AD 6 P ER NUMB ER M

COPY 1AN~ A Unified Interpretation of Room-Temperature

Il Strength of Notched Specimens asL ATIlON nfluenced by Their Size

B. M. WUNDT Lo 2 6 X99A- Structural Engineer, Large Steam

Turbine-Generator Department, FGeneral Electric Company, i

L ,Schenectady, N. Y.

I 'ris paper proposes a generalized concept of material behavior in theW %,presence of sharp notches or cracks, which embraces the notch-strengthening

of small bars and the notch-weakening of large bars, Quantitative explano-(Il | • of notch-strengthening of small bars follows from the experimental work

St•. INN G. Sachs and others, and the interpretation of notch-weakening of largebars, the geometric size effect, is obtainable with the help of Griffith-Irwin

ql approach using the strain-energy-release concept: ',Experimental notch

QýZtength versus size curves for notch-tension and notch-bending tests are• plotted in an especially useful log-log co-ordinate system. An analytical

'10xpression was derived to approximate the foregoing experimentally ob-served, continuous variation of notch strength. A relationship was derivedbetween the notch strength and relative notch dept*for cylindrical tension

C bars with different outside diameters. The plots indicate a continuity ofnotch-strength behavior with varying size and varying notch depth.

i1 dDTIC QUAITY INSPrcTED 2

For presentation at the Metals Engineering Conference, Albany, N. V., April 29 -

"MIU AMMICCA sAMI1 OF MiCHANICAL I I May 3, 1959, of The American Society of Mechanical Engineers. Paper received at29 Wegi*J3dm gemO , New = ot II, N ASME Headquarters, February 24, 1959.

Written discussion on this paper will be accepted up to June 5, 1959.

Copies will be available until March 1, 1960.

Thli document cms been approvedfor public eleose ad sale; in-diutuibutiot is unjimited.

A Unified Interpretation of Room-TemperatureStrength of Notched Specimens as B. M. wuNDT

Influenced by Their Size

Nomenclature Sy = yield strength, psi

The following nomenclature is used in this t = thickness of beam, in.

paper: x, y = co-ordinates

c = depth of notch, in. V = Poisson's ratio

d = notch diameter, also gross depth of

beam, in. Introduction

D = outside diameter of bar, in. In (j),2 the authors have introduced the

E = modulus of elasticity, psi Griffith-Irwin concept for the determination of

FATT = Charpy-V-notch fracture appearance (50 bursting speed of large, effectively notched

per cent fibrous) transition tempera- disks. A new physical quantity, "fracture tough-

ture, deg F ness," 0 cl was experimentally determined from

G = strain-energy release rate, in-lb per bursting tests of such disks made from different

sq in. materials. The authors recognized that the mate-

Gc = fracture toughness, in-lb per sq in. rial behavior in notched disks may be classified

Gco = fracture toughness in the presence of by using the over-all stress field near the notch

crack, in-lb per sq in. apex, at the bursting speed, and comparing it

h = net depth of beam at notch, in. - d - c with the tensile strength and yield strength of

M = bending moment, lb-in, the material. This reasoning resulted in a some-

N - notch depth, ratio of area removed by what arbitrary classification of material behav-

the notch to gross cylindrical area ior into ductile, quasi-ductile, quasi-brittle,1 - (d/D) 2

and brittle. Since then it was recognized that

Nt = notch-strength ratio in tension - Sd/St the foregoing classification is useful and may

P - axial force, lb easily be adapted to apply to other configura-

Pm = maximum axial force in a tension test, tions, like tension tests on sharply notched

lb bars and on notched beams. In addition, a con-

p - coordinate difference = x2 - x1 sistent pattern of no';ch-strength behavior

q = coordinate difference = Y2 - Yl emerged in which the linear size of sharply

r = radius at the apex of notch, in. notched specimens, together with fracture tough-

S - stress, psi ness Gc became the defining parameters. In this

Sd - notch-strength in tension test, psi = paper the experimentally obtained nnotch-strength-

Pm/(7rd2 /4) versus-size" curves are presented for tension

S = nominal bending stress at the notched tests of notched cylindrical specimens and for

beam section of net depth h, psi bending tests of notched beams. A family of such

K/(th2 /6) curves is plotted in an especially suitable log-

Sn - notch-strength, psi log co-ordinate system and the adopted classifi-

St = tensile strength, psi cation of material behavior is indicated in the

diagram. Using the Griffith-Irwin concept, in- 3

1 formative curves were plotted representing theWhen this paper was written the author in- notch-tension strength of cylindrical specimens ......

cluded information and expressed opinions be- as a function of relative notch depth.

lieved to be correct and reliable. Because of Small Notched Tension Specimens Tested at Room

the constant advance of technical knowledge, the Temperature:

widely differing conditions of possible specific There exists considerable literature on the

application, and the possibility of misapplica-

tion, any application of the contents of thispaper must be at the sole discretion and respon- 2 Underlined numbers in parentheses designate

sibility of the user. References at the end of the paper.

o 44'oINt LOADING : TmHICXNESS OF BEAM J'NOTCH M BSENDING M ENT A THE'

NOTCHED SCTION IN -LB

~so 0 6 - 5.Of NOTCH 052;

0 5 C R A, -, 3 " P OIVN T EO A DAG0c, , 0 t, , , , , -• f/ .-'488 . NOTCH

048

INFINILTE PLATE *IT. SEMI-INFINITE PLATE ITHIN DISK-SHAPED CRACK 03 05 1

INTERNAL CRACK WITH EDGE CRACK OF RADIUS R IN STRESS 02 S NMINAL OENING STRESS ATl~~~~1 02-•O.• .. H OCH S", T|O

h STRESS FIELD SO IN STRESS FIELD So FIELD So 02 0.204 T sE C

GS d

I/- -L S i 6 s, A Do 0 28I

(S O S FORMULA)0 01 02 03 04 05 06 O0 08 09 10

Fig.1 Some formulae for strain-energy re-lease rate. Fig.2 Strain-energy release rate for notched

beams.

subject of strength of relatively small notchedcylindrical tension specimens. Kunze in Germany,

McAdam, Sachs, Ripling, Baldwin and their co- straight-line relationship. If combined with

workers in the United States, have contributed very small radii, the resulting notch-strength

to a better understanding of the effect of geome- ratio may decrease to below 1, and especially

try on the tension behavior of cylindrical, so when the notch depth is 50 to 60 per cent.

notched specimens. Readers who intend to study It appears that for the investigated range ofthe foregoing will find references (j_, 16, 17, strength the effects of notch sharpness and

18, 11, 20, 24) useful, stress level are interchangeable (U, Fig. 5, 7,Sachs and his co-workers performed tests on 10) and (20, Fig.6).

heat-treated AISI 3140, 4340 and recently also Increased specimen size results in a more

on other low-alloy steels. Originally, cylindri- or less gradual deviation of the notch-strength

cal diameters varied between 0.300 and 0.500 In.; from the straight-line relationship, especiallyin later experiments diameters were increased to for the high-tensile-strength steels (Uj, Fig.8).

