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Guidelines_for_Fracture_Mirrors_Quinn

Guidelines_for_Fracture_Mirrors_Quinn - 1 July 7,2006...

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Unformatted text preview: 1, July 7,2006 GUIDELINES FOR MEASURING FRACTURE MIRRORS Conference on Fractography of Glasses and George D. Quinn Ceramics, . . Roch ter, NY, Jul 942. 2006 National Institute of Standards and Technology es y Ceramics Division Stop 8529 Gaithersburg, MD 20899 ABSTRACT Fracture mirror size analysis is a powerful diagnostic tool for glass and ceramic fractures. There is considerable variability in published fracture mirror constants, however, especially for ceramics. Mirror—mist or mist~hackle boundaries are not sharp, well—defined transitions and they are subject to interpretation This paper presents some guidelines for mirror boundary inter— pretation and analysis that are from a new NIST Guide to Practice for Fractography. Some recommendations are based on common sense, others are based on solid technical grounds, and some are based upon the experience of other experts and the author. The guidelines are intended to help students, novices, engineers, and materials scientists use fracture mirror analysis to solve practical problems. INTRODUCTION Fracture mirrors are relatively smooth regions surrounding the fracture origin. In glasses and very fine~grained ceramics, the mirror region is very smooth and highly reflective, hence the name “fracture mirror.” In polycrystalline ceramics or composites, the qualifier “relatively” must be used, since there is an inherent roughness from the microstructure even in the area immediately surrounding the origin. Mirrors are circular in ideal loading conditions such as tensir n specimens with internal origins, or near~semicircular for surface origins in tensile specimens or small mirrors in bending as shown in Figures 1 and 2. Fracture mirrors only form in moderate— to high—strength specimens. Weak specimens do not have fracture mirror boundaries since the crack does not achieve sufficient velocity within the confines of the specimen. Fracture mirrors often are elongated or distorted due to stress gradients or geometrical effects. ‘ Fracture mirrors bring one’s attention to an origin, but also give information about the magnitude of the stresses that caused fracture and their distribution. One of the earliest observations in this regard was by Brodmann in 1894:1 “The radially measured size of these mirrors in general was larger, the smaller was the strength.” The relationship between strength and mirror size was gradually refined so that in the 19505 and 1960s, many authors measured mirror sizes and correlated them with stresses in accordance with the relationship12’3’4’5’ 6189 O‘RmzA (1) where e was stress, R was the mirror radius, and m and A were constants. The data was frequently plotted on raphs of log stress versus log radius in order to check for the goodness of fit of equation 1. I was recognized fairly early that m was 1/2 for annealed glasses, and equation I was rewritten as: 0R%:A (2) Figure l Fused silica rod broken in flexure (122 MPa). The origin is a surface flaw located at the bottom of the specimen (a) where the stress was a maximum The mirror—mist boundary is small relative to the cross section size {shown in the insert in (a)} and is approximated by a circle in (b). Close examination of the fracture surface in the Vicinity of the flaw (not shown) showed that fracture started from the deepest part of the flaw. The sizes and arcs were judged while Viewing through a compound optical microscope and then marked on the photographed image. (Some subtle detail in the mist may be lost during printing) The mist~hackle boundary is slightly elongated towards the top. (c) is an SEM image of the same mirror and at the same magnification as (a) and (b). The mist is indistinct in the SEM image. (d) is a composite of two SEM images showing the transition from mirror to mist to hackle. The location of the boundaries as assessed by optical microscopy are marked by dashed lines on the SEM images. Ab A0 Ai ch Figure 2 Schematic of a fracture mirror centered on a surface flaw. The various mirror boundaries and their corresponding fracture mirror constants (A) are marked. The initial flaw at the origin may grow in size from a, to aC at which point the critical fracture toughness, K10, was reached. m .0001 .0002 .0005 001 .002 ‘1' r—i‘ r "Y v H v v i l l «ifi r—r'T—v ~1 '1 _ “f T r ' r ' ROD DtAM tea—INCHES 3 (I) 9— r A Q 9'35 w 200 Q U U.C‘+ , g v 0.39 ' ——’ 0 0,75 s g A [.00 MP8 (9 L50 _ E ° 100 o e. i 0 v.85)“ 3:1 gggeg‘gggfi” " 3 0V .ufijifi‘. . ~ [-— 8 803.3 £619. . A it) .gAC’MA-‘a M .l-SO m o ' 0 LL. :. i j 2 r w j 30 (I) “J l E I i I l _L_.L A l4 Jul-LLJ‘LL I | w .002 .004 .006 .01 0:5 .02 .04 .06 .08 .|0 .