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Fatigue striation spacing analysis
Fatigue Striation Spacing Analysis William C. Connors Sundstrand Aerospace,Rockford, IL 61125 Fatigue crack growth in ductile materials produces features, called striations, on a fracture surface, which can aid greatly in understanding conditions associated with the fracture, including the number of stress variations that produced the fracture. In addition, striations can help to determine the directionality of fracture propagation as well as the location of the origin. Striations can be observed and counted using images from the scanning electron microscope or the transmission electron microscope. Many authors have demonstrated a 1:l correlation between striations and stress cycles. Fracture surfaces typically contain thousands of striations, so that the counting of individual striations tends to be unnecessarily time-consuming. Even if time permitted such individual striation counting, some striations become obscured by rubbing of the fracture surfaces or are so finely spaced as to be very difficult to resolve. Therefore, normal practice consists of measuring striation spacings at a few locations and using statistical methods to estimate the total number of striations. Procedures used for estimating the total number of cycles can be as simple as dividing the crack interval distance of concern by the measured (or average) striation spacing. For a variety of reasons, this approach is not always satisfactory. There are other simple techniques that can be applied, without resorting to fracture mechanics, which enhance both the accuracy of the measurements and aid in understanding the results.
My early experiences with the TEM have been largely supplanted by SEM experience, and therefore, the majority of this presentation is SEM-oriented. Although this is a common fact in many current laboratories performing failure analysis, it is regrettable from the standpoint that resolving fine fatigue striations is an area where the TEM is a clear winner. The current dominance of the SEM in the field of fractography is, however, illustrated by the fact that the latest ASM Fractography Handbook [l] provides over 1300 fractographs in the atlas region with the statistics found in Table 1. Many years after my Sacramento experiences, while attending the 1989International Symposium for Testing and Failure Analysis, a fellow participant told me how she normally determined the number of cycles to failure for a part that has failed in fatigue.
BACKGROUND My encounters with striations began about 28 years ago in the Materials Laboratory at McClellan Air Force Base in Sacramento, California. At that time, we were using a relatively old transmission electron microscope (TEM). Although the TEM has some distinct advantages over the scanning electron microscope (SEM) in resolving high-cycle fatigue (HCF) striations, speed and user friendliness were not among its virtues. At that time, partially due to a lack of knowledge and partially due to conservatism, TE photomicrographs of fatigue striations were used by our laboratory primarily to determine crack direction and to make a judgment call regarding whether HCF or low-cycle fatigue (LCF) was involved in the failure being investigated. 245 0 Elsevier Science Inc., 1994 655 Avenue of the Americas, New York, NY 10010
MATERIALS CHARACTERIZATION
33:245-253 (1994) 1044-5803/94/$7.00
X C.3Connors
246 Table 1
where: Percentage (approx.)
SEM fractographs Light fractographs MacrographslMicrographs TEM fractographs Other
50 23 12 8 7
da = fatigue crack growth rate dN AK = stress intensity factor range E = elastic tensile modulus
The method she used was to simply divide the total crack length by the average striation spacing. While I agreed that this might give a reasonable approximation, I suggested that there might be more accurate methods available. I sympathize with difficulties at finding striations on fracture surfaces. In some materials and under some load spectrum conditions, striations are almost impossible (at least with a SEM) to find much less measure. This is especially true for very high-strength steels such as 52100 or M50, the case region of case-hardened steels, and many cast materials and cemented carbides. Also, under moderately high-cycle loading conditions, small-striation amplitudes and close spacing can present major challenge. However, there are enough higher-ductility materials (e.g., precipitation hardenable wrought-aluminum alloys, medium-strength steels, and some heat and corrosion resistant alloys) that do exhibit well-defined striation patterns that make striation spacing analysis worthwhile.
