Main chemical components and properties of the test materials
A crack length measurement method is very important in the investigation of the fatigue crack growth characteristics of a material and in the evaluation of the fatigue strength of a machine element. Many crack length measurement methods have been proposed. Brown et al. (1966) and Nishitani et al. (1985) measured crack length through the changes in the displacement and compliance of the test piece. Ashida et al. (1996) and Nakai et al. (1989) investigated the changes in electrical properties around a crack during its growth. Lee et al. (1985) and JSME (1986) recommended estimating the crack length from the opening or closing displacement of a crack. In addition, crack length can also be measured by using an optical microscope, an optical grid technology (Bucci et al., 1972, Maustz et al., 1976, James et al., 1981), an acoustic emission method (Masuyama et al., 1994) and an ultrasonic method (Shimada et al., 1983). However, the methods proposed up to now require specific measuring apparatuses and complex calculation processes for crack length, and are applicable to long cracks several millimeters in length, not to small cracks shorter than 1mm in length or cracks with a high growth rate. In addition to the above-mentioned methods, a thin metal film, such as a crack gauge (e.g., KV-25B manufactured by Kyowa Co.), has been used for crack length measurement and fatigue crack initiation detection in some machine elements, such as gears, where cracks are up to several millimeters in length (Deng et al., 1991). Since this metal film is formed on a plastic base film with a thickness of about several tens of micrometers, there is a relatively large error between the actual and measured crack lengths. Increasing the measurement accuracy of the film can only be achieved by decreasing the thicknesses of the metal and plastic base films.
An ion-sputtering device, widely used in a scanning electron microscopy system, is a coating device used to form a nanoscale-thickness metal film on a surface. In this chapter, we introduce methods for crack length measurement using an ion-sputtered film, which are considered as ideal and practical methods applicable to micro-cracks or small cracks in glass and ceramics as well as metals. The measurement principle and measuring system are very simple. As an application of the ion-sputtered film to crack length measurement, cracks in soda-lime glass and alumina ceramics were measured and the microcrack growth characteristics of these materials were clarified. In addition, an ion-sputtered film was also applied to the detection of fatigue crack initiation, and a very small crack that initiated from the notch surface of the acrylic test piece during the fatigue test was detected..
2. Crack length measurement using grid pattern ion-sputtered film
2.1. Measurement principle
Conductive films have been used for crack length measurement. Ogawa et al. (1991a, 1991b) and Nakamura et al. (1993) utilized carbon films to measure the crack length on ceramic surfaces, but their methods are not widely used because the presented relationship between crack length and the resistance of the film is applicable only to the film of specific dimensions. A crack gauge is also a sensor for measuring crack length and has been used to measure the crack length of gears (Deng et al., 1991), but the measurement precision is not satisfied owing to the thickness of the gauge.
An ion-sputtering device, as shown in Figure 1, is commonly used to fabricate a conductive with a thickness of several tens of nanometers. The application of an ion-sputtered film to crack length measurement would contribute to increasing the crack length measurement precision.
The electrical resistance
Thus, at the instant when a crack grows across the film with a grid shape, the electric resistance of the film will increase to infinity and the complex calculation of the electric resistance of the ion-sputtered film with a crack can be avoided; referring to the crack gauge, a grid pattern ion-sputtered film should be available for crack length measurement (Deng et al., 2006). The electric resistance of the grid pattern ion-sputtered film will increase owing to crack growth, crack length can be determined by counting the number of the increasing steps in the electric resistance and measuring the positions of the grids after or before an experiment.
