partdbn

ð

ð

The background fracture studies leading up to Fractal fracture discovery

PARTICLE SIZE DISTRIBUTIONS AND INTERPARTICLE SPACINGS IN 2.XX

DIMENSIONAL SPACE

INCLUSIONS ARE A REALITY! !

Results were used to improve welding practice

(in general) and to develop the welding practice

used on the atomic submarines

iocqCA)w~ n IS pn.JlLr?-.15?~"'DS-~'~ 12/pf8J

II 0.52 0.47 0.37

42 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSESPASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 43

this is not the case when considering a particle sampled from the volume. Tables5 and 6 show a comparison between planar, corrected volume, and fracturesurface measurements. The agreement is not perfect although the corrections dotend to correct the planar measurements in the direction of the fracture surfacemeasurements.

TABLE 5-Comparisons between two-dimensional mean diameters, correctedthree-dimensional mean diameters [6], and fracture surface mean diameters.

and fracture surfaces for the three different cases. The plots are shown ascumulative log normal probability plots. In all cases investigated in this study,the frequency distributions were skewed, asymmetric, and yielded the best linearplots when the cumulative frequency distribution was plotted on log normalprobability paper. It is felt that the distributions are, therefore, all log normaland will be considered as such in the following discussions. Table 4 shows a

TABLE 4-Summary of particle size distribution statistics obtained from extraction replicas.Specimen

II 0.17 0.15 0.20

A. Electropolished -PlanarSpecimen XA1 (µm) XG1 (µm) UA1 (µm) 1n2 uG1

0.64 0.58 0.28 0.20

II 0.52 0.50 0.17 0.11

III 0.38 0.36 0.12 0.11

B. Fracture Surfaces-Room Temperature

XAF (µm) X"GF (µm) uAF (µm) 1n2 uGF

0.53 0.47 0.27 0.26

II 0.37 0.32 0.20 0.29

III 0.36 0.32 0.18 0.23

0.64 0.53 0.53

III 0.38 0.34 0.36

TABLE 6-Comparisons between two-dimensional arithmetic standard deviation,corrected three-dimensional arithmetic standard deviation,

and fracture surface arithmetic mean diameter.

Specimen

0.28 0.24 0.27

III 0.12 0.11 0.18

~It is felt that only fair agreement between the corrected values and measured

values is obtained due to the fact that the probability of observing a particle on afracture surface depends upon the mechanism of particle-nucleated voidformation. Both particle fracture and interface decohesion occur during the voidnucleation step. Thus, the probability of observing a particle on a fracturesurface most likely depends upon both the diameter and the surface area of theparticle.

summary of the statistical data obtained for all the distributions which werestudied. The arithmetic mean and the arithmetic standard deviation werecomputed in the standard manner from the dat~. The geometric mean andstandard deviation were calculated from 3 ~

Discussion

In2uG = (::) 2

InXG = InXA -0.5 In2 uG (5)

In each case it was found that the arithmetic mean diameter of the particlefound on a fracture surface was smaller than that found on a planar surface. Asdiscussed by Ashby and Ebling [6], the diameter of a particle as measured on asurface extraction replica is not the same as the true mean diameter of theparticle for the volume. The difference arises from the fact that probability ofintersecting a particle in a planar section is proportional to its diameter whereas

(4)

Spatial Distribution and Dimple Size

The combined set of measurements (that is, determination of spatialrandomness of the nearest-neighbor interparticle spacing distribution andmeasurement of the mean linear dimple intercept size) constitutes a method by

3 Ashby and Ebling's [6] nomenclature is used here.

D. E. Passoja! and D. CHill!

Comparison of Inclusion Distributionson Fractu re Su rfaces and in the Bu Ikof Carbon-Manganese Weldments

REFERENCE: Passoja, D. E. and Hill, D. C., "Comparison of Inclusion Distributionson Fracture Surfaces and in the Bulk of Carbon-Manganese Weldments," Fractog-

raphy-Microscopic Cracking Processes, ASTM STP 600, American Society forTesting and Materials, 1976, pp. 30--46.

