%rWADTR6.11COPY 0 ~OPIESWADDTR-61I. I 8 I

~part IV

THE TENSILE DUCTILITY-TRANSITIONIN MOLYBDENUM

TECHNICAL DOCUMENTARY REPORT NO. WADD-TR61-18I81

Part IV

July 1964

1/

Air Force Materials Laboratory

Research and Technology Division

Air Force Systems CommandWright-Patterson Air Force Base, Ohio

DDC

Project No. 7351, Task No. 735101 AUG 1 7 196!.

DDC.IRA C

(Prepared under Contract No. AF 33(657)-8424by ManLabs, Inc., Cambridge, Massachusetts:

B. S. Lement and K. Kreder, authors)

NOTICES

When Government drawings, specification, or other data are used for any purposeother than in connection with a definitely related Government procurement operation, the UnitedStates Government thereby incurs no responsibility nor any obliga.;on whatsoever; and thefact that the Government may have formulated furnished, or in any way supplied the saiddrawings, specification, or oher data, is not to be regarded by implication or otherwise as in anymanner licensing the holder or any other person or corporation, or conveying any rights or permis-sion to manufacture, use or sell any patented invention that may in any way be related thereto.

Qualified requesters may obtain copies of this report from the Defense DocumentationCenter (DDC), (formerly ASTIA), Cameron Station, Bldg. 5, 5010 Duke Street, Alexandria,Virginia, 22314.

This report has be released to he office of Tee.hnica Services, U.S. Department ofCommerce, Washington 25, D.C., for sale to the general public.

Copies of this report should not be returned to the Research and Technology DivisionWright-Patterson Air Force Base, Ohio, unless return is required by security consideration,contractual obligations, or notice on a specific document.

U

EU

FOREWORD

This report was prepared by ManLabs, Inc. under USAFContract No. AF33(657)-8424. This contract was initiated underProject No. 7351 "Metallic Materials". Task No. 735101 "Re-fractory Metals". The work was administered under the AF MaterialsLaboratory, Metals and Ceramics Division with Mr. K.Elbaum actingas project engineer.

WThe period covered by this report is 30 April 1963 to 30rApril 1964.

i

i

go-V

MW

97

EF

ABSTRACT

An investigation was carried out to determine the nature of thetensile ductility transition in recrystallized molybdenum strip of threeinterstitial contents. For a fine grain size, the tensile ductility tran-sition temperature (Td) and the brittleness transition temperature (Tb)were found to approximately coincide; whereas with increase in grainsize Td is raised and Tb is lowered. The occurrence of a minimum inthe fracture stress (aF) at Td appears to be associated with the temper-ature dependence of the necking stress (9n). Prestraining above Td, wasfound to result in as much as a 20% increase in OfF as determined at tem-perature below Td. In general, the mode of fracture initiation was foundto be intergranular at Td or below and cleavage above Td. For a testtemperature above as well as below Td, crack initiation appears to be thecontrolling step in fracture. Considering 0fF as a flow stress correspondingto the fracture strainGF), the variation of 07F With temperature above Tdwas predicted within- about 15%. Based on a modification of the Cottrellrelation for crack initiation, the increase in 07F above Td is associatedwith a decrease in both the flow locking parameter (kf) and the effectivegrain size.

This technical documentary -eport has been reviewed and isapproved.

j 4'

I. PerlmutterChief, Physical Metallurgy BranchMetals and Ceramics DivisionAF Materials Laboratory

iii

ITABLE OF CONTENTS

Page

I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . I

1 A. Background . . . . . . .............. 1

B. Scope of Investigation.. ............ .1

I1. EXPERIMENTAL PROCEDURES. . . . . . . . . . . . .. 3

A. Materials . .. .. .. .. .. .. .. .. .. .. . 3

B. Recrystallization-Anneals. . . . . . .. 3II C. Uniaxial Prestrain.. . . . . ......... . .. 3

D. Mechanical Testing.. . . . . . . . . . . . . . .. 3

E. Precracked Charpy Slow Bend Tests. . . . . . . . .. 6

F. Determination of Grain Size. . . . . . ........... 6

G. Fractography .... ................ .

M -I. RESULTSAN DSCUSSION. . . . . . . . . . . . . . 7

I A. Flow and Fracture Characteristics of Mo-EZ Strip.. . 7

B. Flow and Fracture Characteristics of Mo-E3 Strip . .. 26

C. Flow and Fracture Characteristics of Mo-E4 Strip. .. 39

D. Fractographic Characteristics. . ....... ............ 39

E. Theoretical Considerations . . . . . 60

IV. CONCLUSIONS . .. S....................... .... 80

REFERENCES. . . . . . . . .. . . . . . . . . . . . . . . . 81

APPENDIX I ............ ................... . 82

IVI

pf

Ai6

Illustrations

Figure Page

1 Effect of Test Temperature on the Tensile Propertiesof Recrystallized Molybdenum (Mo-E2) Strip (I = 0. 026r71m °

. 8

Z Effect of Test Temperature of Tensile Properties ofRecrystallized Molybdenum (Mo-E2) Strip (1= 0.044 mmnr . 9

3 Effect of Test Temperature on Tensile Properties ofRecrystallized Molybdenum (Mo-E2) Strip (I = 0. 174zam) . 10

4 Variation of Yield Stress (AY ) with Grain Size (I -IZ) ofMolybdenum (Mo-E2 Strip in Test Temperature Range of+Z5 to -1500C ....................... 12

5 Variation of Yield Stress Parameter (ky) and FrictionalStress ((0i) of Molybdenum (Mo-EZ) Strip with Test Temperature.The Parameter KX. and Frictional Stress ai are Based on NormalStress (07y) and Fill Grain Diameter (t) .... ......... .. 13

6 Comparison of Predicted and Experimentally ObservedVariations of the Fracture Stress (0 F) .nd Fracture Strain(*F) with Grain Size (1 -1/2) of Recrystallized -Molybdenu-n(Mo-EZ Strip for a Test Temperature of -40cC Based onData Obtained for Fine Grain Size (I = 0. 026 rm).. .14

7 Variation of the Observed Fracture Stress (0 F) at ConstantStrain with Grain Size (I --1/2) for Recrystallized MolybdenumStrip (Mo-EZ) ............................. 16

8 Variation of Strain Hardening Exponent (n) and Strain HardeningCoefficient (K) with Test Temperature for RecrystallizedMolybdenum (Mo-E2) Strip (I = 0. 026 m) . ............. 22

9 Variation of Strain Hardening Exponent (n) and Strain HardeningCoefficient (K) with Test Temperature for RecrystallizedMolybdenum (Mo-E2) Strip (I = 0.044 mm) ........ ..... 23

10 Variation of Strain Hardening Exponent (n) and Strain HardeningCoefficient (K) with Test Temperature for Recrystallized Molyb-denurn (Mo-E) Strip (I = 0. 174 mm) .... ............. 24

11 Effect of Test Temperature on Tensile Properties of Re-crystallized Molybdenum (Mo-E3 Strip (I = 0.023 mm)..... .28

1Z Variation of Strain Hardening Exponent (n) and Strain HardeningCoefficient (K) with Test Temperature for Recrystallized Molyb-denum (Mo-E3) Strip (t = 0.023 rm)...

V

illustrations (Coninued)

Figure Page

13 Effect of Uniform Prestraining Mo-E3 at -20PC and +25 Conthe Fracture Stress at -100°C, -1500C, and -,96 0 C .. .. 30

14 Effect of PrestrainingMo-E at -ZO)C and +25'C on4 Fracture Strain (tF.)-and Total St.rain (f -- . at- 100°C. ... 32

15 Effect of Prestraining Mo-E -At - 2 0 %. an- +2 onFracture Strain (cF) and Tota-1 Strain (t +c ,)at- 150 oc. . . 33

Ur- r16 ELffect of Prestrainig o- t A?.Ca -°cnd +25°C on

Fracture Strain (F:) and Total Strain (pr + fat -196°C. . . 34

17 Effect of Test Temperature on Tensile Properties of Re -crystallized Molybdenum f bo:- 4) Strip f!=0. 020 mm) 41

I8 Vaiiation ef Straih _Ardening Exponent (n) and Strain HardeningC.efficient(K) with. Test Temperature fbr Recrystallized Molyb-denum (o E4Strii(f-- -. OZi rnm). . ..... . . . 42

i i9" Tensaie Fxachare0,of -Mo-EZ (0. 026 mm grain size) at +25 C--S= ing Several Cleairage Facets (with_ Cleavage steps) andTWO Thtrgranular Facets(3-nooth). 43

20 Same- Specimen as Fig. 19 - Show ng Intergranular FacetsWhichApparently Con-aius Fine PreCipitates. . . 43

21 Tenure Fra , Mo-EZ (0. 026 mm grain size) at -30 0 CShowing Several Clee.vage Facets. . . . . . . . . . . . ... 44

ZZ Same Spec ien as Fig. 21 - Showing Cleavage Steps andSmooth ntergranuiar wa'et. Which Apparently Contains FinePrecipitates. .......... . 44 3

23 Teniile Fractuje of Mo-EZ (0.174 mm grain size) at +25°CShowing Highly Distorted Cleavage Facets. . . ...... . 46

24 TeriaIle Fracture of Mo-EZ (0. 174 mm grain size) at +25°C-hOwi69 a Portion of a Smooth Intergranular Facet (Left)Wir4.ich App.jrently Contains Fine Precipitates. . . . . . . . . 46

2Z" Ten-ile Fracture of Mo-EZ '0. 174 mm rain size) at eC, 37I a Cleavage Facet (upper) and an lntergrantldar

Facet 'lower). . .......................... 47

26 Tensile Fracture of Mo-E2 (0. 174 mm grain size) at -40 0 CShowing a Cleavage Facet Containing Many Cleavage Steps .... 47

vi

1 u N I il l m~l l

Illu strationis (Continued)

Figure Page

27 Tensile Fracture of Mo-EZ (0. 174 mm grain size at -106o%.Showing One Intergranular Facet (Smooth) and SeveralCleavage Face . .. ... . . . . . .. .. .. .. .... 48

28 Tensile Fracture of Mo-EZ (0. 174 -.nm grain5 size) at -1l9 6O CShowing One Intergranular Facet (Sinooth) Surrounded by SeveralCleavage Facets with "Rjver t ' M4arkings Radiating fro itergranular -Facet (Po2ssible Fracture Origin). .. ......... 48

29 Tensile Fracture of Vio-E3 1%0-. 023 mm grain size) at -2-0 CShowing Several Cleavage Facetis and an. lntergranuiiarFacet (Smooth).. .. ........... .. . . . . . .5.z0-

30 Tensile Fracture of Mo-E,;3 (0.023 mm -grain size) at -100 0 CShowing Several Cleavage am-d intergranular Facets .. .... ... 0

31 Tensile Fractti-e of Mo-AE3 (.0.023 m..m grain size) Unifor-alyPrestrained (c = 0. 1151 at +251%1 and Broken at -l00oCShouw-ng Several Highly Distorted C',eavage Facets. ....... 51

32 Tensile Fracture of Mo-FE3 (0. 023 m-m grair; size) UnhiformlyPrestrained (E 0. 110) at -110C and Broken at -100oCShowing Several Cleavage Facets. .. ......... . . . . 5 I

33 Tensile Fracture of Mo -E3 (0. 023 mm.m grain size) Pres-rair-edby Necking (t 0. 28) at +250C and Broken at -1O0 C ShowingSeveraliCleavage Facets. ................... . 52

i34 Tensile Fracture of Mo-E3 (0.023 m-m grain size) Prestreinedby Necking (E = 0. 64) at +-.-5 0 " and Broken at - 1000 C ShowingOne Intergranular Facet (lower right) and Several CleavageFacets . -.. .. .. .. .. ... .. ... ... .. .... 52

35 Tensile Fracture of -Mo-E3 (0.. 023 nmm. grain size) Pre-strainedby Necking (c = 0.64) at +20,Recrystallized, and Broken at-100 0 C Showing Predomni-anty -interera-nular Face........53