3 in. Often, when notched bars are tested in The combined effect of notch angle and notch

tension, after the maximum has been reached the depth for sharp notches is presented in a discus-

load P decreases until the bar fractures. Such slon by McAdam (12, Figs.16, 18). He indicatesbehavior under notched conditions Indicates that that the straight-line relationship holds well

the material exhibits a degree of ductility (20, for angles less than 60 deg, for larger angles

Fig.2). It has been shown that under such condi- a deviation is observed.

tions, the relationship between the notch-strength Sd and notch depth N is approximately Griffith-Irwin Juantitative Approach to Geometric

linear (U, p. 521); namely, it appears that for Size Effect50 per cent notches, the notch-strength Sd is Application of Log-Log Co-ordinates. The

about 50 per cent higher than the unnotched ten- strengthening of notched tension, bars previous-

sile strength St, and for very deep notches, al-' ly described is, as a rule, confined to barsmost 100 per cent deep, Sd is approaching twice with small diameters. With Increasing diameter

St.% This Is shown In Flg.ll(a) by the straight the notch strength decreases and may become evenline ogm. Note that the foregoing applies only lower than the yield strength Sy. This notchwhen the notch is made very sharp and when the weakening is usually accompanied by complete sep-notch angle Is equal to or less than 45 or 60 aration of surfaces and by fast crack propaga-

deg. With increase in notch radius the notch- tion. Often, the main fracture surfaces have astrength Sd passes through a maximum and then smooth and shiny appearance indicative of cleav-

decreases as indicated in Fig.ll(a), curve ogn, age fracturing and the fracture appearance is

and in (1_, Fig.1). For still larger radii, and termed commonly as "brittle" (see bibliographyfor very deep notches, notch-strength Sd may 4, 5, 6, 7, 35, 36, 37, 38, 39 in reference 1).

even approach St, the tensile strength. The lower notch strength of larger bars may

In case of steels with higher strength be qualitatively defined with the help of the

level, above 150,000 psi and up to 290,000 psi, Griffith-Irwin approach (1, page 1647). Newernotch Arength deviates more and more from the references pertaining to this approach are (8, 2.

2

7Z:' IMC,;, AR N3T(.

"STRESS AT NOT.CHED SECTION P U --- P NOTC. CEPrM h:9 1

CIRCULAR NOTCH "•"

P AAIAL TENSION FORCE CIRCULA" "O!

*.% d' F"•

540 G 57

(IN -. B, "

5... (St

6-0.,

02 0.3 0, 0. 0.6

0.

7 0. 6 0. 9 ,. 0 .

~i L ,o : 04 4 3 2 : o~~j8

h o.~7 o'. o t. o. 03 o0. 0., -° (0.3- ____ , .

, ,.o o.__o.___o____o___o__o___o . 55o 5 0.4

13

02S 0 A-

-• F•.• otchstrength of cylindrical tension

10, 11). Reference (23) is another imnportant then for -point loading from curve B, Fi_.2

and very recent paper which discusses stable and

unstable cracks in shear without making use of f(c/d) = 0.317

the Griffith-Irwin approach. For completeness,

two def•iitions will be quoted from (1=): Using Equation (1),

Fracture Toughness Go. The component of

work irreversibly absorbed in local plastic flow Sh2 d = 126 x 106 G psi (2)

to create a unit area of fracture. Fracture

toughness has also been referred to in the liter- The strain-energy release rate 0 for a circular,

atuire as "fracture extension force." sharply notched bar in tension is as follows

Strain-•iergy Release Rate 0. T'he Quantity (13):

Of stored elastic strain energy released from a

cracking specimaen as a result of extension of 0 =" [L( - i.2 )IE' •" ) d 3

the advancing crack by a unit area, where,fd/)dd (•

Fig. 1 summarizes some of the better known

expressions for strain-energy-release rate 0 f~d/D) = (8wN)/(5 + 3W) 2 (4)

(Fig.3 of 1). Equation (27) in (1) is an analy-

tical expression for G, for a notched-beam speci- Sd~d - GE P(d/D) (5)

men with 4-point loadingr F(dAP) = 1/ [(l - v,2)f(d/D)] and Sd 2D = GE F2 (N)

0 = ILl - 12)/EZ f(c/d) Shah ( 1) ( 6)

The notched bend specigen and function (c/d) are w

shown in Pig. 2, curve A. Equation (1) applies F•(N) = CF(d/')2/(I -

to shallow, rintermediate and deep notches.

The analytical expression for 0 for a Functions f(d/D) and F(d/D) are plotted in Fig.3,

notched beam with 3-po int loading was derived in and

B(N) is plotted in Pig. 4. For N = 1, i.e.,

(12). The expression is the same as for the o- for very deep notches f(d/D) = i/8. For very

point loading, but f(c/d) differs. (unction shallow notches d(D - 1, Equation ( 3) practical-

f(c/d) is plotted a es cr

with Irwns equation (page 6 of

o),

In order to investigate the effect of size if it is modified for plain strain.

on strength of notched beams, a series of gradu- Tf a partinc ular specimen geometry is chosen,

ally increasing notched beams is te d in slow e.g., the widely used 50 p er cent notch, then

bending. All dimensions increase proportionally

and the ratio cnconstant. If we

d/u = 0.07, N = 0.500

assume o/d i 0.2, i.e., if we choose a series of

beams with 20 per cent notch depth and h = 0.8 d, and from Equation (a) f(d/D) = 0.297. Ter•Ifore,

tica exresionforG, fr anothedbea spci- d 2 - E Fd/D (5

jARNOT'

ASSUMED 0400I (J)'4L500 P I- ; 300250

S 200 STRAIGHT LINE S'd PRO TIONAL TO GE

405 NOC S•:, GT ý=s2 50 100 ?00 400 150

1 2NNER 9 D 6Z E I S IUASI-BRITTLE OfHIIOR

so40 BR IT T LE IBEHAVIOR

4 20020

'S 07 049 25 3 4 5 7 IC 2

F1.5 Notch strength of 50 per cent notched ten- Fig.6 Notch strength versus size. Schematic rep-sion sRecimens, resentation.

G = 0.297 Di I' -')/EJ Sd2d (7) tions (2, 2) will be represented by a straight

line with a slopeand, because d = 0.7C7 D, d = 0.3, and E = 29 x106 psi tgcM = dy/dx = - 1/2

G = 0.0066 x l0"6 Sd 2D (8) A family of straight lines may be drawn, each

one for a different value of Gc. Using Equationand (9) a number r^ such straight lines were drawn

in Fig.5.

