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METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 34A, APRIL
2003967
Effects of Test Temperature and Grain Size on the CharpyImpact
Toughness and Dynamic Toughness (KID) ofPolycrystalline Niobium
D. PADHI and J.J. LEWANDOWSKI
The effects of changes in test temperature (2196 C to 25 C) and
grain size (40 to 165 mm) onthe dynamic cleavage fracture toughness
(KID) and Charpy impact toughness of polycrystallineniobium (Nb)
have been investigated. The ductile-to-brittle transition was found
to be affected byboth changes in grain size and the severity of
stress concentration (i.e., notch vs fatigue-precrack).In addition
to conducting impact tests on notched and fatigue-precracked Charpy
specimens, ex-tensive fracture surface analyses have been performed
in order to determine the location of ap-parent cleavage nucleation
sites and to rationalize the effects of changes in microstructure
and ex-perimental variables on fracture toughness. Existing finite
element analyses and the stress fielddistributions ahead of stress
concentrators are used to compare the experimental observations
withthe predictions of various fracture models. The dynamic
cleavage fracture toughness, KID, wasshown to be 37 6 4 MPa and
relatively independent of grain size (i.e., 40 to 105 mm) andtest
temperature over the range 2196 C to 25 C.
1m
D. PADHI, Process Engineer-III, is with Applied Materials Inc.,
SantaClara, CA 95054. J.J. LEWANDOWSKI, Leonard Case Jr. Professor
ofEngineering, is with the Department of Materials Science and
Engi-neering, Case Western Reserve University, Cleveland, OH 44106.
Con-tact e-mail: [email protected] and [email protected]
Manuscript submitted June 19, 2002.
I. INTRODUCTION
THE continuing desire for increasing the efficiency ofturbine
engines via operating at elevated temperatures hasled to
exploration into various materials systems. Niobium(Nb) is a
refractory metal with the distinction of pos-sessing excellent
ductility at low temperature, high-temperature strength, and liquid
metal corrosion resis-tance. These properties have encouraged
researchers toinvestigate a variety of Nb-base systems for
potentialaerospace applications. Recently, a number of
researchgroups[16] have investigated the fracture and fatigue
be-havior of Nb-Si systems, which combine a refractory
metalintermetallic, Nb5Si3, with the terminal refractory metalphase
(i.e., Nb with Si in solid solution).
Recent research studies[16] have demonstrated that Nbcan be used
as a tough reinforcement in ductile-phase-toughened Nb5Si3
composites. The success of such a sys-tem is significantly affected
by the mechanical behaviorof the toughening phase (Nb) as well as
the interfacialstrength between the brittle constituent (Nb5Si3)
and thetoughening phase. Considerable efforts have been directedin
the past toward understanding the effects of changes ingrain size,
test temperature, and strain rate on the tensileflow behavior,
cleavage fracture stress, and static planestrain fracture toughness
of Nb.[712] However, the ductile-to-brittle transition and fracture
toughness of Nb underdynamic testing conditions, key considerations
for struc-tural applications, have not been investigated to the
sameextent. The present investigation examines the effects
ofchanges in test temperature and grain size on the Charpyimpact
and dynamic impact toughness (KID) of polycrys-
talline Nb. The studies reported have been conducted onmaterials
identical to those reported previously,[7,8] en-abling direct
comparison.
II. EXPERIMENTAL PROCEDURES
A. Materials Tested, Heat Treatments, and SpecimenDetails
Commercial purity Nb (i.e., Nbcp) was obtained fromCabot
Corporation (Bethlehem, PA) in the form of hot-rolled square plates
having a nominal thickness of 10.5mm. The composition, determined
via wet chemical analy-sis, was identical to that tested
previously[7,8] (i.e., oxy-gen 165 ppm, nitrogen 63 ppm, silicon
0.03 at. pct, bal.Nb). Unnotched bend bar specimens (dimensions: 55
310.5 3 10.5 mm3) were machined from the plates so thatthe long
axis of the bend bar was along the rolling direc-tion. Each bend
bar was wrapped in tantalum foil and heattreated in a vacuum of
1025 torr to minimize oxidation.The temperature and time of
annealing were varied inorder to obtain a range of grain sizes,
measured via thelinear intercept method, and are reported in Table
I. Thespecimens were furnace cooled to 500 C under high vac-uum
followed by cooling in N2 atmosphere to room tem-perature. The
heat-treated specimens were cut in three mu-tually perpendicular
directions, ground, polished, andetched using a solution of 62.5
vol pct distilled water,31.25 vol pct nitric acid, and 6.25 vol pct
hydrofluoricacid for approximately 200 seconds. Representative
mi-crographs of the specimens are shown in Figure 1. Mea-surements
of grain size on the three mutually perpendic-ular directions
revealed homogeneity in grain structureindicating complete
recrystallization.