136 Tensile Fracture of Mo -E3 (0. 023 mm grain size) Having NeckMachined Corresponding to a Necking Prestrain of c= 0. 64,Recrystallized and Broken at -1000 C Showing Prednminantlvlntergranular I-acets. .................... 53

37 Precracked Slow Bend Charpy Fracture oi Mlo-E3 (0.023 mmgrain size) at -1001C Showing a Cleavage Facet Containinga Few Cleavage Steps .. ................... 0

Illustrations (Continued)

F'igurcPage

38 Precracked Slow Bend Charpy Fracture of Mo -E3 (0. 023mm grain size) Prestrained (616 by rolling) at +25 0 C and

Broken at -1000C Showing Cleavage Facets Cn-ntainingMany Cleavage Steps. .... ,...* .*... 56

39 Tensile Fracture of Mo -E4 (0. 020 mm grain size) at +25 0 CShowing Several Cleavage Facets . . . . . . o . . . o 58

40 Tensile Fracture of Mo -E4 (0. 020 mma grain size) at -350CShowing Two Cleavage Facets and Many IntergranularFacets. . . . . ................ . .. . . . . . . . . . 58

41 Schematic Plots of Variation of Fractu~e- Stress (0, YieldStress (0 y), Necking Stress (0Ti), Fracture Strain F'F) andMax. Uniform Strain (eu) with Temperature . . . . . .~.*. 61

42 Plot of Stress and Strain Parameter Bands vs. Temperaturefor Mo -EZ (=0.026 mm). * .** 61

43 Plot of Stress and Strain Parameter Bands vs. TestTemperature for Mo-E2 (I = 0. 044 mm) . . . . . . . . . . 62

44 Plot of Stress and Strain Parameter Bands vs. TestTemperature for Mo-E2 (I = 0. 174 mm) .. . .. 62

45 Plot of Stress and Strain Parameter Bands vs. Test Temperaturefor Mo--3 (I =0. 023 mm) . . . . . . . . . . . . . . . . 63

46 Plot of Stress and Strain Parameter Bands vs. Test Temperatures ~for Mo-E4 (I=0.020mm) .. . . . . . . . . . . . . . . 63

47 Plots of Uniform Flow Stress (Oh)l vs. Grain Size Parameterfor Recrystallized Mo-E2 Strip at Plastic Strains (e of 0. 2

and 0. 4 . ................. . . . . . . . . . . . p 67

48 Plots of Uniform Flow Stress (IlTs) vs. Gxain Size Parameterfor Recrystallized Mo-E2. Strip at Plastic Strains (ep) of 0. 7

49 Variation of Elastic Modulus of Molybdenum (Mo-El Rod)with Temperature...... . ... . . . . . . 72

viii

Tables

T aule Page

I Chemical Composition ................ .4

2 Procedure Used for the Control of Grain Size ........... 5

3 Tensile Test Characteristics of Mo-E2, Mo-E3 and Mo-E4Strip . . . . . . . .. . ....... . ................. 11

4 Calculated Values of Fracture Stress Assuming CompletelyUniform Elongation ................ . . . . . .. 25

5 Calculated Values of Fracture Stress Under Actual Necking

Conditions. . . . . .......................... .... 27

6 Variation of Fracture Stress of Mo-E3 With Total Strain. 35

7 Effect of Necking Prestrains and Simulated Necks onthe Fracture Stress of Mo-E3 at -100 0 C ............ 36

8 Fracture Toughness of Mo-E3 at -100°C ......... 38

9 Effect of Prestrain on the Fracture Stress of Mo-E4Strip at-100 0 C and -196 0 C ....... ............... 40

10 Fractographic Characteristics of Mo-EZ Broken TensileSpecimens . . . . . . ........ .................. . 49

11 Fractographic Characteristics of Mo-E3 Broken TensileSpecimens . . ........ 55

12 Fractographic Characteristics of Mo-E3 Broken PrecrackedCharpy Slow Bend Test Specimens . . ........... . 57

13 Fractographic Characteristic of Mo-E4 Broken TensileSpecimens . . . . . . . . . . . . . . . . . . . . 59

14 Yield Locking Parameter (ky) and Frictional Stress (9j)for Mo-E2, Mo-E3, and Mo-E4 Strip ........... 65

15 Flow Locking Parameter (kf) for Mo-EZ Strip ...... 69

16 Approximate Values of Flow Locking Parameter (kf) forMo-E3 and Mo-E4 Strip ................ ....... 71

17 Calculated Effective Surface Energy for Crack Initiationin Mo-E2, Mo-E3 and Mo-E4 Strip .... ........... . 73

18 Calculated Effective Surface Energy for Crack Propagationin Mo-E2, Mo-E3, and Mo-E4 Strip . . . ........... 76

ix

I. INTRODUCTION

A. Background

9 During the period of 1 November 1959 to 30 April 1963, ManLabsInc. acted as prime contractor on a program entitled "Substructure and Me-chanical Properties of Refractory Metals" under Contracts No. AF33(616)-6383 and AF33(657)-8424. Other research participants on this program wereMassachusetts Institute of Technology, Rutgers the State University, Univer-sity of Liverpool (England) and University of Cambridge (England). The re-sults obtained were presented in three summary technical reports by Lementet al, (1, 2, 3)'

In connection with the above program; ManLabs concentrated on therelation of microstructure to the ductile-brittle transition in refractory met-als. The results obtained on molybdenum that are considered pertinent tothe present investigation are as follows:

a) For recrystallized as well as worked molybdenum strip of re-latively high purity, the effective surface energy (-y') at the tensile ductility-transition temperature (Td) as 2alculated on the basis of the Cottrell fracturerelation is about 3000 ergs/cm ; and the corresponding critical crack lengthas calculated on the basis of the Griffith-Orowan fracture relation is equalto the first-order subgrain size.

b) The discontinuous change in both ductility and fracture stressthat occurs at Td does not appear to correlate with changes in fracture mode,mechanical twinning, or the occurrence of nil-ductility. Rather the tensileducti! ;y-transition seems to be related to the phenomenon of necking which

ii occurs above but not below T- Accordingly, a suggested criterion for theoccurrence of a tensile ductility transition is the intersection of the fracturestress (9. ) corresponding to uniform strain and the necking stress (4 "n) vs.test temperature curves, i.e. aF = (I at Td.

c) The concept of a strain-dependent I temperature-independent)critical fracture stress was used in an attempt to predict the grain size de-pendence of the observed fracture stress and fracture strain based on thevariation of the quantities with test temperature as measured for a fine grain,recrystallized molybdenum. The predicted values of fracture stress and frac-ture strain for a selected test temperature of - 400 C were both found to be ap-preciably lower than the corresponding values actually measured as a functionof grain size. This raised the question as to whether a Cottrell-type fracturerelation actually holds.

B. Scope of Investigation

The present investigation represents a continuation of the researchconducted under Contract AF33(657)-8424. The objective was to elucidateboth theoretically and experimentally some of the basic factors affecting

: Underscored numbers in parentheses designate References given at endof report.

** Manuscript released by the authors May, 1964 for publication as an R&DTechnical Documentary Report.

Ufractur phenomena in molybdenum. The approach used was to study the ef-fects of interstitial content, grain size, and prestraining on the tensile ductility-transition behavior. Attempts were made to determine the effects of plasticstrain on both flow stress and fracture stress. Comparison were made betweeneffective crack propagation energy values as determined by tensile tests andby precracked Charpy slow bend tests.

I2

I

II

I

III

I

!a

TI ~VE~PJMRAL DURES

A. Materials

The interstitial contents of the four 30-mil thick molybdenum stripmaterials used in this investigation are listed in Table 1. The strip fromingot Mo-E2 is relatively high in carbon (about 6 0-ppm); from ingot Mo-E3is relatively high in nitrogen (about 10 ppm) and possibly oxygen (about 20ppm); and from ingot Mo-E4 is relatively high in oxygen (about 145 ppm).

B. Recrystallizaton-Anineals

All recrystailization runs were carried out in a purified argon at-mosphere passing through a vertical Super-Kanthal element furnace control-led within ± 80 C. Specimens were wrapped in tantalum foil and suspendedvertically in the heating zone of the furnace operating at the selected recrystal-lization temperature. After either 0. 5 or 1. 0 hour at temperature (allowingfor heating -up time), the specimens were removed from the heating zone andthen allowed to cool to room temperature in the atmosphere. Recrystallizationtemperatures and times for Mo-EZ, Mo-E3, and Mo-E4 are given in Table 2.

C. Uniaxial Prestrain

In order to strain recrystallized Mo-E2 strips and thereby attainlarger grain sizes on subsequent recrystallization anneal, uniaxial prestrainsin tension were utilized. Flat tensile specimens I inch wide and 10 inches longwere machined from the molybdenum strips with the specimen axis parallelto the rolling direction. These specimens were stress-relieved for I hr. at800 C in a vacuum furnace and then prestrahned in uniaxial tension to about10-15% elongation in a Bgldwin tensile machine. Subsequent recrystallizationswere carried out at 1300 C (medium grain size) and 1600 C (coarse grain size).

D. Mechanical Testing

1. Tensile Tests

In general, the tensile tests were carried out in the range of+ 25 C to - 190 C as described in the second summary technical report(Z).The applied strain rate was maintained at 2. 8 x 10 sec . in analyzingthe stress-strain curves, relatively large discrepancies were found betweenthe measured elastic modulus and the 1961 Metals Handbook value for molyb-denum (E = 47 x 100 psi) which appears to be relatively constant in the testtemperature range of 25 C to at least -80 0 C. in order to correct for thesediscrepancies, it was decided to algebraically add the difference in elasticstrain~as calculated by dividing the measured stress level by the known elasticmodulus and by the measured elastic modulus)to .. e measured strain value(elastic plus p astic).

3

ITable 1

IN Chemical Composition

IS Initial Condition C N 0 Othersppm ppm ppm

Mo-E2 H recrystallized at 12000C~and rolled 87% at 1600

to 400C 65 4 12D recrystallized at 12000C

and rolled 44% at 1250to 9000c 65 2 1

F recrystallized at 1200°Cand rolled 52% at 1250to 4000 C 56 3 8

Mo-E3 H recrystallized at 12000Cand rolled 88% at 1000 to4000C 19 7-15 12-29i0

Mo-E4 C rolled 64% at 125000and rolled 28% at 900to 6000C 12 3 145

*Other elements in ppm are as follows:

Al Cr Cu Fe Mn Ni Pb Si Sn Ti V<50 <5 1 30 <1 <1 <10 <100 10 <50 <10 <10

4

41)

00

S4 ~~ ~1 $4t 0 0 0

' 4 4 -

0,0

.4 ~ - 0 4

14L

bC

I

~E. Precracked Charpy -Iw, w Benid T estt-

WPrecracked Charpy slow bend tests at -100 C were carried outon specimens about 0.030 inch thick, 0. 394 inch wide and 2 inches longcontaining a 450 V-notch. Fatigue precracking to produce an initial crackabout 0.025 inch long at the V-notch was accomplished b; bending in com-pression using a ManLabs precracking machine with the specimen in thereverse position. The slow bend tests were carried out using three point

Iloading to determine load vs deflection characteristics.

F. Determination of Grain Size

Grain size measurements were carried out on both longitudinal andtransverse sections of the recrystallized molybC num strips. Aftermounting.the specimens were electropolished in a solution of 75 cc methyl alcohol and25 cc HS0 4 at a current density of about I amp.icm2 . Etching was carriedout using Murakami's reagent. Grain diameter measurements were madeusing the linear intercept method on photomicrographs taken at 1OX.