striation spacing data can be converted to stress intensity information that can be crucial to an understanding of a failure [2]. Many authors have demonstrated a 1: 1 correlation between striations and stress cycles [3, 41. Analysis of striation spacing data, although relatively simple, merits some detailed consideration such as that presented here. The resulting information can be crucial in postfailure stress analysis and the redesign of components and systems to avoid future problems. Fracture mechanics can be used to determine the number of cycles to failure of a fatigue crack. However, the computed cyclic life is strongly dependent on the starting crack size. The calculation also involves an integration that cannot be performed directly but must be done numerically [5]. Becauseof these and other difficulties, the use of direct striation spacing measurements is usually much easier and probably more accurate. Fatigue crack growth occurs in two stages [6], which usually obey the Paris law: da = CAK” dN where: da -= dN
INTRODUCTION
fatigue crack growth rate
AK = stress intensity factor range
Striations produced by fatigue crack growth can be useful in providing a considerable amount of valuable data to the failure analyst. They can be used to determine the directionality of fracture propagation as well as the location of the origin. These striations can be especially useful when counted while one is using the SEM or the TEM. If one uses empirical relationships such as the BatesClark equation:
(1)
C,n = material constants This law can be very useful because it directly relates the fatigue crack growth rate to the stress intensity factor range through two constants (C,n), which themselves are complex results of material variables, the environment, the cyclic frequency, temperature, and the stress ratio [5]. The first stage of fatigue crack growth is characterized by the initiation of cracks with only coincidental (if any) striations. This stage usually originates at the surface and
Striation Spacing
continues for only a very short distance into the material. The second stage is characterized by striations that normally continue until final fracture or the cessation of cyclic loading. It is the second stage with which we are primarily concerned in this article. Fatigue crack extension begins at a stress concentration that can be considered to be a sharp crack. If one assumes a tensioncompression loading case, during the tension portion of each cycle, the sides of the crack move apart, and the crack lengthens from the sharp crack tip. At this point, plastic strain hardening and plastic flow at the tip produce stress intensity conditions that no longer support crack extension. The crack tip is not sharp but rather rounded and not conducive to further crack growth. However, when the cycle returns to compressive loading, the sides of the crack move back together, and the crack tip radius becomes reduced or sharpened, thereby preparing the crack for another tensile stress portion of the cycle with its attendant crack extension and crack tip blunting. This process (referred to as subcritical crack growth) continues until the crack length reaches the point where the stress intensity at the crack tip exceeds the fracture toughness of the material. At this point, the crack grows catastrophically (critical crack growth) to complete separation of the fracture surfaces. It is the microscopic process of subcritical crack growth that produces the features described as striations.
247
tigue striations from other fractographic features (not always easy) and locate the probable origin(s). There are a number of good references, such as the Air Force Materials Laboratory’s Failure Annlysis Handbook [6], as well as other handbooks of fractography and fractographic atlases published by ASM International [l, 71, ASTM, and others.
MAGNIFICATION SE photomicrographs taken for analysis of fatigue striations typically involve magnifications that range from 1000to x 5000 [6]. TEM magnifications may range up to x 50,000[8]. This suggests that TEM images are better, at least from a practical standpoint. Because measurement of striations on a photomicrograph with a spacing closer than about lmm would be difficult, the closest striations measured on a typical SE photomicrograph would be about 0.2um apart. If this were the average for a fracture with a total length of lcm, the total number of striations for the fracture would correspond to about 50,000 cycles. Although this is well within what is normally considered high-cycle fatigue, it is also very common to have high-cycle fatigue that requires hundreds of thousands of cycles to grow to final fracture. Clearly, a TEM would be the instrument of choice for very high-cycle fatigue and in crack regions very close to the origin,
MEASUREMENTACCURACY MEASUREMENTAND ANALYSIS GETTING STARTED Many people are familiar enough with linear elastic fracture mechanics (LEFM) to understand how stresses and materials properties interact, but they are not sufficiently comfortable with finite element analysis (FEA) to use LEFM confidently. The methods in this article do not require significant LEFM or FEA knowledge but do assume that the reader is already familiar with fatigue as a failure mechanism and can distinguish fa-
Madeyski and Albertin [2] state that fatigue striation spacings may vary widely from point to point even within a small area of the fracture. The local values of striation spacing are governed by the local properties of the material and by the microstress intensities at each specific spot rather than by the calculated macrostress within that region. In view of these and other variations, a 10% accuracy would be excellent. Other references, such as the Air Force Materials Laboratory’s Failure Analysis Handbook[6], suggest an accuracy of between 10% and 50%.
