INTEGRATION OF MECHANICAL ALLOYING AND

INTEGRATION OF MECHANICAL ALLOYING AND EQUAL CHANNEL ANGULAR EXTRUSION FOR PRODUCTION OF NANOSTRUCTURED MATERIALS

A Thesis Presented to The Faculty o f the College o f Graduate Studies Lamar University

In Partial Fulfillment o f the Requirements for the Degree Doctor o f Engineering by Xhemal Kaculi

December 2002

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UMI Number: 3090250

Copyright 2003 by Kaculi, Xhemal

All rights reserved.

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© 2002 by Xhemal Kaculi No part o f this work can be reproduced without permission except as indicated by the “Fair Use” clause o f the copyright law. Passages, images, or ideas taken from this work must be properly credited in any written or published materials.

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INTEGRATION OF MECHANICAL ALLOYING AND EQUAL CHANNEL ANGULAR EXTRUSION FOR PRODUCTION OF NANOSTRUCTURED MATERIALS XHEMAL KACULI

Approved:

Malur N. Srinivasan Supervising Professor

Victor . Zaloom Committee Member

Paul R. Corder Committee Member

V .. A -Malur N. Srinivasarv Chair, Department o f Mechanical Engineering

lYv.




fc->

Figure 9 Workpiece Geometry Change during ECAE Process Source: Anastasios Parasiris, “Consolidation o f WC-Co by Simple Shear” (Masters Thesis, Texas A&M University, 1999) 36.

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Kaculi 32

NOT TO SCALE

b 1

NO ROTATION

13*80

88*30

3P a

N=0

N=1

N=2

Figure 10 Illustration o f the 1A and 2 A ECAE Extrusion Passes Source: Anastasios Parasiris, “Consolidation o f WC-Co by Simple Shear” (Masters Thesis, Texas A&M University, 1999) 38.

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Kaculi 33

CHAPTER 4 NANOSTRUCTURED MATERIALS Nanotechnology Nanotechnology is a new and very fast growing technology with applications in almost any field o f science and industry. Nanotechnology can best be considered as a “catch-all” description o f activities at the level o f atoms and molecules that have applications in the real world. Even in its initial stages o f development, nanotechnology has opened up new worlds o f possibility in engineering the materials that cannot even be imagined before. This science is capable o f manipulating the fundamental building blocks o f nature, inexpensively and in almost any arrangement that we desire. With the help and advancement o f the computer technology, we will be able to fabricate an entire new generation o f products that is beyond the current technology.

Background o f Nanostructured Materials Nanostructured materials, known also as nanomaterials or nanocrystalline materials, have been investigated in numerous studies in recent years. They are defined as materials with grain size less than 100 nanometers, nm (10'9m). The novelty o f these materials is that they have a significant fraction o f the total atoms present at the grain boundaries, and the effect o f other microstructural events such as grain boundary sliding enhanced by grain boundary diffusion, dislocation structure and creep properties affect the formability o f such materials and provide significant improvement in ductility.37 Thus, they may be expected to possess different properties than conventional coarse-grained materials.

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Kaculi 34

Nanostructured materials manifest extremely fascinating and useful properties, which can be exploited for a variety o f structural and nonstructural applications. Scientists have approached the production o f nanostructured materials in two different ways. The first approach starts at atomic level and builds up the material by controlling the way in which atoms are arranged. This is known as the “bottom up” technique and is usually achieved via chemical routes. The second approach generates nanostructured materials from breaking down the materials in bulk form in smaller and smaller fragments until their grain size reaches nanoscale, and then consolidating them by preserving their fine structure. This method is known as the “top down” approach and is usually achieved via mechanical means. The difference between the two methods is that while the first one can mainly be used to produce only thin films and layers for laboratory purposes, the second one can scale up the production on nanostructured materials in bulk form that are very much desirable for industrial applications. Although some progress has been made to shed light on the nature and mechanism o f nanostructured materials, there is still a lot to learn in order to fully understand and utilize these materials. The work done has mainly focused on one and two dimensional nanostructures, but very little has been done to achieve the three dimensional bulk form which is the ultimate desired structure o f these materials for their commercial use. Nanostructured materials may also be considered as the intermediate phase between crystalline and amorphous materials.38 Since the grain boundaries occupy a significant volume in their material, their physical properties greatly influence the overall material. Due to this reason they exhibit quite different properties from crystalline and amorphous