G. Fractography

Fractured surface of tensile and slow bend test specimens wereexamined by both light and electron fractography. Light microscopic ex-amination at magnifications up to 80OX was used to determine where fractureinitiated, mode of fracture, and facet size. Electron microscopy was car-ried out at ZOOOX on shadowed carbon replicas of the fractured surface as ob-tained by a) stripping a parlodion replica from the fractured surface, b)shadowing with chromium, c) depositing a carbon film by evaporation at 90

- and d) dissolving the parlodion in butyl acetate.

tf

6

11. RESULTS AND DISCUSSION

A. Flow and Fracture Characteristics of Mo-EZ Strip

1. Tensile Properties vs. Test Temperature

Plots of yield stress U.), fracture stress ( 0 -F) and fracturestrain(eF) for Mo-EZ molybdenum srrip of fine, intermediate and coarsegrain size (f) are shown in Figs. 1, 2 and 3. Discontinuous yielding wasfound to occur in both the fine and intermediate grain size materials andTy represents the lower yield stress. On the other hand. discontinuousyielding was not observed in the coarse grain material and it was decidedto use the proportional limit for I . This seems iustified on the basisthat the proportional limits of the fine and coarse grain materials werefound to be approximately equal to their respective lower yield stressvalues.

Based on Figs. 1, 2 and 3, the brittleness-transition (Tb),ductility-transition (Td), and fracture stress maximum (Tm) temperatures*as well as both the corresponding fracture strains (EF) and ratios of ("F to0y at Td are given in Table 3. The values obtained for the fine and inter-mediate grain sizes of the Mo-E2 strip are about the same except that Tbis lower for the intermediate grain size. For the fine graih Mo-E2, itwas found that Tj approximately coincides with Td. The coarse grain sizehas the lowest Tb and the highest Td and Tm temperatures. Also, the valuesof eF and 0 F/Cy at Td are highest for t. e coarse grain size.

2. Dependence of Yield Stress on Grain Size

Based on Figs. 1, 2 and 3, plots of Uy vs are shown inFig. 4 for the Mo-E2 strip subjected to test temperatures in the range of+25 to -150 0 C. The corresponding k, values (based on normal stress andfull grain size) are given by the slopes of these plots. As shown in Fig. 5,ky appears to increase linearly with decrease in test temperature, and theextrapolated value at - 196 0 C is about six times higher than at +250C. Theky ratio at -80 0 C is about three, which is about twice that reported formolybdenum by Wronski (5) (about 1. 6). This is tentatively attributed tothe fact that the iterstitial level of the molybdenum (Mo-EZ) used in thepresent investigation is significantly lower than that used by Wronski.

3. Prediction of Dependence of Fracture Stress on Grain Size

In the previous report (Q), a method of predicting the variationof observed fracture stress with grain size over the test temperature rangeof Td to Tm based on data for a single grain size was presented. It was as-sumed that the critical fracture stress (07c) is strain-dependent but tempera-ture-independent, and that the Cottrell (5) relation is obeyed if OC at givenfracture strain (cF) is determined as a function of the grain size (1):

=GL - I2 (1)

*These temperatures are defined in Appendix I.

7

1/)

w I

15 OF I Cr

S-0

I F Q U

XW

: 10-007

,0.4ci:i

500 10 - 5I " .

TEST TEMPERATURE., C

Fas i - Effect of Test Temperature on the Tensile Properties ofRecrysta/lized Molybdenum (Mo-EZ) Stri (1 0. 026 mm).

!8

W1501AU.) 0pF Cr.0

w

b"

5:o 1.Cr)

w

I--

4 - 0.8 U.-- 0.7IIr - -,0 -.6- i

I I ITd in 03-

- , I, -o.0

-200 -150 -100 -50 0TEST TEMPERATURE, OC.

Fig. 2 - Effect of Test Temperature on Tensile Properties ofRecrystallized Molybdenum (Mo-E2) Strip (I =0. 044 rm).

I200

Iw

° I

(15

OF'0

IV 100] O-Y 0 0

w4A

0--

00wA

U- 1 -0.6

T b Td T,,m) II -0.4 D_

; I i-0.3

I-Q

- 200 -150 -100 - 50 0O

00C

i TEST TEMPERATURE, .

i Fig. 3 -Effect of Test Temperature on Tensile Properties ofi Recrystallized Molybdlenum Mo -EZ) Strip (I = 0. 174 mam).

10

LLQ'

i mmm~ m~ mI

Table 3

Tensile Test Characteristics of Mo-E2, Mo-E3 and Mo-E4 Strip

F F yAverage Tat at at at

T T T T T T TStp GrainSize b 0 d m mmm oC OC oC

Mo-E2 0.026 -80 0.04 -80 0.04 -30 0.80 1.00

0.044 -150 0.02 -75 0.07 -25 0.65 1. t0

0.174 -195 0.02 -40 0.18 0 0.95 1.44

Mo-E3 0.023 -80 0.03 -80 0.03 -20 0.90 1.00

Mo-E 4 0.020 -35 0.00 -35 0.00 +25 0.62 1.00

iI

17U5r

6I125 -

10

125*Cmoo

0Io Wo

co

- ---------

25-0 1 2 3 4 5 6 7

GRAIN SIZE PARAMETER (t2)mm 21/

Fig. 4 - Variation of Yield Stress (0Ty) with Grain Size(1/)of Molybdenum (Mo-E2) Strip in Test TemperatureRange of + 25 to 1l500C.

12

W wz % 7 0Ozo 0

OD 4.0 - o

6.0

Wcr3.0I- U)

~2.0 -J4

U) 0

crLL

~1.0- j

-200 -150 -100 -50 0 50

TEST TEMPERATURE, OC

Fi. Variation of Yield Stress Parameter (kv) and FrictionalStress 1.C' i) of Molybdenum (Mo-EZ) Strip with TestTemperature. The Parameter K and FIrictional Stress

1are Based on Normal Stress I(Qy)adFlGriDamtr()

13

4 -f I [ oIE~E

IV)

I I FRACTURESTT FSS

OBSERVED OF forS=E26

- I !YIELD i

/ !STRESSPREDICTED OF 1

-mm 0.8

U o o "- 1 0.7u-,L ./ Zoc- I o4

50- 0.5-a I

GRAIN SIZE PR EDTE I'),mm

A~,r

0--

Size~c 0.2 = .2m)

/ 0.8

10.1LII

I050 I 2o 45n

1b 1

GRAIN SIZE PARAMETER (F 2 ).mm 2'

Fig Comparison of Predicted and Experimentally Observed Variationsof the F r4cture Stress ((T. ) and Fracture Strain (-) with GrainSize (1-/- o/f Recrystaifze Molybdenum (Mo-E21 Strip for aTest Temperature of -40 0 C Based on Data Obtained for Fine GrainSize (I = 0. 026 mm).

14

Fig. 6 is a revised plot showing both the obserxed and predicted values ofthe fracture stress (0FF) and fracture strain (e ) as function of 1 -1/2. Theobserved fracture stresses are as much as 30% higher than predicted; andthe observed fracture strain are as much as four times the predicted values.This raised the question as to whether the critical fracture stress actuallyfollows the relation given in Eq. (1). ln order to clarify this question, plotsof UF vs I-/2 corresponding to iF values of 0.2, 0.4 and 0.6 were madebased on Figs. 1, 2 and 3. As shown in Fig. 7, the slopes (kF) are all about0. 9 x 108 cgs, and there is an intercept (C -) corresponding to infinite grainsize. It appears that the dependence of 0 F at constant fracture strain hasthe following form:

[0=FIE + -kF / (2)

Eq. (2) differs from the form of the Cottrell (5) fracture relation, Eq.(1),according to which "F or 0"c should equal zero at infinite grain size. Thus,it does not seem possible to accurately predict the dependence of 0 F on testtemperature based on data obtained for a single grain size, as was attemptedby this approach.

4. Prediction of Fracture Stress from Fracture Strain

4.1 Previous Approach

In the previous report Q), calculations were made of theratio of the maximum to minimum fracture stress in the transition range forMo-El strip (about 40 ppm carbon, 4 ppm nitrogen and 25 ppm oxygen) rolled5, 46 and 88% (reduction in area) after recrystallization; and for recrystallizedMo-EZ strip in the fine grain condition. For the Mo-El strips, Td and Tm ap-pear to coincide; whereas for the Mo-E2 strip (Fig. I) Tr. is about 50 0 C higherthan Td. It was assumed that the over-all strengthening iactor due to necking(qn) is equal to the following product:

q q, x p x q; = OF)m ax(A.)m in (3)

qp= plastic constraint factor

= strain rate factor

Calculated values of q based on Eq. (3) were found to agree within 10% of thecorresponding measured values.

Subsequent analysis of this approach has led to the conclusionthat the good agreement obtained between calculated and measured values of q1is probably fortuitous. This is based on the following considerations:

a) The strengthening factor associated with substructural

15

x0.15

4E z ,

4E 2 .

ICIW

ICIW

C,)

C,)C,)

50-

0-04

GRI IZ -AMTRM

0i. aito fteOsre atr tes(F tCntnStanwtwri ie(-/) o ersalzdMlbeuStiwAoE)

(I16

changes during strain:ng from the necking stress to the fracture stress,

("'Flmax. at T, was not taken into account.

b) The calculated grain size factor (qc) is probably toolarge since the fracture stress (which is the f1o stress at fracture strain)was assumed to be directly proportional to 1 1- whereas the actual depend-ence of flow stress includes a term representing the flow stress at infinitegrain size.

c) The strengthening factors are more likely to be additiverather thL n multiplicative.

4. 2 Revised Approach

Based on the foregoing considerations, it was decided tomodify Eq. (3) and attempt to predict the variation of fracture stress withtest temperature above Td. Since the fracture stress and the flow stress atthe fracture strain are identical, the factors that influence flow stress can beutilized to calculate the fracture stress provided that the fracture strain isknown. Assuming that the observed flow stress Of is equal to the flow stressdue to substructural changes, Ufs, plus the strengthening contributions of a)decreased grain size during straining, b) plastic constraint due to necking,and c) increased strain rate due to deformation being confined to the neck;the following relation should hold:

0 l [ + (ql- l) + (qp - 1) + (q. - 1)] (4)

I fsp A

where qj, and q. are the strengthening factors due to grain size, plasticconstraint aId strain rate (in the necked region) respectively, correspondingto a given amount of strain e (elastic plus plastic). As is subsequently dis-cussed, qf --z I and therefore can be neglected. For the prediction of frac-ture stre~s (Ur.), the identity of O-. and 0- at t is utilized and equation (4)takes the following form:

F: s % 1 ) + (q. ) (5)A. Fs

where U- is the contribution of substruczural changes to the fracture stress,and qP and q. are maximum values which occur at the fracture strain (rF).

(a) Substructural Strengthening

For the determination of -F_ it is necessary to knowthe relation of the true flow stress (%s) to the truetstrain (1). The simplest

7

uifsumption is that the so called power law holds:

I's = K( })n (6)

where c = total strain (elastic plus plastic)K = strain hardening coefficientn = strain hardening exponent

In particular, 0s is given by substituting ic for c:I

(F K (n (7)Fs KFiI

I Thus it is possible to determine (Y provided K, n and F are known. Thebest way to determine K and n is From a plot of Eq. (6) in the form of log!. vs log c using data corresponding to the portion of the stress-strain curvefrom the yield stress (07 ) to the necking stress (On). (.F can then be deter-

- -mined using equation (7), which is effectively extrapolating the log Oirs vs logeplot to log i F" This assumes that the power law continues to hold from I to4 (or from the strain (Eu ) at Un to EF).

An alternative way to determine 07 - is to utilize therelation between the yield stress (0y7) and the yield strainif

y

n07 K(n (8):-: y

Defining qs as aFs/0 at the fracture strain (zF) and utilizing Eq. (T) and (8)t gives

j nSq = (9)

- Therefore, q represents the substructural strengthening factor and TFs can- be determineS if n, 4E and c F are known.

(b) Grain Size Strengthening Factor

The grain size factor (q) may be defined as follows:

q= fs + fs (0, q, - s(10)JJ

Ii

IZ1

where AU = increase in the flow stress due to the decrease in transverses . IS

grain dimensions. The dependence of flow stress 0" at a given strain andtest temperature on grain diameter is given by the iohlowing relation:

III

9 = 0 + k I(iPfs- f

where 0 = flow stress at infinite grain size

k-. flow stress parameter

Since a decrease in grain size occurs because of the reduction in area duringthe tensile test, the increase in flow stress is at a given strain is given by

(fs = k. - 1/2) (12)

and therefore

=+ (13)

Assuming that k 0.3 k for molybdenum and using the measured value ofk at 20 C for - o-EZ ksi/mm -- ), the corresponding value of kf atL

2 °C ,sO..6ksii 7% For a reduction of area as high as 69% (c = 1.00),A(i- '/ 2 )2mm/ 2 . Since the approximate value of Cs at 20°C is 125 ksi,the value of a, calculated on the basis of Eq. (13) is about 1.01. Since thisrepresents a maximum value, q, can in most cases be considered as equalto unity.

