Astm stp 1085 1990

In this publication, which is based upon that symposium, an overview of recent developments in quantitative fractography and computed tomography in composites is presented by Antolovic

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Library of Congress Cataloging-in-Publication Data

Quantitative methods in fractography/Bernard M Strauss and Susil K

Putatunda, editors

(STP 1085)

Papers presented at a symposium held 10 Nov 1988 in Atlanta,

Ga., sponsored by ASTM Committees E-9 on Fatigue and E-24 on

Fracture Testing

Includes bibliographical references

"ASTM publication code number (PCN) 04-010850-30" T.p verso

ISBN 0-8031-1387-0

1 Fractography Congresses I Strauss, Bernard M., 1946-

II Putatunda, Susil K., 1948- III ASTM Committee E-9 on

Fatigue IV ASTM Committee E-24 on Fracture Testing

NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication

Peer Review Policy

Each paper published in this volume was evaluated by three peer reviewers The authors addressed all of the reviewers' comments to the satisfaction of both'the technical editor(s) and the ASTM Committee on Publications

The quality of the papers in this publication reflects not only the obvious efforts of the authors and the technical editor(s), but also the work of these peer reviewers The ASTM Committee on Publications acknowledges with appreciation their dedication and contribution

of time and effort on behalf of ASTM

Printed in Battimore MD June 1990

Downloaded/printed by

University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized

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Analysis and Interpretation of Aircraft Component Defects Using Quantitative

Fractographic and Metallographic Study of the Initiation of Brittle Fracture in

Weldments P L HARRISON, D J ABSON, A R JONES, AND D J SPARKES

Cracking Mechanisms for Mean Stress/Strain Low-Cycle Multiaxial Fatigue

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Overview

The past two decades have seen the development of fractography of materials from a research tool to an important everyday component of failure analysis and materials characterization The vast body of work in this area has led to volumes of photographs describing fractographic features in general qualitative terms It also has presented researchers with a foundation of evidence that quantitative assignment of selected parameters can relate specific fractographic features to material properties

On 10 Nov 1988, a one-day symposium, sponsored by ASTM Committees E-9 on Fatigue and E-24 on Fracture Testing, was held in Atlanta, Georgia, covering the latest developments and discoveries in both methodology and interpretation of quantitative fractographic methods It sought to provide a benchmark of progress in this science as we enter the 1990s

In this publication, which is based upon that symposium, an overview of recent developments in quantitative fractography and computed tomography in composites is presented

by Antolovich, Gokhale, and Bathias, while Harvey and Jolles relate fractographic features

in HY-100 steel and 2024 aluminum to the critical strain energy density

Alexander has attempted to relate fracture surfaces to mechanical properties by means

of fractals and has found that, while fracture surface profiles are fractal, there does not seem to be a clear correlation between the fractal dimension and the mechanical properties

or the microstructures

Goldsmith and Clark present a discussion of the successful analysis of aircraft components

by means of quantitative techniques that have been employed at the Aeronautical Research Laboratory in Melbourne, Australia, for the past 15 years

Quantitative analysis of specific fracture processes is then discussed in the remaining five papers, which are the following: Ohtsuka and Yamamoto on hydrogen-assisted cracking;

Zhang, Kumar, Armstrong, and Irwin on cleavage; Harrison, Abson, Jones, and Sparkes

on brittle fracture in steel weldments; Kurath and Fatemi on low-cycle fatigue in steel and Inconel 718; and Wanhill and Schra on corrosion fatigue crack arrest in aluminum alloys These works demonstrate the value of applying quantitative methods to fractographic features and utilizing this information in predicting material behavior The examples presented here by these authors further the understanding of fracture processes in polycrystaline materials and provide a sound basis for further studies

Bernard M Strauss

Teledyne Engineering Services, Waltham, MA 02254-9195; symposium cochairman and editor

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Stephen D Antolovich, 1 A r u n M Gokhale, 1 and Claude Bathias 2

Applications of Quantitative Fractography and Computed Tomography to Fracture

Processes in Materials

REFERENCE: Antolovich, S D., Gokhale, A M., and Bathias, C., "Applications of Quan-

titative Fractography and Computed Tomography to Fracture Processes in Materials," Quan-

American Society for Testing and Materials, Philadelphia, 1990, pp 3-25

ABSTRACT: An overview of recent developments in quantitative fractography (QF) and computed tomography (CT) is presented with emphasis on applications of these tools to failure analysis and the identification of fundamental fracture processes QF yields information concerning the geometric attributes of the microstructural features on the fracture surface and quantitative descriptors of the fracture surface geometry By way of example, this methodology

is applied to the case of a composite fabricated [rom an AI/Li matrix and alumina (A1203) fibers to delineate those defects which play the most important role in the fracture process The internal damage state of a material can be studied by CT; such information is not accessible through conventional fractographic approaches CT results for damage detection are given for graphite/epoxy and metal-matrix composites New applications of CT to address important unanswered questions in the fracture field are suggested

Integration of QF, stereology, and CT has the potential to evolve into a very powerful method for the study of failure processes in all classes of materials

KEY WORDS: quantitative fractography, stereology, computed tomography, fracture, crack propagation, fractography