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Kaculi 35

materials. Nanostructured materials are exceptionally strong, hard, and ductile at high temperatures. They are also wear resistant, erosion resistant, corrosion resistant, and chemically very active. They are much more formable than their conventional commercially available counterparts. In Figure 11 is shown the well-known Hall-Petch relationship that correlates the grain size and yield strength for the conventional microstructured materials. Based on this relationship, decreasing the grain size results in the increase o f the strength and the improved mechanical properties o f the material. This is the basis for the excellent mechanical properties displayed by nano structured materials. Theoretically, this means that decreasing the grain size to less than a few nm would result in extreme hardness o f the material. However, as it will be discussed later in this chapter, the Hall-Petch relation may not continue to accurately predict the mechanical properties o f materials when grain size is reduced to less than 10 nanometeres. The Hall-Petch relationship is expressed as: G y ~ GO " t k y d

1/2

where: c y is the yield strength o f the material oo is the yield strength o f an imaginary polycrystal having infinite grain size ky is Hall-Petch coefficient (material constant) d is the material grain diameter

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Hall-Petch Relation 600

'm 500 o. S 400 O) c -

0) h.

A

300

» 200 2 0)

£ 100 0

1

0.5

1.5

Diameter [mm]

Figure 11 Schematic Representation o f Hall-Petch Relation

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Kaculi 37

Engineering Applications o f Nanostructured Materials Almost in any industrial field today there is a great interest on the nanostructured materials owing to the extraordinary properties that they possess. Especially, great interest has been shown in transportation industry, aerospace, and cutting tools for the oil industry. Conventional materials used in automobile industry erode and corrode too soon. The aerospace industry is struggling to get parts that possess excellent properties at high temperatures and in the fatigue strength, which decreases with the age o f the component and increases with the reduction o f the grain size o f the material. Cutting tools made o f nanocrystalline materials, are much harder, more wear-resistant, erosion-resistant, and last longer than their conventional counterparts. They also enable the manufacturer to machine various materials much faster, thereby increasing productivity and significantly reducing manufacturing costs. Also the ductility at high temperatures is a very desirable feature for all the above applications. Nanostructured materials are the best candidates to provide these properties, and therefore it is desirable to develop the technology to produce these materials in industrial quantities.

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Kaculi 38

Modeling o f Nanostructed Materials In the recent years a great interest has been shown in the field o f superhard nanostructured materials, that are defined as materials that possess a Vickers microhardness o f greater than 40 GPa. According to Veprek, the most attracting feature o f these materials is the fact that their microhardness exceeds by a factor o f three to seven times the microhardness given by the rule o f mixture which is given in the following equation for two different materials.39 H(AaBb) = [a H(A) + b H (B)]/ (a+b) where: A and B represent the two different materials a and b represent the number o f atoms o f element A and B respectively H(AaBb) is microhardness o f the mixture o f elements A and B H(A) is microhardness o f element A H(B) is microhardness o f element B The microhardness is proportional to the reciprocal value o f the bulk modulus which is given below by the formula derived from Cohen.40 B = [(Nc)/4 ] (1971 - 220 X) ao'35 where: B is the bulk modulus in GPa N cis the average coordination number X is the polarity o f the bond

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Kaculi 39

a 0 6 0 S + 0 5 - + 2 . OOOa+OS - + 1 . 833*1-05 -■ M .6 6 ? a t-0 5 - H .S O O e + 0 5 - + 1 . 3 3 3 e i-0 5 - i- 1 .1 6 7 « i- 0 5 - + 1 .0 0 0 * 1 -0 5 ~ + 8 . 3 3 3*1-04 - +6 .667S 1-04 - + 5 .0 0 0 « i-0 4 - f3 .3 3 3 f li- 0 4 I B - * 1 .6 6 7 4 + 0 4 + 0 .0 0 0 a + 0 0

Figure 66 Von Mises Stress at 1112 ° F Temperature - Middle Position

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Kaculi 153

s, Hi iA v a . c r i t . i 75%) r * 2 .3 2 9 e - t- 0 5 - + 1 . SDOa+OS -■ c l. 3 7 5 a f 0 5 - + a .2 5 0 a l-O S -+ -1 .1 2 5 e K > 5 - t-J.. CDOei-05 - f 8 .7 5 0 f l i - 0 4 - t-7 ,5 6 0 a + -0 4 - + 6 .2 5 0 e + 0 4 - * 5 . OOOs+04 - +3 . 750e+-04 - +2 .5 0 0 flt-0 4 H S - + 1 .2 5 0 0 + 0 4 + 0 .Q 0 0 « + 0 0