2.2. Bending test piece and crack length measurement
To investigate the precision of the crack length measurement method using a grid pattern ion-sputtered film, three-point bending fatigue tests for acrylic test pieces were performed. Figure 2 shows the loading method, the test piece and the grid pattern ion-sputtered film. In the experiment, first, a notch was introduced into the test piece to easily introduce the fatigue crack from the notch under a cyclic load. The crack growth experiment was performed under a cyclic load for a slow crack growth. The thickness of the grid pattern ion-sputtered film was about 10nm, the grid width was 0.2mm, and the interval between two grids was 0.1mm. The supporting span was 80mm, and the width and thickness of the test piece were 20mm and 10mm, respectively. The cyclic load was a sine wave of 10Hz and the load ratio (
2.3 Precision of crack length measurement with grid pattern ion-sputtered film
The change in the voltage of the grid pattern film during crack propagation is shown in Figure 4. Although fluctuations in voltage signals due to the deformation of the film and the sampling error were observed, a distinct staircase pattern was recorded for the electric resistance. Considering the characteristic of the electric resistance change for a cracked grid as expressed in expression (2), the increasing step in Figure 4 shows the instant of grid snapping. From the positions of the grids that can be measured with an optical microscope before or after an experiment with a very high precision, the crack length at the instant of the increasing step can be accurately estimated. The precision of this method depends on the film thickness and the speed of the measuring system in response to the crack growth. Since the recorded signal upturns vertically and the film is extremely thin, this method can intermittently measure cracks with a very high precision at the instant of grid snapping.
For the application of the crack length measurement method using a grid pattern film to a rapidly growing crack, a fine-pitch grid pattern ion-sputtered film is desirable. Scribing the film using a sharp scriber tip, as shown in Figure 5, can produce grids of 25μm width and 50μm pitch. A film with 40 grids was fabricated and applied to a fatigue test. The change in the voltage of the film during crack propagation is shown in Figure 6, and 40 steps are identified clearly, indicating that 40 points of crack length can be obtained. Tokunaga et al. (2007) have succeeded in fabricating a grid pattern film using an excimer laser micromachining technology where the grid width is about 13μm and the pitch is 20μm for the measurement of cracks in ceramics.
3. Crack length measurement using rectangular ion-sputtered film
Although the grid pattern ion-sputtered film can measure crack length with a high precision, the crack length cannot be determined continuously. In addition, an isolation film is necessary for the application of the grid pattern film to a conductive surface; the formation of the grid pattern without destroying the isolation film would be very difficult. Thus, for measuring the crack length continuously and applying the ion-sputtered film to a conductive surface, such as a metal surface, a rectangular ion-sputtered film is desirable.
3.1. Calculation of electric resistance of cracked metal film
In the case of a cracked film under electric potential difference, the feature of electron flow around the crack, which is similar to that of stress concentration, is shown in Figure 7, and the electric resistance calculation becomes very complex. Ogawa et al. (1991a, 1991b) calculated the electric resistance of an across-cracked carbon film by FEM analysis and presented an approximating formula for the electric resistance of a regulated film where the crack length is in the range of 0.2-0.8
Electrothermal FEM is a practical method for calculating the electric resistance of the film with a crack (Deng et al., 2007). For example, when the mesh of a rectangular metal film and the boundary condition, shown in Figure 8, are prepared, the current density
Figure 10 indicates the electric resistance of a cracked ion-sputtered film on an acrylic piece, where crack length was measured using an optical microscope. The difference between the electric resistances obtained by measurement and FEM analysis is only 2-3%; thus, it can be considered that the electric resistance of a cracked film is calculated correctly by FEM analysis.
Despite the many approaches that can be used to find the expression for the relationship between the electric resistance and the crack length from 0 to the film width, a satisfactory expression was not obtained. Finally, considering practicability, the following expression is introduced to show the relationship in the crack length range from 0 to a portion of the film width.
On the other hands,
However, the physical meaning of expression (4) has not yet been clarified, and such an expression is only a curve-fitting formula and should be applicable to the condition shown in expression (4). Although this approximating expression can calculate the electric resistance of a cracked film in a specific crack length range, it is better to carry out FEM analysis for a good precision in the electric resistance calculation if a FEM software program is available; the necessary physical and electrical properties for FEM analysis can be obtained by using the initial electric resistance and dimensions of the film.