Subsized tension specimens (i.e., gage diameter 53 mm, and gage
length 5 12 mm) were machined alongthe original rolling direction
following ASTM E8M-94.[13]Standard Charpy specimens were machined
from the heat-treated bars in the L-S[13] orientation such that the
notch
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968VOLUME 34A, APRIL 2003 METALLURGICAL AND MATERIALS
TRANSACTIONS A
Table I. Summary of the Heat Treatments and GrainSizes of
Nbcp
Heat TreatmentTemperature Time Grain Size
Material (C) (Min) (mm)Nbcp 1200 45 57 6 7
1200 60 39 6 31300 90 104 6 161300 120 165 6 28
Fig. 1Microstructures of recrystallized Nbcp specimens.
was along the long transverse direction, in accordance withASTM
E23.[13] The dynamic fracture toughness test spec-imens (i.e.,
fatigue-precracked Charpy specimens) wereobtained by introducing a
starter notch of approximately3-mm depth using a
diamond-impregnated wire saw. Thiswas followed by fatigue
precracking at 2125 C in a three-point bend (3PB) configuration, in
accordance with ASTME399.[13] The fatigue precracking was conducted
on a20 Kip MTS (Minneapolis, MN) servohydraulic machineusing an MTS
442 controller and a DEC (Maynard, MA)PDP-11 computer at a
frequency of 20 Hz and a stressratio (R) of 0.1. Based on previous
results for this mater-ial,[8] fatigue precracking was conducted to
achieve a totalcrack length between 0.45 and 0.55 W at 2125 C.
This
ensured a small plastic zone size ahead of the fatigue cracktip
due to the significantly higher yield stress at 2125 C(e.g., 426
MPa) compared to 25 C (e.g., 160 MPa).[8,16]
B. Mechanical TestingIndividual tension tests were conducted at
a strain rate
of 6(1024) s21 at temperatures ranging from 2196 C to25 C on the
Nbcp specimens using an Instron 1142 screw-driven machine and an
MTS servohydraulic machine fit-ted with an ATS
low-/high-temperature cabinet. The lowtemperatures were obtained by
injecting liquid N2 vaporinto the cabinet at intervals controlled
by a thermocouple.Temperature variation during the tests was ,1 C.
Theload-load point displacement traces were used to calcu-late the
0.2 pct offset yield strength (sy).
The notched Charpy and fatigue precracked impactspecimens were
tested in a Wiedemann Baldwin (Summit,NJ) instrumented impact
tester. Load, deflection, absorbedenergy, and velocity of the tup
were acquired as a func-tion of time via the DYNATUP*
instrumentation pack-
*DYNATUP is a trademark of INSTRON Company, Canton, MA.
age. The impact tests were conducted in the temperaturerange of
2196 C to 25 C by using a mixture of 2-methyl
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METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 34A, APRIL
2003969
(a) (b)Fig. 2Schematic of the fracture surface analyses for (a)
fatigue-precracked impact test specimen and (b) Charpy impact test
specimen.
Fig. 3Effect of changes in grain size on 0.2 pct offset yield
stress ofNbcp.
butane and liquid nitrogen in varying proportions. A
non-instrumented Charpy impact tester with a tup of higher
ca-pacity (325.4 J) was used for tests at temperatures wherethe
absorbed impact energy was greater than 81.4 J. Thepeak load,
initial crack length measured from fracturedspecimens, and specimen
geometry were used to computethe dynamic fracture toughness (KID)
according to ac-cepted procedures[14] and K calibrations.[13]
C. Fracture Surface AnalysesThe fracture surfaces of the notched
Charpy specimens
and the fatigue-precracked Charpy test specimens wereanalyzed
using a Hitachi (San Jose, CA) 4500 S high-resolution field
emission gun scanning electron micro-scope. For each sample, a
montage consisting of severalmicrographs was taken in the central 7
mm (thickness di-rection) of the specimen in order to exclude the
area underplane stress condition, as shown in Figure 2. Each
mon-tage was examined to identify the potential nucleation sitesof
cleavage fracture. This was achieved by tracing thecleavage river
lines back to a region from where all theriver lines appeared to
emanate, as conducted previ-ously.[7,8,15] In some cases, multiple
sites of apparent frac-ture nucleation were identified. The
distances of these po-tential cleavage fracture nucleation sites
from the notchtip/precrack front were measured. The relative
amounts ofbrittle (i.e., cleavage) and ductile (i.e., dimpled)
fracturewere also quantified for the entire specimen cross
sections.
III. EXPERIMENTAL RESULTS
A. Mechanical TestsThe 0.2 pct offset yield strength of Nbcp for
different
grain size/test temperature combinations are plotted as
afunction of average grain radius21/2 (d21/2) in Figure 3.No yield
points were observed in any of the tension tests.At a given test
temperature and strain rate, the yieldstrength of Nbcp is found to
be essentially independent ofgrain size in the range of current
investigation (i.e., 40 to165 mm) and a strong function of test
temperature. From
the current investigation, the calculated values for
theHallPetch slope (ky) for Nbcp were found to be verylow, i.e.,
5.6(104) N/m3/2, 2.65(104) N/m3/2, and 4.35(104)N/m3/2 at 2196 C,
275 C, and 25 C, respectively.Adams et al.[9] reported a ky value
of 2.76(104) N/m3/2 at20 C under a strain rate of 2(1024) s21.