The end point of deformation and fracture processes is the generation of fracture surface The geometry of the fracture surface and the associated microstructural features contain information concerning the processes that lead to fracture, in a subtle and complex manner The necessary first step for unraveling this puzzle is quantitative characterization of the fracture surface geometry; this is the basic aim of quantitative fractography There have been significant advances in the theoretical and experimental aspects of quantitative fractography during the past decade It is the purpose of this paper to present an overview of these developments and to point out practical applications of the results The field of stereology will be reviewed as it relates to quantitative fractography, and the developing science of computed tomography, in which the internal defect state can be analyzed, will also be discussed and related to practical problems of current interest

Director and professor, and associate professor of materials engineering, respectively, Mechanical Properties Research Laboratory, School of Materials Engineering, Georgia Tech, Atlanta, GA 30332-

0245

2 Professor of materials science, Conservatoire Nationale des Arts et Metiers 75141 Paris, France

Copyright 9 1990 by ASTM lntcrnational

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Quantitative Fractography

Definition and Applications

Quantitative fractography is concerned with the geometrical characteristics of microstruc-

tural features on the fracture surface such as numbers per unit area, sizes, area fractions,

and so forth It is also concerned with the geometrical characterization of the fracture surface

through parameters such as surface roughness, fracture surface anisotropy, fractal charac-

teristics etc It has been successfully applied to failure analysis, to studies of creep cavitation,

to correlations of surface roughness with mechanical behavior, etc., and it may be used

(although to the best knowledge of the authors this has never been done) to obtain accurate

measures of the surface energies of fracture in brittle systems When successful, quantitative

fractography should lead to a better understanding of fundamental processes that occur in

materials and, thus, to improved materials and to more appropriate applications of existing

materials

Experimental Techniques

A variety of different experimental techniques have been developed in the past to study

fracture surfaces The details of these techniques, their advantages, and limitations are

discussed in some detail by Underwood [1], Exner and Fripan [2], Wright and Karlsson [3],

Coster and Chermant [4], and Underwood and Banerji [5,6] In a broad sense, the basic

approaches can be classified as follows:

(a) methods based on stereoscopic images of the fracture surface and

(b) techniques involving metallographic sectioning of the fracture surface, i.e., profilo-

metric methods

Stereoscopy provides nondestructive techniques for the study of fracture surfaces The

Cartesian coordinates of different points on the fracture surface are determined by using

stereo scanning electron microscope (SEM) pairs, i.e., two micrographs of the same field

taken at small differences in tilt angle The resulting parallax is directly proportional to the

elevation differences between the two points in the image This yields a procedure for

determining the z coordinate of any given point (x,y) on the SEM image The (x,y,z)

coordinates of different points of SEM fractograph can be thus determined The data can

be utilized to generate "carpet" plots of the fracture surface via computer graphics: the

fracture surface roughness and orientation distribution can be calculated [2] from this in-

formation The input can also be utilized to generate fracture profiles [7,8] The stereoscopic

techniques can be automated to reduce the measurement time and effort [9,10]

Profilometry is the study of sections through the fracture surface Depending on the

sectioning geometry, it is possible to obtain vertical [11], horizohtal [12], or slanted [13]

sections The vertical sections can be generated by using standard metallographic techniques,

and they simultaneously reveal the microstructure below the fracture surface Furthermore,

the measurements on such fracture profiles often simplify the subsequent stereological anal-

ysis The quantitative descriptors of fracture surface geometry require a reference direction

for their definition, interpretation, and estimation The natural choice for the reference axis

is the direction normal to an average plane through the fracture surface The vertical sections

contain this reference axis, called the "'vertical" axis Figure la shows a schematic fracture

surface and Figure lb shows a vertical section and corresponding fracture profile The

fracture profile can be quantified via digital image analysis The (x,y) coordinates of the

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ANTOLOVICH ET AL ON COMPUTED TOMOGRAPHY 5

t.Z

Y

FIG 1 (a) Schematic fracture surface and relative orientation of the vertical sectioning plane; (b)

schematic vertical section fracture profile (Z = vertical axis)

points on fracture profile are obtained at preselected length increments (called digitizing ruler length) by tracing the profile image over the digitizing tablet with the help of a cursor [14]; the coupled microprocessor is used to store and process the data The resolution is a function of the ruler length

The profile roughness parameter RL is defined as follows [11]

hp

where, h0 is the total profile length, and hp is its projected length on a line perpendicular

to the vertical axis; overlaps in the projected length are not counted RL can have any value

ranging from one to infinity The orientation of a line element on the fracture profile is specified by the angle between the normal to the line element and the vertical axis, 0- The concept of orientation is illustrated in Fig 2 The orientation distribution function of the line elements on the fracture profile (PODF) gives the fraction of profile length in the orientation range 0 to (0 + dO); hence, it is a measure of the fracture profile anisotropy

RL and P O D F can be calculated from digitized profile data Recently, the horizontal profile

roughness parameter RL H has been defined where the overlaps in the projected length are

Z

d kOg) [

Z dL(~r

w

FIG 2 Specification of orientation of line elements on fracture profile (Z = vertical axis)

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accounted for [15] RL ~ and RL yield the fraction of true profile length [16] having overlaps,