3.2. Crack length measurement using rectangular ion-sputtered film
Three-point bending tests were performed for acrylic test pieces, whose crack lengths were measured using a microscope and ion-sputtered films. The test piece were 100mm in length, 10mm in depth, and 20mm in height, and the supporting span in the tests was 80mm. A V-notch was introduced into the middle of the supporting span. The load ratio Pmin/Pmax was 0.02 and the load frequency was 10Hz. The experimental method and an ion-sputtered film on a test piece are shown in Figure 12. All tests were stopped when the crack grew to about 0.6
The comparison of the crack lengths measured using an optical microscope and an ion-sputtered film is shown in Figure 13. The crack lengths are in very good agreement. Their maximum difference is 0.113mm and their average is only 0.051mm. A relatively large crack length difference occurs when the cracks are very short. This difference is considered to be due to the interruption of the experiment and taking off the test pieces form test rig for crack length measurement using an optical microscope that leads to the changes in the electrical environmental conditions around the test pieces. Although the precision of this rectangle is not as high as that of a grid pattern film, it is greatly higher than that of a commercial crack gauge (Deng et al., 1991). Therefore, a rectangular ion-sputtered film can be used to measure crack length continuously; short cracks or cracks with high growth rate, such as those in glass and ceramics, might be measurable by using a high-frequency sampling system.
4. Evaluation of crack growth characteristics of glass and ceramics based on crack length measurement using ion-sputtered film
It is known that fatigue failures also occur in structure components made of glass and ceramics under a constant load or a dynamic load (Hoshide, 1994). Since a small crack will grow more unstably and crack growth rate may increases more markedly within a small stress intensity factor range in brittle materials than in ductile metals, the understanding of the small crack growth characteristics in brittle materials, such as glass and ceramics, is very important for the prediction of the residual life. Many researches have been performed to clarify the relationship between the crack growth rate and the stress intensity factor for glass and ceramics using fatigue tests (Wakai et al., 1986, Takahashi et al., 1991, Sawaki et al., 1992, Aze et al., 2002, Yoda, 1989, Kimura et al., 1987). However, most of these researches used standard test pieces, such as compact test pieces or double-torsion test pieces, where the crack length is usually over several millimeters; thus, the crack growth characteristics known up to now are considered appropriately restricted to the large cracks that are impractical in the structure components made of glass and ceramics. For investigating the growth characteristics of a small crack with a length shorter than 1mm in glass and ceramics, a high-precision and high-speed crack length measurement method is necessary. Other methods, such as microscopy observation, the compliance method, the opening displacement method and the estimation methods based on the changes in electric properties around the crack are not applicable. However, the presented crack length measurement method using an ion-sputtered film makes it possible to measure the crack growing in glass and ceramics, since the ion-sputtered film is extremely thin that its electric resistance may change owing to a small increase in crack length, and a high-speed sample system is used for recording the electric resistance of the film.
In this section, a concrete example of the application of a rectangular ion-sputtered film to clarifying small crack growth characteristics, namely, the relationship between the crack growth rate and the stress intensity factor, in soda-lime glass and alumina ceramics is discussed in detail.