Johnson[10] in-vestigated the effects of grain size (37 to 138 mm)
and testtemperature (2196 C to 220 C) on the tensile proper-ties of
commercially pure sintered niobium at a strain rateof 1024 s21. No
effect of variation in grain size on yieldstrength was observed.
Churchman[11] conducted tensiontests on high-purity Nb over the
temperature range of2180 C to 280 C. His results showed that the
yieldstrength was unaffected by the change in grain size
fromapproximately 13 to 395 mm. The lack of yield points inthe
present and previous tests[9,10,11] suggests that the lackof
impurity-induced pinning of dislocations is one poten-tial reason
for the low value of ky obtained presently andreported previously.
The yield strength increased with in-creasing strain rate,[16] in
agreement with results reportedelsewhere.[12,18]
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970VOLUME 34A, APRIL 2003 METALLURGICAL AND MATERIALS
TRANSACTIONS A
Fig. 4Ductile-to-brittle transition behavior of Nbcp (Charpy
impacttest). Arrows indicate specimens did not fail.
Fig. 5Absorbed impact energy normalized by initial uncracked
liga-ment area.
Fig. 6Effect of strain rate and test temperature on the yield
stress ofNbcp. *Using empirical constitutive equation.[18]
The impact energy (Cv) obtained from the dial readingon the
Charpy impact machine is plotted as a function oftest temperature
in Figure 4. Two specimens (for eachgrain size) were tested at each
test temperature for re-peatability. The lower shelf regime is
associated with alow value of absorbed impact energy (#6.5 J),
while theupper shelf energy values for the 40 and 105 mm Nbcp
arefound to be nearly equal (,258 J). At 225 C test tem-perature,
the impact energy decreases with an increase ingrain size. The
other test temperatures did not produce aslarge a change as that
obtained at 225 C.
The impact energy normalized by the area of initial un-cracked
ligament is plotted as a function of temperaturein Figure 5 for
both the notched and fatigue-precrackedspecimens. It appears from
this plot that the complete tran-sition to the upper shelf regime
has not occurred at 25 Cin the fatigue-precracked specimens.
Alternatively, theductile-to-brittle transition temperature of
fatigue-
precracked specimens is found to be higher than that ofthe
notched specimens regardless of grain size.
The dynamic fracture toughness (KID) was computedaccording to
accepted procedures.[13,14] The validity of lin-ear elastic
fracture mechanics (LEFM) conditions wasverified using standard
ASTM procedures[13,14] adoptedfor dynamic testing
conditions[17]:
[1]
where
calculated fracture toughness, anddynamic yield strength at a
strain rate j.
The strain rate achieved during the impact test ( j) can
beestimated as[18,19]
[2]
where
W 5 specimen width;S 5 span of loading points (2)2 dBdt R s
#jyd 5
KO 5
LEFM: 4p
aKQs
#jydb2 # B, a0, (W 2 a0)
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Table II. Dynamic Fracture Toughness and Corresponding Plastic
Zone Size Calculations for Fatigue-PrecrackedImpact Tests
Impact PlaneEnergy Strain Validity
Grain Thickness Width (J)2 KID Plastic CriteriaSize Temperature
aavg (B) (W) Pmax (Dial (MP a Zone Size (L)(mm) (C) (mm) (mm) (mm)
(kg)* Reading) **) (mm) (mm) L , B L , aavg L , (W 2 aavg)
40 2195 5.9 10.4 10.1 314.1 3.1 41.4 91 2.2 Y Y Y40 2150 5.5 9.3
10.1 299.3 3.1 39.1 119 2.9 Y Y Y40 2125 5.6 10.4 10.2 329.8 4.4
38.2 142 3.4 Y Y Y40 275 5.0 10.4 10.2 288.2 12.2 27.5 102 2.5 Y Y
Y40 275 5.7 10.3 10.1 297.9 5.3 36.7 182 4.4 Y Y Y40 250 6.0 10.3
10.1 309.5 8.1 43.1 291 7.0 Y N N40 250 5.1 10.3 10.1 337.1 16.4
33.7 178 4.3 Y Y Y40 225 5.6 10.4 10.1 315.4 13.9 37.6 260 6.2 Y N
N40 225 5.4 10.3 10.1 373.4 18.6 41.8 321 7.7 Y N N40 0 3.8 10.3
10.1 540.3 35.6 37.2 297 7.1 Y N N40 25 4.4 10.4 10.1 423.1 77.6
34.8 302 7.2 Y N N
105 2195 5.6 10.5 10.2 351.2 3.4 40.6 88 2.1 Y Y Y105 2125 5.4
10.4 10.2 354.3 4.4 38.1 113 2.7 Y Y Y105 275 5.3 10.3 10.1 316.9
9.8 34.0 156 3.7 Y Y Y105 275 4.8 10.3 10.1 351.4 4.6 32.6 144 3.4
Y Y Y105 250 5.3 10.4 10.2 322.7 13.7 33.9 180 4.3 Y Y Y105 225 4.6
10.4 10.2 358.4 14.6 30.9 149 3.6 Y Y Y105 225 5.0 10.3 10.1 368.2
22.4 35.9 237 5.7 Y N N105 0 4.7 10.3 10.0 378.6 37.8 34.7 258 6.2
Y N N105 25 4.4 10.4 10.2 396.2 41.0 31.8 253 6.1 Y N N
*Instrumented tup reading.**Using Pmax
Using dynamic yield strength at a strain rate of 500
s21.[18]Using Eq. [1].
