On the Fractographic Analysis of

Machining Cracks in Ground Ceramics:

A Case Study on Silicon Nitride

George D. Quinn

Lewis K. Ives

Said Jahanmir

National Institute of Standards and Technology • Technology Administration • U.S. Department of Commerce
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NIST Special Publication 996

On the Fractographic Analysis of

Machining Cracks in Ground Ceramics:

A Case Study on Silicon Nitride

George D. Quinn

Lewis K. Ives Said Jahanmir

Materials Science and Engineering Laboratory

May 2003

U.S. Department of Commerce

Donald L. Evans, Secretary

Technology Administration

Phillip J. Bond, Under Secretaryfor Technology

National Institute of Standards and Technology

Arden L. Bement, Jr., Director
Certain commercial entities, equipment, or materials may be identified in this document

in order to describe an experimental procedure or concept adequately. Such

identification is not intended to imply recommendation or endorsement by the National

Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 996

Natl. Inst. Stand. Technol. Spec. Publ. 996, 107 pages (May 2003)

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TABLE OF CONTENTS

ABSTRACT 1

INTRODUCTION 1

MATERIAL 6

EXPERIMENTAL PROCEDURES 8

Flexural Strength Tests 8

Fractographic Analysis' 9

Specimen Machining Preparation 14

RESULTS 16

Ground Rod Strengths 16

Ground Bar Strengths 38

ANALYSIS OF RESULTS 56

Surface Finish 56

The Size of the SRBSN Machining Cracks 59

A Comparison of Machining Flaw Sizes in Different Silicon Nitrides 60

Fracture Mechanics Analysis of the SRBSN Machining Cracks 67

Fracture Mechanics Analysis of the SSN Machining Cracks 69

Residual Stresses 71

Comparison of Rods and Bars 72

Machining Damage and Scratches 73

Does Fracture Start from a Single Bad Striation? 74

Grinding Damage Maps 75

Machining Conditions and Standard Strength Test Methods 79

Implications for Modeling of Machining Damage 80

Comparisons to Other Selected Studies 81

Telltale Signs of Machining Damage 82

CONCLUSIONS 85

ACKNOWLEDGEMENTS 86

APPENDIX A Fracture Origin Locations in Rods and Fracture Mirror Measurements 87

for Rods and Bars

APPENDIX B Machining Procedures 96

REFERENCES 99

ABSTRACT

Meticulous fractographic analysis of broken flexural strength specimens was used to characterize

the size, shape, and severity of grinding flaws in a commercial silicon nitride. The cylindrical rods and

rectangular bars were prepared by a variety of grinding procedures. Grinding flaw size correlated

strongly with grinding direction and wheel grit size. Cracks depths from as small as 12 |Lim to as large as

80 fim were measured. Copious illustrations of machining cracks are provided. Some grinding

treatments had no deleterious effect on strength since the machining cracks were very small and fracture

occurred from the material's inherent flaws. Telltale signs of machining damage were found with

conventional low power optical microscopy using simple fractographic techniques. The telltale signs are summarized in a new series of schematic drawings that will aid pattern recognition for engineers and

fractographers. These schematics will make detection of machining cracks much easier. Machining

damage maps for silicon nitride are presented.

INTRODUCTION

Micro crack formation in the work piece is an integral part of the process of diamond abrasive

surface grinding of ceramics. Residual surface cracks may act as strength limiting flaws that degrade the

strength of the ceramic component or test piece. Figures 1-3 show several depictions of these machining

cracks. Optimal machining procedures for ceramics allow rapid, cost effective material removal while

minimizing or controlling the residual damage in the work piece. Surface grinding processes often

feature several grinding stages. Rough and intermediate grinding is done with coarse or medium grit

wheels and aggressive removal rates to bring the part close to final dimensions. Finish machining then is

applied to remove the prior damage, to obtain correct final part dimension and finish, and to avoid or minimize introduction of deleterious cracks or residual stresses. The present study was initiated as part of a NIST Consortium program to optimize ceramic

machining practices. Findings from earlier phases of the Consortium program have been presented

previously.[l,2,3 ,4,5,6,7] One component of this program was to investigate machining damage in ground ceramics. Flexural strength specimens are ideal for the study of machining flaws in as much as

they are very sensitive to surface flaws. Both conventional rectangular bar and cylindrical rod specimens were evaluated in the study. The bar specimens were tested in accordance with well-known standard test

methods. Analogous standards for rod specimens do not yet exist, and the present study was undertaken

as part of a prestandization effort to prepare just such a standard test method. Cylindrical test pieces are

preferred to rectangular beam specimens in many instances, particularly if the material is fabricated in

1
Figure 1 Schematic of flaws introduced by machining or scratching a ceramic or glass surface. An

abrasive grit particle moves from left to right. Long coplanar or short overlapping semi-elliptical parallel

cracks form in the direction of abrasive motion. Short orthogonal cracks form perpendicular to the

abrasive motion direction. Orthogonal cracks are either similar in depth or shallower than the parallel

cracks. The parallel cracks are especially severe due to their greater length and stress intensity shape

factor. This causes a dependence of specimen strength on the direction of machining if machining cracks

are strength limiting.

Transversely-ground specimens Longitudinally-ground specimens

Flexure testing activates , Flexure testing activates the parallel machining cracks the orthogonal machining cracks

2
Figure 2 Schematic of machining cracks as they may appear when viewing the fracture surface. The

cracks may link (a); link and extend (b); or overlap (c).

Figure 3 Schematic of machining cracks in a ground surface with a stress applied as shown. The cracks

may interact or link in various ways depending upon their density, relative sizes, locations and

orientations.

3
cylindrical shape or the application is for a cylindrical component. The rods also do not have edges

which are vulnerable damage sites in rectangular beam specimens. One might expect that for cylindrical

component reliability analysis, the strength data from rod shaped specimens would be more useful than

data from rectangular beam specimens

Many studies have investigated the effects of surface grinding and heat treatments on flexure

strength of cylindrical rods (e.g., [8,9,10,11]) or rectangular beam specimens (e.g., [12,13,14,15,16,17,

18,19,20,21,22,23,24,25,26,27]). Although some of these studies have shown a few illustrative machining flaws, more often than not a detailed characterization of the machining flaws such as their size,

shape, and morphology, and density has been lacking. Correlations of flaw characteristics with grinding

conditions are rare. The usual approach is to use several grinding procedures to prepare many test specimens that are then fractured in a bend strength test. Results are shown as Weibull distribution

curves or data tables and machining effects are inferred from strength degradations. Little or no

corroborative fractographic information is given. Notable exceptions to this approach have been the

studies of Hollstein et al.[28]; Rice, Mecholsky and colleagues [29,30,31,32]; and Foley, Pujari and

colleagues [33,34] wherein the sizes and shapes of machining cracks in many specimens were reported.

Nonetheless, very little work has been done to systematically correlate the size and severity of machining

flaw cracks to the grinding conditions that created them. Very little work has been done to compare the

machining flaws created by different machine shops attempting to grind to the same specifications [Refs.

15,18,35,36].^ How consistent is the machining damage from shop to shop?

One important reason for the paucity of good fractographic characterization of machining flaws is

that machining flaws are elusive in many ceramics. They are relatively easy to detect in homogeneous

materials such as glasses, very fine-grained fully dense ceramics, or some very coarse-grained materials

wherein the machining crack may be entirely within one grain. Machining flaws may be quite small; of

the order of 10 [im to 50 \xm in size, and careful microscopy is required to find them in many

polycrystalline ceramics since they often blend into the background microstructural features. It is not uncommon for a fractographer to readily find a fracture mirror centered on a surface origin location, but

not find an obvious defect at the origin. This has led some fractographers to guess that the origin must be

machining damage.'' Sometimes machining cracks are confused with other fracture origin types such as

scratches or handling damage.

Quinn [35] found significant variability in tiie quality and strengths of rectangular bend specimens prepared by five machine shops to the requirements of Military Standard 1942(MR) test method. The variability was traced to billet-tc-billet differences in the material flaws, however, and not to variations in the machining flaws. Allor et al. [15] similarly observed billet-to-billet variations in hot pressed silicon

nitride, but crucial differences between the procedures used in five different machine shops also contributed to variability. Richter [36] was

concerned that five different shops could not produce bend specimens with comparable strengths when working to specifications in a European standard. Breder et al. [18] observed strength variability of as much as 200 MPa with repeated batches from one shop, and

batches from different shops. On the other hand, Ives et al. [3,4] observed fairly consistent strength results for bars prepared by eight machine shops, both with repeated sample batches from one shop and batches from different shops. The origin could be a seam of microporosity, a delamination from a crack in the green state, a contact damage crack, a scratch, or some

other flaw the fractographer does not recognize. A fracture origin located directly on the surface may be machining damage.

4
An ASTM standard [37] for fractographic characterization of fracture origins in ceramics

facilitates machining damage crack identification. Nonetheless, it cannot be denied that machining cracks

are difficult to detect against the background microstructural features in some ceramics, even for

experienced fractographers. These difficulties were underscored in a Versailles Advanced Materials and

Standards (VAMAS) international fractography round robin project that, as one task, asked participants to

identify and characterize machining cracks [38,39].

One objective of the present study was to refine techniques to find machining cracks and to make

their identification easier for engineers and fractographers. Fractographic analysis entails pattern

recognition. Fracture surfaces and fi-acture origins have tell tale markings which may be interpretable by

the fractographer. As we will show, machining cracks do have distinctive features that can aid their

detection and interpretation. Some simple techniques with conventional optical microscopy are effective. Copious illustrations and schematic drawings are furnished of several important classes of machining

cracks in this paper.

Residual stress determinations were unfortunately not part of the study. As will be discussed in

the results section, their influence was thought to be of secondary importance as inferred from fracture mechanics analysis of the machining crack origins.

This program included testing of glass, alumina, silicon carbide, and several silicon nitrides. In

this paper we present detailed results for one particular sintered reaction-bonded silicon nitride with

primary emphasis on the fractographic findings. Results are compared to findings from other silicon

nitrides. How severe are machining cracks, when do they control strength, and how can fi-actographers

find them more easily?

5
MATERIAL

A sintered reaction-bonded silicon nitride (SRBSN)'^''^ containing yttria and alumina was used in

this study. The material is in full-scale production for several applications including cam roller followers

in a diesel engine and pump valve components for the oil extraction industry. This SRBSN has needlelike beta silicon nitride grains, 0.5 jim to 3 |^m wide by up to 10 p,m long, bonded by a second phase as

illustrated in Figure 4. The material was designed to have enhanced fracture toughness as discussed

below. The manufacturer lists the elastic modulus as 310 GPa - 320 GPa, the strength as > 700 MPa,

density as 3.21 g/cm\ and the Vickers hardness as 17.6 GPa and 15.4 GPa at 2.9 N (0.3 kgf) and 49 N (5

kgf) indentation loads, respectively. Silicon starting powders were isopressed into oversized green-body

rods that were nitrided and then gas-pressure sintered. The rods were nominally 7.5 mm in diameter by

111 mm long after sintering. The material was received in two lots in 1999. Two rods were sectioned,

mounted and polished in order to search for any evidence of microstructural gradients. The polished

sections were examined with a reflected-light microscope^ and photographed in bright field, dark field,

differential interference contrast, and fluorescence modes at up to lOOOX. A fluorescent dye penetrant was used to search for microporosity. Slight variations in the microstructure were hinted at by differences

in the reflectivity and translucency of polished specimens as shown in Figure 5.

Figure 5 Reflected light micrographs of a rod cross section showing some minor reflectivity and

transparency variations, (b) is a close up of (a). The white specks are inclusions which have a slightly

greater concentration in the outer I mm of the rod

Ceralloy 147-3 IN, Ceradyne, Cosa Mesa, CA.

Certain commercial materials or equipment are identified in this paper to specify adequately the experimental procedure. Such

identification does not imply endorsement by the National Institute of Standards and Technology nor does it imply that these materials or equipment are necessarily the best for the purpose. Leica model DMRM.

6
No obvious gradient in microstructure was detected with the sole exception that within the outer

0.8 mm to 1.2 mm of the 6 mm diameter specimens, a few more reflective spots were detected, probably

from a slightly greater inclusion content. For comparative purposes, we include data from two sets of rectangular bend specimens that were

cut from SRBSN plates. These specimens were prepared for an earlier phase of the Consortium program.

The fracture toughness of this material has been measured by the three methods in ASTM C

1421 [40] and virtually identical outcomes were obtained. The surface crack in flexure (SCF) and singleedged precracked beams (SEPB) methods gave values of 5.4 MPaVm ± 0.4 MPaVm and 5.6 MPaVm ± 0.2

MPaVm, respectively [41].^ Chevron notch (CN) testing [42] produced 5.3 MPaVm ± 0.2 MPaVm. The

small SCF precracks (50 |j,m - 70 \xm) that were created by the 49 N indentation load prescribed in C

1421 were difficult to detect and required stereo SEM photos. Larger precracks made at indentation loads

of 98 N or greater were much easier to detect since the precracks stood out clearly against the

microstructure. Small amounts of stable crack extension may have occurred in several specimens.

Although these three methods produce converging results for a very broad range of crack sizes (50 fim -

2 mm), there is evidence that the material does have a rising R-curve. [43,44,45]

Figure 6 The four-point fixtures used for the rod flexural strength tests. Cradles on the top (arrows) and

bottom apply the load evenly to the specimens on the top and bottom.

One standard deviation.

7
EXPERIMENTAL PROCEDURES

Flexural Strength Tests

Flexure testing is an ideal method to accentuate surface machining flaws in rod or rectangular bar

specimens. Sample sets of 10 or 30 rod or bar specimens were prepared and tested per grinding

condition. All cylindrical rods were 6.0 mm in diameter by 100 mm long and were transversely- or

longitudinally ground as described below. Rods were tested on a four-point flexure fixture specifically

designed for cylindrical rod specimens (Figure 6). The spans were nominally 40 mm x 80 mm and the

crosshead rate was 1 .3 mm/min. The fixture is a typical semi-articulating design with the key exception

that it has four cradles at the load distribution points.[7] These cradles distribute the load evenly onto a

test piece and avoid severe contact stresses or wedging stresses that would otherwise occur with crossed

cylinders if the rod specimens were placed directly on loading rollers as is normally done with rectangular

bars. The loading geometry is equivalent to the classic four-point configuration and the stress state is

identical except in the immediate vicinity of the cradles. The loading rollers are free to roll to eliminate

frictional constraint forces. In keeping with customary practice, the flexural strengths reported are the

maximum ("outer-fiber") stresses that existed in the rod specimen at the instant of fracture even though

the rods experience the maximum stress only on a very small region (a line) on the specimen bottom. ^

All rectangular bars were "B" sized (3 mm x 4 mm x 45 mm) four-point flexure specimens

prepared in accordance with ASTM C 1161 [46]. Specimens were either longitudinally- or transversely

ground as described below. The four long edges were chamfered in accordance with C 1161. Only a few

specimens fractured from edge damage in this entire study. Specimens were tested with fully-articulating

four-point fixtures with 20 mm and 40 mm spans under laboratory ambient testing conditions (21°C - 25^; 40 % - 70 % R.H.) with a crosshead displacement rate of 0.5 mm/min as per ASTM C 1 161

The rods and bars were different in size but the Weibull effective volumes and effective surfaces were actually quite similar. [47,48] In fact, the bars had greater effective surfaces since they had a large

surface region (4 mm wide x 20 mm long) within the inner fixtures spans whereas the rods only had a tiny

surface region (a line) that experienced the maximum tensile stresses within the inner span. For example,

using a Weibull modulus of 16, the rods and bars had effective volumes of 13.1 mm^ and 7.5 mm,^

respectively. Effective surfaces were 77.4 mm^ and 88.4 mm,^ respectively. Weibull strength scaling

predicts the strengths should agree within a few percent for these volume or surface ratios.'' Hence, any

major differences in strengths must have been due to differences in flaw type, severity, or density and not Weibull size scaling effects.

The maximum stress in the rod is also required for Weibull analyses. The only instances that the stress should be adjusted for the location of fracture are when computing fracture mirror constants and when performing fracture mechanics analysis of the flaw at the origin. Using different Weibull moduli alters the effective surfaces and volumes, but does not change the overall conclusion that the strength differences should be very small. For example, for an m of 27. the effective volumes are 6.0 mm' and 4.4 mm' for rods and bars, respectively. The effectives surfaces are 58.8 mm^ and 85.0 mm^ respectively.

8
The fracture origin locations were monitored in every instance. Origin locations were usually

evenly distributed within the inner gage section with no tendency to cluster at the loading rollers or

loading cradles in the case of the rods. An occasional primary fracture did occur at or near an inner

loading point or cradle. Secondary breakages were quite common at the loading points, but a careful

inspection of specimens with multiple fractures usually confirmed that the primary fracture origin was in

the inner gage section. Interpretation of primary and secondary breakage patterns in flexural specimens is

reviewed in ASTM standards C 1322 and C 1161.'

Fractographic Analysis

The overall fractographic analysis was performed in accordance with ASTM C 1322. All fracture

surfaces of every specimen in this study were examined with a stereo binocular microscope* at

magnifications up to 205X. It was initially felt that optical microscopy would not be effective in finding

and characterizing the machining cracks, but experience proved this notion was wrong. A video camera

fed images to a printer that could make hard copies of the images. Part way through the program, a newer

high-resolution digital camera"^ and a computer replaced the video camera and printer. The newer digital camera recorded very sharp images. We discovered that proper illumination was crucial to finding and

characterizing the machining cracks. It was essential to illuminate the specimen fracture surface from the

side or rear with a bright, low incident angle (vicinal) illumination source as shown in Figure 7. This

low angle illumination accentuated many crucial, tell tale features of machining damage, as the pictures in

this paper will demonstrate. Illumination fi-om directly above the specimen fracture surface washed out many key features. Contrast was reduced and helpful shadows lost. Low angle illumination from the same side of the specimen that contained the machining cracks was also inadvisable, since the

illumination blurred key fracture surface features on the specimen edge at the origin and the material was

partial translucent. Although we used an elaborate discussion stereomicroscope for these examinations

(Figure 7a), the same image quality is obtainable with simpler stereomicroscopes as shown in Figure 7b.

The key to success was having a stereomicroscope that was capable of 100 X -200 X magnifications and

a bright directional illumination source. Simple specimens holders such as shown in Figure 7c were also

helpful in aiding the examination.

Selected specimens (as many as one-half of a sample set) were examined with a scanning electron

microscope (SEM).' Multiple photos were taken with the SEM to ensure that both the fracture mirror and

Secondary fracture planes often were not quite perpendicular to the specimen's long axis or the symmetry of a typical primary fracture plane was missing. The tilts and asymmetries are due to elastic energy reverberations in the specimen. In some instances, the secondary

fracture origins were located on the top side of the specimen, in what was originally the compression side of the specimen since elastic wave reverberations changed the phase of the stress field. With a little experience, secondary fractures can often be identified within seconds, especially if the loading points and tensile and compressive surfaces have been marked before testing. Wild Model M-10 discussion stereomicroscope that allowed two viewers to simultaneously view a fracture surface. Spot Insight, 1600 x 1200 color pixels. Media Diagnostics, Sterling Heights, MI.