W. C. Connors
248 PRECAUTIONS
As in the case of any type of important and serious kind of analysis, it is imperative that the analyst perform frequent “sanity” checks of the results. There are a number of methods of doing this. One of the most important ways is consulting with the customer or other engineering organizations within the company to gather their understanding of the problem. There are frequently others who have a great deal of knowledge regarding a problem. These people (stress analysts, designers, assemblers, program engineers, and many others) should be consulted regularly. On the other hand, there are frequently serious constraints on the failure analyst’s time that seem to work against being as thorough as possible. As with any engineering or scientific endeavor, creativity is helpful in all investigative stages,but common sense should reign supreme when preparing final conclusions. METHODOLOGY
The following methodology is recommended for measuring and analyzing striations: 1. Using a visual/low power binocular mi-
croscope or x 10 loupe, identify the most probable location of the fracture origin(s), intermediate fracture regions, and location of any transition to overload. Carefully clean the fracture surface preparatory to placement in the SEM chamber. 2. Place the fracture in the SEM with the plane of the fracture oriented perpendicular to the electron beam axis. This perpendicular orientation is important because angular orientations can be a source of significant error. This subject has been reviewed thoroughly in the Metals Hundbook on Frucfogruphy [l]. 3. Beginning at the probable fracture origin, examine the fracture surface using the SEM for evidence of fatigue striations. Usually striations in this region will be difficult to detect due to very fine spacing and possible rubbing during latter stages of cracking. 4. Moving away from the origin (with the
SEM), find the location where striations are first observed and take a photomicrograph of the striations at a magnification that will later permit measurement of the spacing between adjacent striations. An ideal magnification will be one that exhibits a number of successive striations that have peak-to-peak spacings of between about 1 and 5mm on the photomicrographs. Repeat this procedure at increasing distances from the origin until the final fracture region (usually overload) is reached. 5. Measure the striation spacing on each photomicrograph and determine the actual spacing on the fracture surface by one of the following three example methods: a. Divide the striation spacing on the photomicrograph by the photographic magnification to obtain the spacing on the fracture surface itself. b. If the SE or TE photomicrographs being used include a magnification scale, this can be used to measure directly the striation spacing. To use this approach, measure the distance between striations on the photomicrograph in whatever units are convenient to use, then multiply this by the ratio of the number of indicated scale bar micrometers and the measured length (in the same units as previously used) of the included micrometer scale. For example, if the photographic striation spacing is lmm, the number inside the micrometer scale indicates lOurn, and the measured length of the micrometer scale is 13mm; the striation spacing on the specimen would be 0.77pm. C. If the analyst is fortunate enough to have accessto an instrument (SEM or TEM) that can directly annotate distances on the photomicrograph, several potential sources of error are completely avoided. 6. Measure the nominal distance from the origin (e.g., use a low-magnification photomicrograph for this) of the previously measured striations (aZzuuys use identical
Striation Spacing
249
units, e.g., inches or micrometers). Tabulate all paired measurements of distance from the origin and striation spacing. The number of measurement pairs should be at least five. If possible, a relatively even spacing of measurement pairs between the origin and final fracture is desirable. The total crack length divided by the average of (evenly spaced) striation spacing measurements can be a convenient "sanity" check of more precise analytical techniques, such as discussed in the next step. 7. Analyze the tabulated measurement pairs using a convenient technique such as the graphical or computer analytical technique elucidated by Tipton and the author [9]. An example of the use of this technique follows:
the base of internal threads (stress concentration). SE photomicrographs and distance/ spacing measurement pairs were made as shown in Figs. I through 5. These were then plotted for further analysis as shown in Fig. 6. The lines shown in Fig. 6 were based on a linear regression best fit of the data, but a visual fit could have been used just as easily. Figure 6 shows both the plotted data points representing the data and two lines drawn to estimate the characteristics of the data. The line segments of interest for analysis are designated as A-B and B-C. Using the following equation for each line segment gives the result shown in Table 2: _ Flny2 | ~ l n yll| Xxl-x2 [ (y2 - yl / [ (3) L \ x 2 - xl! J
EXAMPLE This example is a 7075-T73 aluminum alloy strut that developed fatigue cracks during testing. Macroscopic examination of the fracture indicated that the fracture origin was at
Although it is possible to extrapolate line A-B to the point of the origin and/or line B-C to the point of final fracture, this is not recommended unless further SEM exam|nation and analysis conhrms striations in these regions of the fracture.
Fx~. 1. Distance from origin = 0.71turn; striation spacing = 0.00056ram.
250
W. C. Connors
FIG. 2. Left: distance from origin = 0.91mm; striation spacing = 0.00084mm; Right: distance from origin = 1.30mm; striation spacing = 0.00076ram.
FIG. 3. Left: distance from origin ~ 1.47mm; striation spacing = 0.00081mm; Right: distance from origin = 2.21mm; striation spacing = 0.0011ram.
Striation Spaciny,
251
FIG. 4. Left: Distance from origin = 4.32turn; striation spacing = 0.0011mm; Right: distance from origin = 5.08mm; striation spacing = 0.0015ram.
FIG. 5. Distance from origin = 5.33mm; striation spacing = 0.0033ram.
252
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is important that the report convey all relevant findings, be illustrated with properly annotated photomicrographs, and contain a brief discussion of each step of the analysis. In presenting information derived from striation spacing measurements, it is normally not necessary to provide every detail of the method used.
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INTERNAL
FAILURE ANALYSIS
DATABASES
DISTANCE F R O M O R I G I N ( M I L L I M E T E R S )
Fic. 6. Plotof striationspacing(da/dN)versusdistance from origin (a).