Sd2 D = 152 x 106 Q psi (9)

CONTINUITY OF MATERIAL BEHAVIOR IN THEIt is important to notice that Equations (12), PRESENCE OF NOTCHES(13). (23) in (1), Equations in Fig. 1, andEquations (1), (3), and so on have the same es- Notch-Strength-Versus-Size Curves. We havesential form: "The product of square of stress discussed the strength behavior of small notchedand of a linear dimension is proportional to the specimens at one end of the range of sizes andstrain-energy release rate." The foregoing may the behavior of large notched specimens at thebe interpreted as follows. "If, a series of other end of the range. It is possible to showtests is performed with proportional specimens the notch-strengthening of small specimens andand, if, at the instant when the crack becomes the notch-weakening of large specimens on theunstable and begins to propagate rapidly, all same plot. Such a combined plot becomes espe-dimensions, including the crack length (or - cially useful, if log-log co-ordinates, are usednotch) are proportional, then the product of a for stress and for linear specimen size. Thisnominal stress squared and of crack length is is depicted in Fig.6, where besides the straightproportional to strain-energy-release rate G." line do, also the yield strength Sy, the tensileBut G at this instant becomes fracture toughness strength St and the notch strength Sn are shown.Gc, which is assumed constant and a characteris- It appears to be Justified to assume that thetic of material. The inverse-square law which notch-weakening phenomenon which becomes evidentstates that it takes one half of the stress to when the specimen size is increased takes placecause fracture when all dimensions increase four in a more or less gradual manner. Consequently,times, is usually designated the "geometric size it is supposed that the notch-weakening proceszeffect", (1, p. 1653). may be represented by the dotted line a b c d.

It is helpful to plot S and d in a log-log Point a indicates the first noticeable de-co-ordinate system with abscissa X = log d and viation from the line Sn and at point d theordinates y = log S. For an assumed value of notch-strength begin: to follow the straight lincGc and for a particular geometry any of the Equa- S2D = const. Points b and c are intersection:

14

•! -3

I 1OTC STRENITH

6•i USe ;RTTLE N I0R ,VO ,+ .... .

4I I TTII I iI 00

0I 03 05 h2 3 I 5 0 20LIO('ft •ALUE) 0 0 0

Fig.7 Family of notch strength versus size curves.* LIN,,R SIZE 0schematic representation. IN

Fig.8 Notch strength versus size. Analytical

repres entat ion.

with the two horizontal lines which correspond brittle" and in the region below d as "brittle."to tensile and yield strength, respectively. In The foregoing classification of material be-this manner an assumed curvre a b c d was made to havior into "ductile," "quasi-ductile," nquaai-depict the Intermediate region of material be- brittle," and "brittle" is arbitrary. Hqvever,havior bridging the two eztreme behaviors. The this classification appears to be consistent be-sizes D1 and D2 which define points a and d are cause the grouping is defined by means of theeither obtained experimentally or must be esti- "over-all" stress field which occurs at the 1net-mated. The curve "Sn a b c d e" is designated dent of fractture in the vicinity of the notch.here as "notch-str~ength-versus-size" curve. Besides, these definitions naturally take into

Ibe foregoing Inductive approach considera- account the geometric size effect. in applica-bly helps to visualize the behavior of sharply tion of the roregoing mayT be found elsewhere (pp.notched specimens as influenced by their size. 1645 and 1646 of 1_). It is worthwhile to add

A partial confirmation of this Inductive reason- that am attempt to classify material behavioring, pertaining to material behavior in the similarly by means of fracture appearance will1,presence of notches, may be derived from two for the most part, not be satisfactory. Thesets of experiments with notched tension and main reason for this is that fracture appearanceebend specimens which will be described in later depends not only on the notch geometry and onsections,* the size of the specimen, but is also affected

Nany materials, when sharply notched and to a considerable degrPee by the elastic strainwhen tested in small sizes at room temperature, energy stored in the complete system which con-fracture at stresses above the tensile strength sists not only of the specimen but includes alsoSt, as depicted by the straight line 5 n in Pig.6 the testing machine.and by its continuation--curve a b. The small - The complete "notch-strength-versus-size"sizes are ther~efore notch-strengthened and the curve was origintated to describe test results ofmaterial behavior may be designated as "ductile." a series of very sharply notched but geometrical-However, for somewhat larger sizes the notch ly similar specimens. The relative position ofstrength decreases and falls between the tensile straight line 2na in respect to tensile strengthstrength and yield strength along the curve b c. St. and the location of line d • in respect toIt appears logical to designate the materila be- the abscissa, is defined only when these re•quirze-havior In the region b c as "Quasi-ductile." ments are fuflled. Pig.6 applies to a materialFor larger sizes the notch strength falls below heat-treated to obtain a set of physical proper-the yield strength S•, as indicated by the line ties and which exhibits a corresponding fractureo d. For still larger sizes the full geometric toughness Gc. Therefore, for a particular speci-size effect is evidenced because the notch men geometry, only one notch-st~rength-versus-strength follows the straight line d e. size curve is obtainable, largely defined by the

It is therefore consistent to describe the particular values of St and Qc. It is possiblematerial behavior in the region c d as "quasi- to extend the concept of the single notch-

Ii IhI

ANGKL 45* I<Q003iN purposes such a material behaves in a ductile (-

S- -quasi-ductile manner throughout a large range ofsizes. Specimen geometry, crack depth, and size

. DIA6 FOR 0000•, .0 00.SQ. GI are not sufficient to define material behavior

and, only when In addition fracture toughness Is- --- NOTCH SIR. specified, the material behavior in terms of

TILE._I_ St TENSILE STR stress level becomes established. An important,l •) -0IICTILE BOIE HIMO 8too Sy YIELD STR. but not very obvious conclusion may be inferred

1AIR-TTLE ANR BRITTLE C 0 from the above discussion that theoretically, ir-

o OL3 IN RADIUS G< respective of the value of fracture toughness,0OOT I RADIUS. DOMa 200 o sharply notched specimens will exhibit quasi-

N- FORGIG *A DATA FROM TABE 20 brittle and even brittle behavior If the size0.1 02 04 00810 2 4 6 100 is increased sufficiently.

D Analytical Expression for Notch-Strength-Versus-Size Curve. Having visualized the ap-

Fig.9 Notch strength versus size. Room tempera- Vru-ieCre aigvsaie h pPig. Noch srenth ersu sie. oom em~ra- proximate shape of the notch-strength-versus-

ture; notch-tension tests with 50 per cent notch,. prxmtsheofhenc-teghvru-size curve, an approximate equation will be pro-

posed for such a curve. In Pig.8 a notch-

strength-versus-size curve abd is drawn, in a

strength-versus-size curve to a number of such log-log co-ordinate system with abscissa X = Ig D

curves forming a family. Each of such curves and ordinates y = lg S. It Is prescribed that

corresponds to a different Gc value. This is the curve abd be tangent to the line ah (notch

shown in Fig.7 for four different values of frac- strength) at point a and point d be tangent to

ture toughness Gclc2,Ge3)Gc4- Gc4 is Practi- the inclined line hd, whose slope is tgo = - 1/2.

cally 25 tires as large as Gel, because it is A parabola will fit the requirement that the

proportional to square of the stress for the same curve be tangent at points a and d.

size. Of course, all four curves are for Identi-

cal specimen geometry. Neither the notch- Yl - - q [Lx - x)/p] p/2q (10)strength values nor the location of point a is

definite and may be best represented by a verti- The power of parabola Is p/2q, it is equal

cally hatched area as shown in Fig.7. In draw- to 2 If p - 4, and 3 if p - 6. ifing the curves it was assumed that the four

points of tangency dl, d 2 , d3 , d4 occur at the p - 4q, hb - 0.25q

same stress level $a, below the yield-strength p = 6q, hb = 0.30o

level Sy.