4.1. Four-point bending test piece and fatigue test method
Four-point bending fatigue tests were performed under a constant load. The test pieces were made of soda-lime glass and alumina ceramics. The main chemical components and typical properties of the materials are shown in Table 1. The dimensions of the test pieces are shown in Figure 14. The test piece of soda-lime glass is 100mm long, 12mm wide (
|Material||Soda-lime glass||Alumina ceramics|
|Main components wt%||SiO2||72.0||Al2O3||99.5|
|Grain size μm||Amorphia||10|
|Young’s modulus GPa||71.6||363|
|Bending strength MPa||49.0||441|
Static fatigue crack growth can be observed in glass and ceramic materials owing to stress corrosion. A constant load was applied to the test piece in this experiment. The loading and supporting methods are shown in Figure 14. The upper loading span (
4.2. Calculation of stress intensity factor for surface crack and crack growth rate
A surface crack from a diamond indenter pit takes the shape of a semi-ellipse as shown in Figure 15. The stress intensity factor varies with the position at the edge of a crack. The maximum stress intensity factor at point
The surface crack length was derived from the electric resistance of the film based on the relationship between the crack length and the electric resistance of the ion-sputtered film obtained through the above-mentioned FEM analysis. To remove the effects of the sampling errors included in the electric resistance of the ion-sputtered film, as shown in Figure 16, on the surface crack length, the simple moving average method was used to obtain a smooth relationship between the surface crack length and the loading time, as shown in Figure 17. On the basis of the assumption that the aspect ratio
4.3. Crack growth characteristics of soda-lime glass
The growth of a surface crack in the soda-lime glass test piece is shown in Figure 17. Fracture occurred when the crack length reached about 0.8mm; thus, the critical or unstable crack growth is expected to start from a small crack under a constant load. Moreover, crack growth time was about 25sec from the total fatigue time of about 3,040sec; the crack growth stage occupied less than 1% of the entire fatigue process.
Figure 18 shows the relationship between the crack growth rate and the stress intensity factor for the soda-lime glass under the bending stress of 22.8 and 23.6MPa. It has been very difficult up to now to measure the growth rate of a small crack, particularly the low and high (unstable) growth rates in brittle materials. In this experiment, since the ion-sputtered film can measure a small crack with high precision, and the sampling frequency of the measurement systems is so high that the surface crack can be measured almost continuously, a complete relationship including the three regions of crack growth was obtained successfully. In the stress intensity range from 0.45 to 0.85MPa･m1/2, the crack growth rate changed from very low to very high in the soda-lime glass; thus, the unstable crack growth occurs easily in the soda-lime glass under a constant load.
On the basis of the Paris law indicating that the crack growth rate is proportional to the
4.4. Crack growth characteristics of alumina ceramics
The surface crack lengths measured during the test for alumina ceramics are shown in Figure 19. Brittle fracture occurred when the crack length reached about 0.55mm; thus, the critical or unstable crack growth is expected to start from a small crack under a constant load. Moreover, crack growth time was about 130sec from the total fatigue time of about 15,760sec; the crack growth stage occupied less than 1% of the entire fatigue process.
Figure 20 shows the relationship between the crack growth rate and the stress intensity factor for the alumina ceramics under the bending stress of 86.3MPa. The surface crack length was also measured almost continuously, resulting in the successful determination of a complete relationship in the three regions of crack growth. The stress intensity factors range where the crack growth rate changes from low to high (unstable) in the alumina ceramics is very small (about 0.2 to 0.4 MPa･m1/2), which is similar to that of soda-lime glass; thus, the unstable crack growth occurs easily under a constant load. On the basis of the fact that the stress intensity factor for the crack growth in alumina ceramics is much higher than that in the soda-lime glass, alumina ceramics are considered to have a much higher fatigue strength than soda-lime glass.
Considering that the
The circle in region II in Figure 20 also indicates a decrease in crack growth rate. The shapes of the surface cracks in the soda-lime glass and alumina ceramics are observed using a microscope and shown in Figure 21. The crack grew linearly in the soda-lime glass but meandered in the alumina ceramics. Since the ion-sputtered film can only measure the crack length in the traversing direction of the film, the meandering of the crack would be seen as a decrease in crack growth rate.