|5 MiRROR SIZE. INCHES Figure 3 Fracture stress (adjusted for the origin location) versus mirror size for a borosilicate glass from Kerper and Scuderi.8 This is the original figure from their 1966 paper and it shows the older system of units then in use with a few SI units added on the top and right side. They fitted the data with eq. 2 for 259 rods broken in the three—point bending and obtained a mirror constant of 2.08 MPan (1,891 psi/in”). The rod diameters varied almost by a factor of 10, the mirror sizes by a factor of 50, and the stresses almost by a factor of 10. In this form, A is the “mirror constant” with units of stress intensity (MPan or l<si\/in) and is considered by many to be a material property. It is possible to discern separate mist and hackle regions and the apparent boundaries between them in glasses and each has a corresponding mirror constant A. The most common notation is to refer to the mirror—mist boundary as the inner mirror boundary and its mirror constant is designated A1. The mist—hackle boundary is referred to as the outer mirror and its mirror constant is designated A0. The mirror— mist boundary is usually not perceivable in polycrystalline ceramics and only the mirror~hackle boundary is measured. v This simple relationship has tremendous practical value. It is not necessary to have a—priori information about the how the part was loaded. The smaller the mirror, the larger is the stress at the origin site. A small mirror is proof that the part was strong and had a small strength—limiting flaw. Conversely, large mirrors mean the failure stress was lower and implies a large flaw. In some instances, a part may be so weak that the mirror size is larger than the part cross—section and hence the mirror markings are not visible. That, in and of itself, is valuable information. The existence of a mirror boundary implies that the part was stressed to a moderate or high level. Alternately, very strong parts (e. g., pristine optical fibers) may have such small mirrors that they are not measurable with optical microscopes. The mirror may not even be found due to excessive fragmentation. Errol Shand of the Corning Glass works was a leader in the early analysis work3'5 His 1959 paper presented an early argument for the 1/2 power in equations 1 and 2 based on stress concentrations at the tip of a sharp crack. This paper incorporated early elements of what would become known later as fracture mechanics. Kerper and Scuderi6’7’8 at National Bureau of Standards in Washington performed meticulous experiments on hundreds of glass laths and rods and showed conclusive evidence that equation 2 was applied over a broad range of specimen and mirror sizes as shown in Figure 3. Levengood2, Shands, and later Kirchner10 ‘redited Leighton Orr of the Pittsburg Plate Glass company for equation 2. Orr did not publish his findings until 1972 when he retired,9 but presented equation 2 in empirical form at a Glass Division meeting of the American Ceramic Society in 1955. H So although many associate equation 2 with Johnson and Holloway12 in 1966, the relationship was already in use for over 10 years. Their primary contribution was to use an energy analysis to give some theoretical underpinnings to equation 2. Henry and James Kirchner and James Conwaym’m later presented compelling evidence that a fracture mechanics criterion based on a critical stress intensity (Kl) gives the best fit to data and predicts the exact shape of mirrors in various stress fields. They argued that a more fundamental material parameter might be K18, the stress intensity factor at branching, since equation 2 does not take into account the free surface, geometry factors, and non—uniform stress gradients over the crack surface. Their work is considered again later in this paper. Equation 2 may be used in practice to estimate the stress at an origin. The mirror radius is measured from a fracture surface, the mirror constant found from a data table, and the origin stress calculated. A splendid example of this approach was shown by Morrell et al.15 for hip balls at the last fractography conference in 2000. The calculated stress is the net tensile stress acting on the flaw and the region around the flaw. It may include several stress sources including mechanical, thermal, and residual stresses. The author has compiled hundreds of fracture mirror constants for many materials in an American Society for Testing and Materials Standard16 and more recently in anew National Institute of Standards and Technology (NIST) Guide to Practice for Fractography.17 It became apparent that the reported values for identical materials (even for model materials such as fused silica or soda lime silica) varied by at least 20% (the range), and often much more. For some ceramics, the A values varied by a factor of two. This directly affects accuracy and precision of stress estimates using equation 2. Some of the scatter is due to metrology and judgment issues, but much of it is due to genuine material-to—material variability. Thus, one should not expect all aluminas to have the same mirror constant since there are major differences in the microstructures. The literature review also revealed that many authors were reluctant to show their mirrors with