The previously defined regions of material The author is indebted to Mr. W. G. Sweets

behavior are extended In Fig.7 to embrace all for the derivation of Equation (10).

four curves. The cross-hatched area indicates

that notch strength is hardly affected by the Room-Temperature Tests on Proportional, Sharply

values of fracture toughness Gc. On the other Notched Tension Bars

hand, for large specimens, Gc values define the Room-temperature tests on a series of notch-

strength of sharply notched specimens and, for tension specimens are described in (4). Test

the same size, the notch strength of bars In- bars were taken from a heat-treated, 2.5 pct Ni -

creases with the square root of Ga. A specimen 0.55 pot No - 0.07 pot V forging known as materi-

about 0.4 in. diam has approximately 140,000 psi al A, described in (2) and (14). The following

notch-strength, practically irrespective of frac- physical properties were reported in (14):

ture toughness values and behaves in a ductile Sy = 82,000 psi, St = 110,000 psi, elonga-

manner. In case of a rather low fracture tough- tion 5 to 20 per cent, RA 4 to 55 per cent, 50

ness Gel, the material behavior enters the quasi- per cent fibrous-fracture-appearance transition

brittle range at C1 , when the specimen is about temp. (Charpy - V) - 300 deg F.

2.3 in. diam. However, if the same material has The specimens were provided with a 45-deg

been modified to result in a rather high fracture circumferential V-groove and had a 50 per cent

toughness GO3 , about 8 times Gcl, then the ma- notch; i.e., the ratio of d to D was maintained

terial begins to behave in a quasi-brittle manner constant and equal to 0.707. The radius at the

at point C3 , at a much larger diameter, about 17 bottom of the notch was sharp and was less than

in. A very high fracture toughness Gc4 defines 0.003 in. There were 12 bars tested, two of

curve ab4, which indicates that for practical each of the following six diameters: 0.250,

6

TABLE I-o IT oa ~I9 - KNOI049 MOMENT AT THE NIOTCHED SECTION 145 f..TCHl

TVGION TESTS or NOTCHED aARS AT ROOM TE&OPLAATLIRE I - THCKNSS OF KAN, INii~•

4s5 , Aal,. aoi..u at Notch 0.00),,. S4 ¶.j : '020; S3 1.. J. 1 s0 PSI

"• - D00 CHAMY~ - V INII THK

.ateade Notch Noth Ma... Averast Ax,. -f 250-- . 0 09 0 2r 5 ooo • O /000 S STRENGTHIa&&. 0.,. Ar.e Lod Si ,... Test.

D0 .1ED Pl[IGtSAcros a.c l00 ... .. 'POOTINL SRE

in. I.71 III 37s0 11120.000LE00 TESLESK NS

ISI .17 5 10 37 20 149,000 1 10.o00 so0U0-BRITTLE A0D 0.0 23,6.75 6T 0IS".1711 so 3720 1 .000 60"-BRITTLE KHAV•IOR Ge I. '- 29r• •-G"00

$02 .2838 50 9001 142.000 GC- 00G140

)9.S IS12 49 8860 139.000 14 0~ 40-i*~ 1OC 0.001 I

99 .4!93 -it 16100 131.000 ". V FORGING V. DATA FRWM TA•ES 2 ANO 3 7

198 .4203 51 1480C 134).O00o.O 200L I 0,, I - , 5 too

01o02 04 06 08I 2 4 6 010 1520 30

90 ..6360 so 40400 1 27. ooo.100

9.b339 s0 39000 124vo.000p

l0ot .9200 50 7140, 1 Fig.10 Notch strength versus size. Room tempera-

o .91 S1 5900 9 o00,0 .ture slow-bnd tests.

as* 1.593 so0 146000 7J, 000 73.100

ISO 1.600 49 148000 74.000

Fromn ,.etreace ().

firm that the geometrical size effect does take

place in accordance with Equation (9) It would

D.400, 0.600, 0.900, 1.300 and 2.250 in. The have been desirable to test at least one addi-

test results are summarized in Table 1 and Fig.9 tional bar 5.0 in. In diameter.

is a log-log plot of experimental data. The With the help of the notch-strength-versus-

plot is very similar to P18.5 and the same equa- size curve in Pig.9 It was possible to divide

tion (9) was used to draw the straight lines, the material behavior into the three regions;

The notch strength Sn for small specimens be- namely, ductile, quasi-ductile and quasi-brittle,

comes about 155,000 psi which results in a notch using the horizontal lines which define the ten-

strength ratio of 155,000/110,000 = 1.42 quite sile strength and yield strength of unnotched

close to expected ratio 1.50. specimens. It is of Interest to note that these

It is seen from Fig.9 that the notch- tests, performed at room temperature, Indicate

strength-versus-Size curve a b c e, drawn that the ductile behavior extends Itself up to

through the experimental points Is quite siml- 1 in. diam, in spite of the considerably higher,

lar to one of the family of curves in Fig.?. 300 F FATT.

However, neither point a is definitely located,

nor Is the point of tangency d between the pro- Slow Bend Tests on Notched Specimens

posed curve and the straight line which deter- Room-temperature tests of a series of gradu-

Mines the value of wanted fracture toughness Qc. ally increasing in size, sharply notched, beams

It appears, however, that the six experimental are described In (2) and (1). The test material

points permit defining the required 0 c with suf- was taken from the same forging A as the notched

ficient accuracy as 90 lb-in/sq In. The dashed tension specimens (4). The range of gross beam

line was drawn using the estimated fracture depth d varied from 3/16 to 8 5/8 In. and the

toughness Gc - 90 lb-In/sq in. and this value cross section was square. The beams had a 45-deg

Is assigned to the foregoing forging in the lo- included angle, 20 per cent depth of notch

cation where the specimens were removed. (c/d) = 0.2, the notch radii varied from 0.001

A larger bar from the same forging with to 0.100 in. All tests were performed using 3-

D = 3.82 in., with a 50 per cent V-notch, and point loading, and some of the tests are surnar-

0.007 in. notch radius was tested ( p, P. 160). Ized in Tables 2 and 3. In Table 2 are sui-ar-

thls resulted In Sd = 73,000 psi and Is included ized results of tests on beams vhich were made

Ln Fig.9. The larger notch radius causes a high- strictly proportional to a standard Charpy-V Im-

er fracture strength and may be used to Justify pact specimen whose dimensions are: 0.394 in. x

the choice of 90 in-lb/sq in. for the wanted Gc. 0.394 In., 45 deg V-notch, 0.010 In. radius.