(c) Plastic Constraint Strengthening Factor

Based on the Bridgeman (6) correction, the plasticconstraint factor (nq for a round tensile specimfen is approximately givenby the following rel ion in terms of the fracture strain (

(q) - = . ~d (14)

d 1-0. 1S(F)rd

According to an analysis of Aronofsky's (7) results for a flat specimen, thefollowing relations appear to hold between the plastic constraint factors,(q) r, and (q)rd and between the fracture strains, (cF)fL and (Frd for

I9

Ia flat and round specimen. respectively:

(qp)fl1 =*0.5 [(qp) rd o l] (15)

(I F~f 0.9 (C F)rd (16)

Solving Eq. (14), (15) and (16) fo - in terms of -OFff and dropping thesubscript fV gives

0.50. O(17)

(d) Strain Rate Strengthening Factor

As discussed in the previous report (3) the strain rate( ) in the necked region of a tensile specimen is higher thaitae applied strainrae and the flow stress required to produce a given strain Is increased by afac-tor(q;) given by the following equation:

L = a-C )1/4 rg n n

8 aauexp-n -8oa exp n -4 (c - u (au - a exp n)

(18)

where L = gage lengthgC and c total necking strain and maximum uniform strainn u respectively

a and a = initial specimen semi-width and specimen semi-widtho u corresponding to maximum uniform strain respectively

r strain rate exponent (0.05 for molybdenum according toBechtold's (8) results).

Based on the previous calculations (3), the factor q. has the following depend-ence on plastic strain as given by th- difference betWeenc F and the maximumuniform strain (e ):

20

F - tu qI

0.0001 1.030.0010 1. 060.0100 1.090.1000 1.110.5000 1.11

Since the values of F -cu fall in the range of about 0. 10 to 0.8 for the Mo-E2 strip tensile test results considered, it may be assumed that qZ is equalto 1. 11 for all the cases of interest.

4.3 Calculation of Fracture Stress Assuming_ Completely

Uniform Elongation

As previously defined, 0"Fs represents the fracture stressdue to substructural changes alone, i. e. the flow stress corresponding to theobserved fracture strain assuming completely uniform elongation(no ecing.In order to calculateT- s for a given test temperature, it is necessaff to firstdetermine the strain hardening exponent (n) and strain hardening coefficient(K) from a plot of log Ut. vs log,( at that temperature and then to utilize thepower law as given in lq. (8).

The variations of n and K with test temperature in the rangefrom Td to 20 C are shown in Figs. 8 " to 10 for Mo-EZ (fine, intermediate andcoarse grain sizes). Corresponding sets of n, K and E F values were used tocalculate (IF, at Td, at half-way between Td and TM, at Tm and at 20 C. Theresults given in Table 4 indicate that (F, goes through a maximum with in-crease in test temperature above T d jusl as does the observed fracture stress.However, the calculated ma,6mum in rs occurs at about half-way betweenTd and Tm instead of at T as does the maximum in the observed fracturestress.

From the calculated values of 'IFs and corresponding valuesof observed vield stress (07), it is possible to calculate the substructuralstrengthening factor (qs) which was defined as G FsiY . As shown in Table 4,the variation of q. with increase in test temperature above Td consists of asteady increase up to at least 250 C for the fine grain Mo-E2 strip; whereasqs reaches a maximum and then decreases for the intermediate and coarsegrain Mo-E2 strip.

4.4 Calculation of Fracture Stress Under Actual Necking

Conditions

Based on the revised approach, the relation between thefracture stress under actu.1l necking conditions(F) and the fracture stress due

*The values given in Fig. 8 for n ana K at -90U C (. e., below Td Tb = -85 0 ccorrespond to a specimen that actually necked at -90°C.

ZI

o.18[,C aQ1-

0OJ2 r

E o.1o

Zc 08Wi ao6-0

o0~00X0Q04 -

I-En 0

.240

H220 0z-200-

WLj 80-0

160 K

Z 14 0 0%0

120I

.3100 0cr _ _ _ _ _ _ _ _ _ _ _

~- 80 I Ico -100 -80 -60 -40 -20 0 20

TEST TEMPERATURE, 0C

Fig. 8 - Variation of Strain Hardening Exponent (n) and Strain HardeningCoefficient (K) with Test Temperature for Recrystallized Molybdent(Mo-E2) Strip (1 = 0. 026 mm).

22

0141

z

-0.106

~0~z 00

02

S0

z

LLI0Owr

0

20

z18-00 8 0 0 -0 0 2

- TES TEPEAU60, 0

Fig 9K aito fSri adnn xoet()adSri adnnCofii0 K ihTs eprauefrRcytlie oy

deu 1M40) ti ( .04m )

0Z

z OJ4,

0 O J2

X. nW 0.10

z4

z

O3i~WI-

u_180 _

W0IL K0o 140 "0

Z120°< oo

_Z 80''C -100 -80 -60 -40 -20 0 20

in TEST TEMPERATURE, 0C

Fig. 10 - Variation of Strain Hardening Exponent (n) and Strain HardeningCoefficient (K) with Test Temperature for Recrystallized Molyb-denum (Mo-E2) Strip (I = 0. 174 mi).

24

0~ oo-'tI DOV-4 0 Da oO:1 **- c (Y) Ln en .R4 L 4 m - tr4 cr, -~

-J c- 4 tJ

41

~U)

0 rj) N -4a*,D CT 0 D t - N 0 0 t alf 00 r-I'IV en0 0 -4 0 0 0 - -- - 0 0

CT)

C) ~ ~ r - t o o t o$4 ~ ~ - 0 0_4- 0 O o

%Da, 710 1, 0 e IDC- f--4 ~ 0jy 0 - CID 0

U)

40 '1 v c o v % q O - L C 0 N N - C)I -DS

I

to :.ubftrctuiai haigc s alone (9Fs) is given by equation (5), which requiresthat q and q; be known as a function of F. Eq. (17) was used to calculateqg at he same temperatures at which values of 0 7FS given in Table 4 wereobtained for the three grain sizes of Mo-E2 strip. Taking q* as appror'imately1. 11 based on Eq. (18), calculations were made of OrF as a function of testtemperature. The calculated values of G' shown in Table 5 agree with theobserved fracture stress values within aout 15/ for 10 cases, and withinabouti20%1 for the other two cases. This is considered to be good agreement sincethe precision of measurement of fracture stress is about 100.

The calculated maxima in UF occur about half-way betweenTd and Tm similar to the calculated UFs" maxima. However, there is less ofa difference between the calculated maximum in GF and the calculated value atTm as compared to the corresponding values of UFs. It, therefore, appearsthat the method used to calculate 0 F is correct in principle but suffers frominaccuracies in determing values of qp and 9;

B. Flow and Fracture Characteristics of Mo-E3 Strip

I. Tensile Properties vs. Test Temperature

The effect of test temperature on the tensile properties of Mo-E3stripof finegrainsize (0.023 mm)is shownin Fig. 11. Similar to the fine grainMn-E2 strip, it was found that Tb and Td coincide. As indicated in Table 3, the ten-sile test characteristics of Mo-E2 and Mo-E3 are about the same.

The variations of the strain hiardening exponent (n) and the strainhardening coefficient (K) of Mo-E3 with test temperature are shown in Fig. 12.This information was utilized to calculate the variation of fracture stress (UFs)assuming completely uniform elongation (Table 4) as well as the fracture stress(GF) under actual necking conditions (Table 5). It was found that the substructuralstrengthening factor (q.) goes through a maximum at about -45 0 C. This is re-flected in the occurrence of the calculated maximum U1F value at -45 0 C instead ofat -20 0 C as actually observed.

2. Effect of Uniform Prestraining

Experiments were carried out on Mo-E3 to determine the effectof a uniform prestrain ( e at a temperature above T on the fracture stress(0-F) and fracture strain F) at a temperature below d. The temperaturesselected for the prestraining, -20 0 C and + 250C, correspond to the temperatureat which U, goes through a maximum (Tm) and room temperature respectively.The procedure was to prestrain to increasing values of €pr up to about 0.19 at

0 0 p-20 C or + 25 C, decrease the load by about 900. cool to a final test temperature(-100OC, -150°C, or -196 0 C), and load until fracture occurs.

As shown in Fig. 13, the fracture stress ( F) at -100 0 C increaseswith prestrain (cpr) and goes through a maximum at Epr 0. 1. The maximumin G"F correspons to an increase of about 30% as compared to UF for zero pre-strain as measured at the same breaking temperature of -100 0 C. For abreaking

26

'949P

0 iu

o F. .4 -r Q4 - OD -- - - 4 -Cy% c

-4 0 M 0 m4 t- 0 N~ 0 0 N 0 -4 0 - -

$4 '~ co. ....0...q.. Ol. -~

t~- - - - c-

- IvLA g ~ ; 0 ' rJa \-4 Q . 00 -. .. r ...

0ju ~ ~ ~ 0-~ 0-xf -n

r- 0- r- m

00-- av tm CO

v I noc -0tIn iob fnio -0C~O 0 gn_00

0 I tO r E a o Oto a,'~ 0i ~ o*; ; 000 000 000>-C~ 000- C > 00

GOtA LfOUt COu- En MIN %4 q N OV iNtn

+ ~ + 1 -4 +

En~

C)ii! 04-.-

200-

in 0

U' IICO

in, 1F'0 0 .0.

a:-5~

C, I

- -0.9

5- -0. W

Lb d_ 0.35a

- Q2

I I 0.2I I-

-200 -150 -100 -5C C 50

TES7 TEMPERATURE,OC

F ig. 11- Effect of Test Temperature on Trensile 'rprisof

-Recryrtallized Miols bdenum (Mo-E3 St ip (i = 0.023 mmn).

28

20J8

oOJ4

0 o 00Z 008 n

cQ06 1\ _

Q04

I-.Z

0j

i,1- 240

- 2 20

~200

180K

160

Z140

oz120

Z 100-0I 8 iS8 -100 -80 -60 -40 -20 0 20

(n

TEST TEMPERATURE, 0C

Fig. 12 - Variation of Strain Hardening Exponent (n) and Strain HardeningCnefficient (K) with Test Temperature for Recrystallized Molyb-denum (Mo-E3) Strip (I = 0.023 mm).

29

£80 -20 PRESTRAIN

-o

w 12 25C PRESTRAINI

UNI)R PRES 0CI prES)

w

150L ET EP 10

UNIOR PRESRAI (EPR)SR

116 0FINAL TESTPRESTRAIN0

-205C PRESTRAIN

I--FINAL TEST TEMP :-19%0O

0 0.10 0.20U!NIFORM PRESTRAIN,( E Dr

F ig. 13 -Effect of Uniform Prestraining Mo-E3 at -20oC and +25Con the Fracture Stress at -l00 0 c, -150 0 C, and -1496 0 C.

temperature of -150°C there appears to be a slight maximum in UF at (pr0. 06 for a prestrain temperature of -20°C. A similar trend was found forprestraining at +25 0 C although the position of the maximum is in doubt be-cause of the scatter in the datt. At -196 0 C, 0 9 decreases with prestrainand the rate of decrease is greater for the +25 C than for the -20 0 C prestraintemperature.

The corresponding variations of the fracture strain ((F) and thetotal strain (( r + cF ) with prestrainr are shown in Figs. 14, 15 and 16.After prestrafning at either -20 or + ?50C, F as a function of ir goes througha maximum at all of the final test temperatures (-100 C, -150°t, and -196 0 C).The total strain (ipr + (F ) increases with epr and tends to level off at the highervalues of cpr.