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METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 34A, APRIL
2003971
Fig. 7Effect of test temperature and grain size on dynamic
precrackedfracture toughness (KID).
Validity Criteria Satisfied
Nemat-Nasser and Guos work[18] [Figure 6]. The KID andthe
corresponding plastic zone size data are presented inTable II. The
LEFM criteria are violated at the highesttemperatures tested (e.g.,
225 C to 25 C), and the KIDvalues provide a lower bound estimate
for dynamic frac-ture toughness of the material in this regime.
However, itis important to note that both crack length and
specimenthickness satisfied the LEFM criteria at the highest
tem-peratures, as shown in Table II. The LEFM criteria at
thehighest temperatures were only violated in some of thecases by L
. aavg and (W 2 aavg), as shown in Table II.In the lower shelf
regime, the KID is found to be relativelyunaffected by changes in
test temperature and grain sizeover the range tested, as shown in
Figure 7.
B. Fracture Surface AnalysesScanning electron microscopy (SEM)
fracture analy-
ses at low magnification revealed that all the
fatigue-precracked Charpy impact specimens exhibited a
pre-dominance of cleavage fracture up to test temperaturesof 25 C.
However, above approximately 250 C, thefine- and coarse-grained
specimens exhibited smallstretch zones (e.g., ,100 mm) along some
portions ofthe fracture surface adjacent to the fatigue
precrack.Representative SEM fracture surface montages for the40-mm
grain size Nbcp precracked specimens tested at2196 C and 25 C are
presented in Figures 8(a) and
(b), respectively. For the Charpy V-notch specimens, thefracture
surface was predominantly cleavage in thelower shelf regime, as
shown in Figure 9. Tables III(a)and (b) present the distances of
the apparent cleavagefracture nucleation sites from the stress
concentrator(i.e., notch and precrack, respectively), while
Figures10(a) and (b) plot these data. Quantification of theamount
of cleavage vs ductile fracture present on thenotched Charpy impact
fracture surfaces[16] indicated
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972VOLUME 34A, APRIL 2003 METALLURGICAL AND MATERIALS
TRANSACTIONS A
(a)
Fig. 8Fracture surface montage of an Nbcp 40-mm
fatigue-precracked Charpy specimen. (a) test temperature 5 2196 C
and (b) test temperature 525 C. Apparent cleavage fracture
nucleation sites are shown inside the boxes.
that the transition from predominantly cleavage fractureto
ductile fracture occurred between 250 C (i.e.,.80 pct cleavage) and
225 C (i.e., 100 pct ductiledid not fail) for the 40-mm grain size
Nbcp. In contrast,the 105-mm grain size Nbcp Charpy specimens
revealedthis transition to occur between 225 C (i.e., 75
pctcleavage) and 0 C (i.e., 100 pct ductiledid notfail).[16] The
specimens tested on the upper shelf did notfracture into two
pieces; the extensive plasticity in thesecases permitted the intact
specimen to exit the impactmachine (Figure 4).
IV. DISCUSSION
The present work has investigated the effects of changesin
microstructure, specimen geometry, and stress state onthe
ductile-to-brittle transition, as well as the energy
ab-sorbed/toughness under such testing conditions. The ini-tial
discussion will focus on observations related to
theductile-to-brittle transition, followed by a discussion ofthe
magnitude of fracture toughness possible in the lowershelf regime
for such materials, despite the appearance ofcleavage fracture.
(b)
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METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 34A, APRIL
2003973
Fig. 9Fracture surface montage of a Nbcp 40-mm notched Charpy
specimen tested at 275 C. Apparent cleavage fracture nucleation
site is showninside the box.
A. Ductile-to-Brittle TransitionEarly concepts of the
ductile-to-brittle transition behav-
ior of a material consider the competition between flow
andfracture.[2027] As originally proposed by Ludwik,[20]
brittlefracture occurs when the local stresses exceed the
brittlefracture stress. Considerable work has investigated the
ef-fects of changes in various microstructural features on
themagnitude of the cleavage fracture stress in
ferrous-basedsystems.[15,2328] Work on Nb[7,8] reveals a strong
effect ofgrain size on the cleavage fracture stress, with an
increasein the cleavage fracture stress arising through the
decrease
in grain size. Temperature-independent cleavage fracturestresses
in the range 1150 to 1500 MPa were reported bySamant and
Lewandowski[7,8] on material of nearly identi-cal chemistry and
grain size as that tested presently.