Lhe largest specimens with D - 2.25 In. fractured The smallest beam was 0.197 in. x 0.197 in. and

It Sd - 73,500 psi, which is only slightly lower the largest beam was ten times larger than

than the yield strength Sy = 82,000 psi. To con- Charpy-V specimens.

7

In Table 3 are summarized results of tests TABLE I-

In a series of notched beams with all dimensions ]BEND TESTS OF NOTC•IED SQLAR E SE•A MS ATmroportional, except for the notch radii, which ROOM TEMPERATURE

ALL DIME NSIONS INCLUDING RAO:; - PROPORTIONAL

ore made small, between 0.001 and 0.003 In. 45°V-Not•h. 20% Notch Deptr

Lhe smallest beam was 0.394 in. square and the

Largest about 9.0 in. square. The nominal bend- Grove Notch Nominal comp,.,

Lng strength Sn at the notched-beam section Is • Radio. Bendisten•. s 'aru.. ,..

)btained by dividing the maximum bending moment r A,,.

Lt fracture by the section modulus of the net i in. p., p.,

section. .197 .00o 10S.000 2oo ..

The test data are plotted In Fig.l0 which .1- .0 0 40.o.000 0

Ls a similar representation of notch-strength- .314 .010 10o.ooo 1-.314 .010 19J.000 204.000 )-*

fersus-size curve for bending as Fig.9 is for .394 .010 217,000 Y. L),.nen...a

iotched tension tests. Equation (2) was used to .' . Yos

Iraw the straight lines. The nominal bending 1.960 .0Z5 Z, o000 1.50o 5**

strength of a 3/16 in. unnotched beam was deter- 1.000 .01S 183:000 Ye:

nined (2) as 205,000 psi and 227,000 psi, Table 1.600 .040 161.000 Ye. 4. C

3. The average bending strength, 216,000 psi is 4.000 .100 177.000 Ye, 0o.o(1 ii. thick)

approximately twice 110.000 psi, the tensile

strength 3 t. The foregoing relationship between From r•sfrence (2) Fig. 8 end reference (3) Table 1.

bending and tension strength is generally recog-

riized and the tests confirmed its applicability

to the NI-Mo-V forging. Tensile strength is not

a limiting stress for bending, since for small TABLE 3-

bars which behave in a ductile manner, when the BEND TESTS OF NOTCHED SQUARE BEAMS AT

tensile strength is reached, the bar begins to ROOM TEMPERATUREBEAMS WITH SHARP NOTCHES

neck and the process of necking is not suffi- 450, V-Notch, Z0% Notch Depth

ciently developed in the deformation accompany- Gross Notc h Nomina, Bending Strength Complete

ng bending of square bars (21, 22). It appears Depth Radi.. Separation

that the foregoing does not apply to the yield Asg. Fracture

strength and it is assumed that the yield . .. P* P'i

strength in bending of an unnotched beam is prac- .* .0o1" |9.o00 No

tically equal to the yield strength in tension . 0 .oo- 'h.t 000 169.000 No

of an unnotched specimen. 3.. Goo; 9g0 ooo No3,1. 00 20,000No

The series of notched-beam tests with dimen- 3,1. .0o, 210.000 201.000 No1, .001 194.000 No

sions proportional to Charpy-V bar, summarized 3.,• .O001 175.000 No

in Table 2, are plotted in Fig.10. These tests L6 .003 175.000 175.000 No

form a "proportional" series (double circles); ,. .003 153,000 153.000 ye.

at each point the notch radius is given. It can 3,4 .003 153.000 Y

be seen that only a very small and gradual de- 1.0 .0025 116.500 yes

crease of nominal bending strength with size 1 11. .003 107.o0001 112 .003104.500 :takes place. In other words, the standard I . .oo• 102.000 Ye.

Charpy-V geometry does not lead to appreciable - 4.1 .oo0 60,300 Ye.

notch-weakening due to geometrical size effect. 8.t. .001 43,000 Yes

Ailso, it does not appear to be possible to as- 4.0 .010 94,S00 Ye.

sign a reasonable, even If a very large value of 6. 94." .022, 66. 000 Ye.

fracture toughness, to the curve representing

the proportional series. The series of tests 3:.1, Unnotc.o ZZ7.°000 Zlo.0003 4 205.000 21.0

with beams with small notch radii, between 0.001

and 0.003 in., but otherwise with proportional

dimensions, is ,umaarized in Table 3 and plotted • From relerenme (ýj Fig. S and reference (3) Tables I and 1;

in Fig.10 as the "high-acuity" series. This

series of tests indicates considerable notch the notch-bending strength of a small beam.

weakening, a 0.4-in. beam shows a drop of 20 per The last three points in the high-acuity

cent from approximately 210,000 psi and an 8.62- series seem to define a straight line with suffi.

in. square beam with a 0.001-in. radius has a cient accuracy. The nominal notch-bend strength

notched beam strength of 43,000 psi, a fifth of Sh In the case of the 4 and 8.62 in. beams is

8

ill below the yield strength Sy. This indicates vantageous to plot Sd as an ordinate and a fune-

iat the value of fracture toughness Go, defined tion of increasing notch depth N. The results

r the straight line as 115 In-lb per sq in., is are plotted in Fig.ll; curves c, d, and e were

istified. Tests with "intermediate acuity" con- calculated for notched bars with outer diameters

Lsted of 3 notched beams, 0.197 in., 4.0 in. D = 2 1/4, 9 and 20 1/4, respectively. It is

id 8.94 in., with notch radii 0.005, 0.010 and seen that the shape of these curves is defined

.0225 in. They are summarized in Tables 2 and by the shape of the curve F (N) in Fig.4. For

and plotted in Fig.10. The notch-strength-ver- notch depths between 0.35 and 0.65, notch

is-size curve indicates again considerable notch strength Sd is practically constant and has a

iakening with size. The notch-bend strength for flat minimum. This minimum is especially notice-

ie last point, 66,000 psi, is lower than the able in the case of the two large diameters. Be-

Leld strength, and this test point together with cause of flatness, this region of notch depths

Le one which corresponds to the 4-in. beam de- is most useful for experiments designed to deter-

Lne a straight line with G. = 280 in-lb per sq mine Gc.1. Equation (6) leads to Infinite notch

Again it is seen that the experimentally de- strength for finite Gc and for very shallow

ermined notch-strength-versus-size curves justi- notches, N - 0, and for very deep notches N A 1.

r the concept proposed in Fig.7 that there is a Curves c, d, e are drawn in this manner. How-

)re or less gradual decrease in notch strength ever, the foregoing is devoid of physical mean-•om small to large specimens. ing, and actual boundary conditions derived from

The test results of the three series of known physical behavior must be introduced. Ob-

)tched beams from Ni-No-V "A" forging indicate viously, for unnotched specimens, when N = 0,

iat the nominal bending strength of small the notch strength Sd becomes either equal to

)tched beams of square cross section is slight- tensile strength St in case of small specimens

r lower than the nominal bending strength of un- or, in case of much larger diameters, Sd may be

)tched beams; that is, the notch-strength ratio, somewhat lower. For the large sizes involved it

)r bending of small beams, is slightly less is assumed that the unnotched strength coincides

Lan unity and not considerably more than unity, with point p in the middle between St and S.