The variation of c"F with total strain ((pr + E F) is shown in Table 6for Mo-E3 strip prestrained at -20 0 C and broken at -100, 150, and -196 0 C. Itwas found that Up. increases appreciably at -100 0 C, increases slightly at -150 0 C,and decreases at -196 0 C as the total amount of strain is increased. For thepurpose of comparison, OF values obtained in the range of -80 to -67 0 C withoutany prestrain are listed in Table 6. The ratio of fracture stresses with andwithout any prestrain varies with both total strain and test temperature. Thisis further evidence that OF it not a unique function of strain alone.

3. Effect of Necking Prestrain

Studies were carried out to determine the effect of necking pre-strains at +25 0 C on the fracture stress ( 0 F) and fracture strain ((F) at -1000C.As shown in Table 7, a necking prestrain of 0. 29 at +25'C results in an increasein 0YF at -100 0 C of about 20% and in 'F at -100 0 C of about 500% (0.03 to 0. 18).A larger necking prestrain (0.64) results in a slight increase in 0F along witha 55% decrease in rF as compared to a 0.29 necking prestrain.

In order to determine to what extent the geometry of the neck af-fects 0.F and(F , simulated necking was studied using two procedures: a) pre-straining at +256C to produce a neck corresponding to a strain of 0.64 andrecrystallizing to remove the deformation; b) machining a neck in the rolling planesection of the specimen that corresponds to 0. 64 strain. As shown in Table 7procedures a) and b) resulted in completely brittle fractures ((F = 0) as well asdecreases in 0F of 30% and 12% respectively as compared to a non-prestrainedspecimen tested at -!00°C (OF = 140 ksi). These results indicate that the geom-etrical effect of a neck corresponding to 0.64 strain is to provide a stress con-centration which results in a lowering of UF . It should be noted that the simulatedneck obtained by procedure b) was machined in only one plane, whereas duringtensile deformation necking actually occurs along both the thickness and widthdimensions. Therefore, a greater stress concentration is presumably presentin a specimen that is pre-necked by tensile deformation, procedure a). than bymachining, procedure b).

In view of the simulated necking res,its, it appears that the plasticdeformation associated with prestraining has a greater effect on ratisint: C- at -100 c'than is ir.dicated by the 0% increase shown in Table 7 for 0.6#4 necking prcstrain.

31

Sp +

_nn 0 48

C,,

a OL0

a~~ 0 .0 110.522

z

< .0[ 00 0 .5 02

it 4

I-0.16-0I

0

z

II

0.1 0.20

33

CLp

z 0.16-

< *UfF

A0.1

0

d0.08-

w

z F)

4 1Z 0.I6[

4 0 0.0 5 1 .5 02

cr

UNIFORM PRESTRAIN (lEp) AT-+ 25 0C

T~~~~~jaj5 ~ ~ ~ ~ ~ P -fcto rsrinn oE)t-OCan Z nFatrzriv OjadTtl tan(6+F t100

z -< .t6h .. ~~

-J0.12

0.

z

C,,wCr

0.16

D

0.05 0.0

UNIFORM PRESTRAIN (Epr) AT + 250C

4 0.16-4

0.12

0 1

Fig. 16,- Effect of Prestraining Mo-E3 at -20°C and +250C on Fracture~~Strain (()and Total Strain ( . + ( at -196°C.

oI

34F

Table 6

Variation of Fracture Stress of Mo-E3 With Total Strain

Ratio'of FractureFracture Srse

Test Temperature Prestrain Total Strain Stress With and

TetTmprtr ) {IE+ C (0) Wt nPrestrain Fracture P.F Fpr F Without Prestrain

°C °C

-200 C -1000 C - 0.03 138 1.060.015 0.05 141 1.080.05 0.10 151 1.130.085 0.15 158 1.150.13 0.20 164 1.16

-200 C -150 0 C 0.015 0.05 177 1.350.055 0.10 180 1.340.11 0.15 178 1.290.185 0.20 161 1.14

-200 C -196°0C 0.01 0.05 202 1.540,05 0.10 193 1.440.115 0.15 166 1.200.21 0.20 160 1.11

-800C " 0.03 130

-790C - 0.05 13i

-860C -. 10 134

-730C 0. 15 138

-700C - 0.20 141

-670 C - 0.25 144

Values of fracture stress without any prestrain are given in this table forthe temperature range of -80 to -676C.

i-5 4-

M;4

co 0

444

V 0.

0 0

.41'Q~~ 0) ;

01 -4 C 0

#44 -4

V .410J 4.00(

N0

(d -- 4 414

4 0 ;4 t-J 0 . ; r ,

#4'4

04o 0- '04 >

4 4 4.,4 -4

41

u be

4-1 4)N

t44 + 4.~0 0 0

fz1 z z4 0

~t' C~36

Table 8

Fracture Toughness of Mo-E3 at -1000C

Hartbower (W/A) Irwin GC

Condition in-lbs/in 2 rsc in-lbs/in 2 gjz/M

as -recrystallized 110 i. 9x10 120 2. 1x107

pulled 6% in tension at +25 00 55 9. 6x10 6 120 2. 1x10 7

reduced 6% by roiling 25 4. 4x10 6 85 1. 5xl10at +250 C

38

IIIIII

Assumino[ that the 'eom a-;,- o f of necking is to cause a decrease of 30%,it appears that the necking prestrain per se effectively increases 0"F by about60%.

4. Slow Bend Tests at -1000C

Slow bend tests were carried out on Mo-E3 in the followingconditions: a) as-recrystallized, b) deformed 6% at +25 0 C by tensile pulling,c) deformed 6% at +25 0 C by rolling. V-notch Charpy specimens were machinedto the following dimensions: 0. 030 inch thick, 0. 394 inch wide, and 2 1/8 incheslong.

A 0. 079 inch deep, 450 V-notch was machined perpendicular to therolling direction of the strip (parallel to length direction of specimen). Thesespecimens were precracked by room temperature cyclic bending in compi .ssionfrom zero to about 50 ksi (calculated maximum compressive fiber stress at rootof the V-notch). The average depth of a fatigue crack as obtained by this pro-cedure was about 0.025 inch. Slow bend tests were carried out at -100 0 C andmeasurements of load vs deflection were obtained.

Both the Hartbower and Irwin methods were used to determineresistance to crack propagation from the slow bend test measurements. TheHartbower (2_) method of determining the fracture toughness parameter W/Ainvolves dividing the energy (W) corresponding to the integral of the load vsdeflection rurve by the area (A) of the fractured surface (below the fatigue crack).The Irwin (10) method of determining the fracture toughness parametel Gc in-volves use of the following relation:

Gc PM -119)c B da

where P = maximum loadm

B = specimen thickness

M = spring constant (P/e) where e = deflection

a = notch depth

-I

An approximate value of dM /da was obtained from the initial slopes of theP vs e plots corresponding to different initial crack lengths (a).

The fracture toughness values determined from the slow bend testsO

at -100 C are given in Table 8. The W/A and G values for the as-rccrystallizedcondition show good agreement. However, although decreases in (W/A) of 50 to75% resulted from plastic strains of 0.06 at +25 0 C, the corresponding decreasesin Gc are only 0 to 30%. The fracture toughness values at -100°C fall in the rangeof 25 to 120 in-lbs/in2 or 0.4 to 2.1 x 10-ergs/cm 2 .

37

! I Il I I 1

!

C. Flow and Fracture Characteristics of Mo-E4 Strip

The effect of test temperature on the tensile properties of Mo-E4strip is shown in Fig. 17. For this high oxygen material of fine grain size(I = 0.020 mm), Tb and Td appear to coincide at about -35 0 C, and Tm oc-curs at about + 250C. These are higher temperatures than found for thefine grain Mo-EZ and Mo-E3 materials (Table 3). The Mo-E4 also differsfrom the Mo-EZ and Mo-E3 materials in that eF = 0 below Td and cYF reachesa constant value at about -100 0 C. No evidence was found that twinning isresponsible for the levelling-off in f'F- Therefore, this phenomenum remainsunexplained.

As shown in Table 9, prestraining the Mo-E4 at +25 0 C was found toresult in increases in fracture stress of about 14 and Z0% at -100 and -1960Crespectively. The specimens were observed to fracture without any additionalplastic strain at these test temperatures. This differs from the Mo-E3 be-havior after prestraining since an appreciable amount of strain occurredprior to fracture at -1000C.

The variations of the strain hardening exponent (n) and strain harden-ing coefficient (K) of Mo-E4 strip with test temperature in the range of -25 to+50 0 C are shown in Fig. 18. The strain hardening exponent (n) of Mo-E4 decreasesmarkedly with decrease in test temperature, which is opposite to that found forthe Mo-EZ and Mo-E3 materials. On the other hand, the strain hardening coef-ficient (K) increases with decrease in test temperature similar to the Mo-E2 andMo-E3 materials.

Using the eF , n, and K values for Mo-E4 shown in Figs. 17 and 18respuctively, calculations were made of the uniform fracture stress (9f.) andthe substructural strengthening factor (qs). As shown in Table 4, qs for Mo-E4was found to be considerably higher than for the Mo-EZ and Mo-E3 materials inthe range of 0°C to Z5 0 C. This is attributed to the relatively high strain harden-ing characteristics of Mo-E4, presumably due to its high oxygen content. Thepredicted values of (UF for Mo-E4 under actual necking conditions are shown inTable 5. The predicted values were found to be 27 to 37% higher than the observedvalues of 0"F in the range of -25 to + 50 0 C. The agreement is relatively poor ascompared to that obtained for the Mo-E2 and Mo-E3 materials. This may be dueto a difference between high and rulatively low oxygen materials with respect tothe degree of plastic constraint for the same reduction in area.

D. Fractographic Characteristics

1. Broken Mo-EZ Tensile Specimens

Based on light and electron microscopic observations. thefractographic characteristics of the fine, medium, and coarse grain Mo-EZtensile specimens were determined. As shown in Figs. 19 to 22, the fracturesof the fine grain Mo-E2 specimens tested at +25 to -30 0 C consist of both cleav-age (transgranular) facets and intergranular facets. The cleavage facets con-tain what are called cleavage steps or river markings, which indicate thedirection of crack propagation. On the other hand the intergranular facets

39

ICI

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914

4-b

t4 4.1

td0

00

o 40

c0.34-

0.32 -

wZ0.30

w 0.28 -

Z026-2w Q24--022-

Za020 -ar

U-

50.18

LI)

wiCr

810 .A-1Z 120j-

Wo -80 -60 -40 -20 0 20 40 60

TEST TEMPERATURE 1 C

Fig. 18 - Variation of Strain Hardening Exponent (n) and Strain HardeningCoefficient (K) with Test Temperature for RecrystallizedMolybdenum (Mo-E4) Strip H1 0.0Z0 mm).

42

I

.150

C/)

i- LO i -Qa: I

. -...

,>< Q9 0

-0.7

C/) I

! 00 I I A I

5- 0.0 - 5u 00 -005

w

D 41

LaJ T 0.6'w

Cr

IEE

0 0

-200 -150 -100 -50 0 50

TEST TEMPERATURE, CC

Fig. 17 -Effect of Test Temperature on Tensile Pro perties ofRecrystallized Molybdenum (Mo- E4 Strip (f 0. 020 mm).

41

Light Fractograph 750X

Fig. 19 - Tensile Fracture of Mo-EZ (0.026 mmgrain size)at +250C Showini Several Cleavage Facets (withCleavage steps) and Two Intergranular Facets (smooth).

Electron Fractograph ZOOOX

Fig. 20 - Same Specimnen as 1Fie. 19 -Showing IntergranuiarFacets Which Apparently Contains Fine Precipitates.

At3

Light Fractograph lOOOXFig. 21 - Tensile Fracture of Mo-EZ (0.026 mm grain size)

at -30 0 C Showing Several Cleavage Facets.

Electron Fractograph 2000X

Fig. 22 - Same Specimen as Fig. 21 -Showing CleavageSteps and Smooth Intergranuilar Facets WhichApparently Contains Fine Precipitates.