Hitachi Model S-530.

9
Figure 7 Stereo optical microscopes used to find the fracture origins, (a) shows the Wild MIO

discussion stereo microscope used in the study, (b) shows a more common stereomicroscope. Notice the

intense, directional, low angle illumination applied to the specimens. Machining cracks may be

highlighted by such illumination from the specimen side, (c) shows simple specimen holders such as the

alligator clip mount on the left that enabled specimens to be quickly mounted and tilted around while

viewing through the microscope. The other holders enabled a fractured specimen to be assembled and

lined up in convenient grooves for examination of the ground surfaces, (d) shows low angle grazing

(vicinal) illumination. ;

10
the fracture origin were recorded. Matching fracture halves were frequently examined in the SEM.

Stereo pairs of SEM photos were sometimes taken and were especially valuable in ascertaining the

topography of the machining cracks. This intensive level of fractographic study is warranted for machining damage, which as we have noted above, can be difficult to discern against the background

microstructure. Not every specimen was examined this thoroughly, but within a give set, it was common

to examine as many as 30% of the specimens in the SEM.

As the study progressed, and we gained greater experience in detecting the tell tale features of

machining damage cracks, we were able to speed up our inspection process and optimize photo taking.

By the end of the study, we could immediately identify transverse grinding machining damage on the first

inspection with the stereomicroscope in this SRBSN material. We often followed the guidance of ASTM

C 1322 and took a full suite of three or more photos from each fracture surface showing the entire fracture

surface, the fracture mirror, and the fracture origin.

Fracture mirrors were invaluable in leading attention to the fracture origins. The angular location

of the fracture origin relative to bottom dead center (where the tensile stress was a maximum) was

measured in all the rod specimens. This enabled the stress at the exact fracture location to be calculated

for fracture mirror and fracture mechanics analysis. Details of this procedure and two maps showing the

distribution of fracture origin locations in rod specimens are in Appendix A. Fracture mirror sizes were measured with the stereo binocular microscope, while viewing at 30X - 63X through the eyepieces. In

general, we found it convenient to view the fracture surface with a magnification such that the mirror

region covered one-third to one-half the field of view. Mirrors were plainly evident at low

magnifications, but accurate assessment of their size was difficult. The mirror region was somewhat

bumpy in this self-reinforced silicon nitride, so some judgment as to what was the mirror boundary was

necessary. The criterion used in the present study was that the mirror boundary occurred at the point

where hackle commenced and there was an obvious roughness change relative to the mirror. Full details on the mirror measurements are in Appendix A.

Hereafter in this paper, we will refer to machining cracks as either parallel cracks or orthogonal

cracks. The qualifier denotes the orientation of the crack plane relative to the grinding direction. Figure

1, which is adapted from a figure by Rice and Mecholsky [29],'" is a schematic of flaws introduced by

machining or scratching a ceramic or glass surface. Semi-elliptical parallel cracks form parallel to the

abrasive motion direction. These may either be long coplanar cracks or shorter overlapping cracks. Short

orthogonal cracks form perpendicular to the abrasive motion direction. Orthogonal cracks are either

There are two primary changes to their figure. First, the bowed orthogonal cracks are corrected to bow in the direction of the abrasive motion. Secondly, Rice and Mecholsky used the terms "longitudinal" and "transverse" in a manner that caused some confusion. They used

the terms to describe the cracks with respect to the grinding direction. The long cracks parallel to the machining direction were called "longitudinal cracks", and the shorter orthogonal cracks were called "transverse cracks." Using their nomenclature, flexure testing of

longitudinally-ground bend bars would activate transverse cracks and vice versa. The new nomenclature shown in Figure 1 eliminates this confusion.

11
Figure 8 Orthogonal machining cracks, (a) and (b) show a machining crack in a fine grained hot-pressed

siHcon nitride. The specimen has been tilted back to show the ground surface, labeled "T" for tensile surface. The machining crack (white arrows) is much deeper than the striations. (c) shows a crack in a

hot-pressed silicon carbide. The single striation (black arrow) is helpful in making the interpretation.

(c)

12
similar in depth or deeper than parallel cracks for a given grinding condition [29-31], but the parallel

cracks are much severer due to their greater length and stress intensity shape factor [49]. The difference

in size and shape of the orthogonal and parallel cracks usually causes a dependence of specimen strength on the direction of machining //"machining cracks are strength limiting. Transversely ground specimens

are usually weaker than longitudinally ground specimens.

Parallel machining cracks were not too difficult to detect on fracture surfaces when they were

strength limiting, no matter how small they were. With some experience, we could routinely detect them

even with the stereo optical microscope. Orthogonal cracks may be easy to detect in glasses, some very

fine-grained materials, single crystals, or in very coarse-grained materials in which the crack is within a

single grain. On the other hand, they are very difficult to detect in materials in which the microstructure

masks the cracks, e.g., materials with medium to coarse grain sizes, some toughened ceramics, and

composites. Figure 8 shows orthogonal cracks in fine-grained hot-pressed silicon nitride and silicon

carbide. Unfortunately such cracks, which are typically of the order of 10 |U.m to 50 |j,m in size

(depending upon the grinding conditions), blended in or "hid" very well on the SRBSN fracture surfaces. The SRBSN has rough fracture surfaces even in the mirror region. In any event, only a few sets of

longitudinally prepared specimens were studied in the final phase of the NIST Machining Consortium

program since earlier work had shown that longitudinal grinding had little or no effect upon strength of

this SRBSN. [1-6]

To improve our fractographic skills at detecting small semicircular cracks in this SRBSN, we

tried a series of fracture toughness experiments using artificially created tiny SCF precracks. In this test, which is one of the methods in the ASTM standard C 1421, a Knoop indenter is used to create an artificial

semicircular or semielliptical flaw in a bend bar. The exact fracture location is controlled and subsequent

fractographic analysis can concentrate on finding the markings and features that distinguish the crack

from the background microstructure. [50] The artificial flaw size was controlled by changing the

indentation load. Semielliptical or semicircular precracks made at loads of 98 N or greater (-100 - 150

fim deep) were relatively easy to detect in this SRBSN as shown in Figure 9b. Precracks made with 49 N

(a 60 |j.m deep) were very difficult to discern and required meticulous stereo SEM microscopy. Artificial

cracks made at 29.6 N load (< 50 ]xm deep) could not be detected.

Size estimates of the parallel crack and material flaw origins were made with the 1 }xm resolution

precision traversing stage in the stereomicroscope (Figure 7a) and from SEM photo analysis. Crack

depths (a) could often be measured to within 5 jim or better, although in some problematic specimens the

uncertainty was as much as 10 fim. The crack width (2c, the length along the ground surface) dimensions

had greater uncertainties. Uncertainties of 20 jim - 40 ^m were common, and in some instances the

uncertainty for parallel cracks was as much as 50 fim -100 )j.m. The uncertainty in the width dimension is

of less concern, since the depth dimension is the controlling dimension for determining the stress

intensity, Ki for a long surface crack. [49] Once a crack surface length becomes long, the stress intensity

13
Figure 9 SEM photos of artificially introduced Knoop semielliptical flaws, (a) shows a « 50 jim deep

crack made in a fine-grained hot-pressed silicon nitride (NC 132) with the 25 N Knoop indentation still intact (smaller arrows), (b) shows a 135 \xm deep crack in the SRBSN introduced by 144 N Knoop

indentation (white arrows), with the indentation and residual stress damage zone removed. Despite the

greater surface roughness, the large semielliptical precrack is detectable. Changes in direction of micro

hackle at the boundary (small black arrows) helped identify the critical crack size. Knoop flaws (< 5 N

load, < 50 )im deep) could not be detected in this material.

(a) (b)

shape factor Y approaches 1.99 for the case of a long surface crack and additional length increases along

the surface have negligible effect on the stress intensity factor.

Specimen Machining Preparation

The rods and bars were ground with conventional resin bond diamond abrasive grinding wheels.

Bar specimens were surface ground either perpendicularly (transversely) to or longitudinally to the bar

long axis. Rods were primarily transverse centerless or cylindrical ground, although in one instance,

longitudinal grinding was applied. The well known rectangular bar flexure strength standard test methods

specify longitudinal grinding to control the orientation of machining damage cracks and minimize the

chance that the machining cracks will control strength.

Groups of 10 or 30 specimens were prepared by several shops, designated C, F, N, S, and W,

which participated in the consortium program." Key preparation steps are summarized below, but more

details of the grinding conditions are in Appendix B.

" NISTwas "shopN.

14
Rod specimens were ground down from the 7.5 mm diameter blank rods to 6.00 mm diameter x

100 mm long in several steps. As we will show, the inherent strengths were obtained with one set

prepared by Shop C which used longitudinal centerless finish grinding with a wheel depth of cut of 0.005

mm for 5 passes at an axial feed rate of 3.6 mm/s with a 2000 rpm work piece rotational speed. For

comparison, this shop also prepared one set of 30 specimens with conventional centerless grinding with a 320 grit, 203 mm diameter wheel with 0.05 mm wheel depth of cut to initially grind the rods to 6.025

mm. Rods were then finished down to 6.00 mm by conventional transverse centerless grinding with a

0.005 mm wheel depth of cut for 5 passes at a slow axial feed rate of 2.54 mm/s at a 680 rpm work piece

rotational speed. The work piece rotational speeds were set to approximately match the volumetric rates of material removal obtained in comparable sets of rectangular bars described below.

Other shops also prepared rods by transverse or centerless grinding with various wheel grits.

Three shops used 600 grit centerless or transverse cylindrical finish grinding in order to minimize the

machining crack severity. As we will show, they obtained similar results. Shop F prepared one set by

transverse centerless grinding. Shop N used a three-step procedure, starting with centerless grinding with

a 180 grit, 254 mm diameter wheel with an in feed of 0.050 mm per pass down to 7.05 mm diameter, then

switching to an intermediate step of 400 grit, 250 mm wheel with 0.013 mm/pass down to 6.3 mm

specimen diameter, then finishing the specimens down to 6.00 mm with a 600 grit, 203 mm diameter

wheel with 0.005 mm/pass. Shop W used a two-step process, starting with a 320 grit, 203 mm wheel with

rods mounted on centers, plunge grinding down to 6.30 mm - 6.35 mm diameter, then finish grinding

with a chuck cylindrical grinder and a 600 grit, 203 mm wheel with 0.025 mm/pass and a longitudinal

feed (work piece) of 254 - 305 mm/min.

Shop N prepared one set of 10 transverse centerless ground rods with a 220-grit wheel.

Shop F prepared one set by transverse centerless grinding, but with an unknown, apparently very

coarse grit wheel that was subsequently estimated to have been 150 grit or 1 80 grit judging by the surface

roughness. This set probably was prepared with the shop's normal rough grinding procedure and the

finish-grinding step was inadvertently omitted. The data were useful nonetheless, since they represent the

severe damage that may occur with rough grinding.

In contrast with the grinding processes described above, one shop finished their rod specimens by

lapping. Shop S rough ground their rods by an unidentified procedure, but evidently centerless or

cylindrical transverse grinding. Two separate groups of three specimens were then carefully lapped (with

an unspecified amount of material removed) in an attempt to remove the surface damage.

Several rectangular bend bar sets were ground for comparison to the rod data. Most 3 mm x 4

mm X 50 mm cross-section rectangular bars were cut from the 7.5 mm diameter rod blanks. Shop C

prepared two lots of 30 standard "B" rectangular bar^, one group ground transversely and one group

ground longitudinally in accordance with the ASTM C 1 1 61 "baseline" procedure. Shop F produced one

15
batch of 30 rectangular bars ground transversely with a 600-grit wheel using procedures that closely

matched the transversely ground rods that they also prepared.

Two rectangular bar sets, which were from an earlier phase of this study, are included here for

comparison. Shops C and F prepared rectangular bars by transverse grinding with 150 grit and 80 grit

wheels, respectively. These specimens were cut from SRBSN plates, unlike all other specimens

described in this paper.

Surface roughness was measured with a diamond stylus profilometer, perpendicular to the

grinding direction, on at least three specimens per sample set.

RESULTS

We present a brief discussion of the strength outcomes and the Weibull statistical analyses. Our

primary goal is to not to dwell on the strength or statistics issues, but to document the key fractographic

findings. What did the machining cracks look like? How large and how severe were they?

Each specimen set revealed crucial information about the nature of the strength limiting flaws,

and machining damage cracks in particular. Different types of machining cracks are described below, and

our objectives are to illustrate these machining cracks, correlate them to the machining conditions, and

characterize and document the tell tale features so that other investigators can find them. Our primary

emphases will be on the grinding wheel grit size and the grinding direction since these parameters proved

to be the dominant factors in the creation of the machining cracks.

One set of 320 grit longitudinally ground rods furnished the inherent or "baseline" strength of this

material, which is to say, the strength of the material as controlled by material flaws with negligible or no

influence of machining cracks. Results for all other grinding treatments are compared to this baseline

set. Table 1 lists all flexural strength results for 116 rods and 70 bars from the rod blanks, and 60 bars

cut from plates. Weibull parameters were computed by maximum likelihood analysis in accordance with

ASTM C 1239. [5 1] Tables 2 and 3 show a more reader-friendly summary of the effect of machining in

each case with key fractographic findings. The rod results are reviewed first.

Ground Rod Strengths

The seven data sets and the fractographic findings are discussed in order, starting with the strongest set shown in Figure 10. Shop C prepared thirty 320 grit longitudinally ground rod specimens that fractured

almost exclusively from material flaws. Hence this set will hereafter be termed the "baseline set. " The

material flaws were inclusions (Fe and Ti with a red tinge) Figure 11-12, second-phase compositional

inhomogeneities, Figure 13; large grains; and porous regions, Figure 14. A large subset of these

specimens was examined in the SEM. Many of the origins were well beneath the surface as shown in

Figures 11 -14 and in the origin location distribution map. Figure Al in the Appendix. The material

16
Table 1 Flexural Strength Results for cylindrical rods and rectangular bars. WeibuU parameters

estimates are from the maximum likelihood analysis in accordance with ASTM C 1239. n is the

numbers of specimens per test set.

Grinding Conditions Rods Bars

Shop Wheel Direction Avg

^IVIn CI ]

S. dev. Char.

Str. (MPa)

Weibull Modulus

nn

Avg S. dev.

^ivi 1 dJ

Char.

Str. (MPa)

Weibull Modulus m

30 816 59 843 14.6 655 51 677 15.0

30 670 32 686** 21 .9 550 42 570** 12.5 w 600 grit Transverse 10 764 55 789 13.3

N 600 grit Transverse

Centerless 10 806 49 827 17.6

F 600 grit Transverse 10 735 47 754 18.9 726 19 735 35.9

N 220 grit Transverse

Centerless

10 589 22 600 21.3 C

* 150 grit Transverse 30 458 72 488 6.8*

F

150/180

grit Transverse 10 427 14 433 28.1 F* 80 grit Transverse 30 430 62 443 8.2* S lapped 6 628 76 = 660 = 7

Specimens cut from 2 sets of plates, not rods. Strengths of the two sets differed, accounting for the atypically low Weibull modulus for this material. Threshold strength > 0.

flaws had a wide range of sizes, which is not surprising since there were four different types. The porous

regions ranged from equiaxed shapes with sizes of 25 \xm - 35 \im diameter to elongated shapes of the

order of 20 |j.m wide by 75 jim long. The inclusions and compositional inhomogeneities were often larger

and were sometimes equiaxed with 80 \im - 90 \xm diameter or elongated with sizes up to 20 \xm X 100

fim. Several origins at the surface may have had small orthogonal machining cracks that interacted with

the material flaws, but overall, machining damage was a minor factor in these specimens. The Weibull

modulus was respectable (~ 15) in these longitudinally ground 320 grit rods even though there were four

active flaw populations. These flaw types were uniformly distributed along the strength distribution

curve. Three shops applied 600 grit transverse grinding (centerless or cylindrical). Strengths matched or

nearly matched the baseline strength distribution. Hence controlled 600 grit transverse grinding has

minimal or no deleterious effect upon strength in this material. Shop N's data virtually overlaps the

baseline strength distribution as shown in Figure 10. Shop N and W specimens were only inspected with

the stereo optical microscope, and although red inclusions were detected in a few of the specimens, nearly

all fractured from origins located right at or immediately beneath the ground surface. Specimens from the

shop F set, which was 10% weaker on average than the baseline set, were examined with both optical and

scanning electron microscopes. The fracture origins were shallow 13 \xm - 20 \im deep parallel

machining cracks that interacted with material flaws.

17
Table 2 Rod strengths and fracture origins.

SHOP Specimen

Preparation

Wheel Grit Depth of Cut

Surface finish

Effect on Strength

Average ± std dev (MPa)

Weibull parameters

Char. Str. (MPa)

Modulus, m

Primary Fracture Origins

C

Longitudinal (Centerless) 320 grit 5

0.45 (im ± 0.04 jim

No effect "Baseline Strength "

816 ±59

843 m= 14.6

Inherent Volume

lndusions"composrtional -^^v|^ ^"^^ ''m

Inhomogeneities, Porous ' ^

Regions, Large Grains —^—

N

Transverse 600 grit

0.054 ± 0.002 yfn

No effect.

806 ±49

827 m= 17.6

Parallel machining cracks Minor interaction with ~a '^SC

inherent flaws ^ _

'S^

w

Transverse

(cylindrical) 600 grit 25

0.14 ^m± 0.02 |jm

6% Reduction

764 ±55

789 m= 13.3

Parallel machining cracks Minor

inherent

interaction flawswith V- ^. ^

F

Transverse 600 grit

0,14 t 0.02

10% Reduction

735 ± 47

754 m= 18.9

Parallel machining cracks

13 - 20 ^m deep

Interaction with some — V»ii

inherent tiaws "-.-iTi.-; -

C

Transverse 320 grit 5

0.24 ± 0 02 y.m

18% Reduction

670 ± 32

686 m = 21 9Flat coplanar j^vparallel machining cracks 'z- -- -~

16 - 34 ^m deep _

N

Transverse 220 grit 5 i^m 28% reduction

589 ±22

600 m = 21.3

Long, parallel nnachining cracks ,^?<: - ^lyA- 25 - 40 Jim deep

S

Transverse / Lapped

30 |im grit

0.074 y.m ± 0.05

15-30% Reduction

628 ± 76

?660 m?7 V machining cracks (ffc.

fi'om prior grinding 20 - 35 deep °g

F

Transverse 150 or 180 grit

0.80 ^im ± 0.06 nhi

48% reduction

427 ± 14

433

nn = 28.1 40 - 80 ^m deep: some V cracks

fi-'^' '<t # ^ ^ ^^^i ?'