; it was in the case of notched tension speci- In order to complete the curves, tangents were

ins. Therefore, the foregoing series of tests drawn from point p to curves e, d and c. For

idicates that although the A steel exhibits, by very deep notches, where N is practically 1, it

ifinition, ductile behavior in a notched ten- is assumed that all curves pass through point q

Lon test, Fig.9, by the same definition, the which coincides with tensile strength St. It

;eel does not behave in a ductile manner in a must be understood that under some conditions

ýtched bend test. However, as in the notched point g may be located considerably higher than

:nsion test, the quasi-ductile behavior is evi- the tensile strength, closer to points n or m,

bnced also in the bend test. It is confined to and this may be especially true when the notce.

ie region between the unnotched bending strength radius is very small. As before, tangents were

id the yield strength. As in the notched ten- drawn from point q to complete the curves pcq,

Lon test, the quasi-brittle and brittle behav- pd and peq.

irs extend below the yield strength. These curves in Fig.ll(a) describe the vari-

ation of notch-strength of specimens with threeotch Strength of Circular Tension Specimens different outer diameters made from material A,

.th Variable Notch Depth equipped with sharp notches, for Gc = 90 in-lb

The notch strength of circular tension spec- per sq in., when their notch depth N is varied

tens with sharp, 50 per cent notches is plotted from 0 to 1. It follows that the notch strength

SFig.9. It is of interest to determine the Sd decreases from the assumed value at p with In-

riation of notch strength Sd with variation in creasing notch depth, reaches a broad minimum

*tch depth N while maintaining constant outer level, and then increases again when the notch

akteter D and fracture toughness Gc. Notch becomes much deeper. In case of large diameters,

rength Sd is obtainable from Equation (6) with Sd decreases with increasing depth very rapidly,

e help of F (N) which is plotted in Fig.4. almost abruptly, reaches a broad minimum andacture toughness Gc was assumed 90 in-lb per again very rapidly increasea to reach at leastin., the value determined in Fig.9 for materi- the tensile strength St. or possibly a stillA. The notch strength Sd was calculated for higher stress. In case of large diameters the

ree conveniently chosen outer diameters, D = minimum which the notch strength Sd assumes may1/4 in., 9 in. and 20 1/4 in. It was found ad- be only a fracture of the yield strength S.

9

220f (a) (b) -220G, G -o 90 IN - LSl/tIN' 0• - 20 -O' IN DIA

G IECTED FOR SMAL L WITH A SMALL RADIUS I EXPECTED FOR 420BA0R WS OF DUCTILE $.. INH A LARGER RADIUS SMALL

80LMATERIAL SMAL SARSow~1S 4100

S8 I I!160r. . o ' • P -i i

'D IN 40M? -t4D

0.-lt\ 2-- -ES, -sr -- ___________140 4ESL SIIGT- 4~

b 00 SASSUMC p F /X_~~ASID 12-__ý JASD42

St TENILE STRENGTH -0~C

100',~Ow6 1400u.Y STRENGTH f

20r-ý' - 2 1 IN 'G,01ONBN -420

;91•N Il

200 060i -N OC

oN DEPT H N2-,1 - 0 02 04 06 08

I'0 0.8 0.6 04.4 0 (-------Io o 01 0'6 64, r2 0 0

09 'oo 011 05 o.5 0. o6 '0908 0o 05 a?30

FOR CONSTANT Gc AND VARIABLE SIZE FOR VARIABLE Gc AND CONSTANT SIZE

Fig.1l Notch strength versus notch depth curves for cylindrical bars in

tension.

or a fixed value of fracture toughneas GC# a Fig.ll(b) summarizes how notch strength Sdarticular size (diameter D) may be found for varies when the specimen diameter remains con-

%ich the notch strength will be practically con- stant, 20 1/4 in., but the fracture toughness

bant throughout most of the depth variation, assumes three different values Gc -90*,360 and

t is seen that shallow and very deep notches 720 in-lb per sq in. As before, we assume thatre not suitable for the determination of 0 c. the notch strength is limited by point p for

ie stresses in the neighborhood of the notches shallow notches and by point q for very deepre limited by the yield and tensile strengths notches. Three curves are obtained, puq, pvq,

ad therefore, the calculated fracture toughness and pwq for the three assumed values of Ge.s too small, (1, p. 1653). Curve pwq in Fig.ll(b) is identical with curve

In case of a rather small notched bar, e.g., peq in Fig.ll(a). It follows from Fig.ll(b)

.1 in. diam, the notch strength Sd may follow that the regions of notch depth N, where theie lines ovm or ogn. Fig.9 shows that for D = Griffith-Irwin approach may be used, narrows.25 in., Sd - 150,000 psi and for D = 0.75 in., down considerably from 0.05 to 0.99 to 0.3 to

S= 124,000 psi. These values define points a 0.75 when Gc increases from 90 to 720 in-lb peri.db, respectively, in P1g.ll(a). In the ab- sq in.Rnce of other data, it is assumed that the vari. The author also has plotted the notch-

bion of notch strength for the two specimens strength-versus-size curves for a uniformlyay be represented by curves oam1 and obm2 which think plate in tension, symetrically notched onass through the tensile stress St and through the outside. For this, a somewhat modified formie two experimentally determined points a and of Equation (6) in (1) was used. The same formu-

la was applied to plot notch-strength-versus-A study of the family of curves beginning notch depth curves, similar to Fig. 11. These

Ith the straight-line ogm to the lowest curve will be published at a later date.aq, indicates that there is a degree of continu- A set of curves similar to those in Pig.by in respect to the variation of notch strength 11(a) may be obtained for notched beams with the

r specimens with varying notch depth and with help of Equation (1) and curves A and B in Fig.2.acreasing size. The magnitude of this varia- V

Lon of notch strength will depend on the sharp- G = [(I- 2)/EIl 1-(c/d)I f(c/d)Sh-dess of the notch and on the value of fracture (la)

Dughness associated with the material, and

LO

r ~ - f/r ) V [ (c/d)~ 1Cd had two radial notches with 0.005 in. radius, ex-=2 -L'/(1 -) •2)1 L 1

- C(c/d) (/d) tending from the bore. The net average tangen-(lb) tWal stress of bursting speed was 32,400 psi.