1. Smooth tensile specimensFigure 11 illustrates the effect of
changes in test tem-
perature on reduction in area for the smooth tension spec-imens
and reveals significant ductility (i.e., RA . 50 pct)at 2196 C,
despite the appearance of 100 pct cleavagefracture at 250 C in the
notched/precracked specimens.This is consistent with Ludwiks
concept,[20] because the
Table III(a). Summary of Locations of Apparent Cleavage Fracture
Nucleation Sites: Charpy Impact TestDistance of Apparent Sites of
Average Location of Peak
Grain Test Cleavage Fracture Nucleation from Measured Tensile
Stress Size Temperature Notch Distance from Ahead of Notch (mm) (C)
(mm) Notch (mm) (mm)[30]
40 2195 182 173 77 93 208 221 230 169 6 61 17040 2125 514 216
192 336 384 168 302 6 134 25040 275 239 231 239 296 251 6 30
340
105 2195 215 239 92 110 110 153 6 68 62105 2125 240 275 178 384
240 309 271 6 70 212105 275 374 392 383 6 13 320105 225 637 263 519
473 6 191 310
Table III(b). Summary of Locations of Apparent Cleavage Fracture
Nucleation Sites: Fatigue Precracked Impact TestDistance of
Apparent Sites of Average Location of Peak
Grain Test Cleavage Fracture Nucleation from Measured Tensile
Stress Size Temperature Fatigue Precrack Distance from Ahead of
Crack (mm) (C) (mm) Precrack (mm) (mm)[39]
40 2195 115 18 100 61 61 79 79 73 6 31 7640 275 154 134 189 64
135 6 53 10140 225 269 96 198 243 192 200 6 66 40 25 239 155 183
192 6 43
105 2195 183 163 127 258 139 136 150 165 6 45 148105 275 489 367
165 49 267 6 198 183105 25 377 377
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974VOLUME 34A, APRIL 2003 METALLURGICAL AND MATERIALS
TRANSACTIONS A
(a) (b)Fig. 10Effect of test temperature on the location of
apparent cleavage fracture nucleation sites: (a) Charpy impact test
and (b) precracked impact test.
Fig. 11Effect of test temperature on RA at fracture ( ?j 5
6(1024) s21).
yield stress at 2196 C (approximately 730 MPa) is wellbelow the
cleavage fracture stress (i.e., 1150 to1500 MPa), as determined
elsewhere.[7,8]
2. Notched charpy specimensThe two important considerations in
analyzing the tran-
sition behavior of Charpy impact specimens are (a)
thedistribution of stress ahead of the notch and (b) the criti-cal
cleavage fracture stress as a function of test tempera-ture. Prior
to general yield, the strain rate ( ?j) experiencedby the specimen
can be estimated using Eq. [2] and themeasured velocity of the
impacting tup (i.e., 5.24 m/s),producing ?j value of 380 s21,
several orders of magnitudehigher than that experienced during a
static test. There-fore, the effect of changes in strain rate on
the stress dis-tribution ahead of the notch and sF is required.
Green andHundy[29] have studied the profile of the stress field
aheadof a Charpy notch under static and impact conditions andshowed
that the stress field ahead of the notch is unaf-fected by the
impacting conditions, provided the mode of
deformation was unaltered. However, the increase in theyield
stress due to the increased strain rate experienced bythe material
in the vicinity of the notch increases the mag-nitude of stresses
ahead of the notch tip.
More recent finite element model work[30] has charac-terized the
magnitude and distribution of stresses in anotched Charpy bar
loaded in 3PB to various fractions ofgeneral yield, analogous to
work by Griffith and Owen[31]on notched four-point bend bars. The
maximum stress in-tensification for a notched Charpy bar at general
yield wasshown to be 2.57 for the slip line field solution,[32]
whilean analysis of a notched four-point bend specimen testedto
general yield for a material with moderate linear workhardening
revealed the maximum stress intensification tobe 2.6.[31] Other
work[33,34] on notched four-point bendbars has shown that higher
rates of linear or power-lawwork hardening, beyond those exhibited
presently, in-crease these values. The maximum stress
intensificationat general yield in a notched Charpy bar calculated
usingthree-dimensional FEM[30] for a material with
power-lawhardening (i.e., n 5 0.15) was 2.5. This information
isused subsequently to estimate the Nil Ductility Tempera-ture
(NDT) and is then compared to the present results.
At the NDT, the conditions for general yield and brit-tle
fracture are satisfied[28]:
[3]
[4]
wheremaximum stress intensification ratio ahead ofa Charpy
notch,maximum principal stress along the directionof
loading,dynamic yield strength, andcleavage fracture stress. sF
5
syd 5
smax11 5
R 5
R 5smaxllsyd
Rsyd 5 sF
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METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 34A, APRIL
2003975
Fig. 12SEM photograph of the fracture surface of a Nbcp
105-mmCharpy impact test specimen tested at 225 C. The presence of
a stretchzone prior to cleavage fracture nucleation is clearly
evident.