It should be noted that in the example presented here, the use of two other methods produces similar results, as shown in Table 3. The reason for this correlation is that the striation counts involved were made at relatively uniform spacing across the fracture surface. If, however, the striation measurements had been weighted more toward the final fracture region, analysis based upon an average striation spacing value would not give results that were as accurate as the method used in Table 2 or the STRICOUNT computer program [9]. CONCLUSIONS THE FINAL REPORT Failure analyses are usually performed at the request of some person or organization outside the materials laboratory organization. The requesting organization typically expects a detailed report of the failure analysis. It
It is generally useful for laboratories of any reasonable size to develop a readily retrievable internal data base of photomicrographs and failure analysis reports that can be accessed by engineers performing failure analyses involving fatigue and striation measurements. This is accomplished at Sundstrand through the use of a failure analysis report/ photomicrograph archival system based upon a DEC VAX-based word processor and an index-driven, full-text search program called ForWords. This has been shown to be extremely helpful in analyzing fatigue and other failures and in learning valuable lessons from the past.
USE OF COMPUTERS As in so many areas of metallurgy and other sciences, the availability of computers within the laboratory and at engineers' desks will produce a profound change in how things are done. The analysis of fatigue striations is certainly no exception. An article published by the author and A. Tipton in 1988 [9] presented a simple computer program in BASIC to aid in the analysis of striation spacings. A recent paper by Komai et al. [10] dis-
Table 2 Calculation of the Number of Striations Present in Each Line Segment In Ye lny2 Segment
A-B B-C
Y2
Y7
Y2 -
Yl
x2 -
xl
In Y2
0.0013 0.00071 0.00059 3 . 8 1 -6.65 0.0027 0.0013 0.0014 0 . 8 1 3 -5.91
In Yl
-7.25 -6.65
In Yl
-
In yl
Ye -
Yl
Y2 -
yl
x2 -
xl
x2 -
xl
-
0 . 6 0 0.000155 3871 0 . 7 4 0.00172 430 4301 Total
N
Striation Spacing
253
Table 3 Three Methods Used To Estimate the Number of Cycles
Method
Propagation cycle (N)
Table 2 Striation Average STRICOUNT
4301 3714 4796
c u s s e s the u s e of i m a g e analysis t e c h n i q u e s to identify six different fracture surface m o r p h o l o g i e s i n c l u d i n g fatigue. It is likely that, w i t h i n a v e r y few years, r o u t i n e analysis of fracture surfaces a n d m i c r o s t r u c t u r e s will be a c c o m p l i s h e d o n a h i g h l y a u t o m a t e d basis. W h e n this h a p p e n s , t h e task of the materials e n g i n e e r m a y b e c o m e m o r e like that of t h e analytical c h e m i s t w h o relies h e a v i l y o n a u t o m a t e d i n s t r u m e n t s to d o accurate a n d r a p i d d e t e r m i n a t i o n s of physical s y s t e m characteristics.
The information in this article, although compiled by the author, includes work and ideas from SO many other people that it would be impossible to acknowledge them all. However, I would like to thank several people within my company for their input, including R. Diesner, W. Humy, L. MacDougall, J. Au, and D. Augustine. I would like to dedicate this article to the memory of the late Wilson Leeming, who contributed so much metallurgical understanding to our company and to a number of A M S committees, ForWords is a registered trademark of Computer Associates International Inc. DEC and VAX
are registered trademarks of the Digital Equipment Corp.
References 1. MetalsHandbook,vol. 12, 9th ed., Fractography,ASM International, Metals Park, OH (1987). 2. A. Madeyski and L. Albertin, Fractographic method of evaluation of the cyclic stress amplitude in fatigue failure analysis, in Fractographyin FailureAnalysis, ASTM STP 645, B. M. Strauss and W. H. Cullen, Jr., eds, American Society for Testing and Materials, pp. 73-83 (1978). 3. P. J. E. Forsyth and D. A. Ryder, ACTA Metallurgica 63:117 (1961). 4. J. J. Au and J. S. Ke, Correlation between fatigue crack growth rate and fatigue striation spacing in AISI 9310 (AMS6265) steel, in ASTM STP733, p. 202 (1980). 5. R. W. Hertzberg, Deformationand FractureMechanicsofEngineeringMaterials,John Wiley & Sons, New York (1976). 6. FailureAnalysisHandbook,WRDC-TR-89-4060(1989). 7. MetalsHandbook, vol. 9, 8th ed., Fractographyand Atlas of Fractographs, ASM International, Metals Park, OH (1974).
