 s 60 s 75 s 90 s

Figure 29 Mises stress contours and perforation at various time instants t from 390 m/s bullet impact on a bidirectional fiber plate with fixed edges, resulting in 339 m/s residual velocity. The color blue represents no stress while red is for

1.0 GPa.

time (s)0 25 50 75 100 125 150

bulle

t vel

ocity

(m/s

)

325

350

375

400


Figure 30 Bullet velocities during the perforation from 390 m/s bullet impact on the plates with fixed edges

time (s)0 25 50 75 100 125 150

ener

gy (J

)

0

5

10

15

20

25

IE+KE

IE

KE

Figure 31 Internal energy (IE) and kinetics energy (KE) of the bidirectional fiber plates with fixed edges during

the perforation from 390 m/s bullet impact

When the residual velocities are compared (Figure30), the bidirectional fiber plate still better resists the bullet impact. However, both residual velocities when all edges are fixed are lower than those when only the top and bottom edges are fixed (Figure 26), indicating better resistance from the boundary condition.

Moreover, the energy history of the plate (Figure 31) shows even more variation in internal and kinetic energy components. This further strengthens the possibility that the observed characteristics are geometrical and boundary dependent, which leads to the simulation of the different plate geometry in the next section.

5. Simulation of Bidirectional Square PlateIn order to confirm the size and boundary condition

effects on the simulation with bidirectional fiber material, these effects should be reduced or eliminated by increasing the plate size such that they can not interfere with the perforation mechanism during the bullet perforation.

Thus, 5-mm-thick plates of increasing sizes – 100-mm×100-mm, 200-mm×200-mm and 300-mm×300-mm – are used in the simulation of bullet impact at 390 m/s (Figure 32). The plates are discretized into 50,000, 222,585 and 450,000 8-node hexahedron elements, respectively.

model initial step

Figure 32 The square model setup

Table 4 shows the Mises stress contours and the side-view perforation of the bidirectional fiber plates of different sizes. The smallest plate, 100-mm×100-mm, clearly shows the wave reflections at the edges, indicating that it is not large enough for the purpose. Meanwhile, the two bigger plates experience significant stress at the centers.

When the residual velocities (Figure 33) are considered, it is found that the residual velocity from the 100-mm×100-mm fixed plate is higher than the 45-mm×100-mm fixed plate (Figure 30), further indicating that the better resistance of the smaller plate may be due to the boundary constraint. As the plate gets bigger, the residual velocity decreases slightly at a decreasing rate, showing insignificant differences between the 200-mm×200-mm and 300-mm×300-mm plates.

These results may seem contradicting, but when the energy components in the plates are compared, it is clear that the boundary interference is still present in the 100-mm×100-mm plate (Figure 34a) while these sporadically

changes in internal and kinetic energy components are not presented in the larger plates (Figure 34b and Figure34c). It is also clear that the plate still pulsate long after the bullet punches through, as shown by a longer time axis in Figure 34a. Therefore, larger plates are needed when only the initial impact resistance of the material is studied. In addition, small change in internal energy can be clearly observed when the bullet is about to leave the plate.

This argument also implies that the plate size and boundary condition, i.e. armor plate installation method, must be carefully studied to ensure the true required performances.

6. ConclusionPreliminary results show the capability of extending

the well-calibrated computational model from the unidirectional fiber composite plate to the bidirectional one to better emulate the composite armor prototype under development. The computational model shows that bidirectional plate absorbs more energy, resulting in a lower residual velocity of the penetrated bullet. It is also noted that the plate size and boundary conditions may influence the armor plate integrity.

This investigation serves as a guideline for future optimization of the armor plate prototype. The current framework thus planned is to experimentally measure the values of the composite properties and use them in the simulation for verification and possibly prediction of the plate behavior upon ballistic impact as well as further numerical investigation with parametric studies of the plate properties.

AcknowledgementsThis research is financially supported by MTEC,

contract no. MT-B-48-CER-07-188-I.

References[1] Kumrungsie, P., Maneeratana, K., and Chollacoop,

N., 2007. Simulation of Ballistic Impact on Polymer Composite Armor. 2007 NSTDA Annual Conference (NAC 2007), Thailand Science Park, Pathumthani, March 28-30.

[2] Gu, B., and Xu, J., 2004. Finite Element Calculation of 4-step 3-dimensional Braided Composite under Ballistic Perforation. Composites Part B: Engineering. Vol 35, No. 4, pp. 291-297.

[3] Amonsukchai, T., and Rimdusit, S., 2004., Development of Polyethylene Fiber, Composites from Benzoxazine-Based Alloys and Polyethylene or Kevlar Fiber and Polymer Composites/Metal or Ceramic for Armory, MTEC report.

[4] Livermore Software Technology Corporation, 2005. LS-DYNA Theoretical Manual. Version 970.

[5] Chang, F. K., and Chang, K. Y., 1987. A Progressive Damage Model for Laminated Composite Containing Stress Concentration. Journal of Composite, Vol. 21, No. 9, pp. 834-855.

1

2

Table 4 Mises stress contours and perforation at various time instants t and from bullet impact on a bidirectional fiber square plate with fixed edges at 390 m/s. The color blue represents no stress while and red is for 1.0 GPa.

time 100-mm×100-mm plate 200-mm×200-mm plate 300-mm×300-mm plate

0 s

15 s

30 s

45 s

60 s

75 s

90 s

vr 349 m/s 347 m/s 347 m/s

time (s)0 25 50 75 100 125 150

bulle

t vel

ocity

(m/s

)

340

350

360

370

380

390

400

1002 mm2 plate2002 mm2 plate3002 mm2 plate

Figure 33 Bullet velocities during the perforation of the square plates with 390 m/s bullet impact

time (s)0 100 200 300 400 500 600

ener

gy (J

)

0

5

10

15

20

25

time (s)0 25 50 75 100 125 150

ener

gy (J

)

0

5

10

15

20

25

time (s)0 25 50 75 100 125 150

ener

gy (J

)

0

5

10

15

20

25

IE+KE

IE

KE

IE+KE

IE

KE

IE+KE

IE

KE

(a)

(b)

(c)

Figure 34 Internal energy (IE) and kinetics energy (KE) of the target plate during the

perforation of the (a) 100-mm×100-mm, (b) 200-mm×200-mm and (c) 300-mm×300-mm plates

with bullet impact at 390 m/s.

Documents

หน้าปก - MITweb.mit.edu/nuwong/Public/Armor/F-17_Report_final_sim… · Web viewTel: 0-2564-6500 ext 4700, Fax: 0-2564-6403, E-mail: [email protected] Abstract. This