5. Application of crack length measurement using ion-sputtered film to metal surface
Ion-sputtered films can also be applied to crack length measurement for a metal surface if an insulating film could be fabricated between an ion-sputtered film and a metal surface. The insulating film should be as thin as possible for a high measurement precision. Many methods, such as the vacuum evaporation of silicon and glass, spray pyrolysis using ZnO, painting with quick-drying glue (Krazy Glue) and varnishing using an insulating spray paint, have been used to fabricate a thin insulating film on a steel surface. The method of varnishing using an insulating spray paint was selected finally for the high insulating resistance, thinness and fabrication convenience. The spray paint used in this experiment is the coating agent AY-302 (Sunhayato Co., Tokyo, Japan), which is commonly used in the insulation of printed circuit boards. The main component of the coating agent is polyvinyl resin. Wiping the steel surface with absorbent cotton wetted with the coating agent produces a good-quality and thin isolating film of about 1-2μm thickness. The insulating electric resistance between the ion-sputtered film and the steel surface was measured; its value was as high as several hundreds of ohm for an ion-sputtered film of about 5mm×10mm.
A sectional view of the insulating film, the ion-sputtered film and the wring method used for the crack length measurement on a steel test piece are shown in Figure 22. The insulating film should be fabricated after the setting of the terminal and wiring, and the ion-sputtered film should be fabricated immediately before the experiment.
6. Fatigue crack initiation detection method using ion-sputtered film
Many studies have been performed on the detection method for fatigue crack initiation that is very important in the evaluation of fatigue strength. Makabe et al. (1992, 1994a, 1994b) used a strain waveform for the detection of a fatigue crack with a length of 0.5 to 1mm on a round test piece with a small hemispherical pit. Katayama et al. (1996) and Lee et al. (2002) detected crack initiation using an AC potential method on a sharply notched test piece. Tohmyoh et al. (2001) detected the fatigue crack initiation of a test piece with a surface slit during rotating bending tests using surface SH (shear-horizontal) waves. Papazian et al. (2007) and Zilberstein et al. (2001, 2003, 2005) performed many studies on the application of a meandering winding magnetometer array sensor, ultrasonic techniques and an electrochemical fatigue sensor for the detection of crack initiation for many different types of fatigue test pieces. In addition to the above-mentioned methods, since the ion-sputtered film is very thin, a very short crack can change the electric resistance of the ion-sputtered film; thus, the ion-sputtered film would be practical for detecting the instant of fatigue crack initiation during a fatigue test.
6.1. Principle of fatigue crack initiation detection method
The ion-sputtered film is as thin as several tens of nanometers; thus, a small surface crack is expected to crack the film and change the electric resistance of the film, as shown in Figure 23. The starting point of the increase in electric resistance corresponds to the instant of crack initiation.
6.2. Test piece for fatigue crack initiation detection
Three-point bending fatigue tests were performed to investigate the effectiveness of the ion-sputtered film in crack initiation detection. Considering that the crack initiates from stress concentration regions in machine elements, such as shafts and gears, and the convenience of fabricating an ion-sputtered film, the notch in the test piece should be round instead of being V- or U-shaped. The notches of the test pieces were in the shape shown in Figure 24, and crowned so that the crack could initiate at their centers. The test pieces were 100mm long, 10mm thick and 20mm high, and the supporting span in the tests was 80mm. The radius of the round notch was 4mm, the depth of the notch top
The test pieces were made of acrylic. The ion-sputtered film was formed on the notch surface. The length of the film in the direction of the test piece length was about 10mm, and the width and the thickness of the film were about 5mm and 10-50nm, respectively. The initial electric resistance of the film was lower than 20ohm. As shown in Figure 3, the system was used to record the voltage on the ion-sputtered film.
6.3. Durability of ion-sputtered film
Whether the change in electric resistance or physical damage to the film occurs during the fatigue test before crack initiation was investigated to confirm the suitability of the film. The film was subjected to an endurance test under a light load without fatigue breaks. Figure 25 shows the electric resistance of the film during the test. It is obvious that no physical damage occurred in the film during the test, although a slow decrease in the electric resistance of about 0.5ohm was observed under load cycles of 1×107 (about 90hr). Gradual changes in electric resistance also occurred during some of the subsequent experiments; the reasons for these changes have not yet been clarified. However, considering that the film was made of pure gold (Au) without deteriorations of material properties due to chemical reactions under these test conditions, and that the changes were much slower than that due to crack initiation, the gradual changes might be caused by some unknown environmental factors or the electric shifts of the apparatuses in the measurement system. On the basis of the above-mentioned results, the gradual changes are considered not so severe that the judgment of crack initiation is prevented.