ABSTRACf: Techniques are developed for determining the spatial and sizedistributions of spherical inclusions in mild steel. The relations between thesedistributions as found on electropolished surfaces and as found on fracture surfacesare determined. It is shown that the first neighbor spatial distributions onelectropolished surfaces can be described analytically. The average dimple size on afracture surface is always greater than the most probable first neighbor spacing. Theinclusion size distributions both on electropolished and fracture surfaces are shownto be log-normal. The mean inclusion size on a fracture surface is always smaller thanthat on an electropolished surface. These variations are believed to arise from thenature of the fracture process.

KEY WORDS: fractography, inclusions, crack propagation, fractures (materials),fracture properties, carbon steels, geometric surfaces, weld metal, weldments, particlesize distribution, particle density (concentration)

Nomenclature

tv Volume fraction of inclusionsn Number of eventsr First neighbor separationr* Most probable first neighbor separationr Average first neighbor separationXA

Arithmetic meanXG Geometric mean!AI Arithmetic one-dimensional mean (after Ashby and Ebling [6])!A2 Arithmetic two-dimensional mean (after Ashby and Ebling)!AF Arithmetic fracture surface meanXGF Geometric fracture surface meanD Dimple size (equal to 1.5 [)Ds Average particle spacing (after Kocks [8])K1c

Fracture toughness

I Research scientist, Central Scientific Laboratory, and research supervisor, LindeResearch Department, respectively, Union Carbide Corporation, Tarrytown, N. Y. 10591.

30

PASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 31

LNs

Pen)

Per)

µaaAIaA2aAFaGF

Mean linear intercept dimple sizeAverage planar inclusion densityProbability as a function of nProbability as a function of rNumber of elements in system-average number ofStandard deviationArithmetic one-dimensional standard deviationArithmetic two-dimensional standard deviationArithmetic standard deviation on fracture surfaceGeometric standard deviation on fracture surface

There is considerable evidence to indicate that the fracture toughness ofmetals is related in some Why to a characteristic feature of the microstructure.The feature is thought to be related fundamentally to the fracture process itself,that is, to play a determinant role in the progression of the fracture.Considerations of the physical characteristics of the microstructure usuallyprecede the development of a more specific fracture model and use of such amodel to explain fracture behavior in any system.Several investigators have recognized salient microstructural features and have

related them to fracture toughness. Using Krafft's [1] 2 tensile ligamentinstability theory, Birkle, Wei, and Pellisier [2] measured the spacing betweensulfide particles on extraction replicas and were able to relate the fracturetoughness to the spacing between the particles. Hahn and Rosenfield [3]considered several factors which influenced the toughness of aluminum alloyswhich included:I. the extent of the heavily strained region in front of the crack tip,2. the size of the strained ligaments-which was related to the volume fractionof cracked particles, and

3. the work required to rupture the ligaments.They furthermore recognized that both the size, distribution, and particle typeinfluenced the fracture process. By plotting K

1cversus tv -! /6 ifv being the

volume fraction of cracked particles), the authors were able to developconvincing arguments that fracture toughness in several different material.s couldbe related to inclusions. In his work on high strength steels, Yoder [4] found asomewhat coarser spacing on fracture surfaces which correlated with fracturetoughness. Furthermore, fractographs published in his work clearly indicate thatthe spacing which correlated was considerably larger than the dimple size.In order to determine more definitively the relationship between features

found on fracture surfaces, and those of the microstructure, and to quantify theexistence and nature of such differences, we performed experiments to comparethe features of fracture surfaces with those of plane-polished surfaces in threeferrous materials. In light of the findings just ;eferenced, we chose to use a

2 The italic· numbers in brackets refer to the list of references appended to this paper.

\

46 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSES

The second moment can be written as

(II)

So that

(I2)

References

[1][2]

[3]

Krafft, J. M.,Applied Materials Research, VoL 3, 1964, p. 88.Birkle, A. J., Wei, R. P., and Pellissier, G. E., Transactions, American Society for

Metals, VoL 59, 1966, p. 98L

Hahn, G. T. and Rosenfield, A. R., 5th Spring Meeting of the Metallurgical Society

of the American Institute of Mining, Metallurgical, and Petroleum Engineer's, 29

May to 1 June 1973.