~0

Quantitative Descriptors of Fracture Surface Geometry

The fracture surface roughness parameter, Rs, is equal to the ratio of the true area of fracture surface and its projected area on the plane perpendicular to the vertical axis [13,1 7]; the overlaps in the projected area are not counted The orientation of a surface element on the fracture surface is specified by angles + and 0 referenced to its normal vector ~r (See Fig 3) The fracture surface orientation distribution function (SODF) represents the fraction

of fracture surface area having orientation in any given solid angle range 12 to (~ + dO) (where, df~ - sin + dO d+); hence, it is a measure of the fracture surface anisotropy The SODF can be calculated from the profile data, provided certain assumptions are made concerning its functional form Analogous to RL", one can define Rs H where the overlaps

in the projected area are accounted for [15] Rs n is determined by S O D E The fraction of overlapped fracture surface area 130 can be determined as follows [16]

FIG 3 Specification of orientation of surface elements on fracture surface (Z = vertical axis)

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The SODF g(~b) (by definition, if SODF is symmetric then it depends only on ~b and not O)

can be calculated from measured P O D F f(t~) by using the following relationship [16]

Equation 6 is a generalization of the result given by Scriven and Williams [21] for estimation

of orientation distribution of equiaxed grain boundary facets; the present result is not restricted to fracture surfaces composed of planar facets, it is based only on the symmetry assumption Scriven and Williams [21] have given a detailed procedure for solving Eq 6, to calculate g(+)

If SODF of fracture surface is not symmetric with respect to the vertical axis, then different vertical sections yield different PODF, and different values of RL Recently, Drury [22] has derived the following equation for estimation of Rs from measurements of RL on two perpendicular vertical sections (Fig 4)

to estimate SODF under certain conditions [16]

Applications of Quantitative Fractography

Failure analysis often involves identification of defects or microstructural features responsible for failure; it is also of interest to determine whether the largest defects or a

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significant spectrum of defect sizes control the failure process Quantitative fractography is

an indispensable tool for obtaining such information objectively

consider the role played by defects in the tensile failure of continuous AI.,03 fiber-reinforced

metal-matrix composite material having AI-Li alloy matrix Obviously the fabrication of

such materials is expensive, and it is important to know which defects truly influence the

failure process so that resources can be directed to solving real problems Drury [22] has

studied this problem The virgin material contained the following defects:

(a) voids,

(c) segmented fibers, and

(d) oversized fibers

All of these defects are shown in Fig 5

These defects were also observed on the fracture surface of tensile specimens as seen in

Fig 6, and the real question is what role do these features play in the fracture process In

an attempt to answer this question, Drury [22] made the following measurements:

(a) the number density of above defects, Ns, and their area fraction Aa r on SEM ffac-

tographs, and

(b) the number density of the defects, NA, and their area fraction AA on a metallographic

sectioning plane through the bulk material

An SEM fractograph is essentially a plane projection of a rough fracture surface made

up of non-coplanar segments Thus, the number of defects per unit area in a SEM fracto-

graph, Ns, is not equal to the number of defects per unit area of true fracture surface, Nal;

these quantities are, however, related as follows

N~

Rs

where Rs is the fracture surface roughness parameter Drury [22] estimated Rs by measuring

RL on two perpendicular sectioning planes and using Eq 8 Table 1 gives the values of NA,

different fiber orientations with respect to the tensile axis Inspection of Table 1 reveals the

following:

1 In all the samples the number density of voids NAr and their area fraction on the

fracture surface AA r are significantly higher than their corresponding bulk values This shows

'the affinity of fracture surface for voids In other words, voids play a significant role in the

fracture process, and they are deleterious It is interesting to note that although the average

area per void AI on the fracture surface is higher than its bulk value, the differences are

statistically significant only for 60 and 90 ~ fiber orientation samples It can be said that not

only the largest voids but a significant spectrum of all void sizes affect the failure process

2 The parameters NA I and Aft for oxide particles are also higher than their bulk values,

but differences are statistically significant only for the 60 and 90 ~ orientation Further, the

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ratios ]V.a~/NA and A4tAA a r e much higher for voids than oxide particles This indicates that

voids are more deleterious than oxide particles [3] The parameter AA J for oxide particles

is statistically comparable to its corresponding values for voids However, the bulk value

for area fraction of oxide particles is higher than voids This demonstrates that even if two

types of defects appear on the fracture surface with the same frequency, this does not

necessarily mean that they are equally important in the fracture process The appropriate

conclusion mr/st be drawn after quantitative comparison of the fracture surface parameters

with their corresponding bulk values

Of course such studies could also be done on inclusions on the fracture surface of a steel

to gain insight as to their importance in the fracture process and, consequently, the likely

return that would be obtained in producing a cleaner material

Applications to Creep Crack Growth In some applications, such as pipes in the nuclear

power industry, components are used at moderate temperatures for very long times (e.g.,

20 years and more) This combination of long time and elevated temperature provides a set

of conditions under which creep conditions prevail In particular, cracks can form and extend

by creep processes such as the formation of grain boundary voids and their subsequent

coalescence It is important to be able to predict the rate at which these cracks grow, and

towards that end theories have been developed based on this mechanism [23] In order to

test this theory, experiments have been devised using model materials in which voids can

be made to form on grain boundaries It is important, in testing these theories, to have a

precise knowledge of the various quantitative descriptors of the voids around the crack tip

