Astm stp 1085 1990

STP 1085

Quantitative Methods

in Fractography

Bernard M. Strauss and Susil K. Putatunda, editors

ASTM

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Philadelphia, PA 19103

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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.

TA409.Q36 1990

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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

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Foreword

This publication, Quantitative Methods in Fractography, contains papers presented at the

symposium on Evaluation and Techniques in Fractography, which was held 10 Nov. 1988

in Atlanta, Georgia. Two ASTM committees, Committees E-9 on Fatigue and E-24 on

Fracture Testing, sponsored the event. The symposium cochairmen were Bernard M. Strauss.

Teledyne Engineering Services, and Susil K. Putatunda, Wayne State University, both of

whom also served as editors of this publication.

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Contents

Overview 1

Applications of Quantitative Fractography and Computed Tomography to Fracture

Processes in Materials--STEPHEN D. ANTOLOVICH, ARUN M. GOKHALE,

AND CLAUDE BATHIAS

Relationships Between Fractographic Features and Material Toughness--

D. P. HARVESt ' lI AND M. I. JOLLES 26

Quantitative Analysis of Fracture Surfaces Using Fractals--D. J. ALEXANDER 39

Analysis and Interpretation of Aircraft Component Defects Using Quantitative

Fractography--N. T. GOLDSMITH AND G. CLARK 52

Characteristics of Hydrogen-Assisted Cracking Measured by the Holding-Load and

Fractographic MeIhod--NAOTAKE OHTSUKA AND HIROSHI YAMAMOTO 69

Fractographic Study of Isolated Cleavage Regions in Nuclear Pressure Vessel Steels

and Their Weld Metals--x. J. ZHANG, A. KUMAR ,R. W. ARMSTRONG, AND

G. R. IRWIN 89

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

Loadings--PETER KURATH AND ALl FATEMI

Corrosion Fatigue Crack Arrest in Aluminum Alloys--R. J. H. WANHILL

AND L. SCHRA

Author Index

Subject Index

102

123

144

167

169

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STP1085-EB/Jun. 1990

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.

Susil K. Putatunda

Wayne State University, Detroit, MI 48202;

symposium cochairman and editor.

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Stephen D. Antolovich, 1 Arun 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 Quantitative Fractography and Computed Tomography to Fracture Processes in Materials," Quantitative Methods in Fractography, ASTM STP 1085, B. M. Strauss and S. K. Putatunda, Eds.,

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.

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4 QUANTITATIVE METHODS IN FRACTOGRAPHY

Quantitative Fractography

Definition and Applications

Quantitative fractography is concerned with the geometrical characteristics of microstructural 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 characteristics 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., profilometric 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 information. 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 analysis. 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

(a) (b)

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]

RL = -- (1) 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 PODF 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

d kOg) [

dL(~r

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

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6 QUANTITATIVE METHODS IN FRACTOGRAPHY

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

[RL -- RLn] (2)

~176 = Rz

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 SODE The fraction of

overlapped fracture surface area 130 can be determined as follows [16]

Rs - Rs n

130 - (3) Rs

A significant simplification in the measurements and the analysis is possible when the

SODF is symmetric with respect to the vertical axis. In such a case, all the vertical section

fracture profiles are statistically equivalent; hence, a single vertical section profile contains

the necessary information for estimation of Rs, SODF, Rs n, and [30. The symmetry assumption

has been experimentally verified [18,19] in a number of systems; it is expected to be a good

approximation for fracture surfaces of materials having isotropic microstructure. For fracture

surfaces having a symmetric SODF, Underwood and Banerji [19] and Gokhale and Underwood [20] have developed the following equations to estimate Rs from RL

Rs = 4(RL -- 1) + 1 (4)

Z Z

dS(O,

Y Y

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

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ANTOLOVICH ET AL. ON COMPUTED TOMOGRAPHY 7

Rs = 1.16RL (5)

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

can be calculated from measured PODF f(t~) by using the following relationship [16]

f(t~) = ~2j0 [~2 _ .q2],/2 (6)

where rl = cos 6, ~ = cos t~, and I is a constant which can be determined from the following

condition

'/2f(t~)dt~ = 1 (7)

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).

Rs = f~(RL)~ + (1 - O){4[(RL)~-1]-1) (8)

_ (RL)• - (RL),I (9)

(RL)~ - 1

Equation 8 does involve certain assumptions concerning the functional form of SODF. If

the PODF is measured on two perpendicular vertical sectioning planes, then it is possible

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

FIG. 4--Measurement of profile roughness on two perpendicular sections for calculation of Rs of

anisotropic fracture surface.

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8 QUANTITATIVE METHODS IN FRACTOGRAPHY

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

an indispensable tool for obtaining such information objectively.

Tensile Fracture of Composites--As an example, (and many others could be chosen),

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,

(b) A1203 inclusions,

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

these quantities are, however, related as follows

NA * = -- (i0) 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,

NffA,~, and Aft for voids and oxide particles, obtained in this manner, for samples having

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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ANTOLOVICH ET AL. ON COMPUTED TOMOGRAPHY 9

ratios ]V.a~/NA and A4tAA are 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 measurements 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 obviously 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 materials. 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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10 QUANTITATIVE METHODS IN FRACTOGRAPHY

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