8. MicroscopicFractureProcesses,Fracture,vol. 1, Aca-
demic Press Inc., New York (1969). 9. A. A. Tipton and W. C. Connors, ComputerAnalysis of SEM Striation Spacing Data, Proceedings of the 1988 International Symposium on Testing and Failure Analysis, ASM International, Metals Park, OH, pp. 439-446 (1987). 10. K. Komai, K. Minoshima, and S. Ishii. Recognition of different fracture surface morphologies using computer image processing technique, ]SMEInternational Journal, Series A, 36:220-227.
ReceivedJune 1993; acceptedAugust 1993.
My early experiences with the TEM have been largely supplanted by SEM experience, and therefore, the majority of this presentation is SEM-oriented. Although this is a common fact in many current laboratories performing failure analysis, it is regrettable from the standpoint that resolving fine fatigue striations is an area where the TEM is a clear winner. The current dominance of the SEM in the field of fractography is, however, illustrated by the fact that the latest ASM Fractography Handbook [l] provides over 1300 fractographs in the atlas region with the statistics found in Table 1. Many years after my Sacramento experiences, while attending the 1989International Symposium for Testing and Failure Analysis, a fellow participant told me how she normally determined the number of cycles to failure for a part that has failed in fatigue.
BACKGROUND My encounters with striations began about 28 years ago in the Materials Laboratory at McClellan Air Force Base in Sacramento, California. At that time, we were using a relatively old transmission electron microscope (TEM). Although the TEM has some distinct advantages over the scanning electron microscope (SEM) in resolving high-cycle fatigue (HCF) striations, speed and user friendliness were not among its virtues. At that time, partially due to a lack of knowledge and partially due to conservatism, TE photomicrographs of fatigue striations were used by our laboratory primarily to determine crack direction and to make a judgment call regarding whether HCF or low-cycle fatigue (LCF) was involved in the failure being investigated. 245 0 Elsevier Science Inc., 1994 655 Avenue of the Americas, New York, NY 10010
MATERIALS CHARACTERIZATION
33:245-253 (1994) 1044-5803/94/$7.00
X C.3Connors
246 Table 1
where: Percentage (approx.)
SEM fractographs Light fractographs MacrographslMicrographs TEM fractographs Other
50 23 12 8 7
da = fatigue crack growth rate dN AK = stress intensity factor range E = elastic tensile modulus
The method she used was to simply divide the total crack length by the average striation spacing. While I agreed that this might give a reasonable approximation, I suggested that there might be more accurate methods available. I sympathize with difficulties at finding striations on fracture surfaces. In some materials and under some load spectrum conditions, striations are almost impossible (at least with a SEM) to find much less measure. This is especially true for very high-strength steels such as 52100 or M50, the case region of case-hardened steels, and many cast materials and cemented carbides. Also, under moderately high-cycle loading conditions, small-striation amplitudes and close spacing can present major challenge. However, there are enough higher-ductility materials (e.g., precipitation hardenable wrought-aluminum alloys, medium-strength steels, and some heat and corrosion resistant alloys) that do exhibit well-defined striation patterns that make striation spacing analysis worthwhile.
striation spacing data can be converted to stress intensity information that can be crucial to an understanding of a failure [2]. Many authors have demonstrated a 1: 1 correlation between striations and stress cycles [3, 41. Analysis of striation spacing data, although relatively simple, merits some detailed consideration such as that presented here. The resulting information can be crucial in postfailure stress analysis and the redesign of components and systems to avoid future problems. Fracture mechanics can be used to determine the number of cycles to failure of a fatigue crack. However, the computed cyclic life is strongly dependent on the starting crack size. The calculation also involves an integration that cannot be performed directly but must be done numerically [5]. Becauseof these and other difficulties, the use of direct striation spacing measurements is usually much easier and probably more accurate. Fatigue crack growth occurs in two stages [6], which usually obey the Paris law: da = CAK” dN where: da -= dN
INTRODUCTION
fatigue crack growth rate
AK = stress intensity factor range
Striations produced by fatigue crack growth can be useful in providing a considerable amount of valuable data to the failure analyst. They can be used to determine the directionality of fracture propagation as well as the location of the origin. These striations can be especially useful when counted while one is using the SEM or the TEM. If one uses empirical relationships such as the BatesClark equation:
(1)
C,n = material constants This law can be very useful because it directly relates the fatigue crack growth rate to the stress intensity factor range through two constants (C,n), which themselves are complex results of material variables, the environment, the cyclic frequency, temperature, and the stress ratio [5]. The first stage of fatigue crack growth is characterized by the initiation of cracks with only coincidental (if any) striations. This stage usually originates at the surface and
Striation Spacing
continues for only a very short distance into the material. The second stage is characterized by striations that normally continue until final fracture or the cessation of cyclic loading. It is the second stage with which we are primarily concerned in this article. Fatigue crack extension begins at a stress concentration that can be considered to be a sharp crack. If one assumes a tensioncompression loading case, during the tension portion of each cycle, the sides of the crack move apart, and the crack lengthens from the sharp crack tip. At this point, plastic strain hardening and plastic flow at the tip produce stress intensity conditions that no longer support crack extension. The crack tip is not sharp but rather rounded and not conducive to further crack growth. However, when the cycle returns to compressive loading, the sides of the crack move back together, and the crack tip radius becomes reduced or sharpened, thereby preparing the crack for another tensile stress portion of the cycle with its attendant crack extension and crack tip blunting. This process (referred to as subcritical crack growth) continues until the crack length reaches the point where the stress intensity at the crack tip exceeds the fracture toughness of the material. At this point, the crack grows catastrophically (critical crack growth) to complete separation of the fracture surfaces. It is the microscopic process of subcritical crack growth that produces the features described as striations.