A typical micrograph, showing voids around the crack tip in an Sb-doped Cu alloy, is shown

in Fig 7 Quantitative measures of the void distributions [24] are shown in Fig 8 The

quantities such as number of cavities per unit area, area fraction of cavities, and variation

of these attributes with distance from the crack tip, are the necessary input parameters in

the microstructurally based fracture models It follows that such rigorous stereological mea-

surements are absolutely indispensable in verifying crack growth theories based on growth

and coalescence of cavities

Applications of radiography and Computed Tomography to Fracture in Composites

So far, we have focused our attention primarily on the fracture surface or on sections

containing the fracture surface/crack tip Information obtained by such procedures is ob-

viously of great value However, in many applications it would be of interest to characterize

the formation and growth of internal damage such as microcracks An important example

has to do with composites In many instances damage develops in three dimensions as

opposed to the essentially two-dimensional "fatal flaws" that form in most monolithic ma-

terials In such cases it would be desirable to measure the internal, spatially distributed

damage by nondestructive techniques, if possible

Radiography and Damage Detection

Examples of nondestructive approaches are C-scan, classical radiography, and computed

tomography (CT) Measurement of damage by C-scan gives two-dimensional information,

which is essentially qualitative, and has a low degree of detectability Use of conventional

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ANTOLOVICH ET AL ON COMPUTED TOMOGRAPHY 13

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T A B L E 1 Values of area fraction, number density, and average area per defect on fracture surface

and on a metallographic section through bulk

Number Density, Average Area,

Orientation Voids Particles Voids Particles Voids Particles

u n c r a c k e d a r e a A s a r e s u l t , t h e t r a n s m i t t e d X - r a y i n t e n s i t y will b e t h e s a m e in b o t h r e g i o n s ,

FIG 7 Optical micrograph of Cu-l%Sb alloy sample showing voids around the crack tip during

creep crack growth at 400~C (magnification: x 200; etchent: solution containing equal volumes of nitric acid, acetic acid, and distilled water)

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Geometrical Invisibility absorption

path length

z - ~ z

Z

FIG 9 Schematic illustration of geometric invisibility

and the crack will be invisible On the other hand, the small void shown in Fig 9 would be

visible since the absorption path length is different Geometric invisibility can be eliminated

by use of dye penetrants such as ZnI2 which have different absorption coefficients than the

matrix Such dyes can, of course, lead to interpretation problems through incomplete pen-

etration

An example of radiographic detection of cracking in composites is shown in Fig 10 for

a graphite/epoxy composite in which fibers are present at 0, +45, and 90 deg Fiber cracks

are clearly evident below the principal crack plane in all regions of crack growth Higher

resolution can be obtained by using synchrotron radiation (Synchrotron radiation is essen-

tially relativistically produced X-rays with extremely high intensity and adjustable wave-

length) In Fig 11, a comparison between microfocus and synchrotron radiography of a

fractured graphite/epoxy composite is shown It is quite clear that the resolution is greatly

enhanced when the same area is examined using synchrotron radiation The reason for this

lies in the fact that in the microfocus experiments the specimen is about 30 cm from the

beam, while in the synchrotron the distance is 20 m The greater distance and smaller

aperature (which can be used because of the higher intensity) gives a more nearly parallel

beam

Damage Detection by Computed Tomography

The limitations of two-dimensional information and "geometric invisibility" can be over-

come by use of computed tomography Computed tomography is an extension of radiography

in which radiographs of a "slice" of the part to be examined are made at various angular

orientations from 0 to 360 ~ The radiographic information (which is captured digitally using

sophisticated sensors) can be analyzed using appropriate algorithms to obtain the X-ray

absorption density at each point in space Essentially, a three-dimensional representation

of the X-ray absorption density is obtained Since the absorption density is related to the

presence of defects (low absorption density-high defect density), one has a three-dimensional

representation of the defect distribution A schematic representation of this technique is

shown in Fig 12 In Fig 12 the X-ray source and detectors are rotated around the specimen

It is, of course, equally possible to rotate the specimen and keep the source and the detector

fixed in space and achieve exactly the same results Such an arrangement is shown in Fig

13 In both of these techniques, the size of the slice in laboratory units is typically on the

order of 2 to 5 mm After one "slice" is scanned, the specimen is translated, and the same

procedure is repeated until the entire volume of interest is scanned The three-dimensional

nature of the specimen may be studied by viewing arbitrarily chosen slices (on the computer)

and viewing them with the aid of a CRT display unit The resolution of typical laboratory

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~b

b.,o

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FIG 12 Schematic illustration of X-ray tomography setup involving rotation of X-ray source and

detector

units is approximately 0.02 mm, and meaningful data can be collected in a period of minutes

to hours depending on the specimen being examined

Conventional medical scanners may be adapted to study graphite/epoxy composites with good success; some typical examples of partially fractured graphite/epoxy specimens are shown in Figs 14 to 17 In these figures the Hounsfield density (one measure of X-ray absorption characteristics) is measured The Hounsfield density is linearly related to the linear absorption coefficient more commonly used in X-ray studies On this scale, the Hounsfield density is - 1000 for air, 0 for water, and 1000 for dense bone The apparatus used in these figures has been experimentally demonstrated to be capable of resolving density

sample

co , y X ' l / " - ~ 0

source

FIG 13 Schematic X-ray tomography setup involving specimen rotation

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FIG 14 Reconstructed tomographic image showing cracks in graphite~epoxy composite The variation

in Hounsfield density shown on the left corresponds to the line shown on the "slice" of the upper right The slices shown on the left are parallel to the main crack but at slightly different elevations Regions of isodensity are shown as different colors, with green corresponding to no damage (i.e., H = 386) and other colors corresponding to different damage levels

FIG 15 Histograms of Hounsfield density taken from damaged (broad) and undamaged (narrow) areas of a graphite/epoxy composite, The form of the histogram yields important information on the damage state of the material