Table 3 Bar strengths and fracture origins

SHOP Specimen

Preparation

\MieelGnl Depth of cut Surface finisti

Effect on Strength

Average, std. dev. (MPa)

Weibull parameters

Char. Str. (MPa)

Modulus, m

Primary Fracture Origins

F

Transverse 600 grit 5 ^m 7

0.09 ± 0.01

10% less than tiest rod strengths

same strengths as their 600 grit cods.

726 ± 19

735 m = 36

12 - 18 jimdeep parallel machining cracks, or 20 - 40 um diameter Porous Regnns (bumps at origin)

C

Lonaitudinal 320 grit ASTMC1161

standard

multi-step 5

0.27 ^m± 0.01

10% less than 600 grit, transverse bars above 20% less than

best rods

655 ± 51

677 m= 15

Pores/Porous regions/Co (lapsed Agglomerates

'linear or planar flaws'

wtth 15 - 20 um deep orthogonal machining cracks

'.^ ^; ^ "^^fff^,!0i/ i'lUl'ff^il!

C

Transverse 320 grit 5

0.29 nm± 0.02 iim

24% weaker than best 600 grit transwrse bars above

550 ±42

570 m= 12 5

23 - 40 ^m deep 'zipper cracks' some evidence of stable crack extension ^ -

c

Transverse 150 grit 37% weaker than best 600 grit trans^rse bars above

458 ±72

2 sample k)ts

488 m = 6.8

Meandering parallel and zipper cracks 30 ^m - 70 ^m deep

AH specinnens broke from a single dominant strtation.

F

Transverse 80 grit

41 % weaker than best 600 grit transwrse tiers above

430 ±62

2 sample lots

443 m = 8.2

Meandering paraOel and zipper cracks, 35 um - 80 uHi deep

18
Figure 10 Weibull strength distribution graph for all rod data sets. A unimodal distribution line is fitted to each set of data. Each circle is an individual rod test resuh. The rods ground longitudinally with a 320

grit wheel primarily broke from material flaws and represent the inherent or baseline strength of this particular lot of SRBSN. Three sets of specimens that were transversely ground by different machine

shops with 600 grit wheels had similar strengths. Shop N's 600 grit transverse set matched the baseline

set.

F

Transverse 150/180 grit

n = 10 m = 28.1

cf o

= 433 MPa

Mactilning cracks, 40 - 80 tim deep

X 300 - 500 long. Associated with deep

grooves, not exactly perpendicular

to specinien axis.

N

Centeriess Transverse 220 grit

n = 10 m= 21.3 a^ = 600 MPa

25 - 40 nm deep

X 180- 300 unn long machining cracks Sonne interaction with inherent flaws

c

Centeriess Transverse 320 grit

n =29 m = 21.9

cr 0 = 686

Elongated machining

cracks in nearly all. 16 - 34 nm deep x 100-300+ urn long. A few inherent flavre at the high strength end.

F

Centeriess Transverse 600 grit

n = 10 m= 18.9 <Jo =754

All origins on

surface. MD 13 - 20 tim and

inherent flavra.

w

Cylindrical Transverse 600 grit

n = 10 m= 13.3 a 0 = 789

N

Centeriess Transverse 600 grit

n = 10 m= 17.6 o o

= 827 MPa

Optical exam. Red inclusions (Fe)

only. Need SEM. detected in All origins on several specimens,

surface. Need SEM. 99.9

2

1

0.5

"Baseline Set" C

Longitudinal 320 grit

n = 30 m= 14.6 o 0 = 843 MPa

Inherent flaws: Inclusions (Fe, Ti), 2nd phase Comp. Inhomegeneities. Large Grains, Porous Regions, some deep in interior some deep in Interior

n = 6 m = 7.3

<j o

= 660 MPa

Machining cracks. 20+ to 35 |im deep

by hundreds of \an long

Off axis. Progressively more severe

machining damage

400 450 500 600 700 800 900 1000 1100

Strength (MPa)

19
Figure 11 Material flaw fracture origin (iron inclusion) in a 320 grit longitudinally ground rod with a

strength of 75 1 MPa (684 MPa at the origin). These and the following illustrations follow the guidance in ASTM Standard C 1322 and show: (a) most of the fracture surface; (b), the fracture mirror; and (c), a close-up of the origin.
Figure 12 Material flaw fracture origin (iron inclusion) in a 320 grit longitudinally ground rod with a

strength of 813 MPa (682 MPa at the origin).
Figure 13 Material flaw fracture origin in a 320 grit longitudinally ground rod with a strength of 753

MPa . The origin is a compositional inhomogeneity associated with excess sintering aid. The region has

a greater glass content than normal.

22
Figure 14 Material flaw fracture origin in a 320 grit longitudinally ground rod with a strength of 763

MPa. The origin is a porous region beneath the ground surface.

(a)

(b)

23
More serious machining damage was created with coarser grit wheels in the transverse direction.

Shop C's 320 grit transversely ground rods were 18% weaker than their set of longitudinally ground rods

prepared with the same grit wheel. This strength difference is not surprising, in light of the different

orientations of the machining cracks. Optical examination on all specimens and SEM inspection on over

one-third of the specimens confirmed that the strength limiting flaws in the transversely ground set were

elongated coplanar parallel machining cracks as shown in the top left of Figure 1 and in Figures ISIS. These elongated cracks were fairly uniform in depth (16 |am - 34 ixm) but had variable lengths along

the ground surface (100 |Lim - 300 |im). Some of these cracks showed evidence of stable crack extension.

It cannot be ascertained whether this occurred during the machining process (wherein the crack might

have popped in and then been extended by subsequent grinding) or during the flexural strength test. A

key, telltale aspect of these machining cracks was that they often were tilted or at slight angles to the final

fracture plane which formed the fracture mirror. This change in crack propagation direction confirmed

our interpretation that these were critical crack sizes at the onset of fast fracture. As will be discussed

below, the apparent fracture toughness based upon these crack sizes matched plateau, large crack

toughness values.

The machining flaws sometimes closely overlapped. Several specimens in the high strength

portion of the distribution had material flaw origins and did not break from machining flaws. This is not

surprising since these strengths overlap the baseline strength distribution. The 320 grit parallel machining

cracks were only 16 )u,m to 34 )j.m deep but they were very long and shallow, and thus were more

deleterious to strength than the larger, rounded, or blunter material flaws.

NIST prepared one set of ten 200 grit transverse ground rods that had even lower strengths

(Figure 10). The fracture origins were primarily 25 fim - 40 )j.m deep parallel machining cracks such as shown in Figure 19. Some of these interacted with the material flaws such as pores and agglomerates.

The weakest rod set was inadvertently prepared by Shop F with an unrecorded, but coarse

grinding wheel in the transverse mode. We estimate from the surface roughness that the wheel may have

been 150 grit or 180 grit. The strength limiting flaws were machining cracks 40 \xm - 80 |j,m deep by 300

fj.m - 500 |a,m long. The machining cracks were easy to detect on the fracture surface with the stereo

optical microscope. Figure 20 shows a classic example of a parallel crack. It is deeper that the parallel

cracks shown previously but rather than appearing as a single long elliptical crack, it is serrated as though

it were made up of a number of small crack segments with different orientations or planes. Many of the

specimens from this set had an even more distinctive feature. The mirror region often had pronounced

steps that created a "V" marking (Figures 21 and 22). This crack pattern was caused by specimen axial

displacement relative to the grinding wheel, as illustrated in Figure 23. Grinding with axial feed created

a spiral pattern ("barber pole") of striations and subsurface cracks that were not quite perpendicular to the

specimen axis and the applied sfress axis during flexure strength testing. Consequently, the fracture

24
Figure 15 Coplanar parallel machining crack in a 320 grit transversely ground rod (657 MPa). (b) shows

the mirror region which is centered on a parallel machining crack created by transverse grinding, (c)

shows a close-up of the origin. The crack underneath the dark striation-crack extended to a depth of 17

Jim (arrows). Using that depth, the stress intensity shape factor of 1 .99 for a long surface crack, and the

stress at the origin (653 MPa), the fracture toughness was calculated to be 5.36 MPaVm. The machining

crack can be distinguished from the fracture mirror plane since the machining crack (and possible stable extension from it) is slightly tilted and is more irregular than the plane of final fracture.

25
Figure 16 Coplanar parallel machining crack in a 320 grit transversely ground rod (641 MPa). (b) shows

the fracture mirror region centered on a parallel machining crack, (c) shows a close-up of the origin

which also shows evidence of stable extension. The critical crack size, which is more obvious in (b), is marked in (c) by arrows.

26
Figure 17 Coplanar parallel machining crack in a 320 grit transversely ground rod (63 1 MPa).
Figure 18 Coplanar parallel machining crack in a 320 grit transversely ground rod (634 MPa). The 19

fim deep machining crack leads to an estimate of fracture toughness of 5.2 MPaVm.

28
Figure 19 Parallel 25 fj.m deep machining crack in a 220 grit transversely ground rod (566 MPa

nominal, 557 MPa at origin center), (c) is a composite of two SEM photos of the origin crack.
Figure 20 A parallel machining crack in a Shop F, coarse-grit (150/180), transversely ground rod with a

strength of 409 MPa. The crack has a slight zigzag appearance and can be considered one form of a "zipper crack."
Figure 21 Classic "V" machining crack in a transversely ground rod (42 1 MPa). The arrows in (d)

show the offset parallel machining cracks that are on several tiers as schematically shown in (b). (e) is an SEM image of the origin and the ground surface, (f) is an optical image that shows the ground outer surface at the origin site. The striations are not quite perpendicular to the specimen axis.

(a) (b)

31
Figure 21 continued

32
Figure 22 A similar "V machining crack" in a transversely ground rod. (4 1 9 MPa)

33
mirror had segments on different planes labeled a, b, c in Figure 23b. The steps between the segments in

the mirror created the V pattern. The jogs or steps gradually disappear as the crack segments join and are

analogous to wake or twist hackle markings. These telltale markings are indicative of one class of

machining cracks, which we shall term "V" machining cracks. In some cases, only one leg of the V was

present on a fracture surface.

Shop S lapped two sets of three specimens in an attempt to produce "damage-free" rods, but the

strengths were quite low. Even though the outer specimen surface had a smooth finish, the fracture

origins were obvious "V machining cracks that were 20 |j,m - 35 fim deep by 200 )n,m - 300 \xm long as shown in Figure 24. Telltale, stray striation segments were present on the lapped specimen surface as shown in Figure 25. There was a very strong correlation of strength with final rod diameter that varied

from 5.98 mm to 6.03 mm as shown in Figure 26: the smaller the diameter, the stronger was the

specimen. This confirms that the surface lapping did not remove sufficient material to eliminate damage

from prior transverse grinding. The curve fit through the data shows that had an estimated .060 mm more

of the material been removed from the diameter (.030 mm from each surface) then the inherent strength of

the material may have been reached in all these specimens assuming that the lapping itself did not

introduce damage. That is, however, a lot of material to remove by lapping.

Flat, coplanar parallel "V" machining crack

(a) (b)

Figure 23 The motion of the work piece relative to the grinding wheel during transverse grinding may

create either (a) flat "coplanar parallel cracks" such as in the Shop C, 320 grit transverse-ground rods, or (b), stepped "V machining cracks" such in as the Shop F, coarse-ground rods. The fracture mirror

region is on three offset planes marked "a", "b", and "c." The steps between these three planes create the

V marking.

34
Figure 24 The lapped specimens had deep machining cracks below the surface from prior grinding, (a)

and (b) show double fracture mirrors, an unusual fracture pattern (arrows). The origin in the left mirror is a variant of the "V machining crack" as shown in (c).

35
Figure 25 Lapping did not remove sufficient material to eliminate the prior, deeper damage. These two

figures show the outer lapped surface. Although much of the surface is smooth, a few deep striations remain (arrows). The fracture surface is on the right.

Figure 26 The strength of the lapped specimens was directly related to the final rod diameter.

Extrapolation of the data to the baseline strength suggests that if the rods had been lapped 20 jum to 60

^m more to a final size of 5.967 mm, the subsurface machining damage would have been eliminated.

(0 Q.

c

(0

850

800

750 -

700

650 -

600

550

500 1—I

\—\—I

\—\—\—I—I—I

]—I

\ r

5.940 5.950 5.960 5.970 5.980 5.990 6.000 6.010 6.020 6.030 Diameter (mm)

36
Figure 27 Weibull strength distribution grapii for the rectangular bars. Each square is a bar strength test result. The dashed lines for the baseline rod strength set and the shop F 600 grit transverse rod data sets are shown for comparison.

99.9

99

95

90 +

80

63.2

50

20

10

5

2

1

0.5

Transverse 80

n=30 m = 8.2

: 443 MPa

Meandering parallel cracks

in deep striations 35 - 80 deep

"Baseline Rod Set"

Longitudinal

/ 320 grit

Transverse 150

n=30 m = 6.8 = 488 MPa

Meandering

parallel cracks *

zipper aacks

30 - 70 iim deep

Longitudinal 320

(ASTM)

n = 30 m= 15.0

<J o = 677 MPa

Agglom. + Pore flaws with possible enlargement from

1 5 - 20 urn deep machining cracks. 7 chamfers, 2 incl., 1 scratch, 2 large grain

Transverse 600

n=10 m = 35.9 a o

= 735 MPa

Elongated machining cracks, 12 - 18 |im deep at skip marks

with some interaction with Porous Region and Porous Seam flaws

250 300 350 400 450 500 600 700 800 900 10001100

Strength (MPa)

37
Ground Bar Strengths

Five bars sets were prepared and tested as shown in Figure 27. The strongest set (735 MPa

characteristic strength), which was prepared by Shop F by 600 grit transverse grinding, had nearly an

identical strength to the rod set (754 MPa) that they also prepared with the same grit wheel (dashed gray

line in the same figure). The Weibull modulus for the set of 10 bar specimens was remarkably high (36),

suggesting a very uniform flaw population. Both the bars and rods prepared by this shop with 600 grit

transverse grinding were only 10% weaker than the baseline strengths (816 MPa). Optical and SEM

fractography confirmed that the bars and the rods had 12 |a,m - 18 \xm deep elongated parallel machining

cracks that coincided with slightly deeper than normal skip mark-striations on the specimen tensile

surface." Four bar specimens had such well-formed cracks that it was possible to compute the fracture

toughness based on the crack size and shape, and the stress at fracture. The average was 5.4 MPaVm +

0.4 MPaVm, in good agreement with the measured fracture toughness for this material (This suggests

there were negligible residual stresses present, or that the flaws behaved as though they experienced a

plateau fracture toughness if the material had a rising R-curve.) The machining cracks often linked with

material sintering flaws such as small porous regions or porous seams, causing a slight bump or jog at the

center of the fracture mirror.

Shop C prepared a set of thirty 320 grit longitudinally ground rectangular bars which were machined in accordance with the ASTM C 1 161 standard procedure. The average strength of this set was

655 MPa and the characteristic strength and Weibull moduli were 677 MPA and 15, respectively. We

were surprised that these bars were 1 7% weaker on average than the baseline strength set of 320 grit

longitudinally ground rods prepared by the same shop (816 MPa). On the other hand, the bar strengths were quite comparable with other sets of longitudinally ground bars prepared from earlier batches of the

SRBSN in the consortium program [1-6]. Characteristic strengths previously had been 650 MPa to 723

MPa and Weibull moduli were between 10 and 15. Why then were the strengths of the present set of 320

grit rods and bars different? The flaws or the microstructure must have been different since testing errors were ruled out after careful review of the data. Orthogonal machining cracks may have been in both the

rods and bars, but they could not be discerned. In any case, many of the rod flaws were well below the

surface and unaffected by any possible machining damage. In contrast, most of the bars origins were

located right at the surface and could have been vulnerable to enlargement or alteration by small (15 )im -

20 \xm) semicircular orthogonal machining cracks. A key finding was that the material flaws were somewhat different in the bars and rods in the sets prepared by shop C. The thirty bar origins were pores,

The deep striations did not run across the full 4 mm width of the specimen surface. They were about 0.5 mm long and "skipped" across the ground surface. This distance was probably the contact length of a single abrasive grit for the grinding conditions used.

Fracture toughness, Ki^ = Y cr Va where Y is the dimensionless stress intensity shape factor for a semielliptical surface flaw, a is the

fracture stress and a is the flaw depth. We started with the initial assumptions that there were no residual stresses and the material has

constant fracture toughness. A more detailed discussion of these assumptions is deferred until later in this report.

38
porous regions, or porous seams that often were elongated or oblate. These probably were remnants of

spray-drying agglomerates as shown in Figures 28 and 29. One inclusion, one scratch and two large

grains (Figure 30) also were strength-limiting flaws. A few chamfer fault fractures were also observed.

In contrast, the thirty rods contained many more inclusions and compositional inhomogeneities. Thus,

the possibility of a minor, subtle spatial gradient in flaw origin type cannot be ruled out. Optical

microscopy examination of polished rod cross sections (Figure 5a) suggested that there were more

inclusions in the rim of the rods than in the core region. Since the bar specimens were cut from the

middle of the rods, it is plausible that bars sampled fewer inclusions than the 6 mm diameter rods.'' On

the other hand, shop F's 600 grit transverse ground rod and bars had nearly identical strengths.

As expected. Shop C's thirty 320 grit transversely ground bars were 19% weaker than their

longitudinally ground bars. The transversely ground bar origins were easy to characterize. Most were

classic parallel machining cracks that were offset, overlapping semi-elliptical cracks as illustrated in Figure 2c. Material flaws were detected in several of the high strength specimens, which is not

surprising since the strengths overlap the baseline strength distribution. The machining cracks were 23

)j.m - 40 fim deep and 100 |am to 300 fim long. The strength distribution had a typical Weibull modulus

(13) but had a low strength tail suggestive of a threshold strength of the order of 475 MPa. Six

specimens had sufficiently well defined machining cracks so that an estimate of fracture toughness of

could be determined. A value of 5.04 MPaVm ± 0.31 MPaVm was obtained. This is a little lower than the

fracture toughness measured for this material (~ 5.5 MPaVm). The discrepancy suggests that tensile

residual stresses were present (with an effective contribution of ~ 50 MPa), or possibly undetected stable

crack extension had occurred. Such an extension was detected in a fifth specimen, and if the stable

extension was included in the calculation, the outcome was 5.5 MPaVm. The small elliptical crack

overlaps caused slight steps or jogs in the fracture surface in the immediate vicinity of the origin. These

little steps or jogs created a telltale machining crack feature. As the initial crack extended into the mirror

during fracture, crack segments joined and produced "machining crack hackle'' that may be

characterized as a series of nearly parallel, periodically spaced tails (or "fingerlets") which radiate from

the middle of the flaw, as shown in Figures 31-34. The slight tilt of the micro hackle segments leading

away from the middle of the origin is a telltale feature. Such flaws may be termed "zipper machining

cracks" since they have zigzag kinks that leave a characteristic pattern as the crack opens up as it

propagates catastrophically during final fracture. Zipper cracks are caused by scratches or transverse

machining damage.