247
tigue striations from other fractographic features (not always easy) and locate the probable origin(s). There are a number of good references, such as the Air Force Materials Laboratory’s Failure Annlysis Handbook [6], as well as other handbooks of fractography and fractographic atlases published by ASM International [l, 71, ASTM, and others.
MAGNIFICATION SE photomicrographs taken for analysis of fatigue striations typically involve magnifications that range from 1000to x 5000 [6]. TEM magnifications may range up to x 50,000[8]. This suggests that TEM images are better, at least from a practical standpoint. Because measurement of striations on a photomicrograph with a spacing closer than about lmm would be difficult, the closest striations measured on a typical SE photomicrograph would be about 0.2um apart. If this were the average for a fracture with a total length of lcm, the total number of striations for the fracture would correspond to about 50,000 cycles. Although this is well within what is normally considered high-cycle fatigue, it is also very common to have high-cycle fatigue that requires hundreds of thousands of cycles to grow to final fracture. Clearly, a TEM would be the instrument of choice for very high-cycle fatigue and in crack regions very close to the origin,
MEASUREMENTACCURACY MEASUREMENTAND ANALYSIS GETTING STARTED Many people are familiar enough with linear elastic fracture mechanics (LEFM) to understand how stresses and materials properties interact, but they are not sufficiently comfortable with finite element analysis (FEA) to use LEFM confidently. The methods in this article do not require significant LEFM or FEA knowledge but do assume that the reader is already familiar with fatigue as a failure mechanism and can distinguish fa-
Madeyski and Albertin [2] state that fatigue striation spacings may vary widely from point to point even within a small area of the fracture. The local values of striation spacing are governed by the local properties of the material and by the microstress intensities at each specific spot rather than by the calculated macrostress within that region. In view of these and other variations, a 10% accuracy would be excellent. Other references, such as the Air Force Materials Laboratory’s Failure Analysis Handbook[6], suggest an accuracy of between 10% and 50%.
W. C. Connors
248 PRECAUTIONS
As in the case of any type of important and serious kind of analysis, it is imperative that the analyst perform frequent “sanity” checks of the results. There are a number of methods of doing this. One of the most important ways is consulting with the customer or other engineering organizations within the company to gather their understanding of the problem. There are frequently others who have a great deal of knowledge regarding a problem. These people (stress analysts, designers, assemblers, program engineers, and many others) should be consulted regularly. On the other hand, there are frequently serious constraints on the failure analyst’s time that seem to work against being as thorough as possible. As with any engineering or scientific endeavor, creativity is helpful in all investigative stages,but common sense should reign supreme when preparing final conclusions. METHODOLOGY
The following methodology is recommended for measuring and analyzing striations: 1. Using a visual/low power binocular mi-
croscope or x 10 loupe, identify the most probable location of the fracture origin(s), intermediate fracture regions, and location of any transition to overload. Carefully clean the fracture surface preparatory to placement in the SEM chamber. 2. Place the fracture in the SEM with the plane of the fracture oriented perpendicular to the electron beam axis. This perpendicular orientation is important because angular orientations can be a source of significant error. This subject has been reviewed thoroughly in the Metals Hundbook on Frucfogruphy [l]. 3. Beginning at the probable fracture origin, examine the fracture surface using the SEM for evidence of fatigue striations. Usually striations in this region will be difficult to detect due to very fine spacing and possible rubbing during latter stages of cracking. 4. Moving away from the origin (with the