Yoder, G. R., Metallurgical Transactions, Vol. 3, 1972, p. 185 LHill, D. C. and Passoja, D. E., Welding Journal, VoL 53, 1974, p. 481-s.Ashby, M. F. and Ebeling, R., Transactions, Metallurgical Society of the American

Institute of Mining, Metallurgical, and Petroleum Engineers, VoL 236, 1966, p.

l396.

Hilliard, J. E., Metal Progress, Vol. 85, 1964, p. 99.Kocks, U. F., Philosophical Magazine, VoL 13, 1966, p. 541.

[4]

[5J[6]

[7][8]

(

(V)M

I./)

Zoi=:::)coa:l-I./)

ozoI./)

:::)...JUZ

Zo...J...J

Ioz<!<!-,oI./)I./)

<!(L

I./)

WI./)I./)

WUoa:(L

oz~u<!a:uu(L

ouI./)

oa:u:2:I>-I(L

<!a:ooI-U<!a:u.

NM

'"'" ;::l< 0II 2'" '.0~ 8

'"SN0"'Won.§'-Q)

:>cou>,co

34 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSES

•

0{]

0

0

0 •0 ~'" ". '"

:;: Sl ~". .., .:.-~

H

~-t!

'" ~ ~ '" '" '" ~ Sl ~". .., "'. '"~~


'.

A

>-• <" ...• . . ,

. .:

. .' ..

I'. ..

"....

•

.M<,"

GA. •

.~ .. .,.

. "'. •. ",

.t

~.

•. ..

.. . .~.

, ..•

.- ..

BFIG. 2-111ustrative example of concentric circle measuring technique. (A) shows a tracing

of the unetched, polished metallographic section shown in (B). Five concentric circles are

shown superimposed on a particle marked as A on the micrograph. The magnitude of the

vector R is shown in (A); original magnification, x]OOO.

Appendix II. The agreement between the computed values and measured valuesis fairly good considering that only 200 distances were measured on each sample.It is important to note, however, that the computed curve shape is similar to themeasured values in each case, and that the trends (that is, decreasing values) arethe same for both the computed and measured values. It would appear thediscrepancies between the computed and measured values arise from either a loss

PASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 37 36 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSES

.0.1

;Comparison of Computed

and

Measured lnferpor lie Ie

r--Distribution Spac i n 9 s

) illr-- Opticol- EJectropolished

-r-!!...• •;

'--

• •) •

•; • r- •i-- Il· .

.0.2.0

r .ojI

PI,'

C.'

Comparison of Computed

r- and

Measured interparticle

5Distribution Spacings

I-- I• • Optical Electropolished• •1--....-.0 fT - •

..... ~.; • --, -•• ~

IT • • .Ial_ .. - - .d

1..0 2.0 3.0 4.0

r(lIm) ..

5..0 6.0 7..0 B.C

.0.25

0.21 rPltl

1..0 2.0 3[)

r(pm) - )'

4..0 S.C 6[) 7..0 B.C

.0.05

.0..0

FIG. 3-Frequency distribution for planar first nearest-neighbor interparticle spacing, Steel 1.

t

Comparison of Computed

andr---- Measured Interparticle

Distribution Spacing, IT..- • ITr.- Optical - Electropalished

I-a-'---) • •...