44

are generally smooth, and som etimes contain what appear to be fine pre-cipitates (Figs. 20 and 22). The fractures of the medium grain Mo-E2 wasfound to be similar to the fine- grain M&-1E2. Examples of the coarse grainMo-E2 fractures in the range of +25 to -i96°C are shown in Figs. 23 to 28.At +250C, the fracture consists predominantly of high distorted cleavagefacets (Fig. 23) although a few intergranular facets ,were observed (Fig. 24).Evidence of what is considered to be initiation of facure at an intergranularfacet at -0, 6° C" is shown in Fig. 28.

Table 10 gives a summary of the fractog-raphic characteristicsof the Mo-EZ tensile specimens broken in the range of +250 to 1960C. Withdecrease in test temperature, the relative amount of intergranular facets in-creases from <1 to about 2% for the fine grain size, from <1 to about 6% forthe medium grain size, and from <1 to about 4% for the coarse grain size.The ratio of the average cleavage facet size to the grain size (corrected fortotal reduction in area prior to fracture) varies from 0.7 to 1. 4-for the finegrain size, 0.6 to 1. 1 for the medium grain size, and 0.4 to 0. 5 for the coarsegrain size. The corresponding ratio for the average intergranular facet size-varies from 0.7 to 0. 9 for both the fine and medium grain size, and 0. 1 to 0. 3for the coarse grain size. Thus it appears that although the cleavage and inter-granular facet sizes are approximately equal to the grain size for the fine andmedium grain size Mo-EZ, the cleavage and intergranular facet sizes are sig-nificantly smaller than the grain size for the coarse grain Mo-E2.

For the coarse grain size Mo-E2, the origin of fracturewas traced to a particular intergranular facet from -1960C to Td; whereasfor the fine and medium grain size Mo-E2, it was traced to a group of bothintergranular and cleavage facets. However, above Td the origin of fractureof the three grain sizes was traced to a group consisting of only cleavagefacets. It is therefore concluded that the mode of fracture initiation in Mo -E2is intergranular a Td and below, and cleavage above Td.

The geometrical location of fracture initiation with respectto the specimen cross section was also determined. It was found that fracturegenerally initiated in the interior of the specimen. The approximate locationscan be expressed by the following coordinates: in the width (w) direction, fromw/8 to w/Z; and in the thickness (t) direction, from t/4 to t/2. There wereonly three cases in which fracture initiated at the surface, one at w/3 and theother two at t/2 and t/3.

2. Broken Mo-E3 Tensile Specimens

As shown in Figs. 29 and 30, the fractures of the brokenfine grain Mo-E3 tensile specimens at -20 and -1000C consist of both cleav-age and intergranular facets. Prestraining at +250C followed by breaking at-1000 C results in a greater amount of highly distorted cleavage facets (Figs. 31,33 and 34) as compared to prestraining at -200 C and breaking at -100o C(Fig. 32). Predominantly intergranular fractures (Figs. 35 and 36) were pro -duced by the simulated necking experiments carried out at -1000 C.

The fractographic characteristics of the Mo-E3 tensile

45

7I

-I

I

Light Fractograph 50OX

Fig. 23 - Tensile Fracture of Mo-E2 (0. 174 mm grain size)at +25 0 C Showing Highly Distorted Cleavage Facets.

I

SElectron Fractograph 2000X

Fig. 24 - Tensile Fracture of Mo-E2 (0.174 mm grain size)~at 25S°C Showing a Portion of a Smooth Intergranular

Facet (Left) Which Apparently Contains Fine Precipitates.

46

ama m mo ur Im mm mnm W mu • m n mn n nn n

Electron Fractograph 2000X

Fig. Z5 -Tensile Fracture of Mo-EZ (0. 174 mm grain size)at 011C Showing a Cleavage Facet (upper) and anIntergranular Facet (lower).

Light Fractogr-ph 500X

Fig. 26 -Tensile Fracture of Mo-EZ (0. 174 mm grain size)at -40'C Showing a Cleavage Facet Containing ManyCleav'age Steps.

Light Fractograph r-0ox

Fig. 27 -Tensile Fracture of Mo-E2 (0. 174 mm grain size)at - 1000 C Showing One Intergranular Facet (Smooth)and Several Cleavage Facets.

- 7 boa

Light Fracograp 650

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Light Fractograph lOOOX

Fig. 290 Tensile Fracture of Mo-E3 (0. 023 mm grain size)

at -1060C Show%.ing Several Cleavage and IntergranularFacets.

50

Light Fractograph 75 OX

Fig. 31 - Tensile Fracture of Mo-E3 (0.023 mim grain size)Uniformly Pres trained (c 0~. 115) at +250 C andBroken at - 100 0 C Showing Several Highly DistortedCleavage Facets.

Light Fractograph 75SOX

Fig 3 -Tensile 'Fracture of Mo-E3 (0.023 mm grain size)Uniformly Pres trained (c 0. 110) at 200OC andBroken at - 1 000 C Show-ing Several Cleavage Facets.

Light Fractograph 650X

Fitz. 33 - Tensile Fracture of Mo-iE3 (0. 023 mm grain size)Prestrained by Neckcing 0(= 0.284) at +25 0 C and

Broken at = 1000 C Showing One lntergranular Facet(lower right) and Several Cleavage Facets.

52

iLght Fractograph 650X

Figq. 35 - Tensile Fracture of -Mo-E3 (0.023 mm grain size)Prestrained by Necing (c = 0.64) at +250,Recrystallized, and Broken at -100C ShowingPredomxinantly lntergranular Facets.

Light Fractograph 650X

36 - Tensile Fracture of Mo-E3 (0.023 m. gran size)

Having Neck byachned Corresponding to a NecingPrestrain oft = 064.. Recrystallzed and Brokenat -100C Shomn Predomnantly LntegsranuhrFacets.

53

specimens in the range of +25 to -196°C are summarized in Table 11 Forspecimens that were not prestrained, the fractures are similar to tho f4"grain Mo-k.Z material except that considerably more intergranular facets

_ were found in the Mo-E3 specimens broken at - 85 and at -1960 C(lo and40% respectively,.

After subjecting the Mo-E3 to a uniform prestrain ateither -20 or +250 C and breaking at -1000 C or -1960C, the fracture consistsof only 5-10% intergranular facets. This represents a considerable decreasein intergranular facets as compared to the non-prestrain results. This wouldseem to correlate with the higher fracture stress at -1000 C as compared tothat obtained without prestraining. However, a lower fracture stress wasfound at -1960 C after prestraining.

I0After a necking prestrain at -2S C followed by breaking

at -1000C, the amount of intergranular facets (10-20%) is also lower than

that obtained without prestraining. However, simulated necking (as ac-complished by forming a neck either by prestraining or machining followedby recrystallization) results in a large increase in the amount of intergranularfacets (80-90%6) after breaking at -i00 ° C. This correlates with the lowerfracture stress at -1000 C due to simulated necking as compared to t-e resultsfor either no prestrain or a necking prestrain.

Similar to the Mo-E2 fine grain size, both the intergranularand cleavage facet size in the Mo-E3 broken tensile specimens are approx-imately equal to the grair, size as corrected for the total reduction in areaprior to fracture. This holds for both the non-prestrained and prestrainedspecimens.

3. Broken Mo-E3 Precracked Charpy Slow Bend Specimens

Examples of fractures of Mo-E3 precracked Charpy slowbend specimens broken at -I000 C are shown in Figs. 37 and 38, and theobserved fractographic characteristics are summarized in Table 12. Fortests carried out without prestrain, a greater amount of intergranular facetswas found in the bend than in the tensile fracture at -1000 C (50 vs 30%).After prestraining about 6% at +250 C either by tensile pulling or by rolling,the bend fracture at -1000 C consists of considerably less intergranularfacets than without prestraining (5 vs 50%76), which is similar to the tensileresults (Table 11).

4. Broken Mo-E4 Tensile Specimens

Examples of the fractures oi broken Mo-E4 tensile specimensare shown in Figs. 39 and 40 and the fract'graphic characteristics are sum-marized in Table 13. A sharp change occurt; (om a predominantly cleavagefracture (<1% intergranular facets) at 4-25 ° C to a predominantly intergranularfracture (80% intergranular facets) at O° C. A further increase in the amnountof intergranuiar f;cets to >99% occurs at Td (-350C),and the intergranularfracture remains the same down to -1960 C. It was found that fracture at

54

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55

E

LihIrcorp 0OFi.3 rcakd lwBndCap rcueo oI

(0 Z mgansz)a IOCSoigaCevg

Light Fractograph IQOOX

Fig. 378 Precracked Slow Bend Charpy Fracture of Mo-E3

(0. 023 mm grain size) Pres trained (6%1 by rolling/'at +25 0 C and Broken at - 1000 C Showing CleavageFacets Containing Many Cleavage Steps.

56

000% -

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(Z 0 C) nL

000

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4-,44

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C 000

1.4C> C

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Light Fractograph 50OX

Fig. 490 Tensile F17racture of Mo-E4 (0. 020 mm grain size)

at -35 0 C Showing Two Cleavage Facets and ManyInt,-rgranular Facets.

58

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Wl toT-0$ d t t

04 > W-

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+25oC initiates by a cleavage mode and by an int-rgranular mode at 0°C.

No definite evidence was obtained with respect to the location of fractureinitiation at -35 to -196 0 C; however, it i presumed that the fractureinitiation mode is intergranular since only a few cleavage facets were foundpresent. Prestraining at +250 C and breaking at -100 0 C and at -1960 C wasfound to increase the amount of cleavage facets (50 and 25% respectively),which correlates with the increases in fracture stress obtained by prestrain-ing. Similar to the fine grain Mo-EZ and Mo-E3 materials, both the cleavageand intergranular facet sizes are approximately equal to the grain size ascorrected for the reduction in area prior to fracture.

5. Other Observations

Examinations were carried out for the occurrence ofmicrocracks and twins in the vicinity of the fractures of the Mr,-EZ, Mo-E3,and Mo-E4 materials. No evidence of isolated microcracks was found, al-though branching of secondary cracks from the main fractures was observed.Likewise, no definite evidence of twinning could be found.

E. Theoretical Considerations

1. Relation of Yield Stress to Fracture Stress

As illustrated schematically in Fig. 41, the brittlenesstransition temperature (Tb) corresponds to the intersection of curves I e-presenting the variation with temperature of the observed fracture str,.ss(0 F) and a yield stress parameter (0" ). For each of the molybdenum stripmaterials studied, it was found that &he values of proportional limit (T).lower yield stress (O"iv) or upper yield stress (,) corresponding Foa given test temperature are within about 15% of eac' other. Consideringthat the probable accuracy of measurement L- about * 10% for these threestress parameters, it does not seem to matter whether (7" represents a' 1,0"v or 0 . . In Figs. 42 to 46, the locations of Tb for Vo-EZ (3 grain-stles), ?vO.-E3, and Mo-E4 are shown by the irtersectior.s of a band thatrepresents the accuracy of 07F and a Y band :,hat repre:sents the combint dvariation of 0"pl, 0"uy s , and 0 lys .

2. Relation of Necking Stress at Fracture Stress

Also illustrated schematically in Fig. 41 is the intersectionof the observed fracture stress (9J.) and the necking stress (On), where thelatter is the true stress corresponding to maximum load. This intersectioris shown to occur at the minimum in the 0"F vs. temperature plot. The!temperature at which the minimum occurs has been previoubly defined asthe tensile ductility transition temperature (Td). It was hypothesized byLement (Q) that a n intersects "F at Td because below Td the elongation atfracture was found to be uniform whereas above Td necking occurs priorto fracture. This situaion is schematically indicated in Fig. 41 by theintersection of the fracture strain (cF) and the maximum unifc.,-m strain(CU ) curves at Td.

60

E ui

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0 83

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(,3s s

Bands representing the probably accuracy of fsF, atn, CF,and c u for the various molybdenum strip materials are shown it- -s. 42 to46 as a function of test temperature. For the fine grain Mo-E2, No-E3 andMo-E4 materials, Tb and Td were found to approximately coincide. This isindicated by the intersection of the ., fOn, and OF. bands at Td Figs. 42,45, and 46. On the other hand, Tb alls below Td for the intermediate andcoarse grain Mo-E2 materials. This is indicated by the fact that the inter- V*

I section of the fTy and 0 7F bands occurs below that of the 0 7n and (JF bandsFigs. 43 and 44. For all the materials studied, the cu and EF bands intersect o

at Td Figs. 42 to 46.