SEM), find the location where striations are first observed and take a photomicrograph of the striations at a magnification that will later permit measurement of the spacing between adjacent striations. An ideal magnification will be one that exhibits a number of successive striations that have peak-to-peak spacings of between about 1 and 5mm on the photomicrographs. Repeat this procedure at increasing distances from the origin until the final fracture region (usually overload) is reached. 5. Measure the striation spacing on each photomicrograph and determine the actual spacing on the fracture surface by one of the following three example methods: a. Divide the striation spacing on the photomicrograph by the photographic magnification to obtain the spacing on the fracture surface itself. b. If the SE or TE photomicrographs being used include a magnification scale, this can be used to measure directly the striation spacing. To use this approach, measure the distance between striations on the photomicrograph in whatever units are convenient to use, then multiply this by the ratio of the number of indicated scale bar micrometers and the measured length (in the same units as previously used) of the included micrometer scale. For example, if the photographic striation spacing is lmm, the number inside the micrometer scale indicates lOurn, and the measured length of the micrometer scale is 13mm; the striation spacing on the specimen would be 0.77pm. C. If the analyst is fortunate enough to have accessto an instrument (SEM or TEM) that can directly annotate distances on the photomicrograph, several potential sources of error are completely avoided. 6. Measure the nominal distance from the origin (e.g., use a low-magnification photomicrograph for this) of the previously measured striations (aZzuuys use identical
Striation Spacing
249
units, e.g., inches or micrometers). Tabulate all paired measurements of distance from the origin and striation spacing. The number of measurement pairs should be at least five. If possible, a relatively even spacing of measurement pairs between the origin and final fracture is desirable. The total crack length divided by the average of (evenly spaced) striation spacing measurements can be a convenient "sanity" check of more precise analytical techniques, such as discussed in the next step. 7. Analyze the tabulated measurement pairs using a convenient technique such as the graphical or computer analytical technique elucidated by Tipton and the author [9]. An example of the use of this technique follows:
the base of internal threads (stress concentration). SE photomicrographs and distance/ spacing measurement pairs were made as shown in Figs. I through 5. These were then plotted for further analysis as shown in Fig. 6. The lines shown in Fig. 6 were based on a linear regression best fit of the data, but a visual fit could have been used just as easily. Figure 6 shows both the plotted data points representing the data and two lines drawn to estimate the characteristics of the data. The line segments of interest for analysis are designated as A-B and B-C. Using the following equation for each line segment gives the result shown in Table 2: _ Flny2 | ~ l n yll| Xxl-x2 [ (y2 - yl / [ (3) L \ x 2 - xl! J
EXAMPLE This example is a 7075-T73 aluminum alloy strut that developed fatigue cracks during testing. Macroscopic examination of the fracture indicated that the fracture origin was at
Although it is possible to extrapolate line A-B to the point of the origin and/or line B-C to the point of final fracture, this is not recommended unless further SEM exam|nation and analysis conhrms striations in these regions of the fracture.
Fx~. 1. Distance from origin = 0.71turn; striation spacing = 0.00056ram.
250
W. C. Connors
FIG. 2. Left: distance from origin = 0.91mm; striation spacing = 0.00084mm; Right: distance from origin = 1.30mm; striation spacing = 0.00076ram.
FIG. 3. Left: distance from origin ~ 1.47mm; striation spacing = 0.00081mm; Right: distance from origin = 2.21mm; striation spacing = 0.0011ram.
Striation Spaciny,
251
FIG. 4. Left: Distance from origin = 4.32turn; striation spacing = 0.0011mm; Right: distance from origin = 5.08mm; striation spacing = 0.0015ram.
FIG. 5. Distance from origin = 5.33mm; striation spacing = 0.0033ram.
252
W. C . C o n n o r s
3.s T a~ ~"
-/c
is important that the report convey all relevant findings, be illustrated with properly annotated photomicrographs, and contain a brief discussion of each step of the analysis. In presenting information derived from striation spacing measurements, it is normally not necessary to provide every detail of the method used.
~ ~
2s ~ 2
°t
01.5
I
•
i 1T A
0.5 0
~
•
•
I
0
~
1
2
~
I
I
3
4
5
6
INTERNAL
FAILURE ANALYSIS
DATABASES
DISTANCE F R O M O R I G I N ( M I L L I M E T E R S )
Fic. 6. Plotof striationspacing(da/dN)versusdistance from origin (a).