Sampling uniformity is not a liicely cause for this particular sample set to be different. Although the rods were received in three lots, they were carefully randomized. The lots might have had subtle batch-to-batch differences in inherent material flaws which could account for a few specimens to be different, but not the whole sample set.

39
Figure 28 Fracture origin in a 320 grit longitudinally ground bar (571 MPa). (a) shows an optical image

ot the ground surface. The fracture origin is a pore associated with large agglomerate that caused the

tracture surface to have a jog at the origin, (b) and (c) are SEM close-ups of the origin and the ground

surrace.

(a)

40
Figure 29 Agglomerate/pore type flaw detected in a 320 grit longitudinally ground Shop C bar. These

flaws were ahnost always located at or near the surface of the bars and may have been altered or enlarged

by orthogonal crack machining damage (535 MPa).

41
Figure 30 A large silicon nitride crystal at the origin in a 320 grit longitudinally ground Shop C bar (616

MPa). The orientation of the material flaw caused a jog in the fracture surface at the origin, (a) shows an

optical photo of the ground surface (b) and (c) are SEM close ups. A fracture mechanics analysis

suggests the large grain is too small by itself, and it is possible that a seam or agglomerate in the body

exists just below the ground surface. The white arrows in (b) show that the hackle lines on the right side

of point back to the large grain (large arrow), but on the left side, the micro hackle lines point up to different region beneath the tensile surface.

42
Figure 31 Optical photos of "Zipper machining cracks" in Shop C 320 grit transversely ground bars. The machining cracks are obvious even at these low magnifications, (a) shows both halves mounted back

to back of the next to weakest bar in the set, 487 MPa. (b) is a schematic with close up, and (c) shows a 561 MPa strong specimen with 40 |um deep machining crack (Kic = 5.64 MPaVm). Notice how the steps

between the offset parallel cracks and the machining crack hackle that extend upward into the fracture surface are accentuated by the low angle incident lighting coming from the left side in (a) and the right

side in (c). The machining crack hackle lines are tilted on either side of the origin. They form when

fracture expands outward from middle of the row of machining cracks.

(a)

(b)

Close up of the machining crack

Origin

centerline

Machining wack hackle . ^fT*^^—

rringerlets-) ' ''i^'^

Offset parallel machining cracks "Zipper machining crack"

"Machining cracA

liackle" n

Jogs or steps between segments

(c)

43
Figure 32 (a) and (b) show two optical views of the back-to-back mounted fracture halves of a 516 MPa specimen transversely ground with a 320 grit wheel. A "Zipper machining crack," which is one type

ot parallel machmmg crack, is easy to discern with low angle incident lighting. The elongated shape of

the mirror is evident in (b). (c) and (d) show SEM close-ups of the origin. The 35 um deep crack produces a fracture toughness estimate of 5 .07 MPaVm.

44
Figure 33 Optical and SEM photos of a "Zipper machining crack" in a 487 MPa in a 320 grit

transversely ground bar. This was the weakest specimen in the set. With the 25 jum deep crack, the

fracture toughness was estimated as 4.62 MPaVm. Note how in (a) the illumination from the right side has

highlighted the 5-6 tiny vertical fmgerlets at the origin quite clearly, whereas SEM photos do not show

the steps very well at all.

45
Figure 34 SEM photos of 25 |nm deep "Zipper machining crack" in a 542 MPa Shop C 320 erit transversely ground bar. (Kie= 4.85 MPaVm) In this instance, the SEM images do show the fmgerlets.

(a)

(b)

(c)

46
Even weaker specimens were obtained when shop C ground one sample bar set with a 150 grit

wheel in the transverse direction in an earlier phase of the Consortium program. Unlike the other

specimens discussed here, these specimens were cut out of plates and not rods. Furthermore, 15 of the

specimens were from one batch and the remaining 15 from a second batch. It was subsequently

determined that one batch was 12% stronger on average than the other. This differential existed

irrespective of how the specimens were machined and evidently was due to some microstructural

variation in the two lots. Blending such data caused the lower than typical Weibull modulus for this set

(6.8). All specimens broke from 35 )um to 70 \xm deep parallel machining cracks introduced by the

transverse grinding. Figures 35 and 36 illustrate some examples wherein machining damage created

bumpy, tortuous origins that presumably were made up of interacting short crack segments. The

machining cracks may be considered large zipper cracks whose individual crack segments caused some

meandering and bumpiness. A new telltale fractographic sign of machining damage manifested itself in

these specimens as shown in Figure 35 and 36. The deep machining damage extended not only across

the fracture mirror, but well along the bottom of the fracture surface, along the tensile edge, and often

entirely across the specimen. This thin "machining crack skin zone" could be distinguished from the

fast fracture markings of the crack. Indeed, the depth of this surface damage zone closely matched the

depth of the machining cracks inside the mirror at the origin. Once we recognized this feature, it became

very easy to measure the crack damage depths in these specimens.

A special pattern was detected in these 150 grit transversely ground bar specimens. In one batch,

fracture always started from one particular seemingly innocuous striation as illustrated in Figures 37 and

38. This was noticed when reassembling the specimen fragments as a first step in the fractographic

analysis. Fracture seemed to occur from preferred locations in the inner gage section. Although one wide but shallow striation was prominent on the surface, it was not the cause of fracture. This harmless

striation repeated every 2 mm, corresponding to the cross feed setting of the grinding machine. The

failure initiating striation was in the middle of this repeating 2 mm band. It was a single striation in a group of four closely spaced small striations. It appeared innocuous when viewed in the optical and SEM

microscopes. It certainly was not the largest or deepest striation. It did have much more grain pull out,

fracture, and fragmentation, however. Subsurface damage was manifested as light scattering sources and

the striation appeared in the optical microscope as a fuzzy-blurred region rather than a distinct groove. In

contrast, the other more noticeable striations (labeled C, 1,2, 3a, 3b, 4a) on the tensile surface were

grooves that suggested plastic deformation with negligible subsurface cracking. Figures 35 and 36

reveal what lay underneath the deleterious striations. A different repeating pattern of striations was

detected in the second batch of 1 5 specimens, but again, fracture always commenced from one particular

striation. Other investigators have noticed similar differences between plastically grooved and

fragmented striations [5,52,53] but have not correlated the difference to preferred fracture sites. Xu [5] observed very similar variations in 80 grit grinding striations in two silicon nitrides in an earlier phase

47
of the Consortium program. Grain boundary microfracture and grain pullout were identified as key

material removal processes. These observations raise interesting questions about the nature of damage

formation in coarse ground surfaces. It could very well be that one particularly severe, or "renegade" grit

in the grinding wheel is dominant and accounts for the severest damage, rather than the average wheel grit

size. Shop F used a very coarse, 80 grit wheel to prepare one set of bars in an earlier phase of the

Consortium program. Thirty bars were ground with a depth of cut of 0.050 mm. These specimens had an

average strength of 430 MPa, which is almost 50% less than the baseline strength. This set also was cut from two batches of plates and this accounts for the low WeibuU modulus (8.2). Obviously, machining

damage had to have been strength controlling since the strengths were so low, but the fracture surfaces were at first puzzling. Unlike many of the fracture origins shown above, the origins in this sample set were very bumpy as shown in Figure 39 and 40. The parallel machining cracks were neither sharp

straight cracks nor "zipper cracks." They were a series of wavy offset parallel cracks. The machining

crack depths were usually 40 \xm to 55 \xm deep, although some as deep as 80 \xm caused fracture in the

weakest specimens in the lot. Furthermore, the fracture origins often coincided with unusually deep

machining striations as illustrated in Figure 41. Unlike many of the specimens sets described above, the

striations were quite deep and broad in this set. They were as deep as 1 5 jim and thus the groove itself became part of the overall flaw dimension. The machining crack damage formed underneath the

striations, but meandered from side to side within the striation groove as illustrated in Figure 41.

Offsets between the crack segments as well as the meandering in the groves contributed to the waviness

or bumpiness of the machining damage when viewed on the fracture surface along the tensile edge.

Strakna et al. [6] saw similar overlapping crack segments in their 80 grit transverse ground bar specimens,

and termed these "saw tooth fracture." As with the 150 grit bar specimens, we also noted machining

damage skin zones that ran along the entire bottom of the fracture surface. So whereas the bumpiness of

the machining cracks in the mirror region initially complicated the interpretation, the telltale band along

the tensile surface made identification of machining damage and the depth measurements quite easy.

48
Figure 35 Optical photos of a" zipper crack" in a 150 grit transversely ground bar. Both fracture halves

are mounted back-to-back. The large arrow in (a) identifies the "coarse zipper crack" at the origin, but

the machining crack damage is also visible as a thin band running across the entire fracture surface width

(small arrows) (411 MPa). (b) shows a similar zipper crack in a 412 MPa specimen. Notice the three

vertical fingerlets at the origin in this low magnification optical photo. The low angle directional

illumination highlights these tell tale features.

(a)

(b)

49
Figure 36 Optical photos (a, b) and matching schematic (c) of a 65 jam deep zipper cracks in a Shop C

150 grit transversely ground bar (399 MPa). The mirror and the origin are in the middle, but the thin band

of machining crack damage extends out to either side to the specimens side surfaces marked by the large arrows in (a) and small arrows in (b). (c) is a schematic view which illustrates that the depth of the

machining crack skin zone is similar to the depth of the cracks at the origin.

50
Figure 37 The Shop C 150 grit transversely ground bars had a recurring a recurring striation pattern. In one group of specimens, fracture always occurred from one particular subtle striation. (a) show the origin area on the fracture surface cracks in a 519 MPa specimen, (b) shows the ground tensile surface. The

arrows show the broad but shallow harmless striations "C" that were spaced every 2 mm apart. These did not initiate jfracture. (c) is s close up of this harmless striation. The photo was taken near the specimen's

45° edge chamfer. The striation is broad and shallow and suggests plastic deformation with little or no damage underneath.

A B A B

(b)

(c)

51
Figure 38 Optical and SEM close ups of striations in the ground surface of the bar shown in the previous

figure, (a) shows the group of 4 striations and the fracture origin site, (b) is the same group of 4

striations at another location, (c) and (d) are SEM close ups that show that third and fourth striations are

in fact pairs of smaller closely spaced striations. Note that striations #1-3 are distinct, whereas the

striation #4 is more diffuse, attesting to more light scattering from beneath the surface. Fracture always

initiated from the striation #4b region marked with the arrow in (d).

(a) (b)

(c) (d)

52
Figure 39 Coarse 80 grit transverse grinding created 40 |U,m - 80 jim deep parallel machining cracks that appeared quite bumpy at the SRBSN origin. Three optical microscope view of specimen which fractured

at 476 MPa with a 42 |im deep, very long crack. Notice the roughness and bumpiness even in the mirror

region in this toughened silicon nitride.

53
Figure 40 Fracture origin in an 80 grit transverse ground SRBSN bar. Both halves are mounted back to back. This optical photo shows unusually deep (80 |im) machining damage cracks at the origin (larger

arrow) on the right side in a very weak specimen (357 MPa). The machining damage skin zone extends

along the entire tensile edge of the specimen from side to side (smaller arrows).

100 Mm

54
Figure 41 Fracture in the coarse 80 grit transverse striations often initiated from parallel machining

cracks that emanated beneath unusually deep striations as depicted in (a). The machining crack damage

extended well beneath the striation, but meandered under the striation and caused the fracture origin to appear bumpy on the fracture surface as shown in the previous figures, (b) and (c) show matching SEM

photographs of the origin area in a 463 MPa specimen. The 45 jim deep machining cracks (large arrows)

are associated with a deep striation (smaller arrows). The origin is near to, but not at the chamfer.

55
ANALYSIS OF RESULTS

Tables 2 and 3 rank the strength outcomes and illustrate the strength limiting flaws in descending

order, starting with the strongest data sets. Longitudinal grinding and finer grits led to the greatest

strengths as expected. For the rods, the 320 longitudinally ground specimens had the greatest strengths

and nearly all specimens broke from inherent material flaws. Three different shops either matched this

performance or came close with 600 grit centerless or transverse cylindrical grinding. It is reassuring

that three different shops could obtain comparable performance on the same material.

Coarser wheel grits or more aggressive grinding procedures led to progressively deeper damage

and specimen weakening. Despite all these variations, with a few exceptions, the test sets had similar

Weibull moduli between 12 and 30. Some statistical sampling variability in the Weibull moduli is

expected with small sample sizes (n = 10 or 30). One might expect that machining cracks should be very

consistent in size for a given procedure, and that this would lead to a significant increase in the Weibull

modulus, but only two sample sets had dramatically increased moduli (28.1 and 35.9).

Figure 42 is a customary style graph showing strength versus wheel grit size for both

longitudinal and transverse grinding. Included for comparison are data for other silicon nitrides fi"om the

literature: Allor et al. [14,15]; Anderson and Bratton [16]; Wu and McKinney [17]; Breder et al. [18]; Ota

and Miyahara [19]; Mayer and Fang [21,22]; Thomas et al. [25]; Alfaro et al. [54], and Foley et al. [33].

We also include some earlier Consortium work by Strakna et al. [6] and Ives et al. [55]. The transverse

strength trends are very similar for all studies, a remarkable finding. In general, transverse strengths

decrease for wheel grits coarser than 600 grit. The longitudinal grinding trends varied. Either there was

no effect of grit size and all strengths matched baseline strengths, or strength began to decrease with

wheels coarser than 240 grit. [16,25]

Surface flnish

Tables 2 and 3 include the surface roughness outcomes, Ra, for most sets. In general, the final

surface roughness did not correlate to the strengths. For example, the lapped rods had the finest finish,

but had some of the worst strengths since the flaws that controlled strength were from earlier phase

grinding. The lack of a correlation between strength and surface finish in this SRBSN is consistent with

findings from earlier phases of the Consortium program.[l]

56
Figure 42 Strength versus grit size for (a) transverse, and (b), longitudinal grinding. Average strengths

are shown unless denoted with * in which case the values are characteristic strengths. Baseline strengths,

which presumably are the inherent strengths in each case, varied with material and testing configuration

and are marked on the right if available. Material code designations are shown if available.

strength versus jrit^-ii,-

0 100 200 300 400 500 600 700 800 900 100011001200

1100 H

1 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 1100

(a)

(b)

O)

c

£

153

X

©

u.

1000

900

800 H

700

600

500

400

300

200 H

100

Breder, 1040 MPa

1000

900

800

0» 700 c

i 600

ifiW 500 O 400

300

200

100

0

baseline

strengths

Andareon and Bratton. 849 MPa

~

"SRBSN. This studyy 816 MPa O

Mayer and Fang, 788 MPa

Strakna at al. . 690 MPa

Transverse

• This study, SRBSN, rods

This study, SRBSN, bars

Strakna at al . SRBSN *, Raf. 6, bars Mayarand Fang, HPSN NC 132, Raf. 21, bars Ota and Miyahara, SSN, Raf. 19, bars Andarson and Bratton, HPSN NC 132/HS 130, Raf. 16, bars

Bradaratal., HIP SN GS 44 * savaral sats, Raf. 18, bars

Alfaro at al. HPSN, Raf. 54, biaxial plalas

(

* charactaristic strangth)

1000

900

800

700

600

500

400

300

h 200

100

T I I I ] I 1 I I I I I 0 100 200 300 400 500 600 700 800 900 100011001200

Wheel Grit

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1100 H

^ ^ ^ 1 1 1 ^ ^ 1 1 ^ 1100

_

_ _ - - -® ° ' SRBSN ^

this study, 816 MPa

Mayer and Fang "~ v a

800 MPa ^

Longitudinal

• Thisstudy, SRBSN, rods, shop C

Thisstudy, SRBSN, bars, shop C A Strakna at al, Raf. 6 and Jahanmiratal., SRBSN' o Mayarand Fang, HPSN, NC 132, V Ota and Miyahara, SSN,

Andarson and Bratton, HPSN NC 132 / HS 130, s Thomas, Wast at al., 7 Allor and Baker, A Allor and Baker, B Wu and McKinney, B Ivasatal., e Foley at al..

HPSN NC 132, HPSN NC 132, billet 1322- HPSN NC 132, billet 1324' HPSN NC 132, HIP SN NBD 200

HIP SN NCX5102

Refs. 1,2 bars

Ref. 21 bars

Ref. 19 bars

Ref. 16 bars

Ref. 25 bars

Ref. 14 bars

Ref. 14 bars

Ref. 17 bars

Ref. 55 bars

Ref. 31 Tension Rods

(* charactaristk; strength) —I 1 1 1 1 1 1 1 I

1 1 1

100 200 300 400 500 600 700 800 900 1000 1100 1200 Wheel Grit

1000

900

800

700

600

500

400

300

200

100

0

57
Figure 43 Machining crack size (depth) versus wheel grit for the SRBSN in this study. Only parallel

machining cracks from transverse grinding are shown. Circles denote individual rod specimens and

squares denote individual rectangular bar specimens. The variation in crack sizes for any given set of

conditions was a factor of two. This size variability is consistent with the strength variability. For

comparison, the size range (half minor axis dimension) of the material flaws is shown on the right side.

58
The Size of the SRBSN Machining Cracks

Figure 43 shows the size distribution of all machining cracks measured in this study. The depth

is shown since it is the controlling dimension in fracture mechanics calculations for long shallow surface

cracks in a body. The depth is also an important factor in assessing damage in a finished part. The

critical crack size is shown. In a few instances, cracks showed evidence of stable extension such as shown in Figures 15-18. We could not detect any consistent patterns of stable crack extension in the data

sets in this study. The stable extension, when detected, was usually of the order of 5 \xm to 15 ixm.

Other studies have detected stable crack extension from machining cracks, but only in fine-grained

materials wherein the extension stood out more clearly on the fracture surfaces. Machining flaws with

clear evidence of multiple step propagation are also shown by Rice, Mecholsky, and Becher [30].

Marshall et al. [56] showed clear signs of stable extension driven by strong residual stresses both from

coarse-machining damage cracks and from rows of Knoop indentations.