Figure 67 Von Mises Stress at 1112 ° F Temperature - Final Position

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Kaculi 154

S, Miees [A v e.

c r L t .j

75^)

+2. 465a+0S

+ 1 .5 0 0 a + 0 5 1 -1. 3 7 5 e + 0 5 ii.2 5 0 e + 0 5 + 1 .1 2 5 C + 0 5 + 1 .0 0 0 e + 0 5 + 8 .7 5 0 s + 0 4 1 -7 .5 0 0 3 + 0 4 + 6 .2 5 0 3 + 0 4 -+ 5 .0 0 0 3 + 0 4 + 3 .7 5 0 3 + 0 4 + 2 .5 0 0 3 + 0 4 + 1 .2 5 0 8 + 0 4 + 0 .0 0 0 3 + 0 0

Figure 68 Von Mises Stress at 1652 ° F Temperature - Middle Position

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Kaculi 155

S , H ie a e ( A v a . c r i t . : 75%} • i- 3 .3 J 6 « i- 0 5

•+ \1 .6 0 0 * * 0 5

- * J 1 .4 S 7 a K > 5

•• * 1 .3 3 3 * * 0 5 • * 1 .2 0 0 * * 0 5 M .0 6 7 e * 0 5

• + 8 .3 3 3 * * 0 4 • + 8 .0 0 0 * * 0 4 ■ + 6 .6 6 7 e + 0 4 ' .3 3 3 * * 0 4 • +4 .0 0 0 * * 0 4 • + 2 .6 6 7 * * 0 4 • + 1 .3 3 3**04 +0. 000a +00

Figure 69 Von Mises Stress at 1652 ° F Temperature - Final Position

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Kaculi 156

S, Hiees (A va. c r i t . : 75M ■ + 2 .4 D 5 e -t'D 5 •+ 1 .6 C J 0 4 + O S - + 1 .4 6 7 « - K > S • + 1 . 3 3 341-OS • + -1 .2 0 0 e + 0 5 •+ 1 .0 6 7 e + -0 5 ■ 3334*04 • + 8 . OO O a+04 • + 6 .6 6 7 a + 0 4 . 3 3 3a*04 .0 0 0 a + 0 4 • * 2 .£ 5 7 4 1 * 0 4 ■ ♦ 1 .3 3 3 4 + 0 4 + 0 .0 0 0 * 1 -0 0

Figure 70 Von Mises Stress at 3000 ° F Temperature - Middle Position

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Kaculi 157

S., X i M t

ftwa* C r i t . i ■♦ a . *02*W >'S • ♦ a . ««■?**&% •+ !•. 2 f c © * « » • * 1 .- O * 7 « * 0 5 ■ + 6 : 6 '6 1 * + O i » S , 3 3 3 « * C il ^ ,3 3 3 * * - & 4

S

1

Figure 71 Von Mises Stress at 3000 ° F Temperature - Final Position

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Kaculi 158

APPENDIX E EXPERIMENTAL EQUIPMENTS AND DATA

Photographs o f the mechanical alloying and equal channel angular extrusion equipment used during this research are shown in this appendix. Also, a photograph o f the Vickers microhardness tester, along with the microhardness values at 10 different points for all the experiments are presented. Titanium - Silicon phase diagram is also shown.

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Kaculi 159

Table 14 Vickers Microhardness o f ECAE Powder at 10 Different Points

V

Point 2

3

4

5

6

7

8

9

10

Mean

425.1

362.8

188.7

365.0

404.1

752.6

597.3

207.8

340.3

214.1

385.78

395.8

377.6

457.9

393.3

289.7

179.6

263.2

414.4

389.3

393.3

355.41

417.9

466.1

699.8

419.7

1507.5

423.3

1133.5

684.6

495.8

806.8

705.5

314.4

470.3

228.5

384.6

332.6

405.8

662.8

455.8

546.2

392.5

419.35

257.5

503.8

345.5

331.9

365.0

217.8

266.3

274.7

503.8

302.1

336.84

264.5

159.3

172.1

225.6

165.3

123.3

114.7

198.8

340.3

308.7

207.26

487.7

349.6

719.4

530.6

562.5

570.9

792.7

430.3

899.8

525.6

586.91

446.9

408.3

303.7

508.5

785.8

362.1

355.8

235.0

331.3

666.4

440.38

1 E x p /\ 1 2 3 4 5 6 7 8

Kaculi 160

Figure 72 Mechanical Alloying Equipment Used during the Research

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Kaculi 161

Figure 73 Vickers Michrohardness Tester

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Kaculi 162

Weight Percent Silicon 10

20

2200

30

40

50

60

70

80

90 100

2130'C

2000

T emperature/C

1800

16701 : 1600

1400

m ot 1170°C

1200

03

1000 •

(St>

8651 800

600

20 Ti

100 Atomic Percent Silicon

Figure 74 Titanium —Silicon Phase Diagram

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Kaculi 163

Billet Outer Plug .920 DIA.