labeled photographs. In many instances authors did not document how they had measured their mirrors or critical details were missing. For example, many failed to report whether they corrected stresses for location or how they regressed the data. Confidence bounds on the A estimates were rarely reported. There is a strong subjective element to estimating the location of the mirror boundary even for glasses. Virtually everyone who has written about fracture mirrors has come to this conclusion. Johnson and Holloway12 wrote in 1966: “The position assigned to the boundary between mirror and mist zones depends upon the illumination and the magnification at which the fracture is examined, even within the range of the optical microscope. However, under given conditions a reproducible position for the boundary can be assigned.” Mecholsky and Freiman18 said in 1979: “While one might think initially that the measurements of a mirror boundary using a microscope is quite a qualitative operation and would vary from observer to observer; in fact, experiments performed over a number of years by a large number of investigators have shown that the values of mirror constants obtained in different laboratories are quite nearly tr e same.” They listed some values for a few glasses and ceramics that did in fact vary as much as 20 % to 30 % (range). For example, the soda—lime glass values varied by 23 %. Since many of the early mirror measurements were made while viewing through the optical microscope, it is safe to say that the first perception of a mirror boundary was where the surface roughness was a fraction of the wavelength of light (0.39 pm — 0.80 pm), Threshold levels of detectability have been estimated to be as small as a few tens of nanometers to as much as 0.25 pm. The judgment issue is exacerbated for ceramics, where intrinsic roughness due to the microstructure contributes to interpretation difficulties. Despite these problems, it cannot be denied that fracture mirror measurements are a powerful diagnostic tool for quantitative analysis. The accuracy and precision of the stress estimate is quite variable and depends on the material, the experience of the fractographer, the microscopy and illumination used, and component geometry and stress gradient effects. Stress estimates may be accurate to within 3 20 % with glasses if they form ideal fracture mirrors. The guidelines presented in this paper are intended to bring some long overdue consistency to fracture mirror analysis and improve the precision of this technique. The next two sections address two fundamental questions: 1. Is there really a boundary that can be measured? 2. Is there a theoretical basis for the fracture mirror constant, A? IS THERE A BOUNDARY? The word “boundary” must be used with some caution eVen with glasses. It is now clear that there probably is not a distinct transition point on the fracture surface corresponding to a mirror boundary. The higher the magnification the smaller the mirror seems to be, since fine detail that was washed out or not resolvable at lower power can be discerned at higher power. The mirror— mist boundary in glasses probably corresponds to surface roughness features that are of the order of0.l um to 0.2 pm, which is a fraction of the wavelength of light and at the threshold of observable features with an optical microscope. Mirror size estimates can vary depending upon the type of microscope used, the illumination, the objective power of the lens, and the judgment criteria of the fractographer. Careful electron microscopy and atomic force microscopy have shown that the formation of the mirror is a gradual progression of very—localized crack path deviations from the main plane. Superb transmission electron microscope images of various regions in a mirror have been shown by Beauchamp. ‘9’20 Poncelet21 showed comparable images in 1958, but Golz may have been the earliest with extraordinary electron microscope photos published in 1943.22 Starting well within the mirror, rounded ridges form that are elongated in the direction of crack propagation. These gradually coarsen in amplitude. At some point, they develop slight hackle steps where over running and under running fingerlike crack segments link. This point, where nano scale hackle lines form, could be an important transition point. Close examination of Beauchamp’s Figure 2 of ref. 19 shows they are not preSent inside the mirror, but they are just visible in his Figure 3 near the mirror—mist boundary The explanation below closely follows Fre’chette’s23 general discussion as well as Beauchamp’s19 analysis As the crack accelerates away from the origin, micro portions of the crack front begin to twist slightly or tilt up and down out of the main fracture plane. These local deviations occur as consequence of the stress field in front of a fast crack having maxima that re out ofplane, unlike the case for a static or slowly moving crack.