2021 Volume 62 Issue 12 Pages 1745-1749
The purpose of this study is to investigate a nondestructive method for predicting the fatigue limit of spheroidal graphite cast iron using high resolution X-ray CT. Axial load fatigue test specimens were cut out from a large spheroidal graphite cast iron equivalent to FCD 350, and graphite and defects in the material were detected using high resolution X-ray CT for all specimens. Fatigue limit was estimated from the graphite and defect sizes using the fatigue limit estimation formula based on the four-parameter method.
Axial load fatigue test was performed in accordance with JIS (Japanese Industrial Standards). Repetition frequency was 17 Hz, stress ratio was R = −1, and number of cycles during the test was 1.0 × 107. The specimen used was JIS type 1 of 8.00 mm in diameter. Fracture origins were observed in all fatigue fracture surfaces using a scanning electron microscope (SEM) in order to compare the results between the defects observed by X-ray CT and the fracture origins observed in the fatigue test.
The fatigue limit estimated by the defect with the largest volume detected by X-ray CT was 5% lower than the experimental fatigue limit of 125 MPa, which is considered safe estimation. However, in the fatigue test, the fracture origin was not necessarily the defect with the largest volume. Therefore, the fatigue limit was estimated by the average defect size when the cumulative distribution function of ten defects with the largest volume of each test piece was F = 50%. The result was 11% larger than the experimental fatigue limit, which is considered a dangerous estimation. These results indicate that estimation of fatigue limit using a nondestructive method is feasible.
This Paper was Originally Published in Japanese in J. JFS 91 (2019) 264–269.
Among the material test methods, clarifying the mechanical properties by a simple test method is significant from a practical point of view, and various material evaluation formulas have been proposed.1) Above all, it takes a huge amount of time and effort to determine the fatigue limit of a material from an experiment, so it is desirable to establish a safe and simple evaluation method useful for strength design.2) It is generally said that the fatigue limit of steel materials is 1/2 of the tensile strength σB3) or 1.6 times the Vickers hardness HV,4) but when there are large defects in the material such as spheroidal graphite cast iron, fatigue limit may not be possible to evaluate by tensile strength.5) Therefore, Murakami et al.6) proposed a four-parameter method that estimates the fatigue limit by approximating the defect to a rectangle, setting the square root of the area to $\sqrt{\textit{area}} $, and considering the Vickers hardness of the matrix. It is known that this estimation method enables accurate estimation even when the defect size has a minute defect of about 1000 µm. However, in order to measure this defect size, it is necessary to prepare a large number of fatigue specimens, perform a fatigue test, and observe the fracture surface of all the specimens,7) so it cannot be said to be a simple estimation method. In recent years, X-ray CT has been used to detect defects inherent in castings. By detecting defects inside the material using this X-ray CT8–10) and statistically analyzing the detected defects, it may be possible to predict the fatigue limit non-destructively.11)
Also, when spheroidal graphite cast iron has defects such as graphite and shrinkage cavities, the strength varies, and it is difficult to estimate the fatigue limit with high accuracy, so there is no choice but to design on the safe side.12) If the fatigue limit can be estimated by a non-destructive method using X-ray CT, this method can be a practical fatigue strength evaluation method for using spheroidal graphite cast iron as a structural material without fatigue test.
Therefore, in this study, we statistically analyzed the specimen’s defect size observed by X-ray CT and predicted the fatigue limit from the obtained results using Murakami’s formula. We also conducted an axial load fatigue test on the observed specimens and compared the results to examine effectiveness of non-destructive fatigue limit prediction.