.840 DIA.

.760 DIA.

.350 DIA. T

1.000 .840 DIA.

1 _

.050 .500

.050

V // / .500 J A A

Inner Plug

/ ,

4.500

7

.350 DIA. .250

7

A

r

650

1.000

Drawing o f ECAE Billet

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Kaculi 164 APPENDIX F FINITE ELEMENT ANALYSIS MODELING STRAIN DATA

The strains for nine models with different values o f extrusion angle (60, 90, 120 degrees), temperature (-535, 1112,1652, 3000 °F), and friction (0.05, 0.10, 0.15) are presented in this appendix. The software used for this purpose was ABAQUS. These strains help understand in detail the deformation patterns that the material goes through during the extrusion process.

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Kaculi 165

Axial Strain in Horizontal Direction vs. Stroke Model 1 - Top Section 0.45 0.40 P1 0.35

—'Is--- P2 P3

0.30

P4 P5

c c 0.25

•§ 0.20

;

(/)

P6 P7

1

P8 P9

f

0.15

P10

0.10

'

:% si

*

,

,

2.5

3.0

P11

0.05

0.00 0.0

0.5

1.0

1.5

2.0

3.5

4.0

Stroke (in.)

Figure 75 Transverse Axial Strain vs. Stroke - Top Section Extrusion Angle =90 Deg., Friction Coeff. = 0.10, Temp. = 80° F

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Kaculi 166

S h ear Strain vs. Stroke Model 1 - Top Section

0.70 3K

0.60 -*■- P2 0.50

P3 P4

0.40

5^ P 5 i

- + ~

|

"s/ ^

------

-0.40 - ..... ---

-------

P9 P10 P11

-0.45 -0.50 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

S troke (in.)

Figure 89 Longitudinal Axial Strain vs. Stroke - Top Section Extrusion Angle = 120 Deg., Friction CoefF. = 0.10, Temp. = 80° F

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Kaculi 180

Max. Principal Strain Direction vs. Stroke Model 2 - Top Section 0.04

0.03 P1 •' "£%■■ ■ ■

0.02 c

c

P2 P3

0.01

P4 P5

in 0.00

P6 P7

0.01

P8 P9

E 4->

-

-

P10 P11

0.02 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

S troke (in.)

Figure 90 Max. Principal Strain vs. Stroke - Top Section Extrusion Angle = 120 Deg., Friction CoefF. = 0.10, Temp. = 80° F

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Kaculi 181

Axial Strain in Horizontal Direction vs. Stroke Model 2 - Middle Section 0.30 -

0.20

-

0.10

-

-+ -P 1

0.00 -

0.10

-

0.20

(0

3

a P2 P3 P4 P5 —• —P6

■o « -0.30 o

f P7 P8

_l

-0.40

P9 P10

-0.50

P11

-0.60 -0.70 -0.80 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

S troke (in.)

Figure 91 Transverse Axial Strain vs. Stroke - Middle Section Extrusion Angle = 120 Deg., Friction Coeff. = 0.10, Temp. = 80° F

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Kaculi 182

S h ear Strain vs. Stroke Model 2 - Middle Section 0.50 -^ -P 1 P2

0.40

0.30

P3 P4 —3*6—P5

m et

P6 P7

2 0.20

P8 P9

0.10

P10 P11

0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Stroke (in.)

Figure 92 Shear Strain vs. Stroke - Middle Section Extrusion Angle = 1 2 0 Deg., Friction CoeflP. = 0.10, Temp. = 80° F

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Kaculi 183

Axial Strain in Vertical Direction vs. Stroke Model 2 - Middle Section 0.00 -

0.10

-

0.20

-♦ -P 1 P2

-

P3

— -0.30

P4 -~*s- P5

C -0.40

P6 ~

2

-0.50



+ P7 — P8

0.00 -

0.01

-

0.01

P9 P10

-

0.02

P11

-

0.02 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Stroke (in.)