With the help of Equation (23) in (1), fracturee expression toughness was calculated as Gc - 107 in-lb per

(cd cdjýd 112 sq in., which fails between 90 In-lb per sq in.obtained for tension and 115 in-lb per sq in.,for bending. This rather close agreement is

probably coincidental. Although the disk wasm a minimum for (c/d) approximately 0.30. In quite small, only 9 In. diam, I in. bore, and

;her words, for a constant fracture toughness 3/8 in. thick, the net average tangential burst-Sand total beam depth d, the minimum nominal Ing stress was only 40 per cent of the yield

tndlng stress Sn will be obtained for a 30 per strength, 82,500 psi. This indicates that In

tnt notch depth. A set of curves for notched case of a low value of 000, even a relatively

tams, similar to those In Pig.ll(a), Is pre- small disk may yield quite satisfactory values

rnted In Fig.11 of (2). of fracture toughness.

It Is of Interest that, in the case of The Intermediate acuity series in Fig.10

)tched disks, the curves representing the net results In a much higher Gc - 280 in-lb per sq

terage tangential bursting stress as a function in., obviously because of larger notch radii.

C the relative notch depth (1, Fig.ll) also This difference between the meaning of 0 co and

ave the same appearance as the curves for the of G obtained with manufactured notches must be

Dtch strength of cylindrical bars, Pigs.ll(a) well understood.

nd 12(b). It Is rather difficult to separate the ef-

fect of notch curvature from the effect of size

dditional Remarks Pertaining to Fracture on notch strength. Therefore, it appears logi-oughness cal to define the effect of decreasing notbh

The derived expressions for straln-energy- radius on notch strength by determining experi-

elease-rate, G, postulate that the notches were mentally the resulting shift In 0c to lowerimIlar to natural cracks and that linear elas- values, caused by the change In curvature. The

icity applies. Therefore, to obtain f, -'cture proposal to associate the change In 0 c with a

oughness experimentally in a manner consistent change in notch radius of a series of specimens

Ith Its definition, It is necessary to test a is similar to the established procedure to de-eries of proportional, small and large, spedt- fine the degree of temper brittleness by means

ýens equipped with cracks rather than with me- of a shift In fracture appearance trans. temper-

hanically formed notches with finite curvature. ature. In the foregoing, it Is tacitly assumed

racture toughness obtained experimentally with that the absolute magnitude of notch radius rath-

he help of cracks will be designated Gco. if er than the ratio of the radius to a characteris-

he specimens are equipped with very small radii, tic linear dimension defines the effect on the

.g., 0.001 or possibly even 0.003 in., the ex- notch strength.

erimentally obtained fracture toughness may be It is obvious from FPg.9 that in order to

ufficiently close to Gco to serve, for all prac- obtain a dependable value for 0CO, I.e., to de-

ical purposes, as a substitute. This appears fine a straight line, It Is advisable to extend

o be the case in Fig.9, 0e - 90 in-lb per sq In. the size range far enough to obtain at least two

nd in Fig.10, for the high acuity series, Gc = points which are below the yield strength SY.

15 in-lb per sq in. Although both values may It is also apparent that for small values of Gco,

e considered as practical substitutes for Gco, e.g., 0 cl, any straight line with tgCC = - 0.5

ne was obtained from tension experiments and passing through points like bl, a,, or d1 will

he other from bend tests. However, the values result in an acceptable lower bound for Gcl"ere obtained for the same material A at room However, this i• not true for large values of

emperature, and it appears that this difference Gco, e.g. for Gc3- In this case a straight linef 28 per cent is somewhat large to be accounted through point b3 may not be acceptable, but a

or by scatter. Only additional tests with straight line through pc tnt c3 may be satisfac-

atural cracks may help to dissolve the discrep- tory as a lower bound fc- GO.

ncy.

Table 7 of (14) summarizes disk bursting Summary

ests performed on the same material A. Disk The formulas and the necessary curves for

o. 8 was described as sound (no cracks) and it the calculation of strain-energy release rate

11

fo:" sharply notched beams with 3 and 4-point of Gco will influence the choice of radii. Itloading and variable notch depth were summarized was mentioned that in order to obtain a depend-in Fig.2. Curves and formulas which permit cal- able value for Gco, i.e., in order to define aculation of strain-energy release rate for a straight line, it is advisable to extend thesharply notched cylindrical notched bar in ten- range of specimens into larger sizes, to obtainsion were summarized In Pigs.3 and 4. It is at least two points with fracture stresses belowshown in Fig.5 that a log-log co-ordinate system the yield strength.is especially useful to represent the foregoing It is hoped that the interpretative analy-relation, because the so-called "geometric size sis of material behavior presented in this papereffect," Is represented by a straight line with will contribute to a better understanding of thea slope of - 1/2, somewhat cloudy geometric size effect in the

It appeared that the change of notch presence of notches, and that it will stimulatestrength was more or less gradual from the high- additional experiments to illuminate some of theer values for small specimens to substantially less understood phenomena.smaller values for large specimens. This led togeneralization of strength response to sharp Acknowledgmentsnotches and resulted in the introduction of the The author wishes to extend his appreciationconcept of continuous material behavior as repre- to Messrs. H.P. Bueckner, B.O. Buckiland, R.sented by the notch-strength-versus-size curves Salamoto and D.H. Winne, associates in the Gen-shown in Figs.6 and 7. The somewhat arbitrary eral Electric Company Turbine Division, for theirclassification into ductile, quasi-ductile, aid in forming the new concepts. Especially, thequasi-brittle and brittle material behavior on author desires to thank Dr. S. Yukawa for histhe basis of notch-strength relationship to ten- assistance with available data and for his help-sile and 7ield strength was proposed. It was ful discussions. In addition, the author wouldpointed out that in addition to specimen geome- like to thank Dr. G. R. Irwin, Superintendent oftry and crack depth, the recently recognized and Mechanics Division of the Naval Research Labora-important material property "fracture toughness" tory, Washington, D.C. for his valuable advice.is necessary in order to be able to establishnotch-strength behavior In terms of size. A Referencesconsequential, but not very obvious, conclusion 1 "Application of the Griffith-Irwin Theorywas Intferred, that theoretically, irrespective of Crack Propagation to the Bursting Behavior ofof the fracture toughness, sharply notched speci- Disks, Including Analytical and Experimentalmens are expected to exhibit quasi-brittle and Studies," by D.H. Winne and B.M. Wundt, Trans.even brittle behavior, if the size is increased ASKE, vol. 80, 1958, pp. 1643-1658. Containssufficiently, Fig.7. references pertaining to brittle fracture.