The crack depths ranged from a minimum of 12 ^m to a maximum of 80 yim. Sizes smaller than

10 jam do not appear since specimens with such small cracks broke instead from material flaws. The «

80 |im upper limit is the severest machining damage likely to be encountered with conventional grinding

conditions in this SRBSN. The surface lengths of the machining cracks varied from as low as ~ 50 jim, to

as long as hundreds of micrometers, to the full width of the specimens in some of the coarsest ground

(150 and 80 grit) bar specimens. Rice et al. [29,30] also observed a range in flaw sizes from 15 jam to 89

)im in many ground polycrystalline and single crystal ceramics. Even in glass flexural strength bars

ground with a 1 80 grit wheel, they only found cracks from ~ 10 |im to = 77 \im deep. [31]"^

Several points may be made from Figure 43. In each data set there are only some depth

measurements since we were either unable to obtain a depth measurement in some specimens, or

alternatively, the specimen may have fractured from a material flaw. The coarser the grit size, the more

likely machining damage was strength limiting and the easier it was to measure the machining cracks. So

for example, more than 20 data points are shown for the bar specimens ground with 150 and 80 grit

wheels. A second point is that there was good concurrence of crack depths for rods and bars at 600, 320,

and 150/180 wheel grits. Thirdly, despite the fact that specimens were ground by a number of different

shops with many differences in key machining parameters (e.g., wheel depth of cut or table speeds) all the

data seems to converge. Fourthly, it is fascinating that the range of machining crack sizes was of the

order of a factor of two at each machining condition. This is an interesting finding; since it runs counter

to a widely held expectation that machining cracks should be fairly consistent (e.g., Breder et al. [18] for a

hot-isopressed silicon nitride wherein m varied from 20 to 40). Rice et al. [29,30] also noted a spread of

a factor of two in their 320 grit ground polycrystalline and single crystalline ceramic bend bars. Our

spread of crack sizes was matched by a commensurate spread in strengths. The ground rod sets had

' They reported average cracks depths and standard deviations. The numbers shown above are the average parallel crack size plus two

standard deviations and the average orthogonal crack size minus two standard deviations.

59
WeibuU moduli between 13 and 28 (Figure 10). The bars had moduli typically between 10 and 15

(Figure 27). Figures 10 and 27 show that data sets with moduli of the order of 1 5 had strengths that

varied by a factor of «1.4 from lowest to highest. Since strength scales with the inverse square root of

crack size, the 1 .4 factor is entirely consistent with the factor of 2.0 variation in machining crack size. At the higher strengths (> 600 MPa) the material flaws are dominant. Their spread in size and

severity was such that the material flaw Weibull modulus itself was 15. A bar showing their size range

(10 fim - 45 |um, half minor axis length) is shown on the right side of Figure 43. Material flaws and

machining cracks of the same size may not have the same severity. For example, a 20 |j,m deep

machining crack was far more deleterious to strength than a 20 |am radius material flaw. The machining

crack was sharp, very long, and had a more severe stress intensity. The material flaws were more

equiaxed, partially bonded to the material, or three-dimensional and their stress intensity shape factors were much less. Salem et al. [24] also observed that small machining cracks could control strength even though larger material flaws were present in sintered alpha silicon carbide. In our study, there was

considerable overlap in strengths and flaws sizes for the specimens ground with 600 grit transverse or 320

grit transverse grinding. Some specimens broke from machining cracks, some from material flaws, and

many were hybrid flaws comprising linked machining-material flaws. Machining flaws became dominant

for grinding wheels coarser than 320 grit. A summary map of these results is shown in Figure 44.

Comparison of Machining Flaw Sizes in Different Silicon Nitrides

Figure 45 compares our crack size results on the SRBSN with literature data on other silicon

nitrides.[16,26,28,33, 34,54,56,57,58, 59,60,61, 62,] The literature is sparse. Although several engine

companies (e.g., Westinghouse, Daimler-Benz, Garrett) conducted machining damage studies, they

usually calculated or inferred their flaw sizes from bar strength data, sometimes without furnishing details on how the calculations were performed. A few isolated illustrations of machining damage cracks have

appeared in a handful of papers and we have measured the crack sizes from these photographs. Nearly all

the actual data is for parallel cracks from transverse grinding. Orthogonal crack size measurements from

longitudinal grinding are exceedingly rare. We could not help but notice that many of the original authors were tentative with their identification of the machining cracks or their dimensions. Many were reluctant

to even put arrows on their photos and one is left with the impression that they left the interpretation up to

the reader! This underscores the uneasiness many investigators have had with identifying or

characterizing machining damage. Most the studies featured hot-pressed silicon nitride, and in particular,

Norton's grades NC 132 and HS 130.' These HPSN's were fully dense and had fine, slightly elongated

Norton Co., Worcester, MA. Both HS 130 and NC 132 were hot pressed in the 1970's and 1980"s. The former was the immediate

predecessor to the latter. They had nearly identical microstructures and the primary difference was concentration of impurities such as Ca

and W. They were two of the most studied structural ceramics of all time and were prominent candidates in a number of major engine programs. NIST Standard Reference Material 2100, Fracture Toughness is comprised of NC 132 test pieces.

60
Figure 44 Damage map for the SRBSN for transverse grinding. Machining cracks may be smaller than

the inherent flaws, but they are more severe stress intensifiers (Griffith cracks).

0 100 200 300 400 500 600 700 800

116 78 66 34 22 18 15

Grit size (|j,m)

0 100 200 300 400 500 600 700 800

Grinding Wheel Grit

61
Figure 45 Machining crack size versus wheel grit from a variety of studies for silicon nitride. The

range of outcomes for the SRBSN from this study (previous figure) are included as solid lines. Other data

entries are individual data points or ranges from the other referenced sources. Unpublished new NIST

data on Dow SSN and Eaton SRBSN are also shown. Unless otherwise stated in the key, all grinding was

transverse. Calculated crack sizes from studies by Daimler-Benz and Westinghouse are shown as dashed

lines with "x" or "+" symbols corresponding to the grit sizes at which strength data was collected. The

Daimler-Benz data could be adjusted downward slightly (arrows) if the fracture toughness for the NC 132

that was used was adjusted from 5.0 MPaVm to 4.6 MPawm. Material code designations are listed where

available. For example, many of the studies used Norton's hop pressed silicon nifride (HPSN) grades NC

132 or HS 130. With the exception of the Daimler Benz calculations and the Dow SSN data, nearly all the data fit a single trend.

300

250 -

E 200

N

(J)

O

O

150 -

100 -

MEASURED

NIST data, this study, Dow SSN 30 each 80 grit and 150 grit bars o NIST data, this study, Eaton RBSN 14 bars 80 grit * Hollstein et a!.. SSN, N 3204 Ref. 28, 1 1 bars

ffl Mizuno et al. SSN Ref. 60, 2 bars B Marshall et al.. HPSN NC 132 Ref. 56, 1 bar Kanematsu et al. HPSN Ref. 61 , 2 bars O Kanamatsu et al. HPSN Ref. 62, 11 bars

Alfaro et al. HPSN NC 132 Ref. 54, 1 biaxial plate Quinn, HPSN NC 132, Ref. 59, 8 bars long, ground

Foley et al., HIPSN NCX5102 Ref. 33,34, 1 0 tensile rods, long ® Richerson et al. HPSN NC 132 Ref. 58, 2 tensile rods • Puttick et al.. HIPSN Ref. 26, 3 bars CALCULATED

Daimler-Benz, Morgenthaler, HPSN NC 132 Ref. 57

Westinghouse, Anderson et al., HPSN NC 132/HS130 Ref. 16 Westinghouse, Anderson et al., HPSN NC 132/HS130

long, ground, Ref. 16

CALCULATED

Westinghouse

HPSN

Transverse

Longitudinal

CALCULATED

Daimler Benz HPSN NC 132

50 -

0

0 200 400 500 600 700 800

Grinding Wheel Grit

62
beta silicon nitride grains that made the material conducive to fractographic analysis. Even so, although

finding parallel cracks from transverse grinding was not difficult; detection of orthogonal cracks in NC

132 fi-om longitudinal grinding was difficuh.[63,64] Figures 8a,b show examples. We do not know why

the Daimler calculations for cracks sizes are so different from the other sets, and even correcting the

calculation for a more accurate fracture toughness does not solve the problem.

Figure 45 includes limited data we also collected on two other silicon nitrides that were tested in

an earlier phase of the Consortium program: Dow sintered silicon nitride (SSN)' and Eaton reactionbonded silicon nitride." Properties for these are listed in Table 4. Fractographic examination was very

limited in the earlier work, but we recently reexamined all of the 80 grit transversely ground SSN and

RBSN specimens and all of the SSN 150 grit specimens. Were the crack markings similar and how large were the cracks compared to the Ceradyne SRBSN? Fractography confirmed that the cracks were easy

to find in the SSN, but quite different in the RBSN. The machining crack sizes were dramatically

different in the three materials. These differences were related to the hardness, elastic modulus, fracture

toughness, and microstructures.

The RBSN machining damage zones were relatively easy to detect, but their size and shape were

controlled by the microstructure of the material as shown in Figure 46. This low strength (~ 150 MPa)

pressure-less sintered material is composed of densely packed spherical particles, 40 ^im - 60 \xm in

diameter that are the vestiges of spray dry particles. The machining damage zone was only 35 |j.m - 50

^im deep and was confined to one layer deep of these agglomerates. Hence, this weak, low fracture

toughness material is nonetheless effective in arresting machining cracks, much like a refractory firebrick

is effective in arresting cracks.

The Dow SSN had very similar cracks compared to the Ceradyne SRBSN cracks despite the

different microstructures and fracture toughness as shown in Figure 47. A surprising result was that the

Dow SSN cracks were usually larger than the Ceradyne cracks. We momentarily defer further

discussion of these surprising results until after a brief discussion of fracture mechanics analysis as

applied to the SRBSN data. One group of Dow SSN specimens ground with the 150 grit wheel also

exhibited the same breakage pattern discussed earlier for the SRBSN: every single specimen fractured

from one particular striation that repeated every 2 mm along the specimen ground surface. This confirms

the earlier assessment that a single severe grit in a grinding wheel may be crucial. The maximum machining crack depth detected in our study on the SRBSN was 80 \xm under the

coarsest grinding conditions. The maximum crack size for any silicon nitride from our review of other

literature data was 100 \im.

Dow Chemical Co., Midland, MI.

Eaton Corp., Southfieid, MI.

63
Table 4 Property data for the SRBSN and three other silicon nitrides for comparison.

Material Density

(g/cm')

Grain size

(urn) width X length

Elastic Modulus

(GPa)

Hardness,

(GPa)t

rraciure lougnness

(MPaVm)t

SRBSN

Ceradyne

Ceralloy

147-31

3.21 * 0.5 to 3. X

1 in tn 10 Innn

310-

320*

HK(2) 13.3 ±0.2

HK(1) 13.7 ±0.2

HV(5) 15.4 * HV(1) 15.0 + 0.3 HV(.3) 17.6 *

5.8 ± - *

5.41 ± .54 29 machining cracks

(This study]

5 58 + 024 SCF f411 5.59 ±0.22 SEPB [41] 5.28 ±0.17 CNB [42]

SSN

Dow

3.20**

0.3- 1.3 X

up to 10. long

306**

HK(2) 12.7 ±0.2

HK(1) 13.0 ±0.2

HV(5)

HV(1) 14.5 ±0.3

6.8 ± - * [65,66] 7.25 ± 0.38 28 machining cracks

fThis study] 7.18 ± 0.31 30 machining cracks

[This study]

6.75 ± .29 SCF [67]

RBSN

Eaton

2.36**

\J .\J — 1 . X

1.-2.

**

200 **

HK(2) 4.6 ±0.3

HKC1\ 5 0 + 03

HV(5)

HV(1) 5.2 ±0.4

2.5 ±

-** IS [43]

HPSN

Norton NC 132

3.22-

3.26 < 3. 315-

320

HK(2) 14.3 ±0.3

HK(1) 15.0 ±0.2

HV(5) 15.4 ±1.3 [63] HV(1) 17.3 ± 0.5

4.57 ±0.23 SCF, SEPB, CN,

SRM2100 [68]

* Manufacturer's data ** Consortium preliminary data References [1 -6]. X HV denotes Vickers hardness. HK denotes Knoop hardness. The number in parenthesis is the indentation load (kgf)- t Test method: SCF surface crack in flexure; CNB chevron notched beam; SEPB, single-edge precracked beam;

IS, indentation strength Not available or reported.

[ ] Data source, reference.

64
Figure 46 Fracture origin in an Eaton RBSN specimen transversely ground with 80 grit wheel, (a) and

(b) show that the origin is a small damage cluster near the chamfer, (c) is the same region, but

illuminated differently to highlight the 40 |im - 65 \xm diameter agglomerates from the spray dry process

that comprise this material. The machining damage zone is confined to one layer of these agglomerates.

65
Figure 47 Fracture surface of Dow sintered silicon nitride bars, (a) was transversely ground with an 80

grit wheel. The coarse zipper cracks (90-95 \xm deep) are obvious. From the fracture stress, 352 MPa

and assuming a shape factor Y of 1.99, the fracture toughness is estimated to be 6.7 MPaVm. The

interlocking but very fine (< 2 \\.m) grain microstructure is not evident at this scale in this toughened

ceramic, (b) is a 150 grit transverse bar with a 66 )xm deep crack with a stress of 432 MPa for a fracture toughness of 7.0 MPaVm. Both fractured from "coarse zipper machining cracks as shown in (c). In specimens like these, with such large cracks, the fracture mirror is incomplete since it is large relative to the specimen cross section size.

(a) (b)

(c)

Coarse zipper machining crack

66
Fracture Mechanics Analysis of the SRBSN Machining Cracks

Fracture mechanics may be applied to the interpretation of the machining cracks. In this study we

have taken a simpHstic approach and applied the basic formula for critical stress intensity for a small

crack or flaw in a tension stress field: k,^=yg^4^ (1)

where Kic is the critical stress intensity factor, or fracture toughness, af is the fracture stress at the origin

site, Y is the stress intensity shape factor which takes into account the stress gradient and geometry of the

flaw, and a is the flaw dimension, which is the crack depth for a long shallow surface crack in a beam in

bending. The stress intensity shape factors from the Newman and Raju analysis [46] were used. As a

first approximation, potential residual stresses were ignored, as was any possible rising R-curve behavior.

This simplistic approach is an effective adjunct to fractographic analysis of fracture origins. Any

discrepancies in the outcomes point the way for further review and consideration of such factors as

residual stresses or rismg R-curve behavior. [69,70]

A number of machining cracks had sufficiently well defined shapes and boundaries that apparent

critical fracture toughness could be computed from the measured cracks dimensions a and 2c (width), the

stress at the origin, and the computed Y.' The average for 29 cracks was 5.41 MPaVm ± 0.54 MPaVm.

The results are shown in Figure 48 where they are compared to 35 fracture toughness data collected by

the three test methods in the ASTM standard C 1421 for fracture toughness.[41] One of the three

methods was the surface crack in flexure (SCF) method that involves using a Knoop indenter to make

small semi elliptical surface cracks. These are very close in size (50 fim. Figure 48) to some of the

material and machining cracks. The SCF cracks were used to study the micro-crack fracture resistance in

this material. Notwithstanding our simplifications in the machining crack analysis, the results from the

machining cracks are in superb agreement with the results from the dedicated fracture toughness tests.

This is not an unusual outcome. Using the same assumptions of negligible R-curve effects and negligible

residual stress, Foley et al. [33] also observed a good correlation between calculated and measured (20

|im - 60 ^m) machining crack sizes for longitudinally ground tension strength rods in a hot isopressed

silicon nitride with a modest fracture toughness of 5.35 MPaVm. Rice has remarked that fractographic

analysis of machining cracks is a good way to obtain fracture toughness estimates for ceramics.[71]

In the course of reviewing the literature, we were surprised how many instances investigators improperly applied fracture mechanics to machining damage. Many early studies modeled striations as the machining damage and attempted to analyze the stress intensity factors for the striations. sometimes even using surface roughness data to estimate flaw depths. This is not correct. Machining crack flaws extend well below the machining striations (5x - lOx deeper). It is fhistrating to see a super close up photo of a striation, but not be able to see the genuine machining crack due to the excessive magnification. Even in cases where the correct machining crack is detected, some studies have modeled the flaw as a combined groove with crack extending underneath. In most cases this is not necessary, since the striation grooves are shallow and have negligible influence on the stress intensity factor.

67
Figure 48 Fracture toughness versus crack size. The graph includes data from both 35 dedicated fracture toughness tests as well as estimates from 29 machining flaws. In the lower left comer the size ranges for natural (inherent) flaws in this material and also the mean sizes of machining cracks are depicted.

E

(0 Q.

(OUi

(Dc

rjo

u

(0

Fracture Toughness from Machining Cracks (n = 29)

6

-

5

-

2

-

1 -

4 Bars 1 1 Rods 't Rods 6 Bars

F C N c

600T 320T 220T 320T

\

°0

bo

Q -

O

4 Rods

F 150/180 grit

5kgf Knoop

precracks

SCF

Fracture Toughness

(n=16)

' a

lOkgf Knoop

precracks

15kgf Knoop

precracks

ASTM C 1421

n = 4 SCF

600 320 220 150 80 grit

Mean Size of Orthogonal Machining Cracks

from Transverse Grinding

I

i Size Range of Natural Flaws

(Inclusions, Pores, etc.)

50 100

Crack depth (|a m)

150 200

SEPB CNB

Large Crack

Fracture Toughness

Data

-fll SEPB by C 1421 (n = 8) SEPB by C 1421 (n = 6) T CNB (n = 5)

> 1mm

68
As noted above, a few SRBSN machining cracks showed evidence of small amounts (5 fim - 15

\im) of stable crack extension, but most did not. The critical crack size was used in the calculations. We

could often distinguish the critical crack on the fracture surface by noting where the flaw topography

changed to a flatter mirror plane, and also by observing changes in direction of local micro-hackle lines.

It could not be ascertained whether the stable extension was due to residual stresses, R-curve toughening,

or stepwise pop in during the machining.