•it-- •• •~.I •

0.20

G_ 5-Frequency distribution for planar first nearest-neighbor interparticle spacing, Steel

measured_ It is well known that, during ductile fracture, voids usuallyleate on inclusions, grow, and link-up to form the fracture surface_lsurements of the dimple size should, therefore, be related to the interparticle~ing, in some manner, but should be complicated by the fracture surfacemetry_ We attempted to demonstrate this in the following manner.tereo photomicrographs were taken randomly from ten different areas onldard Charpy specimens fractured at room temperature_ In each instance, aIpled fracture surface was present. three lO-cm circles were located on each"eomicrograph pair. When viewed in the stereo viewer the circles merged andy three circles appeared to be located over the fracture surface. Thersections between the circles and the dimples were marked off and the[section rules outlined by Hillard [7] for measuring grain sizes were followedlustrated in Fig. 6. Table 2 shows a summary of the measured values ..s in the nearest-neighbor planar interparticle measurements, Table 1, theIds exhibited in Table 2 are similar, but in every case the mean-linear-dimplercept size is greater than the nearest-neighbor planar interparticle spacing.differences between the measured distances can be explained in the

owing manner: dimples are created during the void link-up stage upon finallration of the fracture surface. The fracture surface is created as a result ofI nucleation and growth in a volume of material near the crack tip. For thison the spacings between the dimple forming voids do not necessarily'espond to the most probable value of a single nearest-neighbor interparticle;ing, but rather it depends upon a number of factors such as the local stress

0.15

P(r)

0.1

0.0

1.0 2.0 ~O 4~

r0m) •11.0 6.0 7.0 8.0

FIG. 4-Frequency distribution for planar first nearest-neighbor interparticle spacing, SteelII.

of particles during the extraction step or arise from counting only 200 (a limitednumber of) nearest neighbor distances with the concentric circle method.

Dimple Size Measurements

In order to compare the planar nearest-neighbor interparticle spacing withsome meaningful fracture surface feature, the mean linear dimple intercept size


"0<J)

'; I ~ ": «:0-

E0

~IU

~0

"0

~

I<J).... I ~i5l q ~'t;'" N

'" <J)>:>. ~<00

~.l:"-'">:>."-~ "0,S <J)

"- '; I ~ M "!0 0- M"'" EM N

..::::0

,~ ~ U"2 E<00 ~~ 1"-%l "0~ <J)

" ::; I 0\ .-. '<:t..:::: '" N N.... '"<J)"- ~,0.....,<00

".2!'""'1:l

" "0"- <J)::; ';<00 I ~ '"' q%l 0-

E EN N N

'1:l0~ U~

~'"'1:l~ "::; "->:>. "0

E "....0 i5l I N 0 "!" '" N N~ <J)

" ~"

'--- I t""'"~0

FIG. 6-( A) shows polished, etched section of the typical microstructure observed in ,'="

'""-'" ,~teels I through III; original magnification, xl 000. (B) shows one photo of a stereo pair >:>.

'0..'ith two circles used to measure the dimple size, Intersections between the dimples and the E ....... " '" '" t"-

O '" J::t::0 0 0

I ,..., ,..., ,...,'rcles are marked on the micrograph; original magnification, x3250, I E <:: x x x,..., u 0~ ~ N '"' 00

w u 0\,..., ,...,

....l <: ;'! .,., r..:

Ild the particle size distribution. Dimples are thus some irregular shape, such as I a:l ;;:<Cf-< :.:.J

11 n sided polygon, when viewed as a planar projection in the SEM.

Kocks [8] has shown that in some instances the average distance between a

article and its two or three neighbors is more a meaningful distance than thec

earest-neighbor distance. This distance can be calculated by <J)

E'u I - = -D = 1 18 N -1/2 <J)

(3) 0-s . s u:>

40 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSESPASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 41

TABLE 2-Summary of mean linear dimple intercept measurements.