Two informative, experimentally obtained, 2 "Size Effects in Slow Notch-Bend Testsroom-temperature, notch-strength-versus-size of Ni-Mo-V Steel," by J.D. Lubahn and S. Yukawa.curves, were plotted in Pigs.9 and 10 -- for cyl- Preprint no. 79, 1958, American Society for Test-indrical notch-tension bars and for notched beams. ing Materials, presented at the AS3T Annual Meet-In FIg.ll(a) the notch strength of cylindrical ing, Boston, Mass., June 1958.bars was plotted for different outer diameters 3 "Size Effects in Slow Notched Bend Testsas a function of notch depth for a constant G., of Arizona Rotor Steel," by J.D. Lubahn and S.and In PIg.ll(b) the notch strength is plotted Yukawa, General Electric Company Data Folder,for a constant outer diameter and for variable October 21, 1955.Oc. The two plots indicate a remarkable contin- 4 "Experimental Determination of Energy Re-uity of notch strength behavior with varying lease Rate for Notch Bending and Notch Tension,size and varying notch depth. and Applications to Fracturing," by J.D. Lubahn,

As a result of available evidence, it ap- to be Published by ASTM, General Electric Companypeared logical to introduce Gco, fracture tough- Data Folder, October 22, 1958.

ness obtainable for a series of test specimens 5 "Effect of Section Size on Fracturing,"with natural cracks. It was indicated that a by J.D. Lubahn, in "Strength Limitations ofshift to lower values of GC occurs when the notch Metals," pages 143 to 161. Proceedings of theradii are decreased. It was emphasized that in 1955 Sagamore Research Conference, August 24-26,order to obtain experimentally a satisfactory es- 1955, Syracuse University Research Institute.timate of Geo, notches with the smallest possible 6 "Low-Temperature Brittle Fracture," byradii must be used. It seems that not only the J.D. Lubahn. Chapter from the new edition ofspecimen dimension, but also the expected values the ASME Handbook "Metals Engineering - Design."

12

General Electric Company Data Folder, September Strength Stecls," by E.P. Klier, B.B. Muvdi,11, 1958. G. Sachs, Proceedings American Society for Test-

7 "Correlation of Tests Using the Congruen- Ing Materials, vol. 57, 1957, pp. 715-730; Con-

cy Principle," by J.D. Lubahn, presented at the tains references to other papers.

American Society for Testing Materials Annual .17 "Embrittlement of High-Strength Steels,"

Meeting, June 1958, Boston, Mass., General Elec- by E.P. Klier, in "High Strength Steels for Air-

tric Company Report, March 1958. craft," pp. 53-67. Compilatiorn of papers pre-

8 "The Conditions for Unstable Rupturing sented at the Southwestern Metal Congress, May

of a Wide Plate," by G.M. Boyd, Read in London 12-16, 1958, American Society for Metals.

at the Spring Meeting of the Institution of Naval 18 "Survey of Low-Alloy Aircraft Steels

Architects, on March 28, 1957, pp.349 to 366. Heat Treated to High-Strength Levels," "Pdrt 5-9 "Study of Fast Fracture of Centrally Mechanical Properties in the Presence of Stress

Notched Sheet Specimens with Particular Reference Concentrations," by G. Sachs, EP. Klier, Syra-

to Aluminum Alloys L72 and L73," by A.A. cuse University. WADC Tech. Report 53-254 Pt. 5.

Golestaneh, issued by the Technical Information 19 "Factors Responsible for Notch Embrittle-

and Library Services, Ministry of Supply, Decem- ment of High-Strength Steels," by V. Weiss and

ber 1957; issued in USA by NASA, No. N58034. E.P. Klier, final report no. 2, December 1955,10 "Fracture Strengths Relative to Onset Syracuse University Research Institute.

and Arrest of Crack Propagation," by G.R. Irwin, 20 "Notch-Tension Testing," by N.J. Ripling,J.A. Kies and H.L. Smith, U.S. Naval Research in "Materials Evaluation in Relation to ComponentLaboratory, presented at the American Society Behavior," pp. 207-233, Proceedings of the Thirdfor Testing Materials Annual Meeting, June 1958, Sagamore Ordnance Materials Research Conference,

Boston, Mass; also Naval Research Lab Report December 5, 6, 7, 1956, Syracuse University Re-

5222, November 1958, same title as above, search Institute.

11 "Fracture Mechanics," by G.R. Irwin, 21 "Bend-Tensile Relationships for Tool

U.S. Naval Research Laboratory, presented at the Steels at High Strength Levels," by J.C. Namaker,

"First Symposium on Naval Structural Mechanics," Jr., V.C. Strang, G.A. Roberts, Trans. American

August 1958, Stanford University, Stanford, Calif. Society for Metals, vol. 49, 1957, PP. 550-575.12 "The Stress Concentration of a Notched 22 "Relation Between Direct-Stress and Bend-

Bar in Bending," by H.F. Bueckner, Large Steam ing Fatigue of High-Strength Steels," by G. Sachs

Turbine-Generator Department, General Electric and G. Scheven, Proceedings American Society for

Company Data Folder, June 28, 1957. Testing Materials, vol. 57, 1957, pp. 667-681.

"*On the 3-Point Bar Bending Test," by 23 "Ductile Fracture Instability in Shear,"

H.F. Bueckler, Large Steam Turbine-Generator De- by F.A. McClintock, presented at the Annual Meet-

partment, General Electric Company Data Folder, ing of the American Society of Mechanical Engi-

June 14, 1957. neers, December 1958, Paper No. 58-A-12.13 "The Strain Energy Release Rate for a 24 "Resistance to Fracture and Strength of

Circular Notched Bar in Tension," by H.A. Metals," by G.V. Uzhik, Russian Book, chapt. 4,

Bueckner, Large Steam Turbine-Generator Depart- 5, 6, 16. Soprotivlenye Otryvu I Prochnost

ment, General Electric Company; to be published. Metallov, Akad. Nauk SSSR, 1950.

14 "Report of the Investigation of Two Gen- 25 "Symposium on Effect of Temperature on

erator Rotor Fractures," by C. Schabtach, E.L. the Brittle Behavior of Metals with Particular

Fogleman, A.W. Rankin and D.H. Winne, Trans. . Reference to Low Temperatures," American SocietyASME, vol. 78, 1956, PP. 1567-1584. for Testing Materials, STP no. 158, 1954.

15 "The Effects of Notches of Varying Depth 26 "Modified Navy Tear Test for Measuring

on the Strength of Heat Treated Low-Alloy Steeis" the Work of Fracture Propagation in Ductile

by G. Sachs, J.D. Lubahn and L.J. Ebert, includes Metals," by H.E. Romine, Welding Research Supple-

discussion by D.J. McAdam, Transactions of the ment, August 1955, PP. 396S to 408S.American Society for Metals, vol. 34, 1945, PP. 27 "The Crack-Extension-Force for a Crack at517 to 544. a Free Surface Boundary," by G.R. Irwin, Naval

16 "The Static Properties of Several High- Research Laboratory Report 5120, April 15, 1958.

13