According to Ault (UJ, who investigated the tensile propertiesof a fine grain and relatively impure molybdenum strip material, U7uys in-tersects fF at the minimum. in the GF vs. temperature plot (which is definedhere as Td). Based on the present study, this should occur if Td and Tb are oequal as was found for the fine grain molybdenum strip materials. However.the more general condition for Td is the intersection of IT and 0 n as idicated4by the results for the intermediate and coarse grain strip materials Figs 42and 43. For these grain sizes, Td occurs above Tb and 07n intersects (JFat Td.

3. Locking Parameters

3.1 Yield Locking Parameter

According to Cottrell ( F) 07 at Tb and 0 7F isVVinversely proportional to the yield locking parameter (k T he variationof k with test temperature for Mo-EZ as determined by the Petch grain size 'imehod was shown in Fig. 5. An alternative method of determining k v is bythe Owen (12) extrapolation method. This first involves extrapolating the 0oflow stress curve (beyg nd the Liiders strain) back to the elastic line to determirthe f-ictional stress (Uj). Based on the power law, 9i at the intersection ofthe plastic and elastic curves is given by

n -(20)j

(I K (0

EiE

From the Petch relation,

! k = 1

d

Using Eq. (20) and (21), calculations were made ofkv and 9i at test temperatures of +250 C, Td, and Tb for all of the molydenumsf rip materials and the results are given in Table 14. The Tb values of k vand Gi for the intermediate and coarse grain Mo-EZ given in this table are0based on rough extrapolations of the K and n curves down to -150 and -196 C

64

.~~ 0 0 0000 00 00

C: :' . -s -.- %0

C: - PO

~ 00 00 0

CON

1400 00 0

0 0- - ---

X ~ > 0 n % LA Ln I1 L a' N a,

NN

(z4

I0

4n o 0 0

aLn In en r-O 0 0 ND -

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-4* S. ' 0 00 00 0-d0

&j Vo o-- -

4)~r cc 0 z 0

-x -4

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0~ t0 i n 0 Ln 0 0 .n 0 ->Ln1

N 00 rN. j t-LAn N -rCY N 0 N to-I + I - + I- + S + Q

0

k ":2( E E

0* C. 0 0

65

respectively. Corresponding values are given in T'be p 4 for ky and 0"i as__ determined by the Petch grain size method for the Mo-E2 materials(Figs. 4

and 5), which also required extrapolation down to -1960 C. For the Mo-E2materials, relatively good agreement (within 30%) was found between the OTivalues as determined by the Owen extrapolation and the Petch grain size

Mmethods. On the other hand, th.re are much larger discrepancies betweenthe ky values as obtained by these two methods. Furthermore, the extra-polation ky values exhibit anomaious variations with test temperature.

Since the Petch grain size ky values appear to bemore reasonable, it was decided to use these values in subsequent calculations

Lof the effective surface energy for crack initiation. However, this raised thedifficulty that only the Owen extrapolation ky values were determined for theMo-E3 and Mo-E4 materials. As an approximation, it was decided to use theratio of the grain size ky to the extrapolation k for the fine grain Mo-EZ inorder to convert the extrapolation k. values fo~the fine grain Mo-E3 andMo-E4 materials to grain size ky values. For the fine grain Mo-E3, thisratio is about 2; and values of grain size ky for Mo-E3 and Mo-E4 as con-verted on this basis are given in Table 14.

3. 2 Flow Locking Parameter

The flow locking parameter (kf) was determined as afunction of plastic strain (rp) and test temperature for Mo-EZ. This involveddetermination of the variation with grain size of the uniform flow stress (0"fs)as determined by the power law:

a-fs =K (E) n (22)

In Figs. 47 and 48, the values of Ufs corresponding to p v4lues of 0. 2 to 1. 0are plotted as a function of the grain size parameter (1 -1/2) for test tem-peratures of -50, -15, and +250 C. The slopes of these 0"fs vs I T-/2 plotsgive kf as defined by the following relation:

fr -crffs 0l.= -71 (23)

Where g o is a constant for a given value of rp and temperature. As is apparentfrom Figs 47 and 48, the value of kf for a given strain and temperature is notsignificantly affected by plotting Ufs against the final rather than the initialgrain size.

Values of kf based on Fig. 47 are given in Table 15.For each p, kf is approximately equal to k at +250 C and with decrease intest temperature goes through a minimum at about -15°C. The ratio of kfto k was found to decrease from about 1.0 to about 0.4 in the range of +25to -15°C, and from -15 to -500 C there is little change. These results differftrom the work of Armstrong (13), who reported that kf/k y equals about 0.3for molybdenum at room temperature.

66

1501

14o F

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120- T- 50*C

'Is C = .-100- EP0

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0

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120-

110- EpO.4 - C100- Tz -15*C

9 0 - c = .80 T=+250C

0*J 1 2 3 4 5 6 7GRAIN SIZE PARAMETER (1/2 ,mrn-/2

(0 initial grain size) (KOfinal groin size)Fig. 47 - Plots of Uniform Flow Stress ( Of.) vs. Grain Size Parameter

for Recrystallized M,,vo-L2 Strip at Plastic Strains (E)of 0.2and 0.4.

t it

02

920

80 ~ T+2 '5'- cC

70

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top

Table 15

Flow Locking Parameter (kf) for Mo-E2 Strip

Flow Y ield

Plastic Test Locking Lo cking1 31rain T enr-p Parameter Parameter Ratio

('EP) _U__(kf) (k ) k f/ko Cdynes/cm3/27 dynes/cm 3 /2

0.2 +25 6 . OxI 0 4.5xl10 1. 3

-15 3.5x10 8.0x0 0.4

-50 4. 0xI07 13xl10 7 0. 3

0.4 + 2 5 4. 5xl0 4.5x10 7 1.0

D1 3. 0x10 8. OX10 7 0.4

-50 6 . 5x10 13xl10 7 0.5

0.7 +Z5 5. 0xI07 4. 5x10 7 I. 1

-15 3. OxIO 78. OXI 0 0.4

-50 5. 5x! 07 13x10'7 0.4

1.0 +25 4.OxI07 4. 5x10 0.9i

-15 2. 5x10 8. 0x1'7 0.3-50 6.6xl10 7 13x10 7 0.5

69

Values of kf were not determined for the Mo-E3and Mo-E4 materials because these were recrystallized to a fine grainsize only. However, kf for these materials can be approximated by usingthe kf/ky ratio determined for Mo-E2 and the ky values for Mo-E3 andMo-E4 given inTable 14 (converted from extrapolation to grain size kvalues). Approximate values of kf for Mo-E3 and Mo-E4 as determinedon this basis are given in Table 16. These values also show a minimumat -150 C.

4. Calculation of Effective Surface Energy for Crack Initiation

The Cottrell (5) fracture relation for crack initiation atthe brittleness-transition temperature (T b) is as follows:

k I /zT.y' = yF (24)~8G

7where = effective surface energy for crack initiation

k yield locking parameter based on normal stress and fullY grain diameter

EG = shear modulus and is equal to where v is

Poisson's ratio (0.3) 2(1+ v)

I= full grain diameterI

The effective surface energy for crack initiation (-'y) in Mo-EZ, Mo-E3 andMo-E4 at the brittleness transition temperature (Tb) was calculated usinga) values of ciF at Tb given in Figs. I, 2, 3, 11 and 17; b) values of k at

Tb based on tle Petch grain size method (Table 14); and c) values of JatTb as determined from the variation of the elastic modulus (E) with tem-perature for molybdenum (Fig. 49), i.e. G = 0.38 E. Calculations werealso made of -y at temperatures above Tb based on a modification of Eq.(24) which involves substituting the flow locking parameter (kf) for ky inorder to take into account the relatively large plastic strains that occurprior to fracture. Values of kf were obtained from Tables 15 and 16, andthe results of ti l calculations are given in Table 17.

As shown in Table 17, the values of -iy at Tb (based on ky)are in the range of 0. 7 x 104 to 3. 5 x 104 ergs/cm2 . With increase intemperature, an initial decrease in yi (based on kf) occurs which is a mathe-matical consequence of kf being lower than k . Since a lower value ofwould be expected if the initiation mode is intergranular as compared to cleav-age, this casts doubt on the validity of Eq. (24) based on ky. Above Td, Y! forMo-E2 and Mo-E3 ramains essentially constant up to at least +25 0 C and themode of crack initiation is cleavage over this range. On the other hand, there iabout a 75% increase in yi for Mo-E4 between 0oC and +Z5 0 Cwhere the initiatiormode changes from integranular to cleavage. ,It therefore appears that the highoxygen content of Mo-E4 results in different i as well as fracture initiationcharacteristics than the relatively low oxygen content materials (Mo -E2 and Mo-E3)

70

T able 16

Approximzate Values of Flow Locking Parameter (kf) for Mo-E3 and Mo-E4 Strip

Plastic TestStrain Approx. Approx. Approx.

Temp. k/k- kMaterial p (T) f V

°C dynesicm3/2 dynesicm3/2

Mo-E3 0.2-1.0 +25 1.0 2. Zxl07 2. 2x10 7

-15 0.4 3.9x107 1.6x10 7

-50 0.4 5.3x10 7 2. 1x10 7

Mo-E4 0.2-1.0 +25 1.0 19x107 19x10 7

-15 0.4 21x107 8.4x10 7

7

-50 0.4 23xi0 9.0x!07

"* Assumed to be the same as for Mo-E2 strip given in Table 15.

** Approximate grain size ky values given in Table 14 and linear

VN

extrapolations.

71

TEMPERATURE *C

I +25 -50-100 -150 -175 -200

I ~,55-RE 0-

50-

245-

0.0025 0.0050 0.0075 on100 0.0125

INVERSE ABSOLUTE TEMPE RATURESOKI

Fi . 4 Variation of Elastic Modulus of Molybdenum(Mlo-El Rod) with Temnperature.

- 72

14 > cc CI C) m)I

14 Li x ) C)-0 C) U-1 *'j CX xv0 'n -j Ln C) X x

14N v T L

0S

-4Xx x X x X X Xx41 1' 47X . c

0 0 0 C) . Cr0 0

000 01.4

0 0 00q 0 0 0 0-4 -4 - 4 - -4x- -

C);

fn Sn tno% o C' O u - ' 0 0

-o 4-

0 rJ 0 ~ 0 0 000 0

00

N #3 ' N

4) > >

~. 2 v .

4Q

9u 0ISE ~ ~ u54 4 4~

00

* 4 U 4 0 00 5j0 0 0 0 0 0

X X x xC) 0 00 0 c0 . . .

14 0

I 54

-4-N ~ 4

Ct 2 - - 4 C; -: -4 -4 -

Itto

540 0

x x04 v* - N O tA ' r- 0 mi

Lt 9)

> .444-S9

0 '00

en0 0

-474

5. Effective Surface Energy for Crack Propagation

5.1 Based on Tensile Tests

Assuming that fracture of the molybdenum materialsis controlled by crack initiation rather than crack propagation, it followsthat using the value of the observed fracture stress in a Griffith-Orowantype of relation should give an upper limit to thl probable value of the ef-fective surface energy for crack propagation (yp). Accepting this restriction,calculations were made of y under plane strain conditions using the Irwin(14) relation for an interioricrack of radius c that is small with respect tothe section area:

2 24(l - v) cp = E(25)

p E

For the crack radius (c), it was decided to use one-half the measured cleav-age facet size for test temperatures above Td and one-half the measuredintergranular facet size for test temperatures of Td and below.