It should be noted that in the example presented here, the use of two other methods produces similar results, as shown in Table 3. The reason for this correlation is that the striation counts involved were made at relatively uniform spacing across the fracture surface. If, however, the striation measurements had been weighted more toward the final fracture region, analysis based upon an average striation spacing value would not give results that were as accurate as the method used in Table 2 or the STRICOUNT computer program [9]. CONCLUSIONS THE FINAL REPORT Failure analyses are usually performed at the request of some person or organization outside the materials laboratory organization. The requesting organization typically expects a detailed report of the failure analysis. It
It is generally useful for laboratories of any reasonable size to develop a readily retrievable internal data base of photomicrographs and failure analysis reports that can be accessed by engineers performing failure analyses involving fatigue and striation measurements. This is accomplished at Sundstrand through the use of a failure analysis report/ photomicrograph archival system based upon a DEC VAX-based word processor and an index-driven, full-text search program called ForWords. This has been shown to be extremely helpful in analyzing fatigue and other failures and in learning valuable lessons from the past.
USE OF COMPUTERS As in so many areas of metallurgy and other sciences, the availability of computers within the laboratory and at engineers' desks will produce a profound change in how things are done. The analysis of fatigue striations is certainly no exception. An article published by the author and A. Tipton in 1988 [9] presented a simple computer program in BASIC to aid in the analysis of striation spacings. A recent paper by Komai et al. [10] dis-
Table 2 Calculation of the Number of Striations Present in Each Line Segment In Ye lny2 Segment
A-B B-C
Y2
Y7
Y2 -
Yl
x2 -
xl
In Y2
0.0013 0.00071 0.00059 3 . 8 1 -6.65 0.0027 0.0013 0.0014 0 . 8 1 3 -5.91
In Yl
-7.25 -6.65
In Yl
-
In yl
Ye -
Yl
Y2 -
yl
x2 -
xl
x2 -
xl
-
0 . 6 0 0.000155 3871 0 . 7 4 0.00172 430 4301 Total
N
Striation Spacing
253
Table 3 Three Methods Used To Estimate the Number of Cycles
Method
Propagation cycle (N)
Table 2 Striation Average STRICOUNT
4301 3714 4796
c u s s e s the u s e of i m a g e analysis t e c h n i q u e s to identify six different fracture surface m o r p h o l o g i e s i n c l u d i n g fatigue. It is likely that, w i t h i n a v e r y few years, r o u t i n e analysis of fracture surfaces a n d m i c r o s t r u c t u r e s will be a c c o m p l i s h e d o n a h i g h l y a u t o m a t e d basis. W h e n this h a p p e n s , t h e task of the materials e n g i n e e r m a y b e c o m e m o r e like that of t h e analytical c h e m i s t w h o relies h e a v i l y o n a u t o m a t e d i n s t r u m e n t s to d o accurate a n d r a p i d d e t e r m i n a t i o n s of physical s y s t e m characteristics.
The information in this article, although compiled by the author, includes work and ideas from SO many other people that it would be impossible to acknowledge them all. However, I would like to thank several people within my company for their input, including R. Diesner, W. Humy, L. MacDougall, J. Au, and D. Augustine. I would like to dedicate this article to the memory of the late Wilson Leeming, who contributed so much metallurgical understanding to our company and to a number of A M S committees, ForWords is a registered trademark of Computer Associates International Inc. DEC and VAX
are registered trademarks of the Digital Equipment Corp.
References 1. MetalsHandbook,vol. 12, 9th ed., Fractography,ASM International, Metals Park, OH (1987). 2. A. Madeyski and L. Albertin, Fractographic method of evaluation of the cyclic stress amplitude in fatigue failure analysis, in Fractographyin FailureAnalysis, ASTM STP 645, B. M. Strauss and W. H. Cullen, Jr., eds, American Society for Testing and Materials, pp. 73-83 (1978). 3. P. J. E. Forsyth and D. A. Ryder, ACTA Metallurgica 63:117 (1961). 4. J. J. Au and J. S. Ke, Correlation between fatigue crack growth rate and fatigue striation spacing in AISI 9310 (AMS6265) steel, in ASTM STP733, p. 202 (1980). 5. R. W. Hertzberg, Deformationand FractureMechanicsofEngineeringMaterials,John Wiley & Sons, New York (1976). 6. FailureAnalysisHandbook,WRDC-TR-89-4060(1989). 7. MetalsHandbook, vol. 9, 8th ed., Fractographyand Atlas of Fractographs, ASM International, Metals Park, OH (1974).
8. MicroscopicFractureProcesses,Fracture,vol. 1, Aca-
demic Press Inc., New York (1969). 9. A. A. Tipton and W. C. Connors, ComputerAnalysis of SEM Striation Spacing Data, Proceedings of the 1988 International Symposium on Testing and Failure Analysis, ASM International, Metals Park, OH, pp. 439-446 (1987). 10. K. Komai, K. Minoshima, and S. Ishii. Recognition of different fracture surface morphologies using computer image processing technique, ]SMEInternational Journal, Series A, 36:220-227.
ReceivedJune 1993; acceptedAugust 1993.