6.4. Change in electric resistance due to crack initiation
The electric resistance of the ion-sputtered film on an acrylic test piece during the fatigue test is shown in Figure 26. The maximum load was 400N, the loading frequency was 10Hz and the film thickness was about 30nm. The experiment was stopped manually after recognizing a rapid increase in voltage signal on the monitor of the data recorder. Figure 26 clearly shows an increase in the electric resistance of the film, indicating crack initiation. Despite the fact that gradual changes in the electric resistance of the film sometimes occur, as shown in Figure 25, the increase in electric resistance due to crack initiation is clear compared with the gradual changes shown in Figure 25, and the crack initiation point can be confirmed from Figure 26 by observing the upward tendency of the electric resistance. The point where the electric resistance leaves the extension line of the mean electric resistance is considered to be the start point of crack initiation. The notch after the experiment is shown in Figure 27, and a very small round crack, the crack in the primary stage of fatigue, can be observed clearly.
6.5. Shape of detected crack in primary stage of fatigue
A small sample around the notch was quarried out from the test piece to determine the crack front shape. The sample was cut bit by bit from the side using a milling machine. The depth of the sample
The methods for crack length measurement and fatigue crack initiation detection using an ion-sputtered film based on the changes in the electric resistance of the film due to crack growth or crack initiation are presented. On the basis of that the experimental results of crack length measurement and crack initiation detection, and considering the convenience to prepare the measurement and monitoring systems, the presented methods are very practical for investigating crack growth characteristics and crack initiation life.
One of the crack length measurement methods is the use of a grid pattern ion-sputtered film, which is similar to a crack gauge. Since the electric resistance of the film changes only at the point when a grid is entirely snapped by a crack, the calculation of the electric resistance is not necessary, the crack length can be obtained by counting the number of increasing steps in the recorded electric resistance and measuring the positions of the grids. Because the thickness of the ion-sputtered film is only several tens of nanometers, the change in the electric resistance of the film due to grid snapping is more immediate than that of the commercial crack gauge. Grid pattern ion-sputtered films were applied to the crack length measurement for a three-point bending test piece. Very obvious staircase changes in the electric resistance of the film were recorded.
Another crack length measurement method is the use of a rectangular ion-sputtered film, which can measure crack length continuously. The relationship between the electric resistance of the film and crack length is obtained by electrothermal FEM analysis, and an approximate expression is proposed to calculate the electric resistance of a cracked film using the results of electrothermal FEM analysis. Since the film is extremely thin, it is very sensitive to the increase in the length of a small crack and practical for investigating a small crack with high growth rate. As the application of the crack length measurement method using a rectangular ion-sputtered film, cracks in soda-lime glass and alumina ceramics were measured and the crack growth characteristics in these materials were clarified continuously from the crack growth region I to the crack growth region III.
In addition to crack length measurement, an ion-sputtered film can also be applied to the detection of fatigue crack initiation, which is a very important technique for evaluating the fatigue strength of a material. Since the film is extremely thin and can be fabricated directly on a surface, a very small crack can change its electric resistance. As an attempt to confirm the fatigue crack initiation life, an ion-sputtered film was formed on the round notch surface of a three-point bending acrylic test piece; a very small crack that initiated from the notch surface during the fatigue test was detected. From the change in the electric resistance of the ion-sputtered film during the test and the shape of the detected crack, it can be concluded that the ion-sputtered film can be used to detect the initiation of a fatigue crack.