As shown in Table 18, the Y I values are in the rangeof 1.0 x l0 to 12.3 x 104 ergs/cm2. Starting at -q96oC for Mo-EZ aridMo-E3 and at -100°C for Mo-E4, first decreases with increase in tem-perature up to Td, then increases rom Td to Tm, and finally decreasesabove Tm. Thil variation is similar to that of 0 F4 with temperature. Theratio of yO to 7 i at the same temperature varies from I to 43. This in-dicates th? possibility that y' may be larger than -1 even though fractureis controlled by crack initiation.

According to Barrett (5) crack initiation involves thegrowth of a critical size crack until it encounters a major barrier (typicallya grain boundary). In order for the crack to cross the boundary and continueto propagate, an increase in effective surface energy is involved. Thus, itseems reasonable to expect that y' is generally greater than 11 . For frac-ture to be controlled by crack initiation rather than crack propagation, thecondition to be satisfied is (*F)p (4F)i. Based on the results given inTable 17, it appears possible for the ratio of ((TF)p to (KF)i to be as low as1/43 withIZ-y.

5. 2 Based on Precracked Charpy Slow Bend Tests

As was shown in Table 10, the fracture toughnessvalues of Mo-E3 as determined by precracke Charpy slow bend tests fallin the range of 0.4 x 107 to 2.1 x 101 ergs/cmZ. These values are ap-proximately 103 times larger than either t calculated effective surficeenergy for crack initiation (fl) or for cra -'-opagation (-') based on thetensile test results for Mo-E3 as givenir les 17 and ld're.3pectivly.This difference may be due to a greater ari. it of plastic deformation at

75

-4 1 u v N

$4 h4 0

V .. 4 4) $4 m I m 0 m o 0 0 0U ( 0$4 $4 >> > $4 $4 > $4 t4>

41 4 30 4 04 C43 to . .. v o~ (U (U ( gj U (U (U 4 43 ( (U (

u u

- ~ ~ ~ ~ 0 CI - - 4- a,

NU

a.~4 m %0 an %0 v C '. D 0 - %0 - c~ -0

Tx IC.;4 L C'. C;

0 r O0 .O c 0% 00 0 co 0 C7 a, 0 Ln

$4U O O- 0 C) 0 000

to 0 0 0 00 c"00~ 0,a4 L

N- N N3 00 NN N -N- N N N N

E- W x x * x * 9 * x x X .

000l00 C%0 000%0 000

4.

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$0 0 0 0 00 0 00

76- 4 - - 4 4 - 4 ,

5-LI) Ul Ln "I,Ure

Do b4)000 t

94 (U (U (1~cU

oo w Not 0t

u u

a- - 0- - a- 0% -l 0%C

v v x xx x x x x x xx xw co fl No Ln.' ef0 0 0 N N N

au 0 00 00 0 0 000 0oo I. M -0

0

- U 4)(. 0 0 0 0 0 0 0 0 0

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u

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to C:E

o 0)

577

hl1e UP of the fatigue precrack in the rharpy specimen as compared to thetip of the crack that initiates in a tensile specimen. In other words, thefatigue action at +25 0 C may prodice a relatively "blunt" crack tip cor-responding to much lower stress concentration as compared to that forthe tip of a tensile test crack formed at -I 00 0 C.

6. Variation of Fracture Stress with Temperature

6. 1 Decrease in Fracture Stress up to Td

Starting from a relatively low temperature, -196°C,the fracture strees (0 "F) of the various recrystallized molybdenum materialsstudied in this investigation was found to decrease with increase in testtemperature and reach a minimum value at the tensile ductility transitiontemperature (Td). Since M is slightly higher than the proportional limitover most of this temperature range, it seems likely that a) F correspondsto crack nucleation rather than to crack propagation, and b) crack nucleationrequires the prior occurrence of at least ;t small amount of plastic deforma-tion. A crack that initiates at a stress level higher than that required forpropagation would be expected to immediately propagate completely throughthe specimen section. On this basis, the observed decrease in CFF up to Tdis considered to be essentially a consequence of the decrease in yieldstress (T ) which occurs with increase in test temperature.

6. 2 Increase in Fracture Stress T toTm

In the range from Td to Tm, 07 increases from aminimum to a maximum even though 0ly continues to gecrease. These changesare accompanied by an increaje in ductility from a relatively low level at Tdto a relatively high level at Tm. It was observed that below Td the elongationtakes place uniformly over the entire gage length, whereas above Td neckingoccurs prior to fracture. These fracture and necking observations indicatethat Td represents the intersection of the fracture stress corresponding touniform elongation (i.e.,the 0F curve below Td) with the necking stress (On)which is the tensile strength on a true stress basis.

As an aid in understanding the increase in 0F in therange from Td to Tm, UF can be considered as a flow stress, i. e.,theparticular flow stress that corresponds to the fracture strain (EF) at a giventest temperature. On this basis, it was shown that the increase in C"F aboveTd can be attributed to the following effects: a) strain hardening due to in-creased substructure formation, b) plastic constraint due to the necking thatoccurs above Td, and c) increase in strain rate due to the localized nature ofnecking. This approach was first used by Bechtold () and more recently byAult (11)1, although the latter neglected the strain hardening effect.

For a more complete understanding of the increase inUF from Td to Tm, an explanation is needed for the increase in fracturestress per se which permits the flow stress corresponding to iF to increasein the observed manner. Although the plastic constraint and increased local

78

strain rate effects due to necking both increase the flow stress correspondingto a given amount of plastic strain, it seems doubtful whether these effectsalso raise the fracture stress per se. It is generally found that an increasein plastic constraint results in a decrease in fracture stress, which is at-tributed to an increase in the flow stress relative to the fracture stress suchthat fracture occurs at a smaller plastic strain value than without plasticconstraint. Likewise, an increase in strain rate raises the applied stressrequired for a given amount of plastic strain, and appears to act similar toplastic constraint in that the fracture stress is lowered.

Since no micro-cracks were observed above Td, itappears likely that crack initiation rather than crack propagation is the con-trolling step in the fracture of the molybdenum materials studied. in orderto explaii- the increase in 0"F in the range of Td to Tm on the basis of crackinitiation, one might hypothesize that an increase occurs in the effectivesurface energy for crack initiation (-yi). However, calculations of ,y madeon the basis of a modified Cottrell relation using the flow locking parameter(kf) instead of the yield locking parameter (ky) indicate that, with the pos-,sible exception of the Mo-E4 material, there is no significant change in -tiin this range. Instead, the increase in O"F appears to be associated in mostcases with a decrease in both kf and the effective grain size (1) correctedfor the reduction in area that occurs prior to fracture. The decrease in kfwith increase in temperature can be attributed to decreased association ofinterstitials with dislocations.

6. 3 Decrease in Fracture Stress above Tms

It was found that 0F reaches a maximum at Tm and

then decreases above this temperature. Since no evidence of fibrous frac-ture was found at the highest test temperature employed (+25 0 C or 4500C),it does not seem likely that the decrease in 0 F can be associated with achange in fracture mode from cleavage to fibrous. However, a change doestake place from comparatively undistorted to highly distorted cleavage facets.This is accompanied by an increase in kf, which based on the Cottrell rela-tion for crack initiation should tend to lower OF. Further work is necessaryto account for the increase in kf above Tm .

79

IV. CONCLUSIONS

1. As determined by tensile tests, the ductility transition temper-ature (Td) and the brittleness transition temperature (Tb) approximatelycoincide in fine grain, recrystallized molybdenum. With increase in grainsize, Tb is lowered whereas Td is raised.

2. The occurrence of a minimum in the observed fracture stress(07F) at Td is associated with the intersection of the necking stress (9"n) andthe fracture stress corresponding to uniform fracture strain, i.e. neckingoccurs above Td but not below T d . If Td and Tb happen to coincide, theyield stress (0Oy) also intersects at the minimum in O(F since Tb is definedas the intersection of 0 'F and 07y.

3. Taking into account strain hardening due to substructural changesin addition to necking effects such as plastic constraint and increased strainrate, the predicted variation of 0 "F with test temperature above T d was foundto agree (within 15%) with the observed values in most cases.

4. For the molybdenum materials with relatively low oxygen con-tents, the fracture initiation mode is intergranular at or below Td and cleavag(above Td. For a relatively high oxygen content (145 ppm), the fractureinitiation mode is intergranular up to a temperature that is intermediatebetween Td and that corresponding to the maximum in 07- (Tm).

5. By prestraining at a temperature above Td and breaking belowTd, it is possible to increase 0 "F by as much as 20%6 as compared to withoutprestraining. The increase in 0"F due to prestraining correlates with an in-crease in cleavage facets in most cases.

6. For test temperature below T d , fracture occurs after a rel-atively small amount of plastic strain and is apparently controlled by crackinitiation. For test temperatures above Td, crack initiation also appears tobe the controlling step even though the amount of plastic strain prior to fr .c-ture increases markedly.

7. The ratio of the flow locking parameter (kf) to the yield lockingparameter (ky) is approximately unity at room temperature and decreasesto at least 0.3 with lowering of temperature. A minimum in kf was found tooccur between Td and Tm.

8. Based on the Cottrell relation for crack initiation, the increasein 0 F from Td to Tm is attributed to decreases in both kf and the effectivegrain size. The maximum in 0"F at Tm is associated with the increase in kfafter passing through a minimum below Tm.

9. The calculated upper limit of the probable value of the effectivesurface energy for crack propagation (-y) was found to be up to about 40times greater than the correspondingyi' value,

80

References

I. Lement, B.S., Thomas, D.A., Weissmann, S., Owen, W. S. andHirsch, P. B., "Substructure and Mechanical Properties of RefractoryMetals," WADD-TR-61-181, (August, 1961).

2. Lement, B.S., Thomas, D.A., Weissmann, S., Owen, W.S. andHirsch, P. B. , "Substructure and Mechanical Properties of RefractoryMetals," WADD-TR-61-181, Part II (October 1, 1962).

3. Lement, B.S., Thomas, D.A., Weissmann, S., Owen, W.S.. andHirsch, P. B. , "Substructure and Mechanical Properties of RefractoryMetals," WADD-TR-61-181, Part III (April, 1963).

4. Wronski, A. S., and Johnson, A.A., "The Deformation and FractureProperties of Polycrystalline Molybdenum," Phil. Mag. 7 (1962) 213.

5. Cottrell, A.H., "Theory of Brittle Fracture in Steel and SimilarMetals," Trans. AIME, 212 (1958) 192.

6. Bridgeman, P. W., "The Stress Distribut;on at the Neck of a TensionSpecimen," Trans. ASM, 32 (1944) 553.

7. Aronofsky, A., "Evaluation of Stress Distribution in the SymmetricalNeck of Flat Tensile Bars," J. Appl. Mech., 18 (1951) 75.

8. Bechtold, J.H. , "Effects of Temperature on the Flow and FractureCharacteristics of Molybdenum," Trans. AIME 197 (1953) 1469.

9. Hartbower, C.E. and Orner, G.M., "Metallurgical Variables AffectingFracture Toughness in High-Strength Sheet Alloys," ASD-TR-62-868(February 1963).

10. Irwin, G.R., Kies, J.A., and Smith, H.L., "Fracture StrengthRelative to Onset and Arrest of Crack Propagation," Proc. ASTM,58, (1958).

11. Ault, R.T. , "Fracture of Molybdenum," RTD-TDR-63-4088, December,1963.

1Z. Owen, W., et al. "Yield Phenomena in Refractory Metals." Ref. no. 3,page 168.

13. Armstrong, R., Codd, I. Douthwaite, R.M., and Petch, N.J., "ThePlastic Deformation of Polycrystalline Aggregates." Phil. Mag. 7(1962) 45.

14. Irwin, G.R. . "Theoretical Aspects of Fracture Failure Analysis,"ASM Metals Congress, New York (1962).

15. Averbach, B. L. et al., "Fracture", Swampscott 1959 Conference,The Technology Press (1959).

81

Appendix I

__ Definitions of Transition Temperatures Used in Text

Tb..... Brittleness - transition temperature corresponds to intersectionof the fracture stress (U"F) and yield stress (0ig) curves.

Td..... Ductility - transition temperature corresponds to minimum inthe fracture stress (F) curve.

T .... Corresponds to maximum in fracture stress (OF) curve, whichoccurs at a temperature above Td.

82