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ANTOLOVlCH ET AL ON COMPUTED TOMOGRAPHY 21

FIG 16 Cracking in a graphite~epoxy composite similar to Fig 14 Here it is possible to see micro- delaminations on the order o f microns in size extending ahead o f the main crack front

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FIG 17 Tomographic image similar to Fig 14 except that the sampling line is normal to the crack extension direction Note the variation in density as damaged and undamaged regions are sampled

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differences on the order of 10 3 on the Hounsfield scale In Fig 14, the delaminated zone and its contour is easily detected by the color variations (here green was selected to correspond with the density of undamaged material) The two pictures on the right hand side

of Fig 14 represent longitudinal slices at slightly different elevations in the specimen; the full three-dimensional nature of the material is studied by simply examining different slices The damaged zone ahead of the delaminated region is also seen as a variation in color (again each color corresponds to a particular small variation in density) or as decreased density along the sampling line that was chosen The damage state is also conveniently revealed and studied by histograms of the Hounsfield density as shown in Fig 15 In this figure, histograms were obtained from small regions in the damaged and undamaged areas Un- damaged material will exhibit a very narrow distribution, while damaged areas wilt show a very broad distribution of density Even though the slices used in the initial X-ray sampling were 3-mm thick, small microcracks of the order of 10 to 15 microns can be revealed in the longitudinal reconstructions Such microcracks are seen quite clearly in Fig 16 extending ahead of the crack and in Fig 17 at two different levels In Fig 17, the variation in density across a sampling line containing damaged and undamaged material in the upper picture is shown The peaks correspond to undamaged material with a density of about 385 (similar

to Fig 14), while the valleys correspond to severely damaged sites

Improvements in resolution can be obtained by the use of synchrotron radiation to perform

"microtomography." Here the beam has a high intensity, the spot size is small, the detectors are sensitive and close spatially, and sampling times are typically on the order of 4 h, depending on the material being studied The increase in resolution is possible because of the long sample-to-beam distances, the excellent detectors, and the higher intensity which allows small spot sizes to be used The sampling time can be reduced if the spot size is increased A typical reconstructed image [27] is shown in Fig 18 Here a composite specimen

of SiC fibers in 6061 A1 was examined The fiber cores and small cracks are clearly visible The data for the image shown in Fig 18 was taken at the synchrotron facility in Hamburg, West Germany, and the reconstruction was done at Lawrence Livermore National Labo- ratory (LLNL)

Other Potential Applications of Computed Tomography

As CT becomes more available as a routine laboratory tool, some of the vexing questions

in the field of fracture will be able to be addressed with the expectation of obtaining definitive answers One such problem of current interest and considerable controversy has to do with the question of crack closure during fatigue The notion here is that as a crack is unloaded,

FIG 18 Reconstructed image of a lightly bent SiC/AI sample showing the carbon cores of SiC fibers

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the roughness of the fracture surface (which, incidentally can be measured by the techniques

described in this paper) will give rise to crack face contact before the minimum load in a

fatigue cycle If this is the case, then the body containing the crack will not experience the

full range of the stress-intensity parameter AK which is the forcing function for crack ex-

tension in fatigue This premature contact has been termed "crack closure" or "'shielding"

[25] Closure is usually measured using devices such as clip gages or strain gages attached

to the back face of a fracture specimen Deviations from linearity in the load/displacement

curve during loading or unloading are taken as the point of contact or as the "closure load."

The closure load is then subtracted from the maximum load to compute the effective stress-

intensity parameter, AKe,, which is taken as the modified crack extension force Recently,

serious questions have arisen as to the validity of current experimental approaches [26] and

the way in which such measurements can be used Clearly it would be of great value to have

a technique that would allow us to look inside the material in the region of the crack tip

during unloading so that a physical picture of the microprocesses at the crack tip could be

obtained These physical observations could then be correlated with the more global me-

chanics-type measurements It would appear as if CT with synchrotron radiation, having

resolution on the order of a micron, would provide exactly the approach that is needed to

address this issue Loading and unloading experiments could be carried out in a synchrotron,

and a picture of the closure process could be developed in detail These questions are

currently being addressed by researchers in the Mechanical Properties Research Laboratory

at Georgia Tech In a more general sense, it would appear as if many issues related to crack

tip or plastic zone phenomenon could be studied by this powerful new technique

Summary and Conclusions

Conventional fractography yields essentially qualitative information concerning the type

of microstructural features present on the fracture surface as well as the nature of the fracture

surface This information is often not sufficient (and in some cases may be misleading) to

identify the microstructural features responsible for failure It is also difficult to unambig-

uously identify the controlling failure mechanisms by the qualitative approach Quantitative

fractography yields objective, quantitative information concerning the relative frequency of

appearance of any given microstructural feature as welt as other geometric attributes Com-

parison of these parameters with their corresponding bulk values leads to objective conclu-

sions concerning the role of different microstructural features in the failure process

Furthermore, the geometric characteristics of the fracture surface, such as surface roughness

and anisotropy, provide additional useful input for the study of fracture processes With the

availability of modern image analysis equipment, these measurements can be performed on

an essentially routine basis

Computed tomography can yield additional independent information concerning the in-

ternal damage state of a material which is not accessible via fractographic approaches The

sensitivity and speed of computed tomography can be greatly enhanced by using high-

intensity X-ray sources such as are produced in a synchrotron Large-memory, high-speed

computers and sophisticated digital display equipment make it possible to obtain detailed

information that has heretofore not been available An additional advantage of this approach

is that the information that is obtained is direct; no assumptions are needed to calculate

various aspects of the structure or damage state

Acknowledgments

The authors would like to acknowledge useful discussions with numerous colleagues at