Table 1 shows the target components of the test material. The Mn content was 0.9%, the amount of rare earth added was 200 ppm concerning the molten metal, and contained as mish metal in the spheroidizing agent, and late inoculation was not performed. A thick block mold with mold size of h500 × w500 × t500 mm was used, and melt before the spheroidizing in a 10-ton low-frequency induction furnace, and 1500 kg of molten metal was spheroidized by the sandwich method in a ladle to melt it. This molten metal was poured into a furan self-hardening sand mold provided with a pouring box at 1623 K to prepare an ingot. When the temperature of this ingot was measured using a K-thermocouple, the cooling rate from 1623 K to the eutectic temperature was 0.08 K/s. Figure 1 shows the shape of the ingot and the sampling position of the axial load fatigue specimen. Fifteen specimens were cut out from the shaded area in Fig. 1. Table 2 shows microstructure of specimens, mean diameter of spheroidal graphite nodule, graphite nodule count, nodularity, and content of pearlite in matrix structures. The nodularity is 66%, and the matrix has a two-phase structure of ferrite and pearlite with content of pearlite 34%. Table 3 shows the mechanical properties. From the tensile test results, this test material was equivalent to FCD350, and the average Vickers hardness of the matrix structure was HV190. The nodularity is less than 80% specified by JIS,13) and the test material used in this study cannot be defined as spheroidal graphite cast iron. Graphite that is not spheroidized and large shrinkage cavities are intentionally generated in the low nodularity material, and these are samples that X-ray CT can detect, and they are aimed at becoming the fracture origin.
Shape and dimensions of ingot. Axial fatigue test specimens were cut out from the shaded block.
The testing machine is equipped with TOSCANER-33000µFD-Z (micro focus X-ray generator with a maximum tube voltage of 300 kV, FPD <flat panel X-ray detector> with an effective field of view 400 × 400 mm as high-resolution X-ray CT.) was used. The tube voltage and tube current were set to 280 kV and 100 µA, respectively. The slice thickness per cross-sectional image was 0.024 mm, and the slice pitch was 0.012 mm so that there would be no omission in X-ray observation. 3000 cross-sectional images were taken using X-ray CT for 36 mm including the parallel part shown by the hatched area of the axial load fatigue specimen shown in Fig. 2 described later. Then, the black part of the cross-sectional image was assumed to be a micro shrinkage or graphite, and its dimensions were measured. Also, to extract approximately 10 to 20 defects for each specimen, defects with a volume of 0.02 mm3 or more are analyzed using the attached analysis software, and information that satisfies conditions, such as the volume, position and projected area of many defects can be obtained.
Shape and dimensions of axial fatigue test specimen.
An axial load fatigue test was performed using a specimen observed by X-ray CT. Figure 2 shows the shape and dimensions of the axial load specimen. As the axial load fatigue specimen, the No. 1 specimen with a parallel part diameter of 8 mm conforming to JIS Z 227314) was used. The parallel part of the specimen was polished to # 2000 with emery paper, and then mirror-finished with Al2O3 abrasive grains having an average particle size of 1 µm and 0.3 µm. The testing machine used was an electro-hydraulic servo pulsar type fatigue testing machine manufactured by Shimadzu Corporation with a capacity of ±98 kN. The test was conducted using a sinusoidal load control system with a load repetition frequency of 17 Hz, stress ratio R = −1. Also, the test atmosphere was room temperature, and the number of repetitions until the fatigue test was discontinued was 1 × 107 times. The specimen that reached the number of discontinuations was subjected to the stress amplitude 10 MPa greater than the fatigue limit in order to observe the fracture origin.
The approximation method of the S-N diagram obtained by the axial load fatigue test was based on JSMS-SD-6-04.15) After the axial load fatigue test, the fracture surface of the fractured specimen was observed. A scanning electron microscope was used to observe the fracture surface, and the dimensions of the defect that became the fracture origin were measured by observing the fracture origin.
Figure 3(a) shows an example of a cross-sectional image of a specimen taken by X-ray CT. A multi-section reconstruction image (MPR image) is displayed from 3000 cross-section images using the image processing software ImageJ,16) and examples of the obtained A-A′ and B-B′ cross-section images in the longitudinal direction of the specimen are shown in Fig. 3(b). The dotted line in Fig. 3(b) shows the position of the cross-sectional image in Fig. 3(a). By performing image processing, it became possible to observe graphite and defects existing inside the specimen three-dimensionally.
Examples of X-ray CT image observed in axial fatigue test specimens. (a) Cross-sectional image (b) Longitudinal sectional (- - - - - - Cross section).