Figure 95 Transverse Axial Strain vs. Stroke - Bottom Section Extrusion Angle = 120 D eg., Friction Coeff. = 0.10, Temp. = 80° F

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Kaculi 186

S h ear Strain vs. Stroke Model 2 - Bottom Section 0.10 -♦ -P 1 -*■ P2

0.08 0.06 -r c

0.04

1

002 0.00

2 ®

P3 P4 P5 P6 > P7 P8

- 0.02

-0.04

P9 P10

-0.06

P11

-0.08 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

S troke (in.)

Figure 96 Shear Strain vs. Stroke - Bottom Section Extrusion Angle =120 D eg., Friction Coeff. = 0.10, Temp. = 80° F

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Kaculi 187

Axial Strain in Vertical Direction vs. Stroke Model 2 - Bottom Section 0.05

0.00 -0.05

—♦—P1 .K P2

0.10

P3

-0.15

P4

-

7

- V.•• P5

i. ■°-20

P6

.E -0.25 2 w -0.30 -0.35

P7 P8 P9

-0.40

P10

-0.45

P11

-0.50 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Stroke (in.)

Figure 97 Longitudinal Axial Strain vs. Stroke - Bottom Section Extrusion Angle = 120 Deg., Friction Coeff. = 0.10, Temp. = 80° F

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Kaculi 188

Max. Principal Strain Direction vs. Stroke Model 2 - Bottom Section 0.04 -r -* -P 1 P2

0.03

0.02

c

d

P3 P4 ■P5

-

—• —P6

0.01

C 2

i P7

5> 0.00 -

P8 P9 P10

0.01

P11 -

0.02 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

S troke (in.)

Figure 98 Max. Principal Strain vs. Stroke - Bottom Section Extrusion Angle = 120 Deg., Friction Coeff. = 0.10, Temp. = 80° F

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Kaculi 189

Axial Strain in Horizontal Direction vs. Stroke Model 3 - Top Section

-+-P 1

« P2 P3 P4 ~x—P5 ♦ • P6

c c c

< P7

s (/)

— P8 P9 P10 P11

0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Stroke (in.)

Figure 99 Transverse Axial Strain vs. Stroke - Top Section Extrusion Angle =60 Deg., Friction Coeff. = 0.10, Temp. = 80° F

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Kaculi 190

S h ear Strain vs. Stroke Model 3 - Top Section 1.50 P1 ..

1.25

c

f

P2

1.00

P3 P4 ~3K—P5

0.75

— -

0 ~ P6

l

"(5 to 0.50

P7 P8 P9

M

0.25

P10 P11

0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Stroke (in.)

Figure 100 Shear Strain vs. Stroke - Top Section Extrusion Angle = 60 Deg., Friction Coeff. = 0.10, Temp. = 80° F

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Kaculi 191

Axial Strain in Vertical Direction vs. Stroke Model 3 - Top Section 0.20

2

-

0.10

-•-P 1 --a-- P2

0.00

P3 P4

0.10

—m~~ P5

==- -0.20 |

— P6 t P7 — P8 P9 P10 P11

-0 30

-0.40 -0.50 -0.60 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

S troke (in.)

Figure 101 Longitudinal Axial Strain vs. Stroke - Top Section Extrusion Angle = 60 Deg., Friction Coeff. = 0.10, Temp. = 80° F

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Kaculi 192

Max. Principal Strain vs. Stroke Model 3 - Top Section

—♦--P1 --8- P2 P3 P4 -P5 P6 ..t- P7 - P8 P9 P10 P11

c

— jK _

d c

’ -1.50

-

2.00

-2.50 0.0

0.5

1.0

1.5

3.0

3.5

4.0

Stroke (in.)

Figure 121 Longitudinal Axial Strain vs. Stroke - Bottom Section Extrusion Angle = 90 Deg., Friction Coeff. = 0.10, Temp. = 1112° F

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Kaculi 212

Max. Principal Strain vs. Stroke Model 4 - Bottom Section

3.00 2.50 c

d £

-i

2.00 1.50

,-ssH M i—4MM4

---------

/

2 •-

HP « « !§-#-#• H M -St

0.00 0.0

0.5

1.0

1.5

f

-

2.0

& # i-S M I -ft^ * S H K

2.5

3.0

3.5

- ♦ - pi « P2 P3 P4 P5 P6 > P7 ---- P8 P9 P10 P11

4.0

Stroke (in.)

Figure 122 Max. Principal Strain vs. Stroke - Bottom Section Extrusion Angle = 90 Deg., Friction CoefF. = 0.10, Temp. = 1112° F

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Kaculi 21

Axial Strain in Horizontal Direction vs. Stroke Model 5 -Top Section 0.40

-* -P 1 P2 P3 P4 ~m- P5

0.20

P6

w 0.15

f P7 — P8

~

P9 P10 P11

0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Stroke (in.)