Considering that Cottrells model for grain size controlof the
brittle fracture stress is obeyed for Nb as shownearlier,[7] it is
estimated that the sF values for 40- and105-mm grain size Nbcp
specimens are approximately 1800and 1300 MPa, respectively. Using
the values for sF (i.e.,1800 MPa and 1300 MPa) and the values for R
(i.e.,approximately 2.6) in Eq. [3], calculated values for syd
atthe NDT are 690 and 500 MPa for Nbcp Charpy specimenshaving 40-
and 105-mm grain size, respectively. FromNemat-Nasser and Guos
work,[18] the yield strengths ofNbcp at 2100 C and 225 C are
approximately 675 and525 MPa, respectively, at a strain rate of 380
s21 (Figure 6).Similarly, from Briggs and Campbells
experimentaldata,[12] the yield strengths of Nb at 275 C and 225
Care found to be 706 and 517 MPa, respectively, at a strainrate of
100 s21. This estimates that the NDT of a 40-mmgrain size Nbcp
should lie in the vicinity of 275 C, whereasthe NDT of 105-mm grain
size Nb should be near 225 C.
The data reported in Figure 4 are qualitatively consistentwith
the preceding arguments. The NDT, defined as thetemperature at
which the Charpy impact energy first be-gins to rise, appears to be
near 250 C for the 40-mm grainsize Nbcp and is near 225 C for the
105-mm grain sizeNbcp. Quantification of the amount of cleavage vs
ductilefracture present on fracture surfaces[16] indicated that
thetransition from predominantly cleavage fracture to
ductilefracture occurred between 250 C (i.e., .80 pct cleav-age)
and 225 C (i.e., 100 pct ductiledid not fail) forthe 40-mm grain
size Nbcp. In contrast, the 105-mm grainsize Nbcp Charpy specimens
revealed this fracture modetransition occurred between 225 C (i.e.,
75 pct cleav-age) and 0 C (i.e., 100 pct ductiledid not fail).[16]
Inthe present studies, the transition from lower shelf to
uppershelf for Nbcp 40-mm grain size occurs at approximately250 C
to 225 C and takes place between 225 C and0 C for 105-mm grain size
material. Fracture surfaceanalyses revealed that all the Charpy
specimens fracturedvia cleavage mode at test temperatures below the
NDT.However, as the test temperature increased beyond theNDT,
specimens of both grain sizes showed appreciableamounts of stretch
zones immediate to the notch tip(Figure 12). In addition,
increasing amounts of localplasticity were observed at the apparent
cleavage fracturenucleation sites (Figure 13), where evidence of
limitedamounts of ductile fracture was present both at the
ap-parent nucleation site (Figure 13(a)) and along one of
thecleavage river lines (Figure 13(b)). Such features
werenonexistent at the lower temperatures. In the upper
shelfregion, impact specimens exited the machine intact due tothe
extensive plasticity exhibited (Figure 4).
The profiles of load vs time obtained from theinstrumentation
package for tests conducted at temper-atures up to the NDT were
linear to maximum load. Inthese cases, the maximum load (Lmax)
recorded duringthe impact tests conducted below the NDT can be
con-sidered as the load at which cleavage fracture started
toinitiate/propagate. Using Lmax, the nominal applied stressat
fracture for each of the test conditions can be calcu-lated
as[35]
[5]snom 56M
b(W 2 a)2
[6]
where
M 5 bending moment experienced by the bar (N.m),B 5 specimen
thickness (m),W 5 specimen width (m),a 5 notch depth (m),
Lmax 5 load to failure (N), andS 5 span of loading in Charpy
impact test (m).
Using this approach, it is possible to qualitativelycompare the
location of apparent sites of cleavage frac-ture nucleation with
that of the peak stress in a mannerdescribed elsewhere[7] for
specimens loaded under sta-tic conditions. Recent work on Nb[18] is
combined withpresently reported effects of changes in strain rate
onyield stress in Figure 7, showing reasonable justifica-tion in
using an empirical prediction of yield stress ofNbcp as a function
of strain rate and test temperature.[18]Using Eq. [5] and [6] and
the yield stress of Nbcp at 380s21 (during the Charpy test), the
snom/sy values are com-puted for Nbcp specimens having 40- and
105-mm grainsize for test temperatures near and below the NDT.
Com-bining this information with the stress field analyses ofWang
et al.,[30] the distances of the potential nucleationsites are
calculated and summarized in Table III(a); theexperimentally
observed distances of fracture nucleationsites are found to be
close to the location of the peaktensile stress, providing evidence
of a tensile stress con-trolled brittle fracture process, in
agreement with sev-eral investigators.[7,15,23,31] As the test
temperature is in-creased above 2196 C, the yield stress decreases
anda higher nominal bending stress needs to be applied inorder to
achieve the temperature-independent criticalbrittle fracture stress
(sF) for Nb.[7] Thus, snom/sy in-creases and the location of the
peak tensile stress movesfarther away from the notch tip,
consistent with the datapresented in Figure 10(a).