Any R-curve toughening in this material occurred over a very short crack extensions of the order

of 5 |im - 15 \j.m at most. The controlled SCF experiments with residual stress-free 50 |j.m deep Knoop

cracks did not detect any greater extension than this. [41] Preliminary work to evaluate the R-curve and

threshold fracture resistance of this material has shown the fracture resistance may start as low as 2.0 MPaVm, but then rises to the order of 5.5 MPaVm after 500 \xm of crack extension. [43 ,44] We are somewhat surprised by these results, since the fractographic analysis of the machining cracks in our study

(which were as short as only 10 jim) indicated they behaved as though they had reached near plateau

values of fracture toughness resistance when the cracks went critical. Since the silicon nitride grains were

0.5 \Jim to 3 ^m wide by up to 10 fim long, stable crack extension occurred over only a few grain

diameters so only a few bridges would be activated. We surmise that the beneficial effect of enhanced

fracture toughness occurs during the crack initiation, pop in, and initial extension during machining. Very

little additional toughening increase occurs during the subsequent strength test and the crack experiences

a fracture resistance commensurate with a plateau fracture toughness. This interpretation is consistent

with our fractographic findings'* and those of Foley et al. [33] for a different hot isopressed silicon nitride

with similar fracture toughness (5.35 MPaVm). Fett and Munz have also shown that stable crack

extension from natural cracks actually causes only slight crack extensions and has only a small effect upon strengths even in aluminas with pronounced R-curves.[72]

Data from the 35 experiments by three fracture toughness methods in C 1421 plus our analysis of

29 machining cracks converge to a fracture toughness of 5.5 MPaVm to 5.6MPaVm for this SRBSN. It is

reassuring that three different test methods produce such consistent fracture toughness outcomes, and that

these outcomes are relevant to machining cracks. Standardization of fracture toughness and strength

testing methods has improved the quality of mechanical test results. This material is indeed tougher than

a baseline silicon nitride, Standard Reference Material SRM 2100 hot-pressed silicon nitride, which has a

toughness of 4.57 MPaVm ± 0.1 1 MPaVm. [69]

Fracture Mechanics Analysis of the SSN Machining Cracks

The Dow SSN has even greater fracture toughness (6.8 MPaVm or more) due to its very fine (0.3

|im diameter x 1.3 fj.m long) microstructure comprised of elongated interlocking silicon nitride grains.

Yet other dedicated R-curve data [43,44] suggest stable extensions of > 200 are needed to reach the plateau.

69
Nevertheless, the machining cracks were so large that they stood out clearly against the natural roughness

from the interlocking microstructure as shown in Figure 47. There were numerous local jogs and steps

in the machining crack damage zone along the tensile edge of the specimen. These lines were especially

noticeable outside the mirror region. As discussed previously (Figure 31b) "machining crack hackle

lines" arise from jogs or steps and extend upward into the fracture surface. The steps and jogs made the

initial cracks easy to detect and the machining crack hackle tilts helped discriminate the initial machining

cracks from the final fracture markings.

The apparent critical fracture toughness was calculated for every crack in every specimen based on the depth, the fracture stress, and the assumption the crack was a long surface elliptical crack. The

average fracture toughness was calculated as 7.25 MPaVm ± 0.38 MPaVm for all thirty 80 grit ground

specimens which had 72 fim - 95 \xm deep cracks. The average was 7.18 MPaVm ± 0.31 MPaVm for all

thirty 150 grit ground specimens, which had 60 fim to 82 fim deep cracks. Depending upon the

composition and grain sizes, fracture toughness (chevron notch) from 6.5 MPaVm to 9.0 MPaVm have

been reported in the literature for this material. [65,66] The fracture toughness of the particular batch of

material we received was reported to be ~ 6.8 MPaVm (chevron notch) by the vender.[73] We confirmed

this value by five SCF fracture toughness experiments done in accordance with ASTM C 1421 that produced an average of 6.75 MPaVm ± 0.29 MPaVm [67] for single semi-elliptical 75 |j,m deep Knoop

semielliptical precracks. The excellent consistency of the fracture toughness numbers from the dedicated

fracture toughness experiments and the machining cracks confirms that we were observing critical crack

sizes in the latter. There could have been some stable crack extension, but it could not be distinguished on the

fracture surfaces. It is improbable that it would extend so uniformly deep across the specimen's width as

the crack fronts we detected on the fracture surface. It is also unlikely that stable crack extension would

have locally curved out of the fracture plane as much as we detected at the origins. Even though the Dow

SSN machining cracks were surprisingly large, the specimens did require greater stress to break, so there was some benefit of increased fracture toughness. Evidently, the ramp up in increase in fracture

resistance with this likely rising-R curve material occurred during machining crack pop-in in the same

manner as occurred for the SRBSN.

So why were the machining cracks larger in the toughened Dow SSN? Why didn't the

microstructure designed for improved fracture resistance retard crack pop in during machining?" We

offer one possible explanation. There is ample anecdotal evidence from machine shops [74] and

experimental data [75,76,77,78] that toughened ceramics are indeed more difficult to machine. For a

given set of grinding conditions (wheel grit, wheel speed, depth of cut, etc.), greater wheel forces are

generated. High horsepower grinding machines automatically compensate for the increased material

For example, Xu et al. [76] showed that scratch and machining crack penetrations in a toughened silicon carbide were smaller than in a monolithic silicon carbide.

70
resistance and apply greater energy to the work pieces to overcome the material's resistance. Deeper

machining cracks are forced into the material. This is automatic and will not be noticed by the machinist

unless the machine is instrumented, or the motor is underpowered and the machine noise changes, or the

grinding wheel is retarded and does not cut freely. In contrast, less tough ceramics require less energy

and grinding forces are reduced.

Our findings run somewhat counter to recent papers on the influence of fracture toughness on machining that have emphasized short crack length toughnesses [76-78]. For example, Xu et al. [76]

showed that scratch and machining crack penetrations in a toughened silicon carbide were smaller than in

a monolithic silicon carbide. Nevertheless, our fractographic findings suggest that if there is a rising Rcurve for the toughened SRBSN and SSN silicon nitrides, the fracture resistance of smaller cracks must come up the R curve very quickly or even during crack initiation..

Residual Stresses

Residual stress characterization unfortunately was not included in this program. Machining often

creates residual stresses at and just underneath the ground surfaces. These can start with a very

substantial compressive residual stress at the immediate surface, which very rapidly decreases with

distance into the bulk and becomes a low or modest tensile stress 1 0 |j.m or more below the surface. The

net effect of residual stresses on a flaw must take into account the stress gradient and the crack size. So

whereas severe residual stresses may be present, the net effect upon a deep machining crack may be small

and is hard to calculate. The residual stresses are also directional. Stresses in the grinding direction are

typically much less or negligible compared to the stresses perpendicular to the grinding direction.

Characterization of these residual stresses is time consuming and difficult and subject to considerable

uncertainties in large part due to the severe stress gradient or uncertainties in the test method. A sample

review of the literature (e.g., Alfaro [54]; Wobker and Tonshoff [23], Puttick et al. [26], Marshall et al.

[56] Kirchner and Conway [79], Holstein et al. [28], and Pfeiffer and Hollstein [80], Samuel et al.[81],

and Johnson-Walls et al. [82]) shows there is considerable variability in the magnitude and severity of

reported residual stresses. It is not even clear whether the net effect on a machining crack should be

tensile or compressive. Pfeiffer and Hollstein [80] concluded that coarse ground silicon nitride surfaces

had compressive residual stresses extending 5 p.m to 10 fj,m below the surface which created a net

beneficial compression stress of 100 MPa - 150 MPa on the flaws.

The presence of residual stresses could be inferred from the fracture mechanics analysis of the

cracks in the present study. In most cases, the computed fracture toughness (based on the flaw size and

shape and the applied flexure stress at fracture) matched the known fracture toughness, suggesting that

any residual stresses were small. The computed fracture toughness values differed from the fracture

mechanics estimate only for the 320 grit transversely ground bar set. In this set, the combination of

critical flaw size, stress at the origin at fracture, and the shape factor yielded a low estimate of the critical

71
fracture toughness. It was inferred that net residual tensile stresses of only « 50 MPa must have been

acting on the flaws in this case. Foley et al.'s [33] good correlation of calculated and measured

machining flaw size also suggested that negligible residual stresses were present in their study of a in a

hot-isopressed silicon nitride.

Comparison of Rods and Bars

Although the rods were much larger than the rectangular beams, the WeibuU effective volumes

and surfaces were comparable. The 600 transverse grit rods and bars prepared by shop F had almost

identical strengths and the fractographic analysis confirmed that similar machining cracks had been

created. On the other hand, comparably ground rods and bars prepared by Shop C had different strengths.

Their 320 grit longitudinally ground rods were much stronger than their bars. Fractography indicated that

different types or concentrations of material flaws occurred in these bars and rods. We cannot account for why this happened, since some care was taken to randomize all rod blanks at the beginning of this study.

Shop C's transversely ground rods and bars had different strengths, but the cause in this instance was

simply traced to different machining crack depths created in each set.

Bar test piece cross section

Rod test piece cross section

Figure 49 All other things being equal, grinding wheels may leave striations and cracks with different

lengths and orientations in rods and bars.

72
In general, the grinding flaws in rods and bars were similar in some respects, but different in

others. The trends of crack depths for the rods and bars were similar, but the crack lengths varied.

Rectangular bars typically had longer machining cracks, often in the hundreds of micrometers and

sometimes the full 4 mm width of the specimen. This difference is not surprising due to the geometries

involved and the shorter contact length and duration of a round rod contacting a round grinding wheel as

depicted in Figure 49. Furthermore, the rods were more apt to have "V" cracks from the spiral or helical

grinding pattern due to axial motion of the work piece relative to the grinding wheel. On the other hand,

the bars were more likely to have pronounced "zipper cracks" with periodic fmgerlets. It would be an

interesting exercise to try to correlate the fmgerlet spacing to the rates of wheel rotation, the wheel grit

concentration, and the work piece translation during the grinding process.

Machining Damage and Scratches

One is struck by the similar appearance of machining cracks and scratch fracture origins. It may

be difficult to discriminate between the two flaw types if a scratch lines up either parallel or perpendicular

to the grinding direction axis. On the other hand, if the flaw axis is at an irregular angle to the work

piece axis or the grinding direction, then the flaw is likely a scratch. Fractographers should examine not

only the fracture surface, but also the component external surface. Sometimes only a small portion of the

scratch may be revealed on the fracture surface if the scratch is at an angle to the fracture surface. The

mechanism of formation of machining flaws is probably similar to that of scratches [83] or cracks formed

by single point diamond grinding. [8,12,53,56,79] Schinker and Doll [53] showed stunning images of

various striation-scratch grooves and damage patterns. Melting was a prominent factor in some instances.

Changes in the damage modes and the appearance of the groves corresponded to critical depths of cut,

abrasive speeds, and the refractoriness of the glasses. Rice and Mecholsky [29] compared polishing

scratches and machining grinding cracks and noted that the former are often very smooth, and the latter more irregular and stepped. Kirchner and Conway [79] stated that grinding involves a series of events

including crushing, plastic flow, elastic recovery, generation of residual stress, radial, median and lateral

cracking, chipping and gouging. Their contributions vary quite a bit with force and depth of cut.

Although there are similarities in behavior of scratches, single point diamond grinding scratches, and

machining cracks, one should be careful in carrying the analogy too far. Kirchner's single point scratch

damage depths of up to 1000 |im deep have never been observed to the author's knowledge in any ground

silicon nitride part and are certainly 8-10 times deeper than any cracks detected in our study under the

severest grinding conditions. Large residual stresses from huge scratches or indentation flaws with

concentrated plastic zones may overemphasize the influence of residual stresses, and cause much greater

stable crack extension than what occurs in genuine ground surfaces. It should also be remembered that

machining cracks seldom act alone. They are part of a network of closely spaced parallel flaws as shown

in Figure 3. The density and spacing and mutual interaction of these cracks is unexplored at this time.

73
Does Fracture Start from a Single Bad Striation?

As noted above in our discussion of 150 grit and 80 grit transversely ground SRBSN and SSN

bars, a single critical striation can control strength. A simple calculation based on the specimen and

wheel geometries and the table and wheel speeds indicated that the striation may have been formed by a

single abrasive grit/ Hence, the strength and reliability performance of a ground part may be controlled

by a single "renegade" grit in the grinding wheel.

We also have noted over the years that a single large striation, perpendicular to the fracture

surface sometimes coincides with the orthogonal machining cracks in longitudinally ground bars as shown in Figure 8c. Others [17,29,32,33,34] have reached a similar conclusion. The deep striation may

not always be present, however, since subsequent finishing may remove it. Polished plates or window

components often break from handling scratches, scratches from loose abrasives, or grinding flaws.

These flaws may be obvious on the fracture surface, but there often is no indication whatsoever of these

flaws on the finished surface since final polishing removes all traces of the damage. Thermal or biaxial

mechanical stresses will trigger these flaws. Figure 50 shows an example.

Figure 50 Machining damage crack in a lapped NC 132 silicon nitride disk [84]. The disk was broken

in ring-on-ring equibiaxial loading. Although the tensile surface "T" was very smooth and there was no

trace of grinding damage, the subsurface 20 \xm deep "zig zag machining crack" remained (arrows) and was revealed on the fi-acture surface "fs." In this instance, the machining vender did not remove

sufficient material by lapping to eliminate the prior grinding damage.

We did not notice such consistent striation-fracture origin patterns with the finer grit ground bend bars or rods, but we cannot rule them out. A review of all of our SEM photos of fracture origins suggested that fracture origins sometimes, but not always, coincided with deeper than normal striations in 320 grit transversely-ground rods and bars. Fracture origins in Shop F's 600 grit transversely-ground rectangular bars usually did coincide with deeper than normal (2 urn - 3 \i.m) striations.

74
Grinding Damage Maps

Combining the results of the present study and data from other studies on fine-grained, dense

polycrystalHne silicon nitrides, we have constructed several damage maps for fully-dense silicon nitride.

Figures 44, 51, and 52.

Figure 44 condensed the detailed information on crack depth versus grit size from Figures 43

and 45 and key fractographic findings about machining flaws vis-a-vis material flaws. Although it was

prepared for the SRBSN, our review of the literature suggests the general trend may be applied to many

dense silicon nitrides.

Grinding wheel

Machining induced crack 600 grit wheel

13 i^m - 20 urn deep cracks

(.0005" - .0008")

320 grit wheel

14 |im - 40 i^m deep cracks

(.0006" - .0016")

220 grit wheel

25 urn - 55 |am deep cracks

(.0010" - .0022")

150 grit wheel

30 lam - 70 urn deep cracks

(.0012"- .0028")

80 grit wheel

35 lam - 80 i^m deep cracks

(.0014" - .0032")

Figure 51 Damage depths from surface grinding with wheels of various grits. The cracks shown are

parallel cracks that control strength for transversely ground specimens or biaxially-loaded plate or disk

specimens. The cracks are 5X to lOX deeper than the surface roughness striations. The grinding wheel is not drawn to scale.

75
Figure 52 Grinding damage map for silicon nitride. Strengths are normalized to the fast fracture inert strength which may be vary due to billet to billet differences, or specimen size or stress gradient

configurations. The inert strength is typically obtained with longitudinally ground bend or direct tension

specimens that have been prepared with 320 or finer grit finish machining, provided that sufficient

material is removed to eliminate prior coarse machining damage. Longitudinal grinding has minimal

effect on strength unless wheels coarser than 240 grit are used. Transverse grinding may degrade strength

with wheels coarser than 600 grit.

76
Figure 51 is intended to show the effects of surface grinding on flaw generation beneath the

surface for the SRBSN and similar silicon nitrides. This is a simplified variant of an earlier schematic,

based upon calculations that was prepared by Morgenthaler for hot-pressed silicon nitride NC 132. [57]

Unlike Morgenthaler' s, the new figure is based on actual crack depth measurements. This simple

schematic may be useful for demonstrating the significance of subsurface cracking to a general audience

including machine shop personnel.

Figure 52 is a three dimensional damage map for dense silicon nitride in general. Two key

factors are the independent variables: wheel grit size and direction of machining. A normalized strength

axis is used since material-to-material, or batch-to-batch variations in the material flaws, specimen size,

or geometry effects all influence the baseline strengths. The strength trend with grit for transversely

ground specimens is surprisingly consistent over a range of studies (Figure 42a). Parallel cracks from

transverse grinding are particularly severe and begin to control strengths for wheels coarser than «600

grit. On the other hand, although silicon nitrides are more tolerant of longitudinal grinding, the literature shows more variability in the trends (Figure 42b). Small orthogonal cracks from longitudinal grinding can be strength limiting, but usually only for coarser wheel grits (e.g. 240 grit or coarser).^ Quinn

[63,64] showed examples of strength controlling orthogonal machining cracks in 220 or 240 grit

longitudinally ground silicon nitride bars. Orthogonal cracks are more likely to control strength in very

strong materials that have improved process control of the material flaws such that the inherent strengths

are ~ 800 MPa or greater.

Although most of the literature is confined to longitudinal or transverse grinding, there are two

cases that we are aware of that included intermediate angles. Salem et al. [24] systematically studied the

influence of grinding angle in sintered silicon carbide bend bars that were ground with a 320-grit wheel.

The data showed the effect of the angle change was gradual. Parallel machining cracks oriented at 30° or even 45° to the stress axis caused only a minor strength decrease. More pronounced decreases occurred

for cracks oriented 60° and 90° to the stress axis. Their data was supported by finite element and fracture mechanics modeling of cracks oriented at these angles. Thomas et al. [85] also detected a gradual

decrease in strength with grinding angle for hot pressed silicon nitride bend bars ground with a 320-grit

diamond wheel. Specimens ground at a 45° of 90° angle to the specimen axis were 28% and 47 % weaker

on average than the longitudinally ground specimens.

Our data for the Ceradyne SRBSN shows that for a comparable grinding condition the ratio of

transverse to longitudinal strengths are » 0.82 to 0.84. Of course, if material flaws dominate, then the

ratio is ~1. Ratios between these limits may occur for data sets having mixtures of material and

/

There often are exceptions to the general observations. For example, Allor et al's [14] study with longitudinal grinding in hot pressed

silicon nitride showed that very fine a wheel may be deleterious. 1200 grit wheels produced much weaker specimens than comparably machined 600 grit specimens. One possible explanation for this behavior could be that the final finishing did not remove damage from prior grinding.

77
machining flaws. Rice [86,87] lias tabulated ratios of transverse to longitudinal strengths and obtained

values ranging from 0.5 to 1.2. Mayer and Fang [21] obtained ratios of 0.68 to 1.0 depending upon the

grit size. For most fine-grained materials such as the SRBSN in this study, values of 0.60 to 0.84 are the

norm. Material microstructure itself plays a prominent role in determining sensitivity to machining

damage and the strength ratios. Rice has shown that the ratios of transverse to longitudinal strength are

sensitive to grain size particularly when the flaw size is similar to the grain size. [86,87] Xu et al. [76,88]

have shown that grain size has an important effect on hardness and fracture toughness, and in turn, on

subsurface damage, mode of material removal, and grinding forces. Of course, many other factors may play an important role in determining damage and some of the

data scatter in the crack size versus grit size graph in Figure 45 can certainly be attributed to these other

factors such as abrasive bond type, table speed, cross feed, wheel speed, machine stiffness, wheel

trueness, and wheel dressing condition. Often the data is mixed, however, as Li and Liao have pointed

out in their review paper [27]. For example, depth of cut is frequently cited as a key factor. Some

studies have shown it is a major factor for some materials: Kanematsu et al. [89], Mayer and Fang

[21,22]; Xu et al. [5,76]; and Thomas et al. [25]. Others have shown it is not a major factor: Ota and

Miyahara [19]; Mayer and Fang [21,22]; Xu et al.[5,76]; and Allor and Baker [14,15]. Diamond

concentration, diamond bonding (metallic, resiniod, etc), and even operator skill and experience [14,15]

all contribute to variability. Allor and Baker [15] showed that it is crucial to ensure that a machine shop removes sufficient material in the final finishing stages. Phase 2 of our Consortium program

demonstrated that table speed and down feed did not affect longitudinal strength, but did have a small

effect on transverse strength of the SRBSN when 140/1 70 or 80/100 grit wheels were used. [3 ,4] It should

not be surprising that there is so much conflicting evidence as outlined above and more comprehensively

by Li and Liao [27]. The grinding process involves much more than a single grinding wheel and the

work piece. Many variables such as grinding forces, machine stiffness, and a host of operational details

can play a role. A systems approach may be needed to fully appreciate all these factors and their

interactions. [90,91]

A few words on extraneous influences are in order here as well. We have shown that performance may not necessarily be controlled by the average grit size of a diamond wheel. One

renegade abrasive grit could compromise the performance of an otherwise satisfactory 600 grit wheel.