7-Comparison of log normal cumulative probability plot of particle diameters fornd fracture surface for Steels f through fl!.

InclU$lon [)oomeler

Cl.rnulolive Probob,hly

I([>lrocllonRephcosJ

,.,..,.6

.,

•••• O~ 0

• 0• 0

• 0

• 0eEleclropOI,shed

o• DRoam Temperoture

Chorpy

Cumulohve ProbabIlIty

'~r'------------------------,.,6, Inclusion Dio'7'lller

Cumulative PrObability

IT

(E.'roction Replicas)

,.,.8.'.6

• C• 0

• 0• 0o

o

o

o eElecl'opollshod

o Room Temperalur,

Chorpy

.I' 0 I0.01 10 20 JC) 40 50 60 10 00 90 95 99 999

Cumuloli". Probablhty

Cumuklilve Probablhty

m(hlroct_Repllcas)

! '(5.9

~~~, 6

~ 5

,...

:JAoom Tlln'lpe.olureCho'P)'

.11 ' , I

01.1 10 20 30 405060 70 80 90 95 99 ~99

C.."....,lal,ve ProbabIliTy

L(µm)Specimen a(µm)

3.3 0.65

2.6II 0.48

2.5III 0.19

Table 3 shows a comparison between measured D (equal to 1.5 L) and Ds ascalculated by Kocks equation. Thus, it can be seen that the number of nearest

neighbors is important when considering the mean linear intercept dimple size

measurement. There is only fair agreement between Ds and the measured values

due to a number of contributory factors such as:

I. the statistical scatter due to the topographical features (non-planarity),

2. the physical aspects of the fracture process resulting in a physically

meaningful standard deviation, and

3. local differences in the number of nearest neighbors-the most common

number projected in a plane appears to be five.

TABLE 3-Comparisons between measured dimple sizes and computed spacings .

Specimen D (µm)

4.95.0

3.9 4.4II

III 3.7 3.4

Particle Size Distribution

Direct carbon extraction replicas were made of fracture surfaces and

electropolished surfaces taken ~0.5 cm away and parallel td' the fracture surfase.

One thousand particles which could uniquely be associated with dimples were

measured on the fracture surface replicas from each specimen. One thousand

particles were measured on the planar cut and electropolished surfaces from each

specimen. Mechanical polishing was tried, but gave inconsistent results with too

few particles and unreaJistically large mean sizes. Following Ashby and Ebling's

[6] particle extraction efficiency arguments, our assumptions were that the

particle extraction efficienoy was not 100 percent but there was equal

probability of extracting a particle over the entire size range (that is, particle

extraction was not selective).

Figure 7 shows cumulative probability plots of particles extracted from planar


(7)

(8)

which planar surface features can be compared in a meaningful manner with

fracture surface features. Successful application of these methods to our

problem required that two criteria be met.

1. The fracture mode must be related to particle nucleated microvoids.

2. The center-to-center spatial distribution must be random. (This can be and

was checked by means of the Poisson test.)

Differences between planar surface features and fracture surface features can

best be understood by considering the topographical differences which exist

between a fracture surface and a planar surface. The mean linear dimple

intercept, for example, is larger than the most probable planar nearest-neighbor

interparticle spacing due to the fact that voids grow around inclusions and link

up in a volume of material in front of the crack tip. A single planar,

nearest-neighbor interparticle spacing, therefore, does not describe the dimple

formation process since the volume distribution of nearest neighbors is a more

relevant description of the fracture process. For this reason Kocks' correction

appears to bring agreement between planar and fracture surface features.

~PPENDIX I

¥eldment Preparation

Three weldments were made in ASIS baseplate using an E70S-3 electrode4

by

he GMA process according to American Welding Society Standard AS. 18-69.

\.11 welding was done in the flat position using automatic equipment. The

IOminal welding conditions were: current, 200 A; voltage, 27 V; and travel

peed, 30 em/min. The shielding gas composition was varied to provide different