M 5LmaxS
4
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976VOLUME 34A, APRIL 2003 METALLURGICAL AND MATERIALS
TRANSACTIONS A
(a) (b)Fig. 13Higher magnification view of a cleavage fracture
nucleation site in a Nbcp 105-mm Charpy impact specimen tested at
225 C, illustratinglocal plasticity (inside the boxes): (a)
nucleation site and (b) cleavage river line.
3. Fatigue-precracked charpy specimensFrom the plot of absorbed
impact energy (normalized
by initial uncracked ligament area) vs test temperature(Figure
5), it appears that complete transition into the duc-tile regime is
not achieved even at room temperature forthe fatigue precracked
specimens. Furthermore, whencompared with the absorbed energy
values from the V-notch Charpy tests normalized by initial
uncracked liga-ment area, it is clear that for a given grain size,
the tran-sition temperature of Nbcp specimen is higher for
theprecracked specimens tested in impact. This is consistentwith
the higher stress intensification (R) achieved in aprecracked
impact test due to the very small root radius(r V 1 mm) of the
fatigue precrack in contrast to that ofa Charpy notch (r , 250 mm).
The location of apparentcleavage sites ahead of the fatigue
precrack (Table III(b))is discussed in Section B.
B. Dynamic Plane Strain Fracture Toughness (KID)It appears from
Table II that the LEFM criteria (calcu-
lated using the sy values at a strain rate of 500 s21[18]
areonly violated for specimens tested at temperatures above250 C
and 225 C for Nbcp specimens having 40- and105-mm grain size,
respectively. In addition, the load-timehistory of the specimens
tested at 250 C for the 40-mmgrain size Nbcp specimen did not
exhibit any nonlinearityprior to fracture. In contrast, the
instrumented load-timetrace for specimens tested at 225 C revealed
some evi-dence of nonlinearity, indicative of plasticity or
stablecrack growth. Similar observations were made for the 105-mm
grain size Nbcp specimens tested at 225 C or highertemperatures.
Beyond the LEFM validity regime, the KIDvalues probably
underestimate the actual dynamic tough-ness of the material due to
the increased plasticity or sta-ble crack growth.
Over the range of LEFM validity (i.e., 2196 C to250 C for 40-mm
Nbcp and 2196 C to 225 C for105-mm Nbcp), Figure 7 revealed that
KID is virtually in-
dependent of test temperature and grain size. Over thatrange,
Figure 10(b) further revealed that the location ofthe apparent
cleavage fracture nucleation sites were notas affected by changes
in test temperature as demon-strated in the notched Charpy
specimens shown in Fig-ure 10(a). This observation can be
rationalized followingarguments used in the cleavage fracture of
steels[23,3638]and for polycrystalline Nb,[7,8] where a specimen
havinga sharp crack, as in the case of a fatigue precrack,
wouldfail via cleavage when the maximum principal tensilestress
(smaxyy ) ahead of the crack exceeded the criticalcleavage fracture
stress (sF) over a microscopically sig-nificant (characteristic)
distance. The severity of stressstate provided by a sharp crack
results in high stress in-tensification ahead of the crack tip.
Finite element analy-ses of the stress field ahead of a sharp
crack[39,41,42] showthat the maximum stress intensification
achieved in aspecimen having a sharp crack is higher than in a
blunt-notched specimen, and depends on the work-hardeningbehavior
of the material. Thus, the issue of exceeding thesF becomes
secondary, while extending the smaxyy abovethe sF over the
characteristic distance becomes the con-trolling event.
To rationalize the results of the present investigationin light
of the preceding arguments, it is important to con-sider the
distance of apparent cleavage fracture nucleationsites from the
crack tip (x). From fracture surface analy-ses of
fatigue-precracked specimens (Figure 10(b) andTable III(b), it
appears that x is slightly dependent on testtemperature in the
range 2196C to 225C for speci-mens having 40- and 105-mm grain
size. At the highesttest temperatures, this probably arises due to
crack tipblunting and the appearance of stretch zones at the
cracktip (Figure 12). In precracked specimens, the cleavagefracture
can nucleate, stochastically, anywhere in the re-gion where smaxyy
exceeds the sF. Thus, it is reasonable toargue that x is indicative
of the characteristic distance.Previous work has shown that sF is
independent of tem-perature for Nb.[7] The present work indicates
that the
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METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 34A, APRIL
2003977
Fig. 14Comparison of the experimentally obtained dynamic
fracturetoughness (KID) data with the predicted values using
Traceys stress fieldanalyses.[39]
global stress (i.e., applied dynamically) required to prop-agate
a crack in a brittle manner is unaffected by changesin test
temperature (in the range-196 C to 225 C), pro-ducing a nominally
temperature-independent value for thedynamic fracture toughness
over the range of tempera-tures tested.