Georgia Tech and thank them for their permission to use the results of some of their

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unpublished research We w o u l d also like to similarly acknowledge colleagues of the C E A

(Bruyeres-le-Chatel), E C T A (Paris), and the C N R S (Marseille) for their contributions to

the c o m p u t e d t o m o g r a p h y parts of this paper Stephen D A n t o l o v i c h would also like to

acknowledge the financial support of the G e o r g i a Tech F o u n d a t i o n for an academic leave

to carry out research in the area of c o m p u t e d t o m o g r a p h y T h e quantitative fractography

was p e r f o r m e d u n d e r N S F G r a n t No DMR-8504167; this financial support is gratefully

acknowledged Finally, support from U n i t e d Technologies and Pratt and Whitney in the

f o r m of a grant is gratefully a c k n o w l e d g e d for s o m e of the composite results r e p o r t e d here

References

Ed., Van Nostrand Reinhold, New York, 1986, pp 101-122

ed., Vol 12, 1987, pp 193-210

[6] Underwood, E E and Banerji, K., "Fracture Profile Analysis of Heat-Treated 4340 Steel,"

Advances in Fracture Research, S R Valluri, D M Taplin, P R Rao, J E Knott, and R Dubey,

1378

Chameleon Press, London, 1982, pp 591-598

[10] Exner, H E and Bauer, B., Proceedings, Third European Symposium on Stereology, Ljubljana,

Yugoslavia, 1981, pp 255-262

[11] Pickens, J R and Gurland, J., Proceedings, Fourth International Congress on Stereology E E

Underwood R DeWit, and G A Moore, Eds NBS Special Publication 431, National Bureau

of Standards, Gaithersburg, MD, 1976, pp 269-272

[12] Mandelbrot, B B., Passoja, D E., and Paullay, A J., Nature, Vol 308, No 19, 1984, pp 721-

722

[13] Almond, E A., King, J T., and Embury, J D., Metallography, Vol 3, 1970, pp 379-382

[14] Banerji, K., Metallurgical Transactions, Vol 19A, 1988, pp 264-271

[15] Gokhale, A M and Banerji, K., Microstructural Science, Vol 17, 1989, pp 67-79

[16] Gokhale A M., private research, Georgia Institute of Technology, Atlanta, GA, 1988

[17] EI-Soudani, S M., Metallography, Vol 11, 1978, pp 247-336

[18] Underwood, E E and Underwood, E S., Acta Stereologica, Proceedings, Third European Sym-

posium on Stereology M Kalisnik, Ed., 1982, pp 89-101

[19] Banerji, K and Underwood, E E., Acta Stereologica, Proceedings, Sixth International Congress

on Stereology, M Kalisnik, Ed., 1983, pp 65-70

[20] Gokhale, A M and Underwood, E E., Acta Stereologica, Vol 8, No 1, 1989, pp 43-52

[21] Scriven, R A and Williams H D., Transactions of the Metallurgical Society ofAIME, Vol 233,

1965, pp 1593-1602

[22] Drury, W J., M S thesis, Georgia Institute of Technology, Atlanta, GA 1988

[23] Wilkinson, D., Acta Metallurgica, Vol 35, 1987, pp 2791-2799

[24] Staley, J T., Jr and Saxena, A., private research, Georgia Institute of Technology, Atlanta GA,

[27] Stock, S R., Kinney, J H., Breunig, T M., Bonse, U., Antolovich, S D., Johnson, Q C., and

terials Research Society, Vol 143, 1989, pp 273-278

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Relationships Between Fractographic

Features and Material Toughness

REFERENCE: Harvey, D P II and Jolles, M I., "Relationships Between Fractographie Features and Material Toughness," Quantitative Methods in Fractography, ASTM STP 1085,

B M Strauss and S K Putatunda, Eds., American Society for Testing and Materials, Phil- adelphia, 1990, pp 26-38

ABSTRACT: The fracture surfaces of HY-100 steel and 2024 aluminum tensile specimens

with differing gage lengths and gage diameters were examined using scanning electron microscopy Relationships were found between various fractographic features and the toughnesses

of the specimens as quantified by the global critical strain energy density, we which is a measure of the work necessary to fail a material specimen by monotonic loading In both test materials, correlations were made between the percentage of the fracture surface characterized

by a particular fracture mode and the toughness of a given specimen Correlations could also

be made between the toughness of a specimen and other fractographic features such as the linear microvoid density or the aspect ratio of microvoids It was found that both the character

of the fracture surfaces and the specimen toughnesses were dependent on the history of the triaxiality of the stress-strain state which in turn was dependent on the gage geometries of the specimens These results indicate that quantitative interrelationships between the microme- chanical behavior and the global response of a specimen may be derived through the concepts employed in this investigation

KEY WORDS: fractography, strain energy density

Several previous investigations have studied possible relationships between fractographic

relationships between the plane-strain fracture toughness, K~c, and various fracture phe-

of the "'stretched zone" [6, 7] However, substantial scatter in the data has precluded any attempt to quantify these relationships In the present investigation, studies were conducted

on HY-100 steel and 2024 T-351 aluminum in order to determine any possible quantitative relationships between fractographic features and material toughness as quantified by the critical strain energy density, we, in tensile specimens of four different gage geometries