Figure 123 Transverse Axial Strain vs. Stroke - Top Section Extrusion Angle =90 Deg., Friction Coeff. = 0.10, Temp. = -535° F

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Kaculi 214

S h ear Strain vs. Stroke Model 5 -Top Section

0.45 0.35 I

c

0.25

c

S

0.15

JTJf

(/)

0.05 : X i - S . ........

:

'

-

S eriesl Series2 Series3 Series4 Series5 Series6 - Series7 — Series8 Series9 S eriesl 0 S eriesl 1

-0.05 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Stroke (in.)

Figure 124 Shear Strain vs. Stroke - Top Section Extrusion Angle = 90 Deg., Friction Coeff. = 0.10, Temp. = -535° F

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

K a c u li 215

Axial Strain in Vertical Direction vs. Stroke Model 5 -Top Section

0.10

0.05 0.00 P3 P4

Strain (in./in.

-0.05 -

0.10

—'M —P 5

-

-0.15 -

P6 P7 — P8 P9 P10 P11

0.20

-0.25 -0.30 -0.35 -0.40 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Stroke (in.)

Figure 125 Longitudinal Axial Strain vs. Stroke - Top Section Extrusion Angle = 90 Deg., Friction CoefF. = 0.10, Temp. = -535° F

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Kaculi 216

Max. Principal Strain vs. Stroke Model 5 -Top Section

0.50 0.45

-* ~ P 1

0.40

P2 P3 P4 P5 P6 P7 — P8 P9 P10 P11

0.35 d 0.30 d 0.25 c 2

if)

0.20

0.15 0.10

0.05 0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Stroke (in.)

Figure 126 Max. Principal Strain vs. Stroke - Top Section Extrusion Angle = 90 D eg., Friction Coeff. = 0.10, Temp. = -535° F

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Kaculi 217

Axial Strain in Horizontal Direction vs. Stroke Model 5 - Middle Section

2.50 7 P1 P2 P3 P5

2.25 2.00 1.75 c 1.50 c 1.25 c E 1.00

— P8 — P9 P10 P11

0)

-0.80 -

1.00

-1 .2 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Stroke (in.)

Figure 141 Longitudinal Axial Strain vs. Stroke - Middle Section Extrusion Angle = 90 Deg., Friction Coeff. = 0.05, Temp. = 80° F

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Kaculi 232

Max. Principal Strain vs. Stroke Model 6 - Middle Section 1.50 1.25

d d c

-* ~ P 1 -* -P 2 P3 -* -P 4 P5 —* - P 6 -t-P 7 — P8 P9 P10 P11

1.00 0.75 -

2 w 0.50

• t > » ♦«

0.25 0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

S troke (in.)

Figure 142 Max. Principal Strain vs. Stroke - Middle Section Extrusion Angle = 90 D eg., Friction Coeff. = 0.05, Temp. = 80° F

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Kaculi 233

Axial Strain in Horizontal Direction vs. Stroke Model 6 - Bottom Section 1 .0 0

0.90

—

N ss|—

0.60 c

i

p6

1

0.70

— 0.50

!

f

0.80 ^

-♦ -P 1 -*■ P2 P3 P4 P5

* ;~ s b k

p

| - f -

"B-iH...i

'... .............. ^

. . . _._.

j/

S 0.40

..

- 4 ... t~H -+■....t-4- ~s~...f-4

i

W 0.30 0 .2 0

wt! i* se r

'#

,

9

s

t

!

i

0 .1 0 0 .0 0 0.0

0.5

1.0

1.5

2.0

« P7 P8 P9 P10 P11

T------- 1-------1------- 1 2.5 3.0 3.5 4.0

Stroke (in.)

Figure 143 Transverse Axial Strain vs. Stroke —Bottom Section Extrusion Angle = 90 Deg., Friction Coeff. = 0.05, Temp. = 1112° F

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Kaculi 234

S h e a r Strain vs. Stroke Model 6 - Bottom S ection

1.75 1.50

■*~P1

1.25

k l l fcis i w M a H W jw w w w m m *

i

w

< 1 R 1M ' R

m

m

m

™

M r ‘X

m

m

P2 P3

- m 1X

i „ * _

P5 P6 - h-P 7 — P8 — P9 P10 P11

1 .0 0

'§ 0.75