Early work[37] has suggested that the plane strain frac-ture
toughness (KIC) of metals that fail via slip-inducedcleavage can be
predicted using sF, x, and the distribu-tion of stress field ahead
of the crack. The stress analysisdue to Tracey[39] is used for the
present estimation in themanner used previously by Samant and
Lewandowski:[7,8]for static fracture toughness measurements made on
es-sentially identical Nb materials. It should be noted thatthe
work-hardening exponent (n) has a strong effect onthe stress field
profile. From the tensile tests in the pre-sent investigation, n
was found to be between 0.05 and0.08 in the temperature range of
2196 C to 2125 C andbetween 0.15 to 0.2 in 275 C from room
temperature.Based on this, n is assumed to be zero for the
testtemperature range of 2196 C to 2125 C and 0.2 forhigher test
temperatures. The yield stress (at 500 s21) val-ues used in the
estimation are calculated using the em-pirical equation from
Nemat-Nasser and Guos work.[18]The temperature-independent sF
values for the 40 and105-mm grain size specimens are estimated from
datafrom Samant and Lewandowski[7] as discussed earlier inthis
article.
Figure 14 compares the effect of changes in test tem-perature
and grain size on the predicted plane strain dy-namic fracture
toughness (KID) and the experimentally ob-tained data shown earlier
in Figure 7. It is evident thatTraceys model predicts reasonably
well for the low-temperature (2196C to 275 C) tests. This is
consistentwith the observations of catastrophic crack
propagation,without any stable crack growth at these
temperatures.However, at higher temperatures (i.e. T . 225 C),
themodels prediction of fracture toughness is significantlyhigher
than that obtained experimentally. At these temper-atures, the
criteria for linear elastic fracture mechanics are
violated, as shown in Table III, and the experimentally
ob-tained KID values underestimate the predicted toughness inthe
manner demonstrated by Samant and Lewandowski[7,8]for static tests
on similar materials. Attempts at using crackgages to
document/record any stable crack growth duringthe instrumented
impact tests at 275 C were unsuccess-ful due to the difficulty and
space limitations provided bythe impacting tup and specimen
holder.[16] However, crackgages were successfully used to record
stable cracking ofthese materials at high testing velocities and
low tempera-tures on a servohydraulic testing machine. These tests
werenot conducted under the impact conditions used presentlyand are
reported elsewhere.[16,40]
V. CONCLUSIONS
1. Smooth Nbcp tension specimens having grain sizesranging from
40 to 165 mm exhibited ductile fracturewhen tested at a strain rate
of 6(1024) s21 over the testtemperature range of 25 C to 2196 C.
Over thisrange, the HallPetch slope (ky) was found to vary be-tween
2.65(104) and 5.6(104) N ? m23/2.
2. The ductile-to-brittle transition temperature of notchedNbcp
Charpy specimens was grain size dependent. TheNDT of 40-mm grain
size Nbcp Charpy specimens wasnear 250 C, while that of 105-mm
grain size NbcpCharpy specimens was near 225 C. The NDT of
thefatigue-precracked impact specimens was much higherthan that of
notched Charpy specimens, consistent withthe differences in stress
state between the specimenstested.
3. All specimens tested at temperatures below the NDTexhibited
cleavage fracture with multiple sites of ap-parent cleavage
fracture nucleation located ahead ofthe notch tip, consistent with
tensile-stress-controlledcleavage fracture. Increases in test
temperature pro-duced large increases in the distance ahead of
thenotch where the apparent cleavage nucleation siteswere located,
in rough agreement with the locationof peak tensile stress
available from FEM analyses.At temperatures above the NDT, local
plasticity atthe notch and at the apparent cleavage fracture
nu-cleation sites was clearly evident. Extensive plastic-ity was
exhibited on the upper shelf without cata-strophic fracture.
4. The plane strain dynamic cleavage fracture toughness(KID) was
essentially independent of test temperature(over the range 2196 C
to 250 C for 40-mm grainsize Nbcp and 2196 C to 225C for 105-mm
grainsize Nbcp) and grain size (40 to 105 mm). Despite
thepredominance of cleavage fracture, the dynamiccleavage fracture
toughness was approximately 37 64 MPam.
5. The average distances of apparent cleavage fracture
nu-cleation sites from the fatigue precrack exhibited aslight
dependence on test temperature and grain sizeover the range tested.
At the highest test temperatures,this likely results from crack-tip
blunting and thechanges in stress distribution that are produced.
Com-parisons to available models of cleavage fracturetoughness
revealed reasonable agreement for temper-atures below the NDT.
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978VOLUME 34A, APRIL 2003 METALLURGICAL AND MATERIALS
TRANSACTIONS A
ACKNOWLEDGMENTS
The authors thank AFOSR (Grant No. F49620-96-1-0164 and
F49620-00-1-0067) for partial support of thiswork. Partial support
by Reference Metals Companyand supply of materials by Cabot
Corporation are alsoappreciated.
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TITLE: Effects of Test Temperature and Grain Size on theCharpy
Impact Toughness and Dynamic Toughness (KID)of Polycrystalline
Niobium
SOURCE: Metall Mater Trans Part A 34A no40 Ap 20032000
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