Experimental Procedure

The specimens used in this study were round bar tensile specimens of HY-100 steel and

2024 T-351 aluminum with various gage geometries which were from an investigation by Matic, Kirby, and Jolles [8] Typical compositions of the test materials are reported in Tables

la and b, and the typical microstructures are shown in Figs la and b Any minor deviations from the specified chemical compositions within normal quality control standards are not Mechanics of Materials Branch, Naval Research Laboratory, Washington, DC 20375

: Department of Mechanical Engineering, Widener University, Chester, PA 19013

26

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HARVEY AND JOLLES ON MATERIAL TOUGHNESS

TABLE la Typical composition of HY-lO0 steel, in weight percent

a closed-loop servohydraulic test machine under stroke control at a rate of 0.127 cm/min The unique stress-strain curves for the materials used in this study were determined by a hybrid experimental-computational algorithm which uncouples material and geometry in- fluences on observed test specimen deformation [8] Generally, the approach used to determine a unique solution curve for the uniaxial true stress-true strain behavior which would adequately predict the corresponding observed specimen behavior was to treat the uniaxial continuum true stress-true strain curve as the unknown quantity for computational simulations of the tensile specimens A trial continuum stress-strain curve was then generated for the computational simulations The predicted axial load-displacement response and full- field lateral contraction of the tensile specimens were then compared with the corresponding experimental data If the differences between the computational simulations and experiments were greater than desired, the continuum stress-strain curve was revised iteratively until these differences were minimized The final iterate of the uniaxial stress-strain curve was then adopted as the continuum behavior of the material The resulting "continuum stress- strain curves" for the HY-100 steel and 2024 T-351 aluminum used in this investigation are shown in Figs 2 and 3, respectively The symbols represent individual points on the solution curve, and the line is the best fit to these points The critical strain energy density for a given specimen is determined by finding the area under this stress-strain curve out to the fracture strain of that specimen The "global" wc is determined using the fracture strain defined as In ( A J A r ) and represents the deformation across the fracture surface in an

"average" sense Tables 3a and b gives the global fracture strain and the global wc for each specimen The fracture surfaces of these specimens, not including the shear lips, were characterized using scanning electron microscopy The following features were measured: (a) the proportions of the different fracture modes over the entire fracture surface of each specimen,

(b) the average linear density of microvoids in the ductile regions of each specimen, and (c) the average aspect ratio (height/width) of the microvoids on the fracture surface of each HY-100 steel specimen

The percentages of the three groups of fracture features were determined by taking

TABLE lb Typical composition of 2024 aluminum, ib weight percent

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FIG 1 Typical microstructures of the test materials: (a) HY-IO0 steel (x500) and (b) 2024 T-351 aluminum ( x 75)

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HARVEY AND JOLLES ON MATERIAL TOUGHNESS 29

Trang 34

scanning electron micrographs of the fracture surfaces at a magnification of • 100 for the HY-100 steel specimens and • 500 for the 2024 aluminum specimens A grid was then laid over the micrographs, and a manual point count made of the various features In order to determine the linear microvoid density of the specimens, • 1000 micrographs were taken

of randomly selected areas of the fracture surfaces Several manual point counts of microvoids across a given distance were made From these counts, average values were computed Aspect ratios were determined by taking two micrographs (one at 0 ~ tilt, the other at 6 ~ tilt)

of several randomly selected areas at a magnification of x 1000 Once the micrographs were taken, the height w~i~s determined by the parallax stereo-pair method [9], and the width was measured from the micrograph at 0 ~ tilt From these measurements, the average aspect ratio

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HARVEY AND JOLLES ON MATERIAL TOUGHNESS

TABLE 3a Fracture strain and global w, for HY-IO0 steel

Results and Discussion

The damage incurred by a material specimen undergoing mechanical deformation can be attributed to two basic mechanisms The first of these is fracture, which involves the breaking

of atomic bonds along specific crystallographic planes or along interracial boundaries in a material The second mechanism is material flow, which is generally accomplished by slip due to dislocation motion The toughness of a material specimen subjected to loading is determined by the relative proportions of these mechanisms The energy associated with fracture may be expressed as

where crr,,~ is the normal stress required for bond separation, A is the area over which the stress acts, and dfr,~ is the distance required to accomplish this separation The energy associated with elementary flow processes may be similarly expressed as

where r,1ow is the resolved shear stress required for elementary dislocation motion, and

engineering materials, the stresses involved in fracture are generally larger than those involved in flow, but usually not by more than an order of magnitude or so On the other hand, dnow is often several orders of magnitude larger than df,,r consequently, the energy associated with flow is much greater than the energy associated with fracture Thus it follows that the deformation energy of a material specimen subjected to loading is dependent largely

on its ability to flow If flow is able to occur, then a large amount of energy is required to

TABLE 3b Fracture strain and global w~ for 2024 T-351 aluminum

Trang 36

fail a specimen If flow is restricted in some way, then the required amount of energy to

cause failure in a specimen is decreased

Certain fractographic features are associated with a particular failure mechanism Flat

facets and river patterns are associated with fracture, microvoid coalescence and ductile

rupture are associated with flow, and ductile tearing is due to some combination of flow

and fracture Therefore, the relative amounts of material flow and fracture (and thus the

material toughness) should be reflected in the fracture surface of a failed specimen Figures