“ The momentary tilting or twisting does not persist for very long since crack plane deviations are restricted by the energetic cost of creating additional crack surface. The slight tilt or twist variations in crack plane quickly rejoin the main propagating crack plane. These tiny local crack perturbations exist well within the mirror region, but are too small to be optically discernable. As the crack advances, they eventually become large enough to be discernable with the optical microscope as the “mist” zone surrounding the origin. The mist has a slight frosty appearance such as when water condenses on a reflecting mirror. As the crack continues to advance, the local perturbations increase and begin to oscillate and form larger tongue-like segments that may deviate from the average fracture plane to the degree that micro steps are generated running parallel to the direction of crack propagation. Some have described the out-of-plane perturbations as “fingers.” The perturbations gradually coarsen such that the tongue—like elements can over cut other portions of the crack front thereby generating large “velocity hackle” lines that run parallel to the direction of crack propagation. By this time the crack is running at a velocity that is a high fraction of the terminal velocity. Beauchamplg’19 pointed out that many of these features are similar in character from within the mirror out to the hackle zone. They differ only in scale. The transitions between the regions are gradual and are usually described as not abrupt. One intriguing observation by Beauchamp19 was that tilted or twisted hackle segments that relink with the main crack plane may generate elastic pulses and Wallner lines that could trigger additional hackle along the crack front. This could set off a cascade of hackle that forms a mist— hackle boundary. Attempts to make objective determinations of the mirror boundary by quantitative surface roughness characterization have been unsuccessful, since there are different scales of roughness for the various features that comprise the mirror and its apparent boundaries. A single threshold roughness value corresponding to the boundaries cannot be specified although many have tried. Duckworth et al.25 carefully studied mirror sizes in float glass using optical photographs and a conventional surface profilometer. They obtained a good correlation with optical boundary estimates when the surface roughness reached a level of 0.25 pm for the mirror- mist A; boundary, and 5 for the mist~hackle A0 boundary. Hull,26’27 WUnsche et al.,28 and Kuluwansa et al. ) used atomic force microscopy to show that the mist region in glass or brittle epoxy has a roughness of as small as a few tens of nanometers, which is much less than the wavelength of visible light. The scanned regions were quite small, however, and if the AF M scanned a small region between hackle and river line steps, the measured roughness was much less than if the latter were included. Hull pointed out that the large undulations from Wallner lines needed to be factored out when evaluating the intrinsic mist roughness. His study showed that roughness increased continuously and there were no dramatic jumps in roughness at the boundaries, but the rate of change of roughness did increase significantly at the mirror~mist boundar . Hull 6 considered the matter in some detail and pointed out that different surface roughness characterization devices such as atomic force microscopes (AFMS), mechanical profilometers, and laser optical profilometers all have different advantages, disadvantages, sensitivities and scanning zone sizes. AFMs can measure tiny regions with very high sensitivities, but may miss large hackle steps in a mist or hackle zone. These can dramatically alter the average or root mean square roughness. A mechanical stylus profilometer or laser profilometer with a l um spot size may miss the small undulations and be more sensitive to larger hackle steps on the fracture surface. Mist and hackle regions have different roughness at different scales. In summary, there are two potential transition points. The mirror~mist boundary in glass may be a transition Where nanonmicro steps form between ridges that are tens of nanometers tall. The mist~hackle transition boundary may be where a band of microhackle forms that is triggered by self—generated or external elastic pulses and Wallner lines. It is not known whether these possible transition points can be detected or measured accurately and precisely using ordinary microscopy. IS THERE A THEORETICAL BASIS FOR THE F RACTURE MIRROR CONSTANTS? The underlying principal that accounts for the micro and macro branching has been attributed to the crack reaching a critical velocity,24 a critical energy level,12 a critical stress intensity,13’l4’ 30’3 I or a critical strain intensity.32 A velocity criterion for crack branching was discounted by data shown by Congleton and Petch.31 Richter and Kerkhof, 33 Field,34 and Doll35 used ultrasonic fractography to show that cracks approached terminal velocity before the formation of the mist boundary and there w...
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