)xidizing potentials and different levels of inclusions in the weldments. The

.hielding gases used and weld identifications are: CO2, I; Ar-25% CO2, II; and

\r-2% O2, III. Weld compositions are given in Table 7.

TABLE 7 - Weldmetal compositions.

ield Designation c Mn Si o

0.08 0.45 0.12 0.099

II 0.09 0.78 0.32 0.044

III 0.08 1.00 0.46 0.042 Particle Size Distributions

Inclusions which are present in the bulk are the same set of inclusions which

cooperatively participate in fracture and form the fracture surface. The

differences which are observed between inclusion sizes found on a planar surface

and on a fracture surface are believed to result both from the geometrical

differences involved in planar versus volume sampling and from the fracture

process.

\.PPENDIX IIipatial Distribution Function

Equation 2a represents the incremental number of inclusions surrounding a

ingle inclusion in a thin strip of width /::;.r:

/::;.Ns= rrrNs exp (-r2 Ns) /::;.r (6)

lhe exponential term represents the probability that the distance between any

wo inclusions lies between rand r + /::;.r. The distribution can be normalized by

:hanging Eq 6 into a continuous distribution, equating the integrand to I, and

olving for the normalization constant, k:

Conclusions

I = kJ~rrNs r exp (- Nsr2) dr

k= ~rr

Techniques have been developed for quantifying and comparing both the

spatial and size distributions of inclusions on fracture surfaces and in the bulk. A

nearest-neighbor interparticle spacing distribution function of the form

(2b)

4 All terms in this section refer to the American Welding Society designations.

apparently describes a random planar spatial distribution of particles for the

three ferrous materials used in this study.

A correction must be made for two or more nearest neighbors in order to

bring agreement between dimple size measurements performed on a fracture

surface and particle density measurements performed on planar surfaces.

Particle size measurements indicate that the particle sizes are log normally

distributed both on planar surfaces and fracture surfaces. Differences between

the two distributions can be rationalized by considering the details of the

particle sampling process during fracture.

,0 that¢ (r) = 2Ns r exp (-Nsr2) (9)

~quation 9 is the continuous distribution function from which various moments

)f r can be calculated. For instance, the average value of r is'----

r=.r: r¢(r)dr= 1/2 J 1T (10)Ns

I = kJ~ 7TNs r exp (- Nsr2) dr

k = .27T

(7)

(8)


APPENDIX IWeldment Preparation

Three weldments were made in AS IS baseplate using an E70S-3 electrode4

by

the GMA process according to American Welding Society Standard AS. 18-69.

All welding was done in the flat position using automatic equipment. The

nominal welding conditions were: current, 200 A; voltage, 27 V; and travel

speed, 30 cm/min. The shielding gas composition was varied to provide different

oxidizing potentials and different levels of inclusions in the weldments. The

shielding gases used and weld identifications are: CO2, I; Ar-2S% CO2, II; and

Ar-2% O2, III. Weld compositions are given in Table 7.

TABLE 7-Weldmetal compositions.

Weld Designation c Mn Si o

0.08 0.45 0.12 0.099

II 0.09 0.78 0.32 0.044

III 0.08 1.00 0.46 0.042

APPENDIX IISpatial Distribution Function

Equation 2a represents the incremental number of inclusions surrounding a

single inclusion in a thin strip of width I::lr:

I::lNS=7TrNS exp (-r2 Ns)l::lr (6)

The exponential term represents the probability that the distance between any

two inclusions lies between rand r + I::lr. The distribution can be normalized by

changing Eq 6 into a continuous distribution, equating the integrand to I, and

solving for the normalization constant, k:

So that

¢(r)=2Nsrexp(-Nsr2) (9)

Equation 9 is the continuous distribution function from which various moments

of r can be calculated. For instance, the average value of r is

(l0)

4 All terms in this section refer to the American Welding Society designations.

partdbn

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