4a and b are representative of the fracture surfaces of the HY-100 steel specimens with the

largest and smallest global critical strain energy densities, respectively In Fig 4a, the fracture

surface is predominantly microvoid coalescence, while in Fig 4b, larger proportions of

ductile tear and cleavage are visible These observed differences in the fracture surfaces

were quantified in terms of the percentage of the fracture surface characterized by either

microvoid coalescence, ductile tear, or cleavage for HY-100 steel, and ductile tear, fracture,

or void sheeting for 2024 aluminum These values were then plotted versus the global critical

strain energy densities as shown in Figs 5 and 6 for HY-100 steel and 2024 aluminum,

respectively Both Figs 5 and 6 indicate that the percentage of fracture sites characterized

by brittle fracture processes decreases with an increase in the global Wc This is consistent

with the changes in damage mode that would be expected as the energy to failure of a

specimen increases

Figures 7 and 8 show that the linear microvoid densities on the fracture surfaces of both

the HY-100 steel and the 2024 aluminum specimens change with the global we It is generally

accepted that microvoids nucleate primarily at second-phase particles [10, l 1 ] when a critical

value of normal stress is exceeded LeRoy et al [12] have given the value of normal stress

acting at a second-phase particle as

where ~rm is the hydrostatic stress, and cr~oc is the local stress due to incompatibility strains

between the matrix and the second-phase particle The relative magnitudes of these stresses

acting at the particle are dependent on the triaxiality of the global stress state The triaxiality

of the stress state experienced by a material specimen is affected by the geometry of that

specimen As the thickness of a specimen is increased, there is an increase in the transverse

stresses needed to maintain continuity between individual volume elements This decreases

the resolved shear stresses acting in a material which in turn decreases ~o~ However, at the

same time, the hydrostatic stress acting at the particle increases with the stress triaxiality

Therefore, the observed differences in microvoid density are due to the differences in the

specimen geometries which change the nature of the stresses acting at the particle

The linear microvoid density on the fracture surfaces of the HY-100 steel specimens

increases in proportion to the global wc, whereas the opposite trend is observed in the 2024

aluminum specimens This difference may be resolved by considering the mechanisms of

void nucleation in the two test alloys Microvoids can nucleate either by a separation of

material at the particle-matrix interface due to plastic incompatability strains between the

second-phase particle and the matrix or by cracking of the second-phase particles Figures

9a and b are cross sections of failed tensile specimens of HY-100 steel and 2024 aluminum,

respectively HY-100 steel has a ferrite-bainite structure with the light regions being ferrite

and the gray regions being bainite In evidence are a large number of black areas originating

at boundaries between the two phases These dark areas are where separation has occurred

between the ferrite and the bainite These separations are most likely due to plastic incom-

patability strains between the two phases as evidenced by the area to the mid left in Fig

9a, where a lath of ferrite has apparently necked down with resulting voids to either side

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HARVEY AND JOLLES ON MATERIAL TOUGHNESS 33

FIG 4 Fracture surfaces of HY-IO0 steel tensile specimens: (a) high global we ( x 1000) and (b) low global wc ( x 1000)

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F I G 5 Proportions of fracture modes as a function of global w~ for HY-IO0 steel

This mechanism of void nucleation is enhanced by an increase in O'lo c which in turn leads to

a higher we, Consequently, an increase in the wc of HY-100 steel corresponds to an increase

in the obserVed microvoid density on the fracture surface In the cross section of 2024 aluminum (Fig 9b), a fine dispersion of second-phase particles is present These particles appear to be of two types, one type darker than the other Previous metallographic analysis

of 2024 aluminum [13] has identified the lighter particles as CuA12 and the darker particles

as CuMgA12 Intermetallic particles such as these are typically quite brittle Upon closer inspection, cracks may be detected in several of these particles perpendicular to the direction

of loading This behavior is promoted by a high triaxial or hydrostatic stress state (high crm) This type of stress state also leads to a low material toughness because of the corresponding

0

W c (MJ/m 3)

F I G 6 Proportions of fracture modes as a function of global we for 2024 T-351 aluminum

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restraint to material flow Therefore, a decrease in the wc of 2024 T-351 aluminum used in

this study corresponds to an increase in the observed linear microvoid density

Figure 10 shows that the average aspect ratio (height/width) of microvoids increases with

an increase in the global we Under uniaxia! loading, microvoids grow mainly in the tensile

direction; a triaxial stress is required to induce any appreciable lateral microvoid growth

indications of the decrease in the degree of the triaxiality of the stress state as the gage

geometry of the specimens is changed The effects of specimen geometry on fracture mor-

phology have also been observed in H S L A steels [14] In that investigation it was noted

that the aspect ratio of the dimples in tensile specimens was much greater than the aspect

FIG 8 Linear microvoid density versus global wc in 2024 T-351 aluminum

Tiêu đề	Quantitative Methods in Fractography
Tác giả	Bernard M. Strauss, Susil K. Putatunda
Người hướng dẫn	Bernard M. Strauss, Teledyne Engineering Services, Susil K. Putatunda, Wayne State University
Trường học	Wayne State University
Chuyên ngành	Fractography
Thể loại	Bài báo
Năm xuất bản	1990
Thành phố	Philadelphia

Định dạng
Số trang	173
Dung lượng	6,86 MB