Allor and Baker [14] found that how specimens are mounted (clamping or waxing them to a plate) is

critical. Recent unpublished work in the ceramics industry has brought attention to random, stray micro

scratches which can control strength in finely finished bend specimens.^^ These tiny scratches may

compromise parts that are otherwise properly machined. Loose diamond abrasive grits somewhere in the

machining process or subsequent handling of the pieces may cause the damage. Similarly, it is well

Private communication, B. Mikijeij, 2002.

78
known that bend bars are notoriously sensitive to edge damage that can control fracture if the edges are

not prepared carefully.^'' These examples underscore the influences that extraneous factors may have in

controlling performance. There is no guarantee that the performance shown in the maps in this paper can

be realized unless due care is exercised by the machinist. Although Figures 44, 51 and 52 show material

performance potential, these results will not be achieved by an inexperienced machinist using an

improperly trued and dressed 600 grit grinding wheel on a surface grinder with manual controls and with

an out of balance wheel. Experienced machinists often say that one good way of ensuring the machines

are running properly is by listening to the sounds from the surface grinder.

Machining Conditions and Standard Strength Test Methods

The original standard test method for flexure strength of high performance ceramics, MIL STD

1942,[92] and now ASTM C 1 161 and ISO 14704 [93] as well, all prescribe longitudinal grinding if the

goal is to measure or estimate the inherent strength. The detailed specimen preparation specifications were intended to be conservative. Several tension strength methods have even copied the bend bar

specifications. Experience has shown, at least for silicon nitrides, that the specifications may be overly

conservative. It should be borne in mind that the specifications were not written merely for silicon

nitride. Many other structural ceramics such as silicon carbide, aluminum nitride, or boron carbide are

very brittle and sensitive to chipping and machining damage. Indeed, the flexure test standards were

careful to caution that the prescribed grinding sequence was not foolproof. Finer or more careful

processes may be required for some materials. MIL STD 1942 originally stated in 1982:

"Surface preparation can have a pronounced effect upon flexural strength. This occurs due to the

introduction of machining related defects and the creation of residual surface stresses. In

general, the stronger the ceramic, the more likely that machining damage can limit the flexural

strength. Specification of a final surface finish is not adequate because machining damage can

extend well below the surface striations. Lapping or polishing may remove surface striations and generate a perfect finish, but may not remove enough material to eliminate the much deeper

machining damage The wheel grits, speeds and rates of removal specified are intended to

eliminate or minimize severe machining damage or large residual stresses. As the standard

evolves, or is modified in the future, specimen preparation may become more stringent."

The standard test methods specifications have succeeded in managing this problem. They require edge rounding or chamfering parallel to the specimen's long axis with finish grit comparable to the ground flat surfaces. If these specifications are met, then chamfers failures will either be eliminated or minimized. Of course, not every chamfer origin is caused by edge damage. Many material flaws (pores, inclusions,

etc) simply happen to reside there and these are legitimate, normal fractures. In recent years, two problems with chamfer preparation have

arisen in some machine shops, however. Some shops have prepared bars with oversized chamfers in which case mathematical corrections

to the flexure stress must be made. The other problem is when chamfer grinding has not been exactly parallel to the specimen axis, and

small chips or cracks are created on the edges of the chamfers themselves.

79
i' MIL STD 1942 then went on to specify longitudinal surface grinding only with at least two steps

(coarse and fine) with stock removal rates not to exceed 0.030 mm per pass down to the last 0.060 mm.

Final finishing was to be performed with a wheel between 200 and 500 grit and no less than 0.060 mm

was to be removed per face at a rate of no more than 0.002 mm per pass. The finishing wheel range was

tightened to 320 to 500 grit when ASTM C 1 161 was adopted in 1990, and has been further tightened to 400 to 600 grit in early 2002. The newest (2002) version of C 1161 also includes limits on grit sizes and

depths of cut for the coarse and intermediate machining steps. The ISO analogue, ISO 14704 specifies a wheel no coarser than 120 grit for coarse grinding and 320 to 800 grit for final finishing. No less than

0.060 mm must be removed at a rate of 0.002 mm per pass in the final finishing. This seemed like a very

conservative approach back in 1982 when the MIL STD was written, but in reality, a previous ASTM

standard F 417 prepared in 1975 [94] for alumina bend bars for electronic substrate applications specified

longitudinal grinding with a 1 80 or finer grit wheel and put strict limits on the depths of cut (0.005 mm

per pass), the final amount to be removed per face (0.025 mm), and the crossfeed. The key parameters

are the direction of machining, the finishing grit size, and the final amount to be removed. A removal

amount of 0.060 mm (MIL STD 1942(MR), C 1 161, ISO 14704) seemed like a lot of material to have to

grind off in the final stages, but reference to Figures 43, 44, and 51 show that this was probably just

enough to eliminate severe prior rough grinding (albeit damage created in a harmless direction if the bars

are ground longitudinally.) It is interesting that of the five shops evaluated by Allor and Baker [15], two

which fared the worst removed only 0.050 mm during finish grinding of silicon nitride bend bars,

whereas the most experienced shop removed: 0.100 mm - 0.200 mm. This conservatism was prudent and

based on years of accumulated experience.

A new standard intended to evaluate the effect of machining upon strength is ASTM C 1495 [95]

which has a much more conservative approach and specifies 600 grit longitudinal grinding that is

intended to eliminate machining damage as a source of strength limiting flaws.

Salem et al's [24] work is a good example of the successful application of the C 1161 standard

machining procedure to a sintered silicon carbide, a particularly brittle ceramic. Their longitudinally

ground flexure specimens all fractured from volume distributed flaws (agglomerates). Similarly, most of

the two thousand sintered alumina and reaction-bonded silicon nitride specimens tested in a very large,

seven international laboratory Technical Cooperation Program flexural strength round robin based on MIL STD 1942(MR) fractured from material flaws.[35]

Implications for Modeling of Machining Damage

The primary focus of this work has been on the fractographic detection and characterization of

machining cracks and their relationship to grinding conditions. Nevertheless, a few words about the

applicability of the results to modeling are appropriate. Concepts developed for indentation fracture or

single-point scratching have been adapted to construct machining damage models (e.g. [78,96,97].

80
Marshall [78,96] applied conventional indentation mechanics analyses to the machining problem and

showed that machining crack size, c, (depth) can be expressed as [97]:

C = ^

1/3/ p

^2/3

where £, is a constant, E is the elastic modulus, H is hardness, Kic is fracture toughness and F is the force on a single abrasive grit. F varies with the machine conditions such as depth of cut and the abrasive

wheel type, and in particular, the abrasive grit size and concentration. In principal, larger Kjc's should

lead to smaller machining crack sizes, but as we have noted for the case of the very tough Dow SSN, the

opposite may in fact be the case. For a given grinding machine set up, greater material fracture resistance

creates greater applied grinding forces so F is not constant and F = f(Kc). Machining conditions are more

complicated than controlled Vickers indentation experiments where one can control F independently of

all other parameters.

Of course, the above model was developed for materials with constant fracture toughness. Rising

R-curve behavior complicates these issues. Marshall et al. [78] have shown that short crack toughness

may correlate better with grinding resistance than long crack toughness. The lower the threshold fracture

resistance, the lower the grinding forces. As noted above, some experiments [43,44] to measure an R

curve and the threshold fracture resistance of the SRBSN showed the threshold toughness of our

particular SRBSN may be quite low (< 2.0 MPaVm [44] or = 3.0 MPaVm [43]).

It should be borne in mind that the grinding machine-workpiece interaction is a complex dynamic

problem. Residual stresses, microstructural issues (e.g., crack size-grain size ratios), R-curves, and

grinding directionality effects, may all be coupled to the grinding machine response (e.g., the force F).

This problem is much more complex than a simple Vickers indentation experiment.

Comparisons to Other Selected Studies

A recent design project for ceramic diesel valves compared both rectangular and cylindrical

flexure test specimen strengths to valve tension strengths [11]. WeibuU size scaling of strength could not

account for the observed strength differences. It was concluded that microstructural gradients in the rods

created different flaws in different portions of the specimens and components.

Wu and McKinney [17], compared flexural strengths of 180, 320, and 600 grit longitudinally

ground bars in hot pressed silicon nitride grade NC 132. Although the machining flaws were difficult to

positively confirm by fractographic analysis, they were able to ascertain that the dominant flaw type

changed from machining cracks for the 1 80 and 320 grit specimens, to a mixture of machining cracks and

inclusions for the 600 grit specimens. They concluded that finer finishing wheels would not be effective

in increasing strength since the small 600 grit machining flaws were comparable in severity to the

material flaws. This conclusion is consistent with our Figure 44.

81
Figure 53 Schematic views of fracture surfaces of various specimens tilted back to partially reveal the

ground surfaces on the bottom. The following figures show close-ups of the origins.

Telltale Signs of Machining Damage

This study has focused on traditional fractographic methods to detect parallel machining cracks on the fracture surfaces as depicted schematically in Figure 53. These are the methods most likely to be

used by the typical strength tester and fractographer. This is not to say that alternatives do not exist. Dye penetration techniques, which may also help highlight machining cracks during subsequent fracture

surface examination, have good promise.[34,60,61]

The telltale features of fracture origins and mirrors associated with machining damage are

depicted Figures 54 and 55. These schematics are based on the observations of hundreds of flaws in

this study, plus experience gained with a variety of other ceramics and glasses over 25 years of study.The

specimen schematics show the fracture surface tilted back a bit so as to show part of the ground finished.

The schematics show the entire fracture mirror for high strength specimens wherein the mirror is small

relative to the specimen size and any possible stress gradients. Mirrors are incomplete, flared out, or

elongated into the test piece interior (depth) in low to medium strength fractures in bending fractures (not

shown). Appendix A also has several illustrations s\\oW\ng fracture mirror elongations in the direction

of the flaw long axis, another tell tale sign of machining crack damage

Cracks induced by machining, polishing, or scratching extend well below the finished surface.

Traces on the finished surface may not even be present if they have been removed by subsequent grinding

or polishing. Cracks may be as shallow as 2 |im in ground silicon, 5 \xm in polished glass, or as deep as

100 |Lim in scratched or coarse ground surfaces. Finish surface grinding usually produces cracks of the

order of 10 )Lim - 80 |Lim deep depending upon the grinding conditions.

82
Figure 54 Parallel machining cracks in transversely ground surfaces. Parallel cracks lie more or less parallel to the axis of grinding. These cracks are common in biaxial disks, transversely ground uniaxial

flexural or tension strength specimens, or transversely ground components.

(a) elongated "coplanar parallel crack"

A deep striation may or may not necessarily be present.

The fracture mirror may be elongated along the outer specimen surface.

(b) elongated "coplanar parallel crack"

Same as above except the machining crack has linked with a natural flaw. A step in the fracture origin emanates from the material flaw.

(c) "zipper crack"

A type of parallel crack that is made up of a series of short semi elliptical cracks, which have linked. A series of short tails, or "machining crack hackle," emanate

from the links or overlaps of the flaws and extend up into the fracture

mirror. These tails may be tilted to the left or right and help confirm that

fracture originated in the central region of the set. The short tails are

telltale features of slightly misaligned or overlapping transverse machining

cracks (or a scratch) and are often easier to see with an optical microscope

with low angle lighting than with a scanning electron microscope.

The fracture mirror may be elongated along the specimen outer surface or

it may have one or two prominent side lobes. This origin type is common in transversely-ground rectangular

flexure specimens or scratched biaxial disk specimens.

(d) coarse "zipper crack"

A type of parallel crack that is made up of a series of irregular, less coplanar semi-elliptical cracks. Larger tails than in (c ) are created. In severe cases, the tail may extend all the way to the mirror boundary.

The fracture mirror may be elongated.

This origin is common in transversely ground or scratched specimens and

the markings are sometimes termed "shark's teeth."

(e) "V machining crack"

The crack intersects the fracture surface at an angle. Only a portion of the machining crack or crack series is exposed. A pronounced step occurs in the fracture mirror. One or two (shown) tails extend well up into the

fracture mirror. The machining direction is not quite perpendicular to the specimen length and uniaxial stress axis due to grinding

wheel cross feed. This origin is common in cylindrical specimens

prepared by centerless or cylindrical transverse grinding wherein the wheel

and work piece displace axially relative to each other.

(f) "coarse grinding parallel crack"

The ohgin is a deep machining crack that extends along the entire surface. The origin is often bumpy since the origin is comprised of offset parallel cracks. Thin bands of uniform depth extend along the specimen surface on either side of the fracture mirror. The bands have the same depth as

the grinding cracks. Short tails, or "machining crack hackle" which may be

in the thin bands are tilted away from the origin. This origin type is common in coarse ground surfaces. Mr

83
Figure 55 Orthogonal machining cracks in longitudinally ground surfaces. Orthogonal machining cracks

lie perpendicular to the grinding direction. They are much harder to detect than parallel cracks shown in the previous figure.

(a) "orthogonal machining crack"

A semi elliptical surface crack that extends well below the

striation depths.

Depending upon the grain size and microstructure, the short semi elliptical cracks may be difficult to detect in polycrystalline

ceramics since the cracks do not stand out clearly against the normal microstructure. An origin location on the surface is a necessary requirement

but not sufficient proof that the origin is machining damage.

In many instances, (particularly in beams in bending) natural material flaws may reside at the specimen surface.

(b) "orthogonal machining crack"

The same as above, except that an unusually deep machining

striation is lined up with the machining crack. Deep striations may aid interpretation, but they may not necessarily be present since final finishing may eliminate them.

(c) "orthogonal machining crack"

The same as above except that the machining crack has linked up with a natural material flaw such as an agglomerate or pore. The origin may be categorized either as an enlarged natural flaw

or a hybrid natural flaw-machining damage.

The natural flaw may make the material more susceptible to machining crack damage in the immediate vicinity of the flaw .

(d) "orthogonal machining crack"

The same as above, except that the natural flaw created a bump or jog in the fracture mirror. The irregularity at the origin created a step or curve in the fracture mirror that created a tail that extends well up into the mirror or even to its boundary.

84
That routine post fracture optical microscopy of the fracture surface could be so effective was a

surprise result of our project. In many cases, it was much easier to see the machining cracks in a stereo

binocular optical microscope than in the SEM. We hope that fractographers and engineers will try lowangle illumination techniques and will consuh these schematics. Indeed, while reviewing the technical

and engineering literature about machining of ceramics and engine component preparation and testing, the

lead author was struck at how many times these tell tale patterns showed up in old photographs, even in low quality photocopies. The same techniques should work on white translucent ceramics which are

particularly difficult to analyze due to subsurface light scattering. A thin coating of gold-palladium or even staining the fracture surface with a common green felt tip pen may aid the examination.

We conclude by recalling some words written 33 years ago in connection with another study of

the effects of machining damage upon strength. In 1970, Sedlacek et al. [98] pessimistically wrote: "To

examine fi^agments of broken specimens is a futile exercise in microscopy which may, at the best, lead to

only a subjective interpretation of the studied surfaces." A few years later (1974) Rice [99] more

optimistically wrote: "Determination of flaws that are introduced by machining as well as surface

chemical effects is progressing.... Unfortunately, flaw detection in ceramics has not advanced

sufficiently to offer capabilities comparable with those of chemical characterization." We cannot agree

with Sedlacek' s assessment. We have made significant strides in the science of fractographic

characterization of machining flaws, particularly for transverse grinding. We hope others will now

search for machining cracks at fracture origins with more confidence. Subjectivity should be reduced.

Processors and engineers should no longer have to guess whether machining damage is the cause of their

woes.

CONCLUSIONS

The flexural strength of rods and bars of a commercial, toughened SRBSN silicon nitride that were prepared by a variety of machining procedures were evaluated. Fractographic analysis was applied

to every specimen and hundreds of machining cracks were characterized. The dominant factors in

determining flaw severity were the abrasive wheel grit size and the direction of machining. The depth of

machining cracks correlated strongly with the wheel grit. Cracks were as shallow as 12 \im for 600 grit

ground surfaces to as deep as 80 jim for 80 grit transverse ground surfaces. A literature review indicated

that 100 |Lim may be an upper limit for the depth of machining cracks in silicon nitride. Strength limiting

machining flaws varied in size by as much as a factor of two in batches of identically prepared specimens.

This variability matched the strength variability.

The SRBSN's "inherent material strength," whereby specimens nearly all fractured from material

flaws, was obtained from rods ground longitudinally with a 320-grit wheel. Three shops matched or came

close to matching this performance with 600 grit centerless or transverse cylindrical grinding.

85
Cylindrical and centerless grinding of rods may create similar, but not necessarily identical, flaws

to those in surface ground flat bend bars. Strength limiting machining cracks sometimes were associated

with striations that were not necessarily the deepest or most obvious on the ground surface. A single

severe, "renegade" abrasive grit in a grinding wheel may control performance.

The evidence suggests that machining cracks and comparably sized artificial Knoop semielliptical

flaws experience a resistance to fracture commensurate with plateau fracture toughness values. Evidently

the benefits of the enhanced fracture toughness due to the interlocking grain microstructure occur during

machining crack pop in or initiation. Subsequent stable crack extensions prior to fracture are small (5

|am - 15 ]im).

Residual stresses had small or negligible effect upon fracture in the SRBSN.

Most other silicon nitrides had similar sized machining cracks as found in the SRBSN.

Variations occur based upon material properties such as hardness, elastic modulus, and fracture

toughness, upon the microstructure, and upon the energy and forces applied by the grinding machine.

Toughened silicon nitrides may not necessarily have smaller machining cracks.

Damage maps for ground fully-dense silicon nitride were constructed. Hopefully these will aid

machinists and engineers in appreciating the nature of machining damage and its effect upon

performance.