Regarding the dimensional measurement of the defect that is the fatigue fracture origin, the defect is regarded as a microcrack rather than a notch, and the state of crack generation from the micro defect is mechanically equivalent to a crack with the same projected area in the maximum principal stress direction. Evaluation by $\sqrt{\textit{area}} $ is promising as a representative dimension that may be able to evaluate the result of such a complicated defect shape in a unified manner.17) The defects observed by X-ray CT and the defects at the fracture origin of the specimen was broken by the fatigue test were rectangularly approximated as shown in Fig. 4, and the square root of the area was defined as $\sqrt{\textit{area}} $. The defects existing inside have a smaller KI max than the defects on the surface having an area of the same size.18) Considering this, the relationship between the square root of the surface defects $\sqrt{\textit{area}} _{\text{s}}$ and the square root of the internal defects $\sqrt{\textit{area}} _{\text{i}}$ that give the same KI max is shown in the following eq. (1).
| \begin{equation} \sqrt{\textit{area}}_{s} = 0.592\sqrt{\textit{area}}_{i} \end{equation} | (1) |
Example of fracture origin observed by X-ray CT image and SEM analysis in axial fatigue specimen. (a) X-ray CT image (b) SEM image.
In order to investigate the effect of the matrix structure on the fatigue strength characteristics, we conducted a study using a 4-parameter model19) that can quantitatively evaluate the fatigue limit of materials with defects (cracks). In the 4-parameter model shown in Fig. 5, the relationship between the fatigue limit and the defect size is divided into the following three regions.
| \begin{equation} \sigma_{W} = 0.5\sigma_{\boldsymbol{B}} \end{equation} | (2) |
Schematic illustration of relationship between fatigue limit and defect size, $\sqrt{\textit{area}} $ (four-parameter model, σB: Tensile strength, HV: Vickers hardness, ΔKth: Threshold stress intensity factor range).
On the other hand, spheroidal graphite cast iron has defects such as graphite and micro shrinkage. In the case of such a material with defects of several hundred µm or more inside, stress concentration occurs at the edge. It is known that the fatigue limit is lower than the value obtained by eq. (2) because it is affected by the defect size and the hardness of the matrix structure. As a result of examining the fatigue limit of materials with defects of several hundred µm or more, Murakami et al. reported that the fatigue limit of materials with defects of less than 1000 µm can be estimated accurately by eq. (3) (Region II).20)
| \begin{equation} \sigma_{\text{w}} = \frac{\alpha (HV + 120)}{\sqrt{\textit{area}}^{\frac{1}{6}}} \end{equation} | (3) |
However, eq. (3) is an evaluation formula for fatigue limit by rotating bending fatigue test, and the stress distribution differs between the rotational bending fatigue test and the axial load fatigue test. Therefore, Sugiyama et al. focused on the difference in stress distribution and reported that the fatigue limit of the axial load fatigue test can be estimated accurately by modifying eq. (3) to eq. (4).21)
| \begin{equation} \sigma_{\text{w}} = \frac{\alpha (HV + 120)}{\sqrt{\textit{area}}^{\frac{1}{6}}} \cdot \frac{r - \sqrt{\textit{area}}}{r} \end{equation} | (4) |
In estimating the fatigue limit using a 4-parameter model, we focused on the defects with maximum volume existing inside the specimen. Since defects are observed three-dimensionally in X-ray CT, the projected area of the defect differs depending on the cross-section observed even for the same defect, and as a result, the measurement result of $\sqrt{\textit{area}} $ differs. Therefore, when estimating the fatigue limit from a defect with the maximum volume, $\sqrt{\textit{area}} $ was measured at the position where the cross-sectional area of the defect was maximum, and this was defined as $\sqrt{\textit{area}} _{\text{max}}$. The $\sqrt{\textit{area}} _{\text{max}}$ of the defects of 15 specimen was measured from the photographed cross-sectional images, and the estimated fatigue limit of each test piece was calculated by eq. (4). However, if the defect was present inside the specimen, the defect dimension $\sqrt{\textit{area}} _{\text{i}}$ at the fracture origin was calculated by replacing the defect dimension $\sqrt{\textit{area}} _{\text{i}}$ of the defect starting point with the defect dimension $\sqrt{\textit{area}} _{\text{s}}$ of the defect near the surface from eq. (1). The α of eq. (4) was calculated as 1.43. As a result, the arithmetic mean of all 15 estimated fatigue limits were 119 MPa, the median was 122 MPa, and the standard deviation was 19.9 MPa.
4.2 Results of axial loading fatigue testFigure 6 shows the S-N diagram obtained by the axial load fatigue test. As a result of the test, the fatigue limit was 125 MPa. Since the estimated fatigue limit based on the maximum defect size $\sqrt{\textit{area}} _{\text{max}}$ of each specimen detected by the above-mentioned X-ray CT is 119 MPa, it was estimated on the safe side with an error of about 5%.
Results of S-N curve conducted using axial fatigue test.
We compared the maximum volume defect observed by X-ray CT with the fracture origin observed by a scanning electron microscope on the fracture surface of the specimen subjected to the fatigue test. The fracture origin of destruction observed this time were all micro shrinkage. Figure 7 shows the macroscopic fracture surface when the defect of the maximum volume in the specimen and the fracture origin of the fatigue test match. On the other hand, Fig. 8 shows the macroscopic fracture surface when the defect of the maximum volume in the specimen and the fracture origin of the fatigue test do not match. In this case, when the defect corresponding to the fracture origin was searched from the cross-sectional image obtained by X-ray CT, it was confirmed that it coincided with the fifth defect in the top volume.
Example in which fracture origin coincides with maximum defect observed in X-ray CT.
Example in which fracture origin (fifth largest volume defect observed in X-ray CT) did not coincide with maximum defect observed in X-ray CT.
As a result of the same comparison for all 15 specimens, 3 specimens had the fracture origins matching the defect with the maximum volume, 7 specimens matched with the defect with the top 10 volumes, and up to the 10th place with the top volume. Five of them did not match the defects.
4.4 Fatigue limit estimation by a statistical method using X-ray CTAs a result of observing the fracture surface of the fatigue specimen, it became clear that the maximum volume defect detected by X-ray CT may not always coincide with the fracture origin of the fatigue test. Therefore, we estimated the fatigue limit of the specimen used in this study, targeting the $\sqrt{\textit{area}} $ of the maximum cross-sectional area of the defects up to the top 10 in the volume of each specimen. There is a little mechanical or statistical basis for targeting the top 10 defects by volume. However, 10 defects, which is two-thirds of the 15 specimens used this time, are included. Therefore, we decided to consider this as appropriate. Figure 9 shows a total of 143 data plotted on Gumbel distribution paper, with the volume of each specimen exceeding 0.02 mm3 and 15 defects up to the top 10 in volume. As a result, $\sqrt{\textit{area}} _{\text{F} = 50\%}$, the average defect size of the cumulative distribution function F = 50%, was 474 µm. The estimated fatigue limit calculated by eq. (4) using this value was 139 MPa. Compared with the fatigue limit obtained by the axial load fatigue test, the error was estimated to be 11% on the dangerous side. The reason for this is that although the actual fracture origin was a large defect, it was estimated including the top 10 defects smaller than the defect size of the actual fracture origin. In addition, when the maximum defect dimension $\sqrt{\textit{area}} _{\text{max}}$ was used as described above, the evaluation was on the safe side with an error of about 5%. This is because the largest defect shown by X-ray CT is not always $\sqrt{\textit{area}} _{\text{max}}$. Equation (4) is an equation obtained from the results of testing by introducing artificial micro-defects of regular shape into the smoothing material.23) The micro shrinkage present in spheroidal graphite cast iron have a complicated shape.22,24) It will be necessary to study the definition and estimation method of defect dimensions, including eq. (4).
Plotting on Gumbel distribution paper indicating defect size to tenth largest volume of each specimen.
As a result of detecting defects in the specimen by X-ray CT, estimating the fatigue limit from the defect dimensions by Murakami’s formula, and comparing it with the experimental results, the largest defect detected may not be the fracture origin so to some extent. It was suggested that the fatigue limit could be estimated by a non-destructive method using X-ray CT, although errors would occur.
As a result of finding the defect existing inside the fatigue specimen by X-ray CT, estimating the fatigue limit from the defect size, and comparing it with the fatigue limit obtained by the axial load fatigue test, the following was clarified.
Part of this research was funded by Grants-in-Aid for Scientific Research (Basic Research (C) Project No. 16K06815), and we would like to express our gratitude to all concerned parties.