Simple fractographic techniques may find parallel machining cracks on fracture surfaces. Their

telltale markings are tabulated in a series of new schematic illustrations. These will help engineers and

analysts find and characterize machining damage flaws with greater confidence. Orthogonal machining

cracks, created by longitudinal grinding still remain difficult to detect.

ACKOWLEGEMENTS

The authors thank the members of the Ceramic Machining Consortium who participated in this

program. We especially recognize Dr. B. Mikijelj of Ceradyne Inc., Mr. Richard Allor of Ford Motor

Company, and Drs. Ron Chand and C. Guo of Chand-Kare Technical Ceramics. Partial support for this

project was furnished by the U. S. Department of Energy, Office of Transportation Technologies, under

contract DE-AC05-84OR21400 with Oak Ridge National Laboratory.

Dr. Hockin Xu and Mr. Robert Gettings assisted with earlier phases of the Consortium project

and with fracture toughness testing. Dr. W. Luecke kindly furnished a micrograph of the microstructure.

Over the course of this multiyear project, we were privileged to work with the following enthusiastic

postdoctoral and guest worker colleagues who contributed a great deal to the success of this project: Dr.

Phillip Koshy, Dr. Tim Strakna, Mr. Jeffrey Swab, and Dr. Kang Xu.

p. 86
Appendix A

Fracture Origin Locations in Rods and

Fracture Mirror Measurements for Rods and Bars

The stress at the origin site was used for computations of fracture toughness at the flaw location

or for fracture mirror analysis. For the bar specimens, the origins were always at or very close to the

tensile surface, and hence, the stress used was the same as the maximum stress in the beam, CTmax- This is

the nominal value used for reporting strength and conducting Weibull analyses. On the other hand the rod

origins sometimes were located in the interior or partway up the side surface. The stresses at the actual

origin site, Gq, were used for the fracture mirror calculations. From simple beam theory, stress decreases

linearly with the origin's distance from the rod bottom to the neutral axis of the rod (which passes

through the center of the rod): <Jo = (2y/D) Gmax where D is the rod diameter and y is the distance from the

neutral axis (Figure Al).

Fracture origin locations were determined by projecting the fracture surface image onto a

television monitor that had a superimposed angular grid. The angular location of the fracture origin

relative to bottom dead center (the maximum stress location) and the rod center in all the rod specimens was also measured. The specimen was tilted slightly so that the camera, which viewed the specimen

through only one light path in the stereomicroscope, was perpendicular to the fracture surface. The

angular location of the origin was measured to within ±

1°.'^'^ The repeatability of this procedure was

verified by multiple measurements on the same and the opposite fracture halves of several specimens.

Nearly all specimens broke within ± 25° of bottom center so that the stress at the origin site was 90% or more of the maximum outer fiber stress. Figure Al shows the distribution of fracture origin sites for two

different sets of thirty rod specimens.

Fracture mirrors were measured with the stereo binocular microscope, while viewing at SOX - 63X through the eyepieces. Even though the microscope was capable of greater magnifications (205X),

we found it optimal to not us such large magnifications, but to "step back" and view the fracture surface

from a distance, so to speak. We viewed and measured the mirrors when they occupied about 1/3 to 1/2

of the field of view when looking through the stereo microscope.

Mirror constants are important properties that can aid in fractography interpretation of fractured

components or lab test specimens. In general, stress and the mirror radius are related through the

expression:

Type B estimate, 95% confidence level.

87
Figure Al Rod cross section views showing tiie distribution of origin locations, (a) is for a set of 30

specimens ground with a 320 grit wheel in the transverse direction. Stress decreases linearly with

distance towards the neutral axis (mid plane). Nearly all specimens broke in the portion of the rod that experienced stresses 95% or more of the maximum stress near the bottom center of the rod. Most of the

specimens broke from machining damage on the surface. A single large inclusion caused fracture in an

unusually weak specimen and is marked as the hollow point that is well up the side of the rod. (b) is for a

set of 30 specimens ground longitudinally with 320 grit wheel. More material flaws were activated in this set and several inclusions were well below the surface.

Transversely

ground

320 grit

m = 22

Longitudinally

ground

320 grit

m = 15

88
where Gf is the fracture stress at the mirror site, Ri, is the mirror radius (the mist-hackle boundary in this

instance), and Aq is the mirror constant.

Mirrors were plainly evident at low magnifications, but accurate assessment of their size was

difficult. The mirror region itself was somewhat bumpy in this self-reinforced silicon nitride, so some

judgment as to what was the mirror boundary was necessary. The criterion used in the present study was

that the mirror boundary occurred at the point where hackle commenced and there was an obvious

roughness change relative to the mirror. Figure A2 shows schematics of the mirrors. The mirror size

measurements were made while viewing the specimen with the binocular stereomicroscope. The

microscope cross hair was used in conjunction with a micro positioning X-Y traversing stage on the

microscope platform that read out to 0.001 mm. The fracture surface was positioned so that it was

parallel to the traversing stage's axes of movement. Illumination was from a fiber-optic light source

positioned at a low incident angle to the fracture surface. The mirror radii were calculated as follows.

For the rectangular bars, the overall diameter (Ri + R2) was measured on the tensile surface as well as the

radius into the depth, R4. An average radius Rh was computed as {(Ri + R2)/2 + Rd}/2. All the origins on

the rectangular bars were at or very close to the surface, so no stress adjustment was needed. For the

cylindrical rods, the diameter on the surface (Ri + R2) was measured as well as the radius into the depth,

R<i, and an average mirror size computed as above. The two segments Ri and R2 were often unequal,

especially for origins that were partway up a rod side. For origins located in the rod interior, the average

of two orthogonal mirror diameters was used to compute the radius. The stress at the origin was corrected

for the distance away from the bottom center for all rods for the fracture mirror size analysis. Bottom

center was ascertained by viewing the entire fracture surface with special attention to the telltale

cantilever curl on the opposite compression side of the fracture surface. The fracture mirror data are shown in Figure A3 and A4. The graphs include data from many of

the specimens in the study and cover a very broad stress and mirror size range. The mirror constant is the

slope of the lines. The rod and bar data have slightly different (8.7 %) slopes. We cannot account for the

difference at this time. The same eyes, same microscope, same illumination conditions, and similar

averaging criteria were used in each case. There was no deviation from the overall trend for any data

subset. All bar data fell on the bar line, and all rod data fell on the rod line. Potential residual stresses

from machining extend only shallow distances into the depth, and are unlikely to affect mirror sizes.

89
Figure A2 Schematics of fracture mirrors. In very fine grained or glasses materials, mirror boundaries

are not too difficult to delineate as shown in a, where the mist hackle boundary is marked. The SRBSN in the present study had bumps and roughness even within the mirror region as suggested by (b) for bars and

(c) for rods.

90
Figure A3 Fracture mirror sizes for most of the rods tested in the study. The mirror sizes varied from

test set to test set, but were in accordance with the general trend for this material. The slope of the line is the mirror constant A©. Uncertainties for a single measurement are indicated by an error bar on the single

rod datum at 587 MPa. The uncertainty bar corresponds to two limits for the datum: the minimum

possible mirror size and absolute maximum size that in this case was the branching distance.

Mirror Radius ( |i m)

1000 600 400 300 200 150 100 80 60

1000

0 20 40 60 80 100 120 140

1./V(Radius) (m'''^^)

91
Figure A4 Fracture mirror data for rods o, and bars . The solid lines show the linear regression lines with a zero intercept. The slopes of the lines are the mirror constants. The uncertainties, which are the

standard deviation of the slopes of the line, are very small due to the large number of data points. The

dashed lines are regressed lines with non zero intercepts. The intercept for the bars is 153 MPa for the

rods, 123 MPa.

Mirror Radius ( \i m)

1000 600 400 300 200 150 100 80 60

0 20 40 60 80 100 120 140

1./V(Radius) (m-''^^)

92
Kirchner and Conway noted that fracture mechanics stress intensity factors around surface connected

semicircular and semielliptical flaws, could account for differences in mirror shapes in rods and bars. Hence, apparent mirror and branching constants from the two geometries could be slightly different. One surprising observation was that the transversely ground bar specimens often had mirrors that were noticeably elongated along the specimen surface (Figure A5 a-c). Elongations into the specimen

depth are common in flexure specimens (Figure A5 e,f) and are due to the stress gradient, but the lateral

elongation of the mirror dimension is noteworthy. The elongations were less noticeable in the rod

specimens. The degree of mirror elongation along the bar specimen surface was directly related to the

length and severity of the grinding flaws as shown in Figure A6. Weaker specimens had depth to width

ratios much less than 1. Ellipticity is the ratio of the mirror radius into the depth to the radius along the

surface. Weak specimens with shallow but very long surface cracks (e.g., "zipper cracks") had

ellipticities as low as 0.68. From our experiences with the SRBSN and also with other glasses and

ceramics, we conclude that flattened, elongated mirrors are telltale signs of scratches or transverse machining damage. We have even detected severely elongated and lobed mirrors in stress-free annealed

glass disks. In some instances, a side lobe may even jut out from the side of the fracture mirror as shown

in Figure A5c.

Figure A7 illustrates two mechanisms by which elongated mirrors could form: either fracture

unzips along the surface (a), or fracture starts and radiates outward from the two ends of the machining

cracks. We believe the (a) is more plausible, especially since machining crack hackle lines on top of the

"zipper machining cracks" (Figures 31b and Appendix Figures C2c, d, f) often "lean" or tilt to the left

or right within the mirror. The tilts suggest that the origin crack unzips to the left and the right from the

middle of the origin.

H. P. Kirchner and J. C. Conway, Jr., "Criteria for Crack Branching in Cylindrical Rods: I, Tension," 7. Amer. Ceram. Soc, 70 [6] (1987) 413-18.

93
Figure A5 Elongated fracture mirrors, (a) - (c) show the lateral elongations that may arise from long

machining cracks or scratches, (d) - (f) shows the usual elongation patterns into the depth of the

specimens as a results of the stress gradient in flexure specimens. If the mirror is relatively small (high

strength specimen or the specimen itself is large), the mirror will be semicircular (d). If the specimen is smaller or is weaker, then the crack advances into a decreasing stress gradient as it penetrates into the

depth. In such cases mirrors may be elongated in the depth direction (e) or may not form boundaries at all

(a) (b) (c)

(d) (e) (f)

semicircular Flared into the depth

and incomplete

Flared Into the depth and

incomplete

94
Figure A6 Fracture mirror ellipticity for 30 rectangular bars with a 320 grit shop C transverse ground

surface. The flaws were long shallow surface machining cracks in these specimens.

Q.

0)

o

'>55

1.20

1.10

1.00

0.90 —

0.80 —

0.70

0.60

mirror is semicircular

°

cm °

mirror is elongated

along the tensile surface

400 500 600

Stress (MPa)

700

Figure A7 Possible mechanisms to account for elongated mirrors associated with long surface scratches or machining cracks, (a) shows how crack propagation at the instant of fracture could commence from

the flaw middle portion, but advance rapidly along the flaw ("unzip") before moving into the bar interior, or alternatively, (b), fracture could initiate simultaneously from both ends of the crack.

(a) (b)

95
Appendix B

Machining Procedures

RODS

SHOP

preparation Machining Procedure

C

Longitudinal

(Centerless)

320 grit

Initial grinding;

Conventional Transverse centerless qrinding

Wheel: SD 320R100B, 12.7 mm wide, 203 mm diameter, resin bond

Rods ground down to 6.025 mm diameter by

Wheel depth of cut: 0.050 mm per pass

Wheel surface speed: 38.8 m/s (3650 rpm)

Workpiece rotation speed: 1100 rpm

Axial feed rate: 7.62 mm/s

Volumetric removal rate: 3.6 mm^/s

Finish grinding:

Same wheel

Centerless Longitudinal Grinding

Wheel depth of cut: 0.005 mm for 5 passes

0.025 mm removal

Workpiece Rotation Speed: 2000 rpm

Axial feed rate: 3.6 mm/s

Volumetric removal rate: 0.17mm^/s

N

Transverse

Centerless

600 grit

Initial grinding:

Wheel: D180-L100-B1/8, 19 mm wide, 254 mm diameter, resin bond

Wheel Surface Speed: 26.8 m/s (2015 rpm)

In feed: 0.050 mm per pass

Axial feed rate: 30 mm/s

Roughing final diameter: 7.05 mm

intermediate grinding:

Wheel: ASD400B100B, 9.5 mm wide, 254 mm diameter, resin bond

Wheel Surface Speed: 32 m/s (2425 rpm)

In feed: 0.013 mm per pass

Axial feed rate: 30 mm/s

Workpiece rotational speed: 2890 rpm

Intermediate step final diameter: 6.3 mm

Finish grinding:

Total removal: .300 mm from diameter, .150 mm from each surface Norton D10/20MIC-R75B61 9-1/8, 203 mm x 12.7 mm wheel, resin bond

Wheel surface speed: 25.8 m/s (2425 rpm)

In feed: 0.005 mm per pass

Axial feed rate: 23 m/s

Total removal: 0.300 mm from diameter, 0.150 mm from each surface w

Transverse

(cylindrical)

600 grit

Initial grinding: Norton 6" x 12" chuck cylindrical grinder

320 diamond wheel, 100 concentration, 8" diameter x 1/2" wide, resin bond

Rods mounted on centers, plunge ground (no traverse)

Final roughing diameter: 6.305 mm - 6.356 mm

Finish grinding:

Cincinnati Milacron MD600-P100-B-1/8, 8" x 1/4" wheel

Surface speed: 18.6 m/s (1750 rpm)

Wheel in-feed: 0.025 mm per pass

Axial longitudinal feed rate: 4.2 to 5.1 mm/s (work piece)

Workpiece Rotational Speed: 950 rpm

Final finish diameter: 6.00 mm

Total removal: 0.300 mm from diameter, 0.150 mm from each surface

96
F

Transverse

Details not reported.

c

Transverse

Centerless

320 grit

Initial grinding;

Conventional Transverse centerless qrindinq

Wheel: SD 320R100B, 12.7 mm wide, 203 mm diameter, resin bond

Rods ground down to 6.025 mm diameter by

Wheel depth of cut: 0.050 mm per pass Wheel surface speed: 38.8 m/s (3650 rpm)

Work rotation speed: 1 100 rpm

Axial feed rate: 7.62 mm/s

Volumetric removal rate: 3.6 mm^ls

Finish finishing:

Same wheel

Wheel depth of cut: 0.005 mm for 5 passes

Work Rotation Speed: 680 rpm

Axial feed rate: 2.54 mm/s

Volumetric removal rate: 0.12 mm^/s

N

Transverse

Centerless

220 grit

Wheel: Norton AD 220-R175B61 9-1/8, 12.7 mm wide, 203 mm diameter, resin bond

Depth of cut: 0.005 mm per pass Wheel Surface speed: 30 m/s (2800 rpm)

Axial Feed Rate: 20 mm/s

Workpiece rotational speed: 2500 rpm

Removal rate: 0.94 mm Is Total removal: 0.300 mm from diameter (final size 6.00 mm)

s

Transverse

Centerless then Lapped

30 grit No details other than rods were centerless transverse ground

then lapped with 30 |im abrasive grit.

F

Transverse 150 or 180 grit?

Details not reported.

97
BARS

SHOP Specimen

Preparation

Grit/

Depth of cut Machining details

F Transverse 600 grit

5 |im?

Bars cut from Rods.

No details. Probably ASTM C1161 standard procedure,

but with 600 grit resin bond wheel final finish added to only one 4

mm X 45 mm face.

Final removal with 600 grit wheel: 0.125 mm (specified) Bars cut from Rods.

C

Longitudinal

320 grit

5 urn

ASTM C 1 161 multi-step sequence

Finish grinding with 320 grit longitudinal

Wheel: 320 grit, 100 concentration, 203 mm diameter, 12.7 mm

wide

Wheel Surface speed 36 m/s (3400 rpm)

Wheel depth of cut: 0.005 mm per pass

Cross feed: 0.5 mm per pass

Table speed: 200 mm/sec

Volumetric removal rate: 0.5 mm^/s

C Transverse 320 grit

5 |im

Bars cut from Rods.

ASTM C 1161 multi-step sequence

Except finish grinding with 320 grit wheel in transverse direction

Wheel: 320 grit, 100 concentration, 203 mm diameter, 12.7 mm

wide

Wheel Surface speed 36 m/s (3400 rpm)

Wheel depth of cut: 0.005 mm per pass

Cross feed: 0.5 mm per pass

Table speed: 200 mm/sec

Volumetric removal rate: 0.5 mm^/s

Transverse Bars cut from 2 sets of SRBSN plates, not rods

c 150 grit Wheel surface speed: 30 m/s

Table speed: 0.025 m/sec

Down Feed: 0.050 mm per pass

Cross feed: 2.0 mm per pass

Transverse Bars cut from 2 sets of SRBSN plates, not rods

F 80 grit Wheel surface speed: 30 m/s

Table speed: 0.025 m/sec

Down Feed: 0.050 mm per pass

Cross feed: 2.0 mm per pass

98
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21 Nov. 1983, U. S. Army Materials Research Center, Watertown. MA. (This standard was

superceded by ASTM C 1 161 in May 1998.)

93 ISO 14704 (2000) "Fine Ceramics (Advanced Ceramics, Advanced Technical Ceramics) - Test Method for Flexural Strength of Monolithic Ceramics at Room Temperature," International

Organization for Standards, Geneva, SW, 2000.

94 ASTM F 417-75, "Standard Test Method for Flexural Strength (Modulus of rupture) of ElectronicGrade Ceramics," Annual Book ofStandards, Volume 15.02, ASTM, West Conshohocken, PA, 2001.

103
95 ASTMC 1495-01, "Standard Test Method for Effect of Surface Grinding on Flexure Strength of

Advanced Ceramics," Annual Book of Standards, Volume 15.01, ASTM, West Conshohocken, PA,

2001.

96 D. B. Marshall, "Failure from Surface Flaws," pp. 190 - 220 in Fracture in Ceramic Materials:

Toughening Mechanisms, Machining Damage, Shock, ed. A. G. Evans, Noyes Publ. NY, 1984.

97 R. W. Rice, "Monolithic and Composite Ceramic Machining Flaw-Microstructure-Strength Effects: Model Evaluation," J. Eur. Ceram. Soc, 22 (2002) 141 1-1424.

98 R. Sedlacek, F. A. Halden, and P. J. Jorgensen, "The Effect of Grinding Variables on the Strength and

Surface Finish of Alumina," pp. 391-398 in The Science of Ceramic Machining and Surface

Finishing, Special Publication 348, NBS, Gaithersburg, MD, 1970.

99 R. W. Rice, "Machining of Ceramics," pp. 287-343 in Ceramics for High Performance

Applications, " eds. J. J. Burke, A. E. Gorum, and R. N. Katz, Brook Hill Publ. Co., Chestnut Hill,